tag:blogger.com,1999:blog-57273287491904372162024-02-07T21:28:13.823-06:00Paging Doctor MathPaging Doctor Math is an extension of my Twitter account, @Doctor_Math. When 160 characters just aren't enough, come to Paging Doctor Math to see what I am using in my classroom, my views on the world of mathematical education, and examples of useful mathematics in the real world. Please comment on everything you read at this blog with your own ideas, views, and reactions to the content!Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.comBlogger41125tag:blogger.com,1999:blog-5727328749190437216.post-28123832052289598412017-05-09T07:31:00.002-05:002017-05-09T07:33:55.636-05:00Whiteboard TaskI don't claim to be a great creator of these mathematical tasks...in fact most of the tasks I use I adapt from the Internet. Every once in awhile I will come up with a situation that the students will enjoy or be excited about that I can parlay into a task, and in this case the situation came from difficult experience from the previous year for my students. I left for a year to teach at the collegiate level, which I enjoyed, but I decided to come back this year to the middle school. I was in my old classroom last year a lot, and I wanted to come in so much as a college professor to still have the credibility of having a connection with middle school students. I think my college students appreciated this and knew what I was telling them was relevant and not coming from someone who hadn't worked with a middle school student in 20 years. Anyway, my classroom was much different last year in philosophy by the person who replaced me. I am not sure if it was necessarily bad, just very different. I had noticed that many of my students got bored or something during class and would write middle school type phrases on the back of my whiteboards (if you watch intro video one, you will see my favorite...it's hard for me to even be mad because it was clever). These whiteboards were clean on the wooden backs the year before, and now the whiteboard backs were covered with writing. I wanted to get rid of this writing, because I wanted the students to see that this wasn't how we operated, so I decided to cover the backs with contact paper that doubled as a whiteboard. This wasn't cheap to do, so I decided to incorporate this covering of whiteboards into a task.<br />
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When the students were watching the videos for this task, I could see a lot of smiles on faces because these were the same students who had written on the backs of these boards the year before. This was a great chance for them to reflect on how much had changed in just a year's time.<br />
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<span style="font-size: small;">Here is the task:</span><br />
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<div dir="ltr" id="docs-internal-guid-80d9c596-6851-6a94-7228-0bebf69a2b49" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: small;"><span style="font-family: inherit;"><a href="https://youtu.be/_i2yeivz_WU" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Intro Video One</span></a></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><a href="https://youtu.be/306hIPDxE0I" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Intro Video Two</span></a></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><a href="https://youtu.be/cAyQ6ekfnNw" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Intro Video Three</span></a></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><a href="https://youtu.be/5YZLsbRtFvw" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Intro Video Four</span></a></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Info One: 20 Whiteboards needed to be covered…</span></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Info Two (the price has changed since we did this task): </span><a href="https://www.amazon.com/Tact-Readi-Write-Contact-18-Inch-06F-C82010-06/dp/B0068BO3IA" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Contact Paper Specs</span></a></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: cyan; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Question One:</span><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> How many rolls did I need to cover the boards?</span></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: cyan; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Question Two:</span><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> How much contact paper was left over?</span></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: cyan; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Question Three:</span><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> Draw a real-sized rectangle that the remaining pieces could cover.</span></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: cyan; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Question Four:</span><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> How much did I spend on contact paper?</span></span></span></div>
<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: cyan; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Question Five:</span><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> If the store let me take back the extra contact paper, how much money would I get back assuming that the cost/amount received is proportional?</span></span></span><br />
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">There were a different ways students approached this task. Some of the students found the total area of the boards and fit them into the rolls. This made everything a lot cleaner and easier, but not as interesting. A few students created an actual picture showing where the white boards fit onto the paper, and then showed how the scraps were utilized. Other students figured out how many boards could fit in one roll in a numerical value, and saved the leftover in number form until there was enough square inches to trade in for another board. Students are always amazed when discussing with other students and groups how different some of these methods are while having many similarities. </span></span></span><br />
<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"><br /></span></span></span>
<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">While I may not be the best task creator, this task checked many of the objectives I look for (not related to content). These objectives include multiple entry points, something interesting for the student to discuss both mathematically and situationally, and a situation the students would enjoy. Not bad for one of my first attempts creating from scratch! I have included a variety of student work below to give you an idea of what I expect. </span></span></span><br />
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"><span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhH1JOUkWWKZZWxLG7KwSgBIjB6dUjRslZMt7v5GcqeGFyzGi6ZmtvQ8I_W8xd-YptxhS4rrYcdboZmSXl-EmKFyeCvPJWIpo0Ly5FfwwFWoNGx54TkDJeCBaWejmn1ccI1WAiynarVFHSY/s1600/IMG_2201.JPG" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhH1JOUkWWKZZWxLG7KwSgBIjB6dUjRslZMt7v5GcqeGFyzGi6ZmtvQ8I_W8xd-YptxhS4rrYcdboZmSXl-EmKFyeCvPJWIpo0Ly5FfwwFWoNGx54TkDJeCBaWejmn1ccI1WAiynarVFHSY/s640/IMG_2201.JPG" width="476" /></a></span></span></span> </span></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> </span></span></span><span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRvygYMDJQHnoAb3Ber0Tb3UV7679lh943jQRD5L3RXm10kE87L0OM7tb2uoh5Fxz4nsXbsCGDSfA_kHacwUDHRATh-zqD1-bMPUA7dwgzWnUbYAuQ6YOyN1Qu53lyHi0TEBJKW-JlSufR/s1600/IMG_2202.JPG" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRvygYMDJQHnoAb3Ber0Tb3UV7679lh943jQRD5L3RXm10kE87L0OM7tb2uoh5Fxz4nsXbsCGDSfA_kHacwUDHRATh-zqD1-bMPUA7dwgzWnUbYAuQ6YOyN1Qu53lyHi0TEBJKW-JlSufR/s640/IMG_2202.JPG" width="478" /></a></span></span></span></div>
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<span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Dr. Clayton M. Edwards<br />Grundy Center Middle School<br />Middle School Mathematics Instructor<br /><a href="https://docs.google.com/document/d/16THWEeMiU_NWflzhC-EjWUK-_3Xj8sx5LBlJ7S_upYI/edit?usp=sharing" target="_blank">Curriculum Vita</a><br />-<br /><a href="http://www.nctm.org/Publications/mathematics-teaching-in-middle-school/About-Mathematics-Teaching-in-the-Middle-School/" target="_blank">National Council of Teachers of Mathematics Editorial Panel</a><br /><a href="http://www.iowamath.org/about/board.htm" target="_blank">Iowa Council of Teachers of Mathematics Regional Director AEA 267</a></span></span><br />
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<span style="font-family: "cambria"; font-size: 12.0pt;"></span><a href="https://www.educateiowa.gov/pk-12/content-areas/mathematics/statewide-mathematics-leadership-team" target="_blank">Iowa Department of Education Statewide Mathematics Leadership Team</a><br /><a href="http://www.ifets.info/reviewers.php" target="_blank">Journal of Educational Technology and Society Executive Peer Reviewer</a><br />-</span></span></div>
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<span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Ed. D. Curriculum and Instruction (UNI)<br />MA Middle Level Mathematics (UNI)<br /><a href="http://www.uni.edu/newsroom/uni-confers-yager-exemplary-teaching-recognition-awards-0" target="_blank">Yager Exemplary Teaching Award</a></span></span></div>
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<span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://www.grad.uni.edu/sites/default/files/program14_-_final_for_the_web_0.pdf" target="_blank">Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa</a><br />-</span></span></div>
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<span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://twitter.com/Doctor_Math" target="_blank">@Doctor_Math</a></span></span></div>
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<span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://tinyurl.com/grundymsmath" target="_blank">Classroom Math Website</a></span></span></div>
<span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://pagingdoctormath.blogspot.com/" target="_blank">Blog</a></span></span><span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span></span></div>
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<span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://bit.ly/2bxMG5T" target="_blank">Problem-Solving Tasks Document One</a></span></span><span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="https://t.co/9QdPKgBoSU" target="_blank">Problem-Solving Tasks Document Two</a></span></span></div>
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<span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://tinyurl.com/1to1mlmath" target="_blank">1:1 Math Philosophy</a></span></span></div>
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<span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://tinyurl.com/taskmathpresent" target="_blank">Task-Based Mathematics Presentation</a></span></span></div>
<span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="https://docs.google.com/document/d/12m3kTMqEz0UjQdNwswhzNZR48vrG4nxO0Nmp85nlo3E/edit?usp=sharing" target="_blank">Student/Parent Expectations - About Dr. Edwards</a></span></span></div>
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Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-29608706970453498052017-02-14T09:58:00.001-06:002017-02-14T09:58:47.129-06:00Nardo RingToday's task comes from Dane Ehlert and his page of <a href="https://whenmathhappens.com/3-act-math/" target="_blank">3-Act Tasks</a>. I have been messing around with his <a href="http://dailyoverviewmath.weebly.com/nardo-ring.html" target="_blank">Nardo Ring</a> task since last year when I was at the University of Northern Iowa, and I finally got to implement my adaptive version with my 8th graders. This task was interesting for most students because they had never heard of this track (and neither had I). The ideas of fast cars, or in my case slow cars racing is exciting, and many students took a few minutes before getting started to do a little research on the track. Having tasks that are interesting for middle school students helps with engagement, which in turn makes the math content more meaningful. See <a href="http://pagingdoctormath.blogspot.com/2014/12/man-versus-squirrel.html" target="_blank">exhibit A</a> and <a href="http://pagingdoctormath.blogspot.com/2015/04/doritos-roulette.html" target="_blank">exhibit B</a> for more examples of tasks that middle school students enjoy. I also like the implementation of <a href="https://www.desmos.com/" target="_blank">Desmos</a>, even if it isn't a major part of the task. I use a lot of the <a href="https://teacher.desmos.com/" target="_blank">Desmos Teacher</a> activities, but I don't use Desmos for much more than that. I was happy to find some other uses.<br />
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Here is what the students saw upon entering the classroom:<br />
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">The Nardo Ring is a high speed test track in Italy. Use this link to Google Maps to get an idea of what it looks like...</span></div>
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<a href="https://www.google.com/maps/place/SP219,+73010+Nard%C3%B2+LE,+Italy/@40.3223507,17.8174497,4919m/data=!3m1!1e3!4m2!3m1!1s0x134691ae985997cf:0xb1dc2295dcb7dcb" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Nardo Ring</span></a></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Today, witness a race between my old high school car, the </span><a href="http://i.ytimg.com/vi/JJvCJgmUT_g/maxresdefault.jpg" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Chevy Celebrity</span></a><span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">, and the new Shelby Cobra Mustang (</span><a href="http://mustangsdaily.com/blog/wp-content/uploads/2012/04/03-shelby-cobra-reunion-mustangs.jpg" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">pic one</span></a><span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> and </span><a href="https://s-media-cache-ak0.pinimg.com/736x/7a/f9/c9/7af9c9ba092037994f8e2ea2517ac7f0.jpg" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">pic two</span></a><span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">). As you can tell from the pictures, my old ride will need a slight headstart to keep this race close.</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Chevy Celebrity Speed - 40 mph (if it doesn’t fall apart first)</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Shelby Cobra Speed - 90 mph</span></div>
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<a href="https://whenmathhappens.files.wordpress.com/2015/06/diameter.jpg" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Race Track Specs</span></a></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline;">How to Use This Map:</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">The large orange dot is the Shelby Cobra, which is at the starting line and finish line. The large light blue dot is the Celebrity, which is where the head start is at. You can take the slider on the left hand side labeled </span><span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline;">r orange</span><span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> and move orange line to see the angle it makes with the starting line, or the green line (the angle measurement is also displayed on the right hand side). </span></div>
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<a href="https://www.desmos.com/calculator/iftqbnmixn" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Map</span></a></div>
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<span style="background-color: cyan; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Q1</span><span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">- Who wins the race? Use appropriate minutes and seconds to convey you answer. </span></div>
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<span style="background-color: cyan; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Q2</span><span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">- At what degree does the Celebrity need to be placed at so the race is a tie (or as close to a tie as you can get)?</span></div>
<br /><span style="background-color: cyan; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Q3</span><span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">- How much less space is contained inside the track at the old 1910 </span><a href="https://upload.wikimedia.org/wikipedia/en/f/fb/Los_angeles_motordrome_postcard.jpg" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Los Angeles Motordrome</span></a><span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> than the Nardo Ring? The Motordrome is 1 mile around the track.</span><br />
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"></span>A few of the tougher spots for students on this task:<br />
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1. When finding the degree that the Celebrity should start at for the race to roughly be a tie, many students figure out how many degrees the car would take to get to 5 or so minutes to match the Cobra, but not where the car should start at on the track. It took a lot of conversation to understand that those numbers were not the same thing.<br />
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2. Finding the radius of the track that is 1 mile around was difficult because students had to use decimals without whole numbers to eventually get the circumference to be 1. I think if the track would have been 10 or so miles around, the radius would have been easier to find and made more sense, but there isn't anything wrong with using decimals. 8th graders should be able to do that. <br />
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3. Some students had to do a triple conversion of degrees being equal to miles being equal to minutes, which was different. Normally my students set up ratio tables for percentages and proportional relationships, but not normally in groups of three.<br />
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Some of the reasoning I really enjoyed from this task:<br />
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1. A few students also related the degrees of the track to fractional pieces of the track like 1/8th of the track or 1/16 of the track to help with conversions.<br />
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2. Students were all over the board on what information was used to solve the problem. For instance, you can find the time for both cars by only using the miles per hour, but some students ended up using miles per hour and degrees.<br />
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3. We were able to have a nice discussion on some of the variables that we did not factor into this race (like time taken to get to top speed for instance). These are valuable discussions that let students know that math isn't always as simple as it can sometimes be presented.<br />
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Enjoy the student work...especially the ones you can actually read without straining your eyes! <br />
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<span style="font-size: xx-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Dr. Clayton M. Edwards<br />Grundy Center Middle School<br />Middle School Mathematics Instructor<br /><a href="https://docs.google.com/document/d/16THWEeMiU_NWflzhC-EjWUK-_3Xj8sx5LBlJ7S_upYI/edit?usp=sharing" target="_blank">Curriculum Vita</a><br />-<br /><a href="http://www.nctm.org/Publications/mathematics-teaching-in-middle-school/About-Mathematics-Teaching-in-the-Middle-School/" target="_blank">National Council of Teachers of Mathematics Editorial Panel</a><br /><a href="https://www.educateiowa.gov/pk-12/content-areas/mathematics/statewide-mathematics-leadership-team" target="_blank">Iowa Department of Education Statewide Mathematics Leadership Team</a><br /><a href="http://www.ifets.info/reviewers.php" target="_blank">Journal of Educational Technology and Society Executive Peer Reviewer</a><br />-</span></span></div>
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<span style="font-size: xx-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Ed. D. Curriculum and Instruction (UNI)<br />MA Middle Level Mathematics (UNI)<br /><a href="http://www.uni.edu/newsroom/uni-confers-yager-exemplary-teaching-recognition-awards-0" target="_blank">Yager Exemplary Teaching Award 2014</a></span></span></div>
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<span style="font-size: xx-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://www.grad.uni.edu/sites/default/files/program14_-_final_for_the_web_0.pdf" target="_blank">Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa 2014</a><br />-</span></span></div>
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<span style="font-size: xx-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://twitter.com/Doctor_Math" target="_blank">@Doctor_Math</a></span></span></div>
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<span style="font-size: xx-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://tinyurl.com/grundymsmath" target="_blank">Classroom Math Website</a></span></span></div>
<span style="font-size: xx-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://pagingdoctormath.blogspot.com/" target="_blank">Blog</a></span></span><br />
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<span style="font-size: xx-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://tinyurl.com/mathematicstasks" target="_blank">Problem-Solving Task Spreadsheet</a></span></span><br />
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<span style="font-size: xx-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://tinyurl.com/1to1mlmath" target="_blank">1:1 Math Philosophy</a></span></span></div>
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<span style="font-size: xx-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://tinyurl.com/taskmathpresent" target="_blank">Task-Based Mathematics Presentation</a></span></span></div>
<span style="font-size: xx-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="https://docs.google.com/document/d/12m3kTMqEz0UjQdNwswhzNZR48vrG4nxO0Nmp85nlo3E/edit?usp=sharing" target="_blank">Student/Parent Expectations - About Dr. Edwards</a></span></span></div>
Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-66833822044876540902017-01-28T11:29:00.002-06:002017-08-09T14:35:17.061-05:00Tug-Of-War TaskFollowing <a href="https://twitter.com/mburnsmath" target="_blank">@mburnsmath</a> on Twitter has paid off. This time the payment was an older task of hers, A Mathematical Tug-of-War. I did this task with my 7th graders, and while this may not have been the most difficult task I have ever presented, it may be the most accessible. When discussing this task during class with individual students and groups, I counted four distinctive approaches, with different variations of those four approaches present. I would categorize different ways as informal substitution, Algebra/combining like terms, unit rates, and assigning values (some of these overlap between the student work). I have examples of each posted at the end of the post. <br />
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<span style="background-color: cyan; color: black; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Q1</span></div>
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<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> </span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"><img alt="Screen Shot 2017-01-16 at 7.31.20 AM.png" height="444" src="https://lh6.googleusercontent.com/iWWFpwf56VdxEoTqfqFW4QEEEFCnK0OnxTfxgkA33CIEqUEW05edVBoUC8_5d-7xN-m5YZxr_IgsLvrLn-lKd2JGoPf4gM39MfAcdBX2BdE4a2A81ONqdByQYRRZVNRBTVwFm3SQ" style="-webkit-transform: rotate(0.00rad); border: none; transform: rotate(0.00rad);" width="561" /></span></div>
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<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 10.666666666666666px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Can be found in 50 Problem Solving Lessons for Grades 1-6 Marilyn Burns Math Solutions Press 2003</span></div>
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<span style="background-color: cyan; color: black; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Q2</span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> What character(s) could you add to the losing side of round three to make the round a draw?</span></div>
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<span style="background-color: cyan; color: black; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Q3</span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> Dr. Edwards is teaming up with Ivan to form a tug-of-war dream team. Dr. Edwards is twice as strong as Ivan. You are forming your own team to tie Dr. Edwards and Ivan’s team. Give </span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline;">TWO</span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> possible team formations of Grandmas and/or Acrobats to TIE Dr. Edwards and Ivan’s team. </span></div>
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This is also a great example of a task that isn't necessarily real-world, but it is interesting for the students. Not everything has to be real-world all the time. The important thing is that the students are discussing the math involved. Maybe some will argue with me that this is real-world...I have seen a lot of wacky things on ESPN 2 late at night, but never the International Tug-Of-War Competition where animals and people are allowed to enter, although that would be interesting television. Same goes for this <a href="http://pagingdoctormath.blogspot.com/2014/12/man-versus-squirrel.html" target="_blank">task</a>...<br />
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A few of my students struggled to get started and were hung up on both sides needing to have an equal number of people in physical number and not in amount of strength. I gave the example of myself having a tug-of-war match with one of my student's kindergarten sisters. There would be one person on each side, but it wouldn't necessarily be equal. That worked well.<br />
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This task is also a good way to organically get away from a problem being on one side of the equals sign and one number being on the other side. The equal side doesn't necessarily mean question and answer like many students come to me thinking, but both sides being the same amount. When I previously taught 6th grade, problems like 3 + 5 - 2 = 1 + 1 + x would be difficult, and I think this task would help solidify what the equals sign really means.<br />
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I was disappointed that some of my students called me out on being as strong as two Ivan's, but in rethinking the reality of the situation, it probably depends on what four grandmas and what two acrobats I would be facing!<br />
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<span style="font-size: xx-small;">(The 100% reference loses its meaning after the first round, and we discussed that after this was submitted)</span></div>
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Other Task Posts Examples (more available in previous entries)...<br />
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<a href="http://pagingdoctormath.blogspot.com/2016/11/mathematics-tasks-for-2016-2017the.html" target="_blank">Pokemon Go</a> <br />
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<a href="http://pagingdoctormath.blogspot.com/2014/12/man-versus-squirrel.html" target="_blank">Man Versus Squirrel</a><br />
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<a href="http://pagingdoctormath.blogspot.com/2015/02/shrinking-dollar-task.html" target="_blank">Shrinking Dollar</a> <br />
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Dr. Clayton M. Edwards<br />Grundy Center Middle School<br />Middle School Mathematics Instructor<br /><span><a href="https://docs.google.com/document/d/16THWEeMiU_NWflzhC-EjWUK-_3Xj8sx5LBlJ7S_upYI/edit?usp=sharing" target="_blank">Curriculum Vita</a></span><br />-<br /><a href="http://www.nctm.org/Publications/mathematics-teaching-in-middle-school/About-Mathematics-Teaching-in-the-Middle-School/" target="_blank">National Council of Teachers of Mathematics Editorial Panel Chair</a><br /><span><span style="font-size: x-small;"><span style="font-family: arial,helvetica,sans-serif;"><a href="https://www.iowamath.org/about/board" target="_blank">Iowa Council of Teachers of Mathematics Regional Director Central Rivers AEA</a></span></span></span><br /><a href="https://www.educateiowa.gov/pk-12/content-areas/mathematics/statewide-mathematics-leadership-team" target="_blank">Iowa Department of Education Statewide Mathematics Leadership Team</a><br /><a href="http://www.ifets.info/reviewers.php" target="_blank">Journal of Educational Technology and Society Executive Peer Reviewer</a><br />-</div>
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Ed. D. Curriculum and Instruction (UNI)<br />MA Middle Level Mathematics (UNI)<br /><a href="http://www.uni.edu/newsroom/uni-confers-yager-exemplary-teaching-recognition-awards-0" target="_blank">Yager Exemplary Teaching Award</a></div>
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<a href="http://www.grad.uni.edu/sites/default/files/program14_-_final_for_the_web_0.pdf" target="_blank">Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa</a><br />-</div>
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<a href="http://twitter.com/Doctor_Math" target="_blank">@Doctor_Math</a></div>
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<a href="http://tinyurl.com/grundymsmath" target="_blank">Classroom Math Website</a></div>
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<span><span style="font-size: x-small;"><span style="font-family: arial,helvetica,sans-serif;"><a href="http://bit.ly/2bxMG5T" target="_blank">Problem-Solving Tasks Document One</a></span></span><span><span style="font-size: x-small;"><span style="font-family: arial,helvetica,sans-serif;"><a href="https://t.co/9QdPKgBoSU" target="_blank">Problem-Solving Tasks Document Two</a></span></span></span></span><div>
<a href="http://tinyurl.com/1to1mlmath" target="_blank">1:1 Math Philosophy</a></div>
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<a href="http://tinyurl.com/taskmathpresent" target="_blank">Task-Based Mathematics Presentation</a></div>
<a href="https://docs.google.com/document/d/12m3kTMqEz0UjQdNwswhzNZR48vrG4nxO0Nmp85nlo3E/edit?usp=sharing" target="_blank">Student/Parent Expectations - About Dr. Edwards</a></div>
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Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-75936436533001878372017-01-10T10:27:00.001-06:002017-01-10T10:33:49.607-06:00Toothpick Task 2017I had an icy two-hour delay this morning, and when you operate off the a combination of getting to school by 6 every morning and living 40 minutes away from school, I never find out about the delay until after I arrive. I enjoy these mornings because I get to catch up on some work. I had a few students come in 3 hours before school started to work, I submitted a manuscript review for Mathematics Teaching in the Middle School, and worked on questions for an upcoming <a href="https://twitter.com/search?f=tweets&vertical=default&q=%23mtmschat&src=typd" target="_blank">MTMS Twitter chat</a> (which you should join the 3rd Wednesday of each month at 9ET/8CT with using #MTMSchat).<br />
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To the task...<br />
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<div dir="ltr" id="docs-internal-guid-b79f5e56-88d1-2a3f-5b2a-9a25a67f2e30" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<a href="https://vimeo.com/56821540" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Informational Video</span></a></div>
<a href="http://threeacts.mrmeyer.com/toothpicks/act2/toothpickcount.jpg" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Additional Information</span></a><span style="background-color: transparent; color: #1155cc; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;"> </span><br />
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<div dir="ltr" id="docs-internal-guid-b79f5e56-88d9-d203-f829-a502d54dae24" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: cyan; color: black; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Q1</span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">~How many complete rows of toothpicks can you make with the amount given?</span></div>
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<span style="background-color: cyan; color: black; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Q2</span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">~Will there be any extra? How many?</span></div>
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<span style="background-color: cyan; color: black; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Q3</span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">~How many more would you need to complete the next full row?</span></div>
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<span style="background-color: cyan; color: black; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Q4</span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">~How many toothpicks would the container need to create 20 rows?</span></div>
<span style="background-color: cyan; color: black; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Q5</span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">~If someone wanted to know how many toothpicks would be in the 75th row and you didn’t want to build that big of a pyramid, what could you do to find that answer fast? How do you know that will work?</span><br />
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The first part of this toothpick task (by <a href="https://twitter.com/ddmeyer" target="_blank">@ddmeyer</a> <a href="http://bit.ly/2jzv0sZ">http://bit.ly/2jzv0sZ</a>) begins innocently enough, with students trying to find out how many full rows could be made with the given amount of toothpicks. The interesting part to this is how students choose to solve this first problem. Almost all of the students (I did this with 7th grade, but could work for 5-8 or more). will start by dividing 250 by 3, not fully thinking what the result will mean. Once it is understood what this answer of 83ish means (asking a quick question about what does the 3 mean normally brings light to this problem), students branched off into three different ways to solve: a full blown picture, a chart, or a combination. Within these three options, most students either went with the tooth pick totals, or the total number of triangles. While many of these options will be similar, the different number of ways to solve this problem speaks to the accessibility of this task. <br />
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Question 5 is a great question as well because you can get into some generalizing. Some students automatically search for patterns, but some don't think of that as an option. Making it more explicit helps students understand that finding patterns is an option that can always be looked for. Patterns may not always be prevalent, but at least now students know that option exists.<br />
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This task will help us move into some tasks with some equation/expression writing built in such as <a href="https://teacher.desmos.com/centralpark" target="_blank">Central Park</a>, <a href="http://pagingdoctormath.blogspot.com/2015/01/in-n-out-burger-task.html" target="_blank">In-N-Out Burger</a>, and <a href="https://tapintoteenminds.com/3act-math/the-detention-buy-out/" target="_blank">Detention Buy-Out</a>.<br />
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Enjoy the student work below! I especially like the one towards the middle where the students exclusively used triangles instead of individual toothpicks like many of the students used. <br />
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Note: As I was typing this, we are now cancelled :-(<br />
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Other Task Posts Examples (more available in previous entries)...<br />
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<a href="http://pagingdoctormath.blogspot.com/2015/02/shrinking-dollar-task.html" target="_blank">Shrinking Dollar</a> <br />
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<span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Dr. Clayton M. Edwards<br />Grundy Center Middle School<br />Middle School Mathematics Instructor<br /><a href="https://docs.google.com/document/d/16THWEeMiU_NWflzhC-EjWUK-_3Xj8sx5LBlJ7S_upYI/edit?usp=sharing" target="_blank">Curriculum Vita</a><br />-<br /><a href="http://www.nctm.org/Publications/mathematics-teaching-in-middle-school/About-Mathematics-Teaching-in-the-Middle-School/" target="_blank">National Council of Teachers of Mathematics Editorial Panel</a><br /><a href="https://www.educateiowa.gov/pk-12/content-areas/mathematics/statewide-mathematics-leadership-team" target="_blank">Iowa Department of Education Statewide Mathematics Leadership Team</a><br /><a href="http://www.ifets.info/reviewers.php" target="_blank">Journal of Educational Technology and Society Executive Peer Reviewer</a><br />-</span></span></div>
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<span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Ed. D. Curriculum and Instruction (UNI)<br />MA Middle Level Mathematics (UNI)<br /><a href="http://www.uni.edu/newsroom/uni-confers-yager-exemplary-teaching-recognition-awards-0" target="_blank">Yager Exemplary Teaching Award 2014</a></span></span></div>
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<span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://www.grad.uni.edu/sites/default/files/program14_-_final_for_the_web_0.pdf" target="_blank">Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa 2014</a><br />-</span></span></div>
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<span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://twitter.com/Doctor_Math" target="_blank">@Doctor_Math</a></span></span></div>
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<span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://pagingdoctormath.blogspot.com/" target="_blank">Blog</a></span></span><br />
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<span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://tinyurl.com/mathematicstasks" target="_blank">Problem-Solving Task Spreadsheet</a></span></span><br />
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<span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://tinyurl.com/1to1mlmath" target="_blank">1:1 Math Philosophy</a></span></span></div>
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<span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://tinyurl.com/taskmathpresent" target="_blank">Task-Based Mathematics Presentation</a></span></span></div>
<span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="https://docs.google.com/document/d/12m3kTMqEz0UjQdNwswhzNZR48vrG4nxO0Nmp85nlo3E/edit?usp=sharing" target="_blank">Student/Parent Expectations - About Dr. Edwards</a></span></span></div>
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<br />Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-56252939101732245512016-12-02T10:01:00.002-06:002016-12-02T10:01:21.311-06:00Sticky Note Task Expanded<span style="font-size: small;"><span style="font-family: inherit;">With my 7th graders, we recently finished the sticky note task, which is a compilation of tasks by <a href="https://twitter.com/mr_stadel" target="_blank">Andrew Stadel</a> and <a href="https://twitter.com/MrOrr_geek" target="_blank">Jon Orr</a>. I have done this in the past, but added the part by Jon this year. Surface area is probably the predominant math concept, but I found question 4 to be particularly interesting. Before we talk about that, here is the task...</span></span><br />
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<span style="font-size: small;"><span style="font-family: inherit;"><a href="https://vimeo.com/40917688" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Introductory Video</span></a></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><a href="http://www.estimation180.com/uploads/1/3/8/8/13883834/fc-act2a.018.jpg" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Information One</span></a></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><a href="http://www.estimation180.com/uploads/1/3/8/8/13883834/fc-act2b.020.jpg" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Information Two</span></a></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: lime; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Q1:</span><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> How many sticky notes are needed to cover every exposed face of the cabinet?</span></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: lime; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Q2:</span><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> How many pads would you need to have enough sticky notes?</span></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><a href="http://101qs-media.s3.amazonaws.com/videos/3044-r2d2-postits.mp4?_=1" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Introductory Video</span></a></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><a href="https://drive.google.com/file/d/1MJHX11MnzGIDZpcrUmwe_kmZoIWI4v-ZaNsUOULCcYrjge-E_XB8QdB2jmIiTmZK8ObYzldU6PxxFLsx/view?usp=sharing%20https://drive.google.com/file/d/1KX4GPTYHVw7RH1v1uKHCDIYJh-cmGnBB6qrh8aQe5_OY5iKcp2BFSQpNO2E44gpqLLu2EfdfsPQsFM-W/view?usp=sharing" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Information One</span></a></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><a href="https://drive.google.com/file/d/1KX4GPTYHVw7RH1v1uKHCDIYJh-cmGnBB6qrh8aQe5_OY5iKcp2BFSQpNO2E44gpqLLu2EfdfsPQsFM-W/view?usp=sharing" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Information Two</span></a></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: lime; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Q3:</span><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> How many sticky notes fit on the whiteboard?</span></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: lime; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Q4:</span><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> If you had 120 of the 1.5 inch by 2 inch sticky notes, what is one size of board that you could cover (dimensions and area)?</span></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><a href="http://mrorr-isageek.com/wp-content/uploads/2014/06/IMG_2395.jpg" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Information One</span></a></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: lime; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Q5:</span><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> What fraction and percent represents the following categories? </span></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">*Pink and blue Combined?</span></span></span></div>
<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">*All colors that are not pink or blue?</span></span></span><br />
<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"></span></span></span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 18.666666666666664px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"><span style="font-family: inherit;"><span style="font-size: small;"> </span></span></span><br />
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"><span style="font-family: inherit;"><span style="font-family: inherit;">For question <span style="font-family: inherit;">4</span>, stu<span style="font-family: inherit;">dents had a variety of amounts of sticky notes on the boards...anywhere from<span style="font-family: inherit;"> 12 notes by 10 notes to more of a ribbon board look of 120 notes by 1 note or 60 notes by <span style="font-family: inherit;">2 notes. The unexpected part for the students came when figuring <span style="font-family: inherit;">out how much space the board they created took up. No matter the configuration of the 120 stick notes, the area <span style="font-family: inherit;">of the board was al<span style="font-family: inherit;">ways 360 square inches. This makes sense since all of the boards have the same number of <span style="font-family: inherit;">sticky notes<span style="font-family: inherit;">, and each note<span style="font-family: inherit;"> has an indivi<span style="font-family: inherit;">dual area of 3, but this took some time <span style="font-family: inherit;">for everyone to <span style="font-family: inherit;">comprehend</span>. A great discussion piece for sure. </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;">The other thing I <span style="font-family: inherit;">think was</span> inter<span style="font-family: inherit;">e<span style="font-family: inherit;">sting</span> <span style="font-family: inherit;">about this task <span style="font-family: inherit;">was</span> if the students chose to find the<span style="font-family: inherit;"> sticky notes by finding the area <span style="font-family: inherit;">of the board/face of the cabinet first, or find the number of sticky notes along the length and the width first. Some student did one method for question 1 and the other for question 3. </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;">This was a great task that would be appropriate for almost all levels of middle school<span style="font-family: inherit;">. <span style="font-family: inherit;">I have included some student work be<span style="font-family: inherit;">low. </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
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<span style="font-size: xx-small;"><span style="font-family: arial,helvetica,sans-serif;">Dr. Clayton M. Edwards</span></span><br /><div dir="ltr">
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<span style="font-size: xx-small;"><span style="font-family: arial,helvetica,sans-serif;">Grundy Center Middle School<br />Middle School Mathematics Instructor<br /><span><a href="https://docs.google.com/document/d/16THWEeMiU_NWflzhC-EjWUK-_3Xj8sx5LBlJ7S_upYI/edit?usp=sharing" target="_blank">Curriculum Vita</a></span><br />-<br /><a href="http://www.nctm.org/Publications/mathematics-teaching-in-middle-school/About-Mathematics-Teaching-in-the-Middle-School/" target="_blank">National Council of Teachers of Mathematics Editorial Panel</a><br /><a href="https://www.educateiowa.gov/pk-12/content-areas/mathematics/statewide-mathematics-leadership-team" target="_blank">Iowa Department of Education Statewide Mathematics Leadership Team</a><br /><a href="http://www.ifets.info/reviewers.php" target="_blank">Journal of Educational Technology and Society Executive Peer Reviewer</a><br />-</span></span></div>
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<span style="font-size: xx-small;"><span style="font-family: arial,helvetica,sans-serif;">Ed. D. Curriculum and Instruction (UNI)<br />MA Middle Level Mathematics (UNI)<br /><a href="http://www.uni.edu/newsroom/uni-confers-yager-exemplary-teaching-recognition-awards-0" target="_blank">Yager Exemplary Teaching Award 2014</a></span></span></div>
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<span style="font-size: xx-small;"><span style="font-family: arial,helvetica,sans-serif;"><a href="http://www.grad.uni.edu/sites/default/files/program14_-_final_for_the_web_0.pdf" target="_blank">Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa 2014</a><br />-</span></span></div>
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<span style="font-size: xx-small;"><span style="font-family: arial,helvetica,sans-serif;"><a href="http://twitter.com/Doctor_Math" target="_blank">@Doctor_Math</a></span></span></div>
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<span style="font-size: xx-small;"><span style="font-family: arial,helvetica,sans-serif;"><a href="http://tinyurl.com/grundymsmath" target="_blank">Classroom Math Website</a></span></span></div>
<span style="font-size: xx-small;"><span style="font-family: arial,helvetica,sans-serif;"><a href="http://pagingdoctormath.blogspot.com/" target="_blank">Blog</a></span></span><div>
<span style="font-size: xx-small;"><span style="font-family: arial,helvetica,sans-serif;"><a href="http://tinyurl.com/mathematicstasks" target="_blank">Problem-Solving Task Spreadsheet</a></span></span><div>
<span style="font-size: xx-small;"><span style="font-family: arial,helvetica,sans-serif;"><a href="http://tinyurl.com/1to1mlmath" target="_blank">1:1 Math Philosophy</a></span></span></div>
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<span style="font-size: xx-small;"><span style="font-family: arial,helvetica,sans-serif;"><a href="http://tinyurl.com/taskmathpresent" target="_blank">Task-Based Mathematics Presentation</a></span></span></div>
<span style="font-size: xx-small;"><span style="font-family: arial,helvetica,sans-serif;"><a href="https://docs.google.com/document/d/12m3kTMqEz0UjQdNwswhzNZR48vrG4nxO0Nmp85nlo3E/edit?usp=sharing" target="_blank">Student/Parent Expectations - About Dr. Edwards</a></span></span></div>
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Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-67661170579162187902016-11-14T09:58:00.002-06:002016-11-14T09:58:30.482-06:00Mathematics Tasks for 2016-2017/The Pokemon Go TaskI've been doing a lousy job of blogging. I've thought to myself many times that I have no idea how I blogged in previous years. Last year at my university job, I always made a point to tell my preservice teachers just how much time and effort it takes to even do an adequate job teaching. I may have even underestimated that point, because clearly I forgot how much time this job takes up.<br />
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With that being said, I think it is important to get the tasks that my students have done this year out to other math teachers so they know what is possible. I have had multiple groups of teachers come into my classroom this year, and the comments are always the same...<br />
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1. I wish my students communicated like that...<br />
2. I wish my students showed understanding like that...<br />
3. I wish my students stayed on task like that...<br />
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I am very proud to hear these comments, and I always pass the kind words along to my students. One of the comments I don't hear are that my students are geniuses or rocket scientists. I am glad this is recognized by teachers as well, because teachers think that you can only do these tasks with the highest level of student academically (I've heard that comment many times at different presentations I have done). This certainly isn't true, because frankly a lot of my "lower level" students figure these tasks out faster than my traditional "successful" students. My students struggle in general with these tasks, but given time and the allowance of communication, everyone figures them out.<br />
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This process of getting students to communicate, show justification, and stay focused doesn't happen the first time you do one of these tasks. It's a process...sometimes even a slog. I think that problems happen when a teacher gives up on these tasks after the first try. You must keep plugging away. The benefits will far outweigh any struggles you have. All of these positives that teachers pick out carry over into everything else you do. These tasks aren't novelties, but an expectation of how everything should go in class. Even on days we don't do these tasks, my students display these desirable traits (for the most part...they are middle school students :-) ).<br />
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I think from here on out, I will post one task every so often, talk very briefly about it, and post some student work. Feel free to use these tasks, ask questions about these tasks, give suggestions to make these tasks better, etc. I will make sure to link where each task was adapted from so you can go right to the source if you wish.<br />
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I did the Pokemon Go task with my 8th grade students. I adapted this from <a href="https://vimeo.com/178429549" target="_blank">Dan Meyer</a>. I polled my students before I did this task, and only a small percentage had ever played Pokemon Go, so I was initially worried that some students wouldn't understand what I was going for. I ended up having very few question about the mechanics of the game, so don't worry about that. One idea that many student brought up after the fact was that we didn't calculate for the middle of the fan. I did not take this into account when I went through my task either, so I will have to account for it next time. As sad as the last two question are, they are both true depictions of my weekends these days. I have included a few pieces of student work along with my notes that I took the first time I prepared for this task. Hopefully I will have time to include these tasks a little more frequently, but here are links to both of my task pages for the year (updated as we do more tasks) in case you are curious what else we have done. <br />
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<a href="https://docs.google.com/document/d/18W8oZxaCETimqG7Tphksh3Dmrk4M0Bc-qnlJ0qtz02M/edit?usp=sharing" target="_blank">7th Tasks</a><br />
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<a href="https://docs.google.com/document/d/11x8i6mk7T1cq60SNjNX2I8_R9N090WY5aLtM-t2R8lw/edit?usp=sharing" target="_blank">8th Tasks</a><br />
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 14.666666666666666px; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline;">Task Nine ~ Pokemon Go (Dan Meyer)</span></div>
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<a href="https://vimeo.com/178429549" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 18.666666666666664px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Info One</span></a></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 18.666666666666664px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Info Two ~ 100000 cm = 1 km</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 18.666666666666664px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Info Three ~ 1 mile = 1.61 km</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 18.666666666666664px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Info Four ~ 1 mile = 5280 feet</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 18.666666666666664px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Info Five ~ Each of the fan’s blades is 45 cm long</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 18.666666666666664px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Info Six ~ The fan spins at a rate of 10 rotations for every 8 seconds</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 18.666666666666664px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Info Seven </span><a href="https://docs.google.com/document/d/1e5AxV7e-iVTPjd0QDvEnqLbZDDCg0hKoQoSNpwYG8_o/edit?usp=sharing" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 18.666666666666664px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline;">Target Map</span></a></div>
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<span style="background-color: cyan; color: black; font-family: Arial; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Q1</span><span style="background-color: transparent; color: black; font-family: Arial; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> ~ How long would it take to hatch the 5 km egg using the ceiling fan?</span></div>
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<span style="background-color: cyan; color: black; font-family: Arial; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Q2</span><span style="background-color: transparent; color: black; font-family: Arial; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> ~ My daughter was sleeping in the car while my wife went into Target. If I stop the car, my daughter will wake up, so I kept driving around the Target building until my wife was finished. If I kept at an average speed of around 6 miles per hour, how many laps did I make in the time she was in Target if she was in the store for 20 minutes?</span></div>
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<span style="background-color: cyan; color: black; font-family: Arial; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Q3</span><span style="background-color: transparent; color: black; font-family: Arial; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;"> ~ I had my Pokemon Go app on as I was driving around Target (I wasn’t playing...it was just on). How many 2km eggs (I started with 4) did I hatch in the 20 minutes if all of my 2km eggs started at 0km?</span><br />
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<span style="font-size: x-small;"><span style="font-family: arial,helvetica,sans-serif;">Dr. Clayton M. Edwards<br />Grundy Center Middle School<br />Middle School Mathematics Instructor<br /><span><a href="https://docs.google.com/document/d/16THWEeMiU_NWflzhC-EjWUK-_3Xj8sx5LBlJ7S_upYI/edit?usp=sharing" target="_blank">Curriculum Vita</a></span><br />-<br /><a href="http://www.nctm.org/Publications/mathematics-teaching-in-middle-school/About-Mathematics-Teaching-in-the-Middle-School/" target="_blank">National Council of Teachers of Mathematics Editorial Panel</a><br /><a href="https://www.educateiowa.gov/pk-12/content-areas/mathematics/statewide-mathematics-leadership-team" target="_blank">Iowa Department of Education Statewide Mathematics Leadership Team</a><br /><a href="http://www.ifets.info/reviewers.php" target="_blank">Journal of Educational Technology and Society Executive Peer Reviewer</a><br />-</span></span></div>
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<span style="font-size: x-small;"><span style="font-family: arial,helvetica,sans-serif;">Ed. D. Curriculum and Instruction (UNI)<br />MA Middle Level Mathematics (UNI)<br /><a href="http://www.uni.edu/newsroom/uni-confers-yager-exemplary-teaching-recognition-awards-0" target="_blank">Yager Exemplary Teaching Award 2014</a></span></span></div>
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<span style="font-size: x-small;"><span style="font-family: arial,helvetica,sans-serif;"><a href="http://www.grad.uni.edu/sites/default/files/program14_-_final_for_the_web_0.pdf" target="_blank">Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa 2014</a><br />-</span></span></div>
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<span style="font-size: x-small;"><span style="font-family: arial,helvetica,sans-serif;"><a href="http://twitter.com/Doctor_Math" target="_blank">@Doctor_Math</a></span></span></div>
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<span style="font-size: x-small;"><span style="font-family: arial,helvetica,sans-serif;"><a href="http://tinyurl.com/grundymsmath" target="_blank">Classroom Math Website</a></span></span></div>
<span style="font-size: x-small;"><span style="font-family: arial,helvetica,sans-serif;"><a href="http://pagingdoctormath.blogspot.com/" target="_blank">Blog</a></span></span><div>
<span style="font-size: x-small;"><span style="font-family: arial,helvetica,sans-serif;"><a href="http://tinyurl.com/mathematicstasks" target="_blank">Problem-Solving Task Spreadsheet</a></span></span><div>
<span style="font-size: x-small;"><span style="font-family: arial,helvetica,sans-serif;"><a href="http://tinyurl.com/1to1mlmath" target="_blank">1:1 Math Philosophy</a></span></span></div>
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<span style="font-size: x-small;"><span style="font-family: arial,helvetica,sans-serif;"><a href="http://tinyurl.com/taskmathpresent" target="_blank">Task-Based Mathematics Presentation</a></span></span></div>
<span style="font-size: x-small;"><span style="font-family: arial,helvetica,sans-serif;"><a href="https://docs.google.com/document/d/12m3kTMqEz0UjQdNwswhzNZR48vrG4nxO0Nmp85nlo3E/edit?usp=sharing" target="_blank">Student/Parent Expectations - About Dr. Edwards</a></span></span></div>
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Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-4111775144217287762016-06-29T11:35:00.000-05:002016-06-29T11:49:10.850-05:00What to Expect From the Blog and Me in 2016-2017It is still June, but I am very excited to get the school year started. I had a great year at UNI as the middle level coordinator. UNI is a first class institution with great faculty, staff, and most importantly, wonderful students. I felt like I was able to make a difference in my classes and with the middle level program, but I missed working with middle school students, so I was lucky enough to be able to get my job back. <br />
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I am busy revamping my classroom website, locating and testing new tasks, and getting prepared for the grind that is the school year. The great thing about summer as a teacher is I can still work 3 or 4 hours a day (compared to the 12 or 13 during the school year) and still have time to spend doing summer type activities. <br />
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If you are new to my blog, I normally post about mathematical tasks I have done in the classroom. I post student work, and let you know what went well and what could be improved so if you try these tasks, you will know what to expect.<br />
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Here are a few of my previous posts to give you an idea...<br />
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<a href="http://pagingdoctormath.blogspot.com/2015/01/in-n-out-burger-task.html" target="_blank">In-N-Out Burger Task</a><br />
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<a href="http://pagingdoctormath.blogspot.com/2014/12/man-versus-squirrel.html" target="_blank">Man Versus Squirrel</a><br />
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<a href="http://pagingdoctormath.blogspot.com/2015/04/doritos-roulette.html" target="_blank">Doritos Roulette</a><br />
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I look forward to doing these tasks again, along with the many tasks on my spreadsheet I have tested...<br />
<a href="https://docs.google.com/spreadsheets/d/1odw5amLUL77vBwOIt8bw72WRntZBWxwVHLAmeyMGAME/edit#gid=0" target="_blank"><br /></a>
<a href="https://docs.google.com/spreadsheets/d/1odw5amLUL77vBwOIt8bw72WRntZBWxwVHLAmeyMGAME/edit#gid=0" target="_blank">Mathematical Task Spreadsheet</a><br />
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I found some new tasks as well that I know my students will enjoy...<br />
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<a href="http://fawnnguyen.com/vroom-vroom/" target="_blank">Vroom Vroom</a><br />
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<a href="https://docs.google.com/document/d/1CSWG-r7BwOI4xxlDZROzSDTWanmEkU1VYSWUIstlvxw/edit" target="_blank">The Nardo Ring</a><br />
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<a href="http://blog.mrmeyer.com/2016/gas-station-ripoff/" target="_blank">Gas Station Ripoff</a> <br />
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<a href="https://teacher.desmos.com/marbleslides-lines" target="_blank">Marble Slide</a><br />
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The nice things about these tasks is that many come with base questions, but you can expand your questioning to include what students are wondering about the situation. By the way, a big thanks to the <a href="https://twitter.com/hashtag/mtbos?f=tweets&vertical=default" target="_blank">#MTBoS</a> and other math professionals on Twitter for consistently pumping out these tasks for my students to enjoy. <br />
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I will also be involved in a few professional development and speaking opportunities where I will be discussing <a href="http://tinyurl.com/1to1mlmath" target="_blank">1:1 Mathematics</a>, and <a href="http://tinyurl.com/taskmathpresent" target="_blank">Task-Based Mathematics</a>.<br />
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Finally, I am in year two of being on <a href="http://www.nctm.org/Publications/mathematics-teaching-in-middle-school/About-Mathematics-Teaching-in-the-Middle-School/" target="_blank">NCTM's MTMS Editorial Panel</a>. This is such a great opportunity for me to get involved with middle level math on a national level and meet other math professionals I wouldn't normally get the chance to meet.<br />
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I look forward to blogging this year and hopefully helping you feel good about implementing tasks into your <span style="font-size: small;">classrooms</span>! Have a great summer!<br />
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<span style="font-size: small;">Dr. Clayton M. Edwards<br />Grundy Center Middle School<br />Middle School Mathematics Instructor</span><br />
<span style="font-size: small;"><a href="http://www.nctm.org/Publications/mathematics-teaching-in-middle-school/About-Mathematics-Teaching-in-the-Middle-School/" target="_blank">National Council of Teachers of Mathematics Editorial Panel</a></span></div>
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<span style="font-size: small;">Former Middle Level Coordinator (UNI)</span><br />
<span style="font-size: small;">Ed. D. Curriculum and Instruction (UNI)<br />MA Middle Level Mathematics (UNI) </span><br />
<span style="font-size: small;"><a href="http://www.uni.edu/newsroom/uni-confers-yager-exemplary-teaching-recognition-awards-0" target="_blank">Yager Exemplary Teaching Award 2014</a></span></div>
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<span style="font-size: small;">Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa 2014</span></div>
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<span style="font-size: small;"><a href="mailto:cedwards@spartanpride.net" target="_blank">cedwards@spartanpride.net</a></span></div>
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<span style="font-size: small;"><a href="http://twitter.com/Doctor_Math" target="_blank">@Doctor_Math</a></span></div>
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<span style="font-size: small;"><a href="https://docs.google.com/document/d/16THWEeMiU_NWflzhC-EjWUK-_3Xj8sx5LBlJ7S_upYI/edit?usp=sharing" target="_blank">Curriculum Vita</a> </span></div>
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<span style="font-size: small;"><a href="http://tinyurl.com/grundymsmath" target="_blank">Classroom Math Website</a></span></div>
<span style="font-size: small;"><a href="http://pagingdoctormath.blogspot.com/" target="_blank">Blog</a></span><br />
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<span style="font-size: small;"><a href="http://tinyurl.com/mathematicstasks" target="_blank">Problem-Solving Task Spreadsheet</a></span><br />
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<span style="font-size: small;"><a href="http://tinyurl.com/1to1mlmath" target="_blank">1:1 Math Philosophy</a> </span></div>
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<span style="font-size: small;"><a href="http://tinyurl.com/taskmathpresent" target="_blank">Task-Based Mathematics Presentation</a></span></div>
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</span><span style="font-size: small;"><a href="https://docs.google.com/document/d/12m3kTMqEz0UjQdNwswhzNZR48vrG4nxO0Nmp85nlo3E/edit?usp=sharing" target="_blank">Student/Parent Expectations - About Dr. Edwards</a></span></div>
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Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-27049758291972225652016-01-04T14:29:00.000-06:002016-01-04T14:30:15.397-06:00Cube Net Task and the Excitement of Substitute TeachingI miss working with middle school students on an everyday basis.
There, I said it. Don't get me wrong, I enjoy my new job as a middle
level coordinator in higher education. I get to work closely with middle
level preservice teachers and make an impact on their future teaching
and the successes of all the students they will ever have in a
classroom. I had a wonderful group of students for my first semester who
I thought were genuinely curious to learn about what really goes on in a
middle level classroom and how to best serve middle level students.<br />
<br />
One
of the preservice teachers asked me point-blank "if you liked teaching
middle school students so much, why did you leave?" That was a great
question, and of course the answer was to have a more widespread impact
on middle level education and NOT because I was trying to get away from
middle school students. I took that question as making sure I had a
genuine connection to middle school students, which I appreciated. Just
like middle school students, college students will be brutally
honest...and that is why we get along well.<br />
<br />
I still
have a strong connection to my previous school district, and I am very
grateful for that. I enjoyed working with the students and staff. I go
back frequently for many reasons, with the most important being access
to the classroom...making sure I don't lose touch with the reality that
is middle school. I feel like this gives me a lot credibility with my
preservice teachers, and I enjoy it as well. I also went back for a few
open gyms over break...I am only 30 something, but I felt like I was
near the end after that experience. I didn't know my feet could fit so
many blisters.<br />
<br />
Recently, I had a unique opportunity
to actually be a substitute teacher in my old classroom. I didn't have
class scheduled in the morning when I was needed to sub, so I jumped on
the opportunity. The day I was there was the start of a new trimester,
so the current teacher left it up to me what to plan for the day. As you
can tell from my previous blog posts, I am into <a href="https://docs.google.com/spreadsheets/d/1odw5amLUL77vBwOIt8bw72WRntZBWxwVHLAmeyMGAME/edit?usp=sharing" target="_blank">robust problem-solving tasks</a>, so I thought I would go that route.<br />
<br />
From
my past experiences, my sixth grade students always seemed to lack in
justification, collaboration, and problem-solving skills (not so much in
math content knowledge). I don't know why that was (maybe the middle
school transition or using a more traditional curriculum?), but when I
gave them one of these <a href="https://docs.google.com/spreadsheets/d/1odw5amLUL77vBwOIt8bw72WRntZBWxwVHLAmeyMGAME/edit?usp=sharing" target="_blank">tasks</a>,
you would have thought I gave them something in an unfamiliar
language. For example, when I first get my 6th graders, I would ask
them to justify an answer, and many would write, "I used a calculator"
or "mental math." They would give up at the drop of a hat when something
was difficult (which it always was). It generally took a month or so
for most of the 6th graders to be comfortable with what justification
and perseverance, but when they did, we were able to reach some truly
amazing mathematical heights.<br />
<br />
I decided to select a
task dealing with nets and if they could be folded into cubes. The
closest 6th grade standard to this would be<span style="font-size: small;"><span style="font-family: inherit;"><b> </b></span></span><span style="font-size: small;"><span style="font-family: inherit;"><b><span style="font-family: inherit;"><b id="docs-internal-guid-0636172e-d040-ff86-4430-e357c4617c28" style="font-weight: normal;"><a href="http://www.corestandards.org/Math/Content/6/G/A/4/" style="text-decoration: none;" target="_blank"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">6.G.A.4</span></a></b></span></b>,
but that is probably a stretch. You would only focus on the solving
problems with nets and ignoring the rest. I wasn't too worried about the
standard anyway, because I was more concerned with the mathematical
understanding and collaboration. This task is very accessible to many
different grade levels and that helps to focus on the process standards
without worrying about the content <span style="font-family: inherit;">so much</span>. </span></span><br />
<span style="font-size: small;"><span style="font-family: inherit;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: inherit;">Here are the directions for the task (note: this task comes from </span></span><span style="font-size: small;"><span style="font-family: inherit;"><span style="font-family: inherit;"><b id="docs-internal-guid-0636172e-d045-0fd5-f369-7a40902313a7" style="font-weight: normal;"><a href="https://twitter.com/NCTMIllum" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">@NCTMillum</span></a></b></span>):</span></span><br />
<span style="font-size: small;"><span style="font-family: inherit;"><br /></span></span>
<a href="https://docs.google.com/document/d/15_KoeEJ9hkW3-fn9AhUm6Vgo7PYGeRe-3AQgGeWKUq4/edit?usp=sharing" target="_blank"><span style="font-size: small;"><span style="font-family: inherit;">https://docs.google.com/document/d/15_KoeEJ9hkW3-fn9AhUm6Vgo7PYGeRe-3AQgGeWKUq4/edit?usp=sharing</span></span></a><br />
<br />
Before
we started, I put up a simplified version of my classroom expectations.
My expectations are centered on students improving and not worry about
their current standing compared to others...just getting better all the
time. This is a strange concept for most students who I haven't had. I
can keep making mistakes and correcting until I understand? You won't
leave me behind? I still get full credit if I end up showing
understanding even if it isn't on the first try? I had no idea another
person with this philosophy existed until I ran into <a href="https://twitter.com/rickwormeli2" target="_blank">Rick Wormeli</a> at <a href="http://amle.org/" target="_blank">AMLE</a>. <br />
<br />
They
are always louder than a whisper, but if you are going for a 2 on a
1-10 scale with 10 being the loudest they could be, and they want a 10,
I'll happily take a 4 so everyone can have a meaningful discussion and
hear themselves think. <br />
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<br />
<br />
<span style="background-color: white;">I
generally let students work with others they were comfortable talking
with so there aren't a lot of conversational barriers. I printed off
two copies of this sheet off of the </span><span style="font-size: small;"><span style="font-family: inherit;"><span style="font-family: inherit;"><b id="docs-internal-guid-0636172e-d045-0fd5-f369-7a40902313a7" style="font-weight: normal;"><a href="https://twitter.com/NCTMIllum" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">@NCTMillum</span></a> <a href="http://illuminations.nctm.org/Activity.aspx?id=3544" target="_blank">website</a> so students had plenty of room to write</b><span style="font-weight: normal;"><span style="font-family: inherit;">, draw, and explain. </span></span></span></span></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-PQCkwIZGr5G5AatUl9LpGzwrOLrOY_lI7BmjBkcjrR438ZniXbln7c8upTWChjSeDADwJBkzxuq7BoJ3A9bfI9PmoAFcLes_IZasW09S9dp9jUiECgXFg4NYCP7VqQAfl9TBh8oVeyix/s1600/Screen+Shot+2015-12-23+at+1.44.35+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="111" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-PQCkwIZGr5G5AatUl9LpGzwrOLrOY_lI7BmjBkcjrR438ZniXbln7c8upTWChjSeDADwJBkzxuq7BoJ3A9bfI9PmoAFcLes_IZasW09S9dp9jUiECgXFg4NYCP7VqQAfl9TBh8oVeyix/s200/Screen+Shot+2015-12-23+at+1.44.35+PM.png" width="200" /></a></div>
<br />
<br />
<span style="font-size: small;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-weight: normal;"><span style="font-family: inherit;">Keep in mind that the order of the nets shifts around ever<span style="font-family: inherit;">y time you start the online portion of the activity over, but it is easy to find which <span style="font-family: inherit;">net
the students are talking about. We did not use their 1:1 laptops for
this activity even though the activity was online. I like to save that
for the<span style="font-family: inherit;"> discussion at the end. There are 11 nets<span style="font-family: inherit;"> that make cubes and 13 nets where something is <span style="font-family: inherit;">incorrect (not enough faces, too many t<span style="font-family: inherit;">ops, e<span style="font-family: inherit;">tc)</span></span>. I did not tell them how many did or did not<span style="font-family: inherit;">. </span></span></span></span></span></span></span></span></span></span></span><br />
<br />
<span style="font-size: small;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-weight: normal;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;">This activity really takes 60+ minutes to do it right. I was there on an early out day with 40 minute classes<span style="font-family: inherit;">,</span> and by the <span style="font-family: inherit;">time we did a few introductions and went over expectations<span style="font-family: inherit;">/task objectives, we ha<span style="font-family: inherit;">d about 30 minutes<span style="font-family: inherit;"> of student work time<span style="font-family: inherit;">/discussion.</span></span></span></span></span>
I had the students put the sheets in a safe place in case I got an
opportunity to come back and finish the task (I know what you are think<span style="font-family: inherit;"><span style="font-family: inherit;">ing</span>...fat chance a 6th grader could hold onto a piece of paper for 2 m<span style="font-family: inherit;"><span style="font-family: inherit;">onths</span>...it could happen :-)</span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<span style="font-size: small;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-weight: normal;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"> <span style="font-family: inherit;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<span style="font-size: small;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-weight: normal;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;">Right away, I could tell that some of the students were not strong with sp<span style="font-family: inherit;"><span style="font-family: inherit;">atial</span> thinking. <span style="font-family: inherit;">I
try not to butt in too much, but listen to the ongoing conversations.
One of the students who was confident in spatial thinking was trying to
help a student by <span style="font-family: inherit;">explaining that it made thinking about the cube easier if you picked o<span style="font-family: inherit;"><span style="font-family: inherit;">ut</span> one of the faces to be the bottom before starting, and go <span style="font-family: inherit;">from
there. I thought this was sound advice, so I let this student explain
to the class what she was thinking. I think this idea helped jump start a
few individuals. </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<br />
<span style="font-size: small;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-weight: normal;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;">I enjoy using tasks from @jstevens<span style="font-family: inherit;">009 and his site, <a href="http://www.wouldyourathermath.com/">www.wouldyourathermath.com</a><span style="font-family: inherit;">, and I saw a lot of that argumentative<span style="font-family: inherit;"> sp<span style="font-family: inherit;"><span style="font-family: inherit;">irit</span> come out in these students when I am not sure they had ever thought about math this w<span style="font-family: inherit;"><span style="font-family: inherit;">ay</span> before. Two boys were paired up, and<span style="font-family: inherit;"> they were<span style="font-family: inherit;"> not getting very far in <span style="font-family: inherit;">making a decision on this net...</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-weight: normal;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span> </span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<br />
<span style="font-size: small;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-weight: normal;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;">This seems pretty cut and dry to me, but from a 6th graders perspective who has been us<span style="font-family: inherit;">e<span style="font-family: inherit;">d to going with a gu<span style="font-family: inherit;">t feeling, I could see why he thought it was a cube.<span style="font-family: inherit;"> The conversation between these two boys was basically a yes it was, no it wasn't back and forth<span style="font-family: inherit;">, which was going no where. <span style="font-family: inherit;">I
noticed this as I was walking around and stopped to talk with them. I
reiterated the need for justifications, and told them to separate for a
few minutes, come up with their best <span style="font-family: inherit;">arguments</span>,
and come back together to make a decision. I gave no indication of who
was correct and who was not. When they got back together, they had
actually both came up with the same reasoning for it not being a cube,
meaning that after taking the time to think and justify, one of the boys
change<span style="font-family: inherit;">d positions. Both boys actually pictured the top<span style="font-family: inherit;">/middle squ<span style="font-family: inherit;">are as being the bottom and stated that there could never be a back side <span style="font-family: inherit;">and the top would overlap. This is a great example of the power of individual think time be<span style="font-family: inherit;">fore talking with a group. It <span style="font-family: inherit;">arms every<span style="font-family: inherit;">one with ideas instead of just accepting what someone else has or d<span style="font-family: inherit;"><span style="font-family: inherit;">enying</span> someone's suggestions just because a gut feeling told you so. </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<br />
I
had been in this classroom before helping out, and like any 6th grade
classroom, there are some student who just need to be doing something.
Listening to someone talk at them for 40 minutes doesn't work for them. I
noticed those students really shining. They were free to talk and
discuss, and they were getting to create the knowledge. These types of
tasks are perfect for middle school students and their unique needs.<br />
<br />
I
wanted to keep letting them work, but we were running low on time. I
put the computer version of this task on the screen and called on random
students to select one of the nets and tell me yes it makes a cube, or
no it does not and why. The students had plenty of time to work through
justification with each other, so I did not feel bad at all calling on
different individuals. They were prepared because I gave them plenty of
time. Some of the answers were simplistic but to the point. "This cannot
be a cube because it only has 5 sides (note: we did have a conversation
about what a face is to clarify)." Some of the students thought it
would be best to show a model of what they were doing, so one student
actually grabbed some textbooks and started folding them up like each
book was a face. After the student explained, I click on yes or know and
the animation folded up. In one instance, a student was incorrect, but
we had a discussion on what their misconception was based off of the
animation. This is another value of the improvement mindset. It's more
of an environment, really. Sometimes you feel bad if someone has a
faulty explanation and you have to correct the student, but when the
goal is improvement, students don't see it as being so bad. It gives
them a chance to learn and it gives other students a chance to further
explain misconceptions. I only knew these students for a short time, and
to them, this concept of improvement was an epiphany. <br />
<br />
Overall,
this is a very accessible task to start addressing the concept of
justification with your students. This would be one of the first tasks I
would do to make that point. If your students are not used to
justifying, you will get weak justifications at first, but you have to
understand that your students probably don't know any better. It is your
job to get them to that point. Trust me, it will get better. Here is a
collection of student work from that day. Hopefully you will notice how
quickly we were able to go from "this is a cube because it folds into a
cube," to some of the justifications listed on the student work.<br />
<br />
(Notes:
not all of the student work is correct...but I hope to have more time
in the future to discuss, and some of the incorrect work was discussed
during our discussion portion of class. Some of the justifications have
letters like B to represent bottom or back and so forth...you have to
look closely. There was a wide variance in how far the student got,
which was alright. I would allow for as much time as needed normally).<br />
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: white; color: #222222; display: inline ! important; float: none; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;">Dr. Clayton M. Edwards</span></span></span>
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<div style="background-color: white; color: #222222; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 1; word-spacing: 0px;">
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: white; color: #222222; display: inline ! important; float: none; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;">Assistant Professor of Curriculum and Instruction </span></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: white; color: #222222; display: inline ! important; float: none; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;">Middle Level Program Coordinator </span></span></span></div>
<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: white; color: #222222; display: inline ! important; float: none; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;">University of Northern Iowa</span></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: white; color: #222222; display: inline ! important; float: none; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;">Schindler Education Center/Nielsen Field House</span><br /><a href="https://drive.google.com/file/d/0B4KWbB3Q5yolSHo1MU9KUmVlUWc/view?usp=sharing" style="color: #1155cc;" target="_blank">Middle Level Major Requirements</a><br /><a href="http://www.nctm.org/About/President,-Board-and-Committees/Committees-and-Appointees/Mathematics-Teaching-in-the-Middle-School-Editorial-Panel-%28MTMS%29/" style="color: #1155cc;" target="_blank">National Council of Teachers of Mathematics Editorial Panel</a></span></span></div>
<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: white; color: #222222; display: inline ! important; float: none; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;"><a href="https://docs.google.com/document/d/1GtUIPZ4xdXsdyTD61bSwetxDJkjPsZ5dyVg4ABlNT1g/edit?usp=sharing" style="color: #1155cc;" target="_blank">Curriculum Vita</a></span></span></span></div>
<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: white; color: #222222; display: inline ! important; float: none; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;"><a href="https://twitter.com/doctor_math" style="color: #1155cc;" target="_blank">@doctor_math</a></span></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><a href="http://pagingdoctormath.blogspot.com/" style="color: #1155cc;" target="_blank">Blog</a></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: white; color: #222222; display: inline ! important; float: none; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;"><a href="http://www.linkedin.com/in/doctoredwards" style="color: #1155cc;" target="_blank">Linkedin</a></span></span></span></div>
<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: white; color: #222222; display: inline ! important; float: none; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;"><a href="http://tinyurl.com/mathematicstasks" style="color: #1155cc;" target="_blank">Mathematical Tasks Spreadsheet</a></span></span></span></div>
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<span style="font-family: inherit;"><span style="background-color: white; color: #222222; display: inline ! important; float: none; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: 1; word-spacing: 0px;"><a href="http://tinyurl.com/1to1math" style="color: #1155cc;" target="_blank">1:1 Mathematical Philosophy</a></span></span></span>Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-33695245170332853082015-12-08T11:33:00.000-06:002015-12-23T13:33:33.549-06:00The 12 Math Tasks of Christmas...I have a lot to be thankful for this holiday season:<br />
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<li>A new daughter</li>
<li>A new job where I can prepare middle level educators while still having many chances to get back into the classroom and work with/teach middle school students </li>
<li>A group of math professionals scattered around the web that pump out mathematical task after mathematical task for classroom use <a href="http://tinyurl.com/mathematicstasks" target="_blank">TASK SPREADSHEET</a></li>
</ul>
For this blog, we will focus on the last bullet. Over the next 12 days (school days), I will be linking a task to this post each day, which should take us up to December 23rd. Hopefully this will be a great opportunity to start thinking about implementing these tasks after your holiday break. I also hope that this introduces you to the lovely people out there who have made my students' mathematical experiences that much better. The ties to the holidays are VERY loose :-) I am short on actual holiday related tasks. Happy holidays!<br />
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<b>Day One ~ You can feed your leftover fruitcake to this giant squirrel...</b><br />
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Courtesy of <a href="https://twitter.com/emergentmath" target="_blank">@emergentmath</a> and also adapted by <a href="https://twitter.com/DaneEhlert" target="_blank">@daneehlert</a><br />
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<a href="http://bit.ly/1yOk5er" target="_blank">Man Versus Squirrel Blog Post With Student Work</a><br />
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<a href="http://bit.ly/1AXtDqk" target="_blank">Man Versus Squirrel Student Directions </a><br />
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<b>Day Two ~ Mmmmm...holiday cookies (use your imagination)</b><br />
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Courtesy of <a href="https://twitter.com/MathletePearce" target="_blank">@mathletepearce</a><br />
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<a href="http://pagingdoctormath.blogspot.com/2015/03/cookie-cutter-task.html" target="_blank">Cookie Cutter Task Blog Post With Student Work</a><br />
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<a href="http://bit.ly/1MhEopX" target="_blank">Cookie Cutter Task Student Directions</a><br />
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<b>Day Three ~ Instead of serving ham for the holidays, try this big stack of beef...</b><br />
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Courtesy of <a href="https://twitter.com/robertkaplinsky" target="_blank">@robertkaplinsky</a><b> </b><br />
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<a href="http://pagingdoctormath.blogspot.com/2015/01/in-n-out-burger-task.html" target="_blank">In-N-Out Burger Task Blog Post With Student Work</a><b> </b><br />
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<a href="https://docs.google.com/document/d/10x4cpP4wtwo75HbE9JKly8TEg7kfUEVIlJ-olZ5zdPE/edit?usp=sharing" target="_blank">In-N-Out Burger Task Student Directions</a><br />
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<b>Day Four ~ It would be nice if I could print money to buy presents for the holidays...</b><br />
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Courtesy of<b> </b><a href="https://twitter.com/ddmeyer" target="_blank">@ddmeyer</a><br />
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<a href="http://pagingdoctormath.blogspot.com/2015/02/shrinking-dollar-task.html" target="_blank">Shrinking Dollar Task Blog Post With Student Work</a><b> </b><br />
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<a href="https://docs.google.com/document/d/1gkd4v2-ClRAmYW9e5E-O67vQSb5L0xqohqEFSLD8yxE/edit?usp=sharing" target="_blank">Shrinking Dollar Task Student Directions</a><b> </b> <b> </b><br />
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<b>Day Five ~ Buying presents can be expensive, especially if your budget consists of only pennies in a cube 6 inch cube...</b><br />
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Courtesy of <a href="https://twitter.com/mikewiernicki" target="_blank">@mikewiernicki</a><b> </b><br />
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<a href="http://pagingdoctormath.blogspot.com/2015/02/penny-cube-task.html" target="_blank">Penny Cube Task Blog Post With Student Work</a><br />
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<a href="https://docs.google.com/document/d/1RVUfzL1s9QHa4DyxAovkguNI-BE4ZQuVkxA58-nD4V4/edit?usp=sharing" target="_blank">Penny Cube Task Student Directions</a><br />
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<b>Day Six ~ The ultimate holiday party game...Giant Jenga!</b><br />
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Courtesy of <a href="https://twitter.com/DaneEhlert" target="_blank">@daneehlert</a><br />
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<a href="http://pagingdoctormath.blogspot.com/2015/02/jenga-task.html" target="_blank">Jenga Task Blog Post With Student Work</a><br />
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<a href="https://docs.google.com/document/d/1c5y6oDjbD8s8veZYFJL6sWPlNSHxKCtJB9im7nUX-rk/edit?usp=sharing" target="_blank">Jenga Task Student Directions</a><br />
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<b>Day Seven ~ The weather has been so nice in Iowa that I might have to mow in December...</b><br />
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Courtesy of <a href="https://twitter.com/MathletePearce" target="_blank">@mathletepearce</a><br />
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Lawn Mowing Task Student Work Example (for whatever reason I didn't keep all the student work for this, but here is one example...good luck reading it :-)<br />
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<a href="https://twitter.com/Doctor_Math/status/535796489885216768" target="_blank">Part One of Student Work</a><br />
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<a href="https://twitter.com/Doctor_Math/status/535911193282502657" target="_blank">Part Two of Student Work</a> <br />
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<a href="https://docs.google.com/document/d/1hAaSTkwQEDbZR71l1JiXTKSbocaphhCYrbrSPJC-KNs/edit?usp=sharing" target="_blank">Lawn Mowing Task Student Directions</a><br />
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<b>Day Eight ~ Inflatable Holiday Decorations...How Long to Inflate?</b><br />
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Courtesy of <a href="https://twitter.com/DaneEhlert" target="_blank">@daneehlert</a><br />
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<a href="http://pagingdoctormath.blogspot.com/2015/03/air-pump-task.html" target="_blank">Air Pump Task Blog Post With Student Work</a><br />
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<a href="https://docs.google.com/document/d/1Om65Y_0ut4gwqsq0w8SzghjJl4v18a1sxbIaaGRyVE0/edit?usp=sharing" target="_blank">Air Pump Task Student Directions</a><br />
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<b>Day Nine ~ Laying some new tile? I don't know what that has to do with the holidays, but it was a great task...</b><br />
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Courtesy of Santa??? I am not really sure where this came from, but I would like to know.<br />
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<a href="http://pagingdoctormath.blogspot.com/2015/02/tile-floor-task.html" target="_blank">Tile Floor Task Blog Post With Student Work</a><br />
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<a href="https://docs.google.com/document/d/1RX4H5tPXcxw18HvZHuKkY3F4Bv-jRKef1URmGsfqFxM/edit?usp=sharing" target="_blank">Tile Floor Task Student Directions</a><br />
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<b>Day Ten ~ This is going to turn into the 11 tasks of the holiday season...I didn't have time to post today. Sorry for the inconvenience! </b><br />
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<b>Day Eleven ~ These toothpicks make a festive tree for the holiday season...</b><br />
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Courtesy of<b> </b><a href="https://twitter.com/ddmeyer" target="_blank">@ddmeyer</a><br />
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<a href="http://pagingdoctormath.blogspot.com/2014/12/toothpick-task.html" target="_blank">Toothpick Task Blog Post With Student Work</a><br />
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<a href="https://docs.google.com/document/d/1suYKZCu67Xcovu4Ugxd3B6x-USABokDhZnkG0QRbnMw/edit?usp=sharing" target="_blank">Toothpick Task Student Directions</a><br />
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<b> Day Twelve ~ These blocks might be a popular holiday gift...</b><br />
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Courtesy of <a href="https://twitter.com/fawnpnguyen" target="_blank">@fawnpnguyen</a> and <a href="https://twitter.com/mr_stadel" target="_blank">@mr_stadel</a><br />
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<a href="http://pagingdoctormath.blogspot.com/2015/05/hotel-snap.html" target="_blank">Hotel Snap Task Blog Post With Student Work</a><br />
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<a href="http://fawnnguyen.com/hotel-snap/" target="_blank">Hotel Snap Directions</a><br />
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<b>I hope this post collection gave you an idea of what students are capable of as well as tasks/task creators to help you plan out the best experience possible for your students. Doing something like these tasks where students get to explore and collaborate makes the entire classroom experience more enjoyable. Middle school students like "doing" and not being led to something, and these tasks provide this type of "doing" experience. Have a wonderful holiday and get your students "doing" after the break!</b><br />
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<b>Here are some other relatable posts if interested:</b><br />
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<a href="http://pagingdoctormath.blogspot.com/2015/05/tasks-and-standardized-tests.html" target="_blank">Tasks and Standardized Testing</a><br />
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<a href="http://pagingdoctormath.blogspot.com/2015/03/how-i-implement-tasks-in-mathematics.html" target="_blank">How to Implement a Mathematical Task</a><br />
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<a href="http://pagingdoctormath.blogspot.com/2014/11/written-and-verbal-mathematical.html" target="_blank">How to Get Your Students Talking and Writing One</a><br />
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<a href="http://pagingdoctormath.blogspot.com/2014/11/written-and-verbal-mathematical_28.html" target="_blank">How to Get Your Students Talking and Writing Two</a><br />
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: white; color: #222222; display: inline ! important; float: none; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;">Dr. Clayton M. Edwards</span></span></span><br />
<div style="background-color: white; color: #222222; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 1; word-spacing: 0px;">
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: white; color: #222222; display: inline ! important; float: none; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;">Assistant Professor of Curriculum and Instruction </span></span></span></div>
<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: white; color: #222222; display: inline ! important; float: none; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;">University of Northern Iowa</span></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: white; color: #222222; display: inline ! important; float: none; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;">Schindler Education Center/Nielsen Field House</span><br /><a href="https://drive.google.com/file/d/0B4KWbB3Q5yolSHo1MU9KUmVlUWc/view?usp=sharing" style="color: #1155cc;" target="_blank">Middle Level Major Requirements</a><br /><a href="http://www.nctm.org/About/President,-Board-and-Committees/Committees-and-Appointees/Mathematics-Teaching-in-the-Middle-School-Editorial-Panel-%28MTMS%29/" style="color: #1155cc;" target="_blank">National Council of Teachers of Mathematics Editorial Panel</a></span></span></div>
<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: white; color: #222222; display: inline ! important; float: none; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;"><a href="https://docs.google.com/document/d/1GtUIPZ4xdXsdyTD61bSwetxDJkjPsZ5dyVg4ABlNT1g/edit?usp=sharing" style="color: #1155cc;" target="_blank">Curriculum Vita</a></span></span></span></div>
<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: white; color: #222222; display: inline ! important; float: none; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;"><a href="https://twitter.com/doctor_math" style="color: #1155cc;" target="_blank">@doctor_math</a></span></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><a href="http://pagingdoctormath.blogspot.com/" style="color: #1155cc;" target="_blank">Blog</a></span></span></div>
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<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: white; color: #222222; display: inline ! important; float: none; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;"><a href="http://www.linkedin.com/in/doctoredwards" style="color: #1155cc;" target="_blank">Linkedin</a></span></span></span></div>
<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: white; color: #222222; display: inline ! important; float: none; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;"><a href="http://tinyurl.com/mathematicstasks" style="color: #1155cc;" target="_blank">Mathematical Tasks Spreadsheet</a></span></span></span></div>
<span style="font-size: small;"><span style="font-family: inherit;"><span style="background-color: white; color: #222222; display: inline ! important; float: none; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: 1; word-spacing: 0px;"><a href="http://tinyurl.com/1to1math" style="color: #1155cc;" target="_blank">1:1 Mathematical Philosophy</a></span></span></span>Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-85169492745557961772015-10-23T21:00:00.003-05:002015-12-03T04:57:39.365-06:00Animal Crossing Amiibo Cards...Can You Collect All 100?I recently collected all 100 of the <a href="http://animal-crossing.com/amiibo-cards/#" target="_blank">series one Animal Crossing Amiibo Cards</a>. Here is a look at my haul (Timmy is probably my favorite)...<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtf5Gv_RQCLcpC6ywpLgLAnjl7Tx77HRa1VvNFzHgoz3Q2ZQ8_tiZLiO0ATYCDlx6YgryQ6DsqOim-jAEJDUEyliFYPPXI3zEbpL-I-TTsMgRSCHXqH0wDiqo0t-6xgMYPpackxTeTTnd4/s1600/FullSizeRender.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtf5Gv_RQCLcpC6ywpLgLAnjl7Tx77HRa1VvNFzHgoz3Q2ZQ8_tiZLiO0ATYCDlx6YgryQ6DsqOim-jAEJDUEyliFYPPXI3zEbpL-I-TTsMgRSCHXqH0wDiqo0t-6xgMYPpackxTeTTnd4/s640/FullSizeRender.jpg" width="480" /></a></div>
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Most people use these cards to interact with different video games that the cards are compatible with. Me...I store them in a box. Probably the more important question is why do I collect these cards in the first place? The short answer is that I am a nerd and we can leave it at that. Here is another painful reminder of my nerdiness, as I collect the Amiibo figures as well.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4y2F_C2F7HXDjOla04Rw4Qhkac-GoEz4_PI9aUmfLDSOrvbJqAX64O4apHcZZr7xUvGRhE7WNx5E4KrdGlGV_bwAqC-Hr8HnZyJqHx-CL2SEz3u-EG-PfKVVxl9N8FEpcpD7FOlslAcUO/s1600/IMG_0393.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4y2F_C2F7HXDjOla04Rw4Qhkac-GoEz4_PI9aUmfLDSOrvbJqAX64O4apHcZZr7xUvGRhE7WNx5E4KrdGlGV_bwAqC-Hr8HnZyJqHx-CL2SEz3u-EG-PfKVVxl9N8FEpcpD7FOlslAcUO/s640/IMG_0393.JPG" width="480" /></a></div>
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Here is a little background on the cards. The cards come in packs of 6 for *gasp* $5.99. For cards 1 through 15 of the series, you will get 1 card per pack out of the six cards. For cards 16 through 100 of the series, you will get 5 cards per pack out of the 6. Cards 1 through 15 are considered special and are sort of glittery (again...nerdy I know).<br />
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The cards are also readily available on eBay in exchange for various amounts of money. Some of the dealers sell <a href="http://www.ebay.com/sch/i.html?_from=R40&_sacat=0&_sop=15&LH_BIN=1&_nkw=animal%20crossing%20amiibo%20cards&rt=nc&LH_PrefLoc=1&_trksid=p2045573.m1684" target="_blank">individuals</a> and some make you choose <a href="http://www.ebay.com/itm/Animal-Crossing-Amiibo-Card-Lot-Pick-3-Please-Read-Finish-Your-Sets/111790894733?_trksid=p2047675.c100011.m1850&_trkparms=aid%3D222007%26algo%3DSIC.MBE%26ao%3D1%26asc%3D33431%26meid%3Dcf74e462a38f4a6b871664af01bac2cd%26pid%3D100011%26rk%3D1%26rkt%3D5%26sd%3D191717697429" target="_blank">multiple amounts</a> at a time. Either could be better depending on what you need.<br />
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When I started collecting these cards, I did not have a plan. I just started buying packs without thinking. To get all 100 cards, I ended up buying 37 packs (37 * $5.99 *1.07 tax = about $237). Within those 37 packs I didn't even get all of the cards. I ended up with 85 card and 137 doubles (<a href="https://drive.google.com/file/d/0BwmHJLTQdr_IcGQwWFBjN0tJeHM/view?usp=sharing" target="_blank">here are my doubles if anyone is interested...each red box is one card</a>). To get the remaining 15 cards I went on eBay and averaged about $3 per card (cards 1 through 15 are a little pricier) for an eBay total of $45.<br />
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My grand total was $282. I did not plan out this experience, but it got me thinking...<b>what would be the cheapest way to get all 100 cards?</b><br />
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$5.99 per pack + tax gets you 1 of cards 1 through 15 and 5 of cards 16 through 100<br />
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Most cards 16 through 100 can be had on eBay for $2 per card<br />
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Most cards 1 through 15 can be purchased on eBay for $4 per card<br />
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Lucky for me, I will get to experience this card buying process again when <a href="http://animalcrossingworld.com/2015/09/animal-crossing-amiibo-cards-series-2-releasing-october-29th-in-japan-take-a-look-at-the-characters/" target="_blank">series two</a> comes out in the near future. That's right, another series of 100 cards following the same format (it looks like there may be 17 special cards this time instead of 15).<br />
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I thought about this problem mathematically from a few perspectives, and I think your students would have a good time with this as well.<br />
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If I had purchased the entire first series on eBay...<br />
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15 specials * about $4 per card = $60<br />
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85 regulars * about $2 per card = $170<br />
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Total eBay amount = $230<br />
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Clearly I did not get a good deal in spending $282.<br />
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Although pretty much impossible, I thought about the fewest number of packs I would need to buy to get all 100:<br />
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I would need at least 15 packs to get all the specials and assuming I didn't get any doubles so far, I would be at 15 special cards and 15 * 5 = 75 regular cards for a total of 90 cards. I would then need two more packs to get the remaining 10 regular cards (and I would have 2 special cards as doubles).<br />
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17 pack * $5.99 * 1.07 = about $109<br />
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I would probably have a better chance of winning the lottery than getting all the cards in 17 packs, so this isn't really feasible, but it does give us a minimum amount of $109 and we already figured out a maximum amount of $230 through eBay.<br />
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Now we need to somehow find that sweet spot. When do you stop buying packs and start hunting on eBay? There are a lot of ways you could do this, and it would probably take smarter people than me to figure out an exact answer, but if you were proposing this problem to 6th graders, I would think more about presenting an argument at their level...and depending on the grade level there could possibly be a different argument made using a different math strand.<br />
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I am specifically thinking about those always difficult <a href="http://www.corestandards.org/Math/Content/6/SP/" target="_blank">6th grade statistics and probability standards</a> that focus on data collection and being able to interrupt the data. For the data collection, I think this could be done by the entire class so a lot of data is present.<br />
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If you go to <a href="https://www.random.org/integers/">random.org/integers</a>, we can set up a simulation.<br />
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For the cards 16-100, it would look like this. The top number would have to be 5 times larger than the bottom number so it sorts it into sets of 5 cards<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8h7PjNk5b1IVpIDiAL0M4nOYLXRIr5U3yKErMHtHHjDgtliLBoRyXaK7bdD9OTY0pCyxFyTAt129EiR0PSPLfAQqqVkSBnMR8jFFl0sU7bi45sloYPHOvcGxur-jNf_KlDV_zOd6SfUPU/s1600/Screen+Shot+2015-10-23+at+1.18.37+PM.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="152" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8h7PjNk5b1IVpIDiAL0M4nOYLXRIr5U3yKErMHtHHjDgtliLBoRyXaK7bdD9OTY0pCyxFyTAt129EiR0PSPLfAQqqVkSBnMR8jFFl0sU7bi45sloYPHOvcGxur-jNf_KlDV_zOd6SfUPU/s640/Screen+Shot+2015-10-23+at+1.18.37+PM.png" width="640" /></a>You will get a list similar to this:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgg-YwtDn6l6ScM8EC48Eb25fBYMeTNuUa641sdaS0mfS8Sl0nGCSXy1jIyCkHRes01cj0i5yAtAfDMTVOIO6kO3GgDUNP53_cbh2jMQUJjYHtrnyj0G5_ufaZmg35ffIxT3ACByOuWAW2/s1600/Screen+Shot+2015-10-23+at+1.20.17+PM.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="65" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgg-YwtDn6l6ScM8EC48Eb25fBYMeTNuUa641sdaS0mfS8Sl0nGCSXy1jIyCkHRes01cj0i5yAtAfDMTVOIO6kO3GgDUNP53_cbh2jMQUJjYHtrnyj0G5_ufaZmg35ffIxT3ACByOuWAW2/s640/Screen+Shot+2015-10-23+at+1.20.17+PM.png" width="640" /></a></div>
You would have to do the same thing for for cards 1 through 15. The top and the bottom numbers would now need to be the same so you get only one special card per column.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVmu3uEyMocudHyumc_O7CBd6oyzpIt2o1w1aVceRR-W0sqlBJpnsp4eUlDmWxQovYSKf1NhfxYChAwEYlafU3LVxbxJV03qIY0W6cLe3ok8pl815hMitU2R1Q5tujftCAhsqycY5MvDoX/s1600/Screen+Shot+2015-10-23+at+1.24.54+PM.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="142" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVmu3uEyMocudHyumc_O7CBd6oyzpIt2o1w1aVceRR-W0sqlBJpnsp4eUlDmWxQovYSKf1NhfxYChAwEYlafU3LVxbxJV03qIY0W6cLe3ok8pl815hMitU2R1Q5tujftCAhsqycY5MvDoX/s400/Screen+Shot+2015-10-23+at+1.24.54+PM.png" width="400" /></a></div>
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You'll end up with something like this:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMN7H4fJa6GlVipJITy-v9y5IbHZs58sh1yN947ZdEPDDD2D7CCnokfupX4A1xW1u0URcQVlLRKXr7fyZ8GXHlFAInN2w44ptEDSZdlpcjeBnhzQG2gND87mziQ-fW2wU4I-5eZCDiCBwi/s1600/Screen+Shot+2015-10-23+at+1.26.31+PM.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="38" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMN7H4fJa6GlVipJITy-v9y5IbHZs58sh1yN947ZdEPDDD2D7CCnokfupX4A1xW1u0URcQVlLRKXr7fyZ8GXHlFAInN2w44ptEDSZdlpcjeBnhzQG2gND87mziQ-fW2wU4I-5eZCDiCBwi/s640/Screen+Shot+2015-10-23+at+1.26.31+PM.png" width="640" /></a></div>
Now you can collect your data. How many packs in your situation would it take to get all 100 by just buying packs? If each student did this twice, you would have a lot of data to draw from. From my experience with middle school students, you wouldn't want to have each student do this 100 times, but if you did it twice I feel like they would be excited to see if they could take the fewest packs to get all the cards. <br />
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Once you have the data, it would really be up to the student(s) to take what you have most definitely been talking about with all of these data concepts and have them make an argument on what they think would be the best way to get all the cards with spending the least amount of money.<br />
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Another factor I will be throwing in myself is selling these cards on eBay to make some of my money back, and this could be a factor you use as well. While doubles are not desirable, it does give you plenty of chances to make some of your money back. Do I try to undersell everyone and chance $1 per card (maybe $2 for special cards)? I won't make all my money back, but they may sell faster. Maybe I will do a normal or higher price and wait out the market? What about shipping? Most of the cards I got were just sent in regular envelopes and placed between two pieces of cardboard making the shipping cost cheaper...but if something happened to the cards during shipping you would get a lot of refund requested and lose inventory. There is also the flip side as well. You could also think about bundling the cards in sets of so many. The possibilities are endless.<br />
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However you choose to take this problem (I would have the student discover all of the ideas that I presented before doing anything else), there are many variables involved, which in my opinion makes for a good situation. There doesn't have to be one correct answer, the most important aspect is the level that you can defend your decision.<br />
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If nothing else this has caused me to think before I purchase series two. What is that sweetest sweet spot I can find? Maybe your student can help me save some money!<br />
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<div style="background-color: white; color: #222222; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 1; word-spacing: 0px;">
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Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-41091114947031973862015-08-06T14:50:00.000-05:002015-08-06T14:50:30.095-05:00Estimation via SplatoonI am a huge fan the website <a href="http://www.estimation180.com/" target="_blank">Estimation 180</a> and the various estimation tasks it provides my students. I am always impressed by the ideas that come to mind when looking at real world objects and what could be estimated. Every once in awhile I will see something that I think is interesting and submit the picture to the <a href="https://twitter.com/Estimation180" target="_blank">@Estimation180 </a>Twitter feed for others to enjoy. <br />
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Whenever I have a little free time, I enjoy sitting down and playing a video game. It doesn't happen very often, but playing a game provides a relaxing 15 or 20 minutes before it's back to the grind. The game I am currently playing is <a href="http://splatoon.nintendo.com/" target="_blank">Splatoon by Nintendo</a>. Splatoon is a paintball type game where you and 3 other players try to cover the floor of the arena you are in with more ink than the 4 other players you are battling. You can also ink the opposing players causing them to be in sort of the penalty box for a few seconds before they can start shooting again. Here is some <a href="http://splatoon.nintendo.com/#!/trailer/" target="_blank">game footage</a> to give you an idea...<br />
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The game is very entertaining in short burst, but as I played a little more, I noticed something in the end match screen that screamed estimation. When the match is over, you look at an overhead view of the arena and the winner is decided by whichever team has the most paint splattered on the floor. A cartoon cat is the judge, and he gives you a little time to estimate who was the winner before he declares a winner. After every match I found myself trying to quickly calculate which team won and what the percentages were. It is possible for the percentages to not equal 100% if some of the arena floor is left unpainted. Some areas like grates cannot be painted.<br />
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I am thinking about creating my own site with pictures posted for estimation goodness. I think these pictures could also be useful for working with complex area on a larger scale. For now, here are some images that you can use with your students to start your school year!<br />
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<span style="-webkit-text-stroke-width: 0px; background-color: white; color: #222222; display: inline !important; float: none; font-family: arial, sans-serif; font-size: 12.8000001907349px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: 1; word-spacing: 0px;"><a href="http://tinyurl.com/1to1math" style="color: #1155cc;" target="_blank">1:1 Mathematical Philosophy</a></span>Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-32771675040967814652015-06-22T17:16:00.002-05:002015-06-22T17:24:58.663-05:00Sticky Note TaskSince our school year is over, this is being posted after the fact, but regardless, this was the final task for my 6th grade students. The sticky note task comes courtesy of <a href="https://twitter.com/mr_stadel?lang=en" target="_blank">@mr_stadel</a>. The task involves placing sticky notes on a cabinet and deciding how many pads/packs of sticky notes you would need to cover said cabinet. I thought it was very helpful having a similar filling cabinet in the room just so students could look at the cabinet for a visual during the process, but it wouldn't be necessary. The videos provided are more than enough to get the point. Here is what my students saw on my television as they entered the classroom and the connecting standards:<br />
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<a href="http://bit.ly/1HgG3wC">http://bit.ly/1HgG3wC</a></div>
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<span id="docs-internal-guid-2ac46af3-1d1d-4e9e-0634-bf09c78d92e1"><span style="font-family: Times, Times New Roman, serif;"><a href="http://www.corestandards.org/Math/Content/6/NS/B/4/" style="text-decoration: none;"><span style="color: #1155cc; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">6.NS.B.4</span></a></span></span></div>
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One interesting thing I have noticed from doing these tasks with video introductions is that my students will rely on the videos in different ways that I had not thought of. For instance, the video included shows the first 48 sticky notes being placed on the front of the cabinet. My feeling is that the introductory videos are normally used to just set the situation. I found a lot of my students taking those 48 sticky notes and trying to estimate how many sets of 48 would fit from top to bottom. Since the side is half as wide as the front, it was that many sets of 24. I guess all of my work with <a href="http://www.estimation180.com/" target="_blank">Estimation 180</a> (created by the same <a href="https://twitter.com/mr_stadel?lang=en" target="_blank">@mr_stadel</a>) has put them in this mindset, which isn't a bad thing. </div>
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For the most part we had two different approaches to discuss. One involved the area of the sticky note while the other dealt with how many columns and rows of sticky notes could fit on each face. It's interesting to see which the students choose because we have actually done a task earlier in the year that prominently featured both approaches. Even though we shared both methods during the <a href="http://bit.ly/1DWAtvL" target="_blank">Tile Floor Task</a>, when I went back to the previous student work, about 80% of the students used the same method for both tasks. I'm not sure what to think about that or if there really is anything to analyze, but it is interesting. </div>
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Finding how many packs of sticky notes needed should be easy, but this is one of those cases where a student that does a division problem on a calculator really has to think and justify why I would round up to the next pack of sticky notes. Without context, the "rule" would generally say round down, so this gives the students a real look at a decimal answer and the purpose of rounding. </div>
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I added the third question in hopes that students would see that not all sizes of sticky notes would fit perfectly on the cabinet without needing to be cut...some factor/multiple thinking. Many students jumped into this question without considering the fitting in perfectly component. When it was time for the justification, some students had to go back to the drawing board. The number of notes worked out, but upon further review, that dreaded 4 wouldn't go into the side of 18. The 6 by 4 was a popular sticky note with this problem. If you chose the 6 by 4, students discovered that you could turn the note a different direction and make it fit. Those selecting 4 by 4 weren't so lucky. </div>
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Below is the final set of student work for the year. I am finding new tasks all the time to try out next year. I can't wait to get started again! If you are on the fence about implementing mathematical tasks into your classroom, the benefits will outweigh any concerns you have. My students are better problem-solvers, communicators, and have an overall toughness to them where they do not give up. These are all great traits to have in the mathematics classroom as well as society. If you ever need any tips on implementing these tasks, feel free contact me and/or consult some of my previous posts. All my contact info and other pertinent links are below. </div>
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<b><span style="font-family: Times, 'Times New Roman', serif;"><br /></span></b></div>
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<b><span style="font-family: Times, 'Times New Roman', serif;">Student Task Work Examples</span></b></div>
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<span style="line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2015/03/air-pump-task.html" style="color: #888888; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Air Pump Task</span></a></span></div>
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<span style="line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2015/02/jenga-task.html" style="color: #888888; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Jenga Task</span></a></span></div>
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<a href="http://pagingdoctormath.blogspot.com/2015/05/hotel-snap.html" style="color: #888888; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Hotel Snap</span></a></div>
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<a href="http://pagingdoctormath.blogspot.com/2014/12/toothpick-task.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Toothpick Task</span></a></div>
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<a href="http://pagingdoctormath.blogspot.com/2014/12/man-versus-squirrel.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Man Versus Squirrel </span></a></div>
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<span style="color: #888888;"><a href="http://pagingdoctormath.blogspot.com/2015/01/in-n-out-burger-task.html" style="color: #888888; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">In-N-Out Burger</span></a></span></div>
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<a href="http://pagingdoctormath.blogspot.com/2015/03/shower-versus-bath-task.html" style="color: #888888; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Shower Versus Bath</span></a></div>
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<a href="http://pagingdoctormath.blogspot.com/2015/03/cookie-cutter-task.html" style="color: #888888; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Cookie Cutter Task</span></a></div>
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<a href="http://pagingdoctormath.blogspot.com/2015/03/elevator-or-stairs-task.html" style="color: #888888; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Elevator or Stairs?</span></a></div>
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<span style="font-family: Times, 'Times New Roman', serif;">Dr. Clayton M. Edwards</span></div>
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<span style="font-family: Times, 'Times New Roman', serif;">Ed. D. Curriculum and Instruction (UNI)</span></div>
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<a href="http://www.nctm.org/Publications/mathematics-teaching-in-middle-school/About-Mathematics-Teaching-in-the-Middle-School/" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">National Council of Teachers of Mathematics (NCTM) Middle School (MTMS) Editorial Panel</span></a></div>
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<a href="http://www.uni.edu/newsroom/uni-confers-yager-exemplary-teaching-recognition-awards-0" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Yager Exemplary Teaching Award 2014</span></a></div>
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<span style="font-family: Times, 'Times New Roman', serif;">Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa 2014</span></div>
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<span style="font-family: Times, 'Times New Roman', serif;">MA Middle Level Mathematics (UNI)</span></div>
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<span style="font-family: Times, 'Times New Roman', serif;">Middle School Mathematics Instructor</span></div>
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<span style="font-family: Times, 'Times New Roman', serif;">Grundy Center Middle School</span></div>
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<a href="mailto:cedwards@spartanpride.net" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">cedwards@spartanpride.net</span></a></div>
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<a href="http://twitter.com/Doctor_Math" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">@Doctor_Math (Twitter)</span></a></div>
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<span style="font-family: Times, 'Times New Roman', serif;"><a href="https://drive.google.com/file/d/0B13SidoEAHM3MUNzanhUcVlSOUE/view?usp=sharing" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Curriculum Vita</a></span></div>
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<span style="font-family: Times, 'Times New Roman', serif;"><a href="http://tinyurl.com/edwardsbio" style="color: #1155cc; text-decoration: none;" target="_blank">About Dr. Edwards</a> </span></div>
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<a href="http://tinyurl.com/edwardspub" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Dr. Edwards' Publications</span></a></div>
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<a href="http://tinyurl.com/edwardsmath" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Dr. Edwards' Math Website</span></a></div>
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<a href="http://youtube.com/bucs2812" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Dr. Edwards' YouTube Channel</span></a></div>
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<a href="http://tinyurl.com/1to1math" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Dr. Edwards' 1:1 Math Philosophy</span></a></div>
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<span style="font-family: Times, 'Times New Roman', serif;"><a href="http://pagingdoctormath.blogspot.com/" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Blog</a></span></div>
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<a href="http://tinyurl.com/mathematicstasks" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Dr. Edwards' Problem-Solving Task Spreadsheet</span></a></div>
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<span style="color: #1155cc; font-family: Times, 'Times New Roman', serif; text-decoration: none;"><a href="http://www.linkedin.com/in/doctoredwards" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Linkedin</a></span></div>
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Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-29226077931261699222015-06-01T14:38:00.003-05:002015-06-01T16:56:25.191-05:00What My Students Would Say About Me...Last week I was having a conversation with another educational professional when I was posed this question..."If I asked your students about Dr. Edwards, what would they say?" I answered the question how I assumed they would answer, but the question left me wondering exactly what the students would say. I normally end the year with some kind of survey to help me make decisions for the following year, but I am not sure I have ever asked the question quite like this.<br />
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I ended up asking the question at the end of each of my class periods the day before we got out of school for the summer. I can't claim the results are the most accurate, but I am posting them below verbatim to see if their are any patterns...be kind on the spelling/grammar :-). Is what I try to bestow on my students rubbing off? Do they enjoy/dislike my class for those reasons or for something entirely different? Are there differences in grade levels? Do opinions hinge on system likes or dislikes and not necessarily something specific about me? Do students this age really notice the "little things." Let's find out.<br />
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The two biggest ideas I stress in my classroom are improvement and understanding. In looking through the responses, 12/42 6th graders (28.5%) and 13/33 (39.3%) 7th graders (I had a lot gone or doing things for other classes) specifically mentioned improvement or becoming better mathematically. Only 4.7% of 6th graders and 3% if 7th graders said something about their level of understanding. An equal number of students said something about me liking candy as did the mathematical understanding! I'm not sure if that means anything, but it is interesting to me that improvement is mentioned much more even though I speak about both of those concepts hand in hand.<br />
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One of my main focuses as a teacher is to not give too much information. We do a lot of mathematical tasks, and students have a tough time at first not getting immediate information from me. My 6th graders were actually a little confused at the start of the year...thought I didn't like them because I wasn't telling them everything. Eventually they caught on. It was interesting to see that 3 students mentioned something about this...although this one may or may not count:<br />
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"but when he gives me help, usually he doesn't explain it very well"<br />
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No matter what we are doing in class, I use self-pacing as my philosophy. That doesn't mean that students have all year to complete something, but it does mean that I create loose deadlines for completion allowing plenty of time for understanding, and it also means students can be pushed or challenged at the same time without being held back. 16.7% of 6th graders mentioned something to do with self-pacing and no 7th grader mentioned this. Could this be because 7th graders are so used to being pushed that they do not even think about it being different anymore?<br />
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I didn't know I was so funny. Maybe the students mean funny looking. It didn't work for <a href="https://youtu.be/5yYPCi9pyNY" target="_blank">Joey in Full House when he was a substitute</a>, but maybe if this teaching gig doesn't pan out I have a career in comedy because 17% of 6th graders thought I was funny. I must get less funny the older the students get because only one 7th grader thought I was funny. <br />
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Here are a few random words I found that described me that show that these middle schoolers at least thought about the question: motivator, persistent, realistic, stressful, flexible, strict, and efficient...I can live with all of those. <br />
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I even got a Rocky reference from a kid who I doubt has seen any of those movies...<br />
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<a href="https://www.youtube.com/watch?v=E-WHW-QNswE" style="background-color: white; color: #1155cc; font-family: arial, sans-serif; font-size: 12.8000001907349px;" target="_blank">https://www.youtube.com/watch?<wbr></wbr>v=E-WHW-QNswE</a><br />
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Doing something like this can get you thinking going into the summer. I'm not sure how much I actually learned from this, but I am very proud of the relationships I build with my students and how they lead to success. If you are looking for a way to improve on your teaching and to hone your craft over the summer, you might want to focus little on curriculum, a little on classroom culture, and some with your relationships with students. All students are different, you just need to find something each student as an individual can latch onto ensuring that all the potential in your classroom is fulfilled. One piece of advice though...watch out for this student:<br />
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"Dr. Edwards is my favorite teacher in the whole entire world.. and I hate teachers."<br />
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<b><u>6th Grade</u></b><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">I think that dr. Edwards is a great teacher Because he has helped me improve in math and being a better student and he Is a very good motivator overall i think he is a great teacher and best teacher i have had. </span><br />
<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;"><br /></span>
<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">Weel He is a grate teacher he helps you if you have a question if you fnish your work he lets you go on to do higher level math. He is in my eyes the best midle school teacher. </span><br />
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<span style="background-color: white; font-family: verdana, sans-serif; font-size: x-small;">I would say that you are awesome and ​i learned a lot from you... You are funny and always make me laugh even if i am in a bad mood. You are my favorite teacher... And FYI I want you to teach me next year for sure...</span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">He is the best teacher ever because I hated math and I was horrible at it through PK-5th grade know with him being my teacher I am now at a A he is the best</span><br />
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<span style="background-color: white; font-family: verdana, sans-serif; font-size: x-small;">I have to say you are my favorite teacher. I always have hated math and I never liked it because I couldn't understand things well, but when this year rolled around math was my favorite subject. You help me understand things more better and because of that my math scores have improved a lot! Thank you for being the best math teacher ever! </span><br />
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<span style="background-color: white; color: #ff9900; font-family: 'comic sans ms', sans-serif; font-size: medium;">Dr.Edwards is a great teacher and he can explain things so it makes scene and I remember how. I like the ways he teaches because with his website you can work at your own speed.</span><br />
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<span style="background-color: white; color: blue; font-family: monospace, monospace; font-size: 12.8000001907349px;">I think that you are a really good teacher because you challenge us and help us. You give us work that I enjoy and the units are really fun. My favourite day of the week is Thursday because I like the Facts and Computation.</span><br />
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<span style="background-color: white; color: magenta; font-family: monospace, monospace; font-size: 12.8000001907349px;">You are a great teacher. Your really fun and the way you teach math is fun because it lets you work at your own pace. Also I didn't really like math but now I really like math because you have helped a lot. Your really awesome!</span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">grate teacher</span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">nice funny I learn a lot from you and is my favorite teacher. </span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">Persistant because he wants you to improve.</span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">He is helpful funny and a motivator </span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">That you are the best teacher and you make the day way better </span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">I would say that you are the best math teacher ever.</span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">i would say he is an awesome math teacher, he is really nice, and he cares about improvement</span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">I think that you are the best teacher I have had I won't be able to be taught by you next year which is sad but you are the coolest most realistic and caring teacher I know.</span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">Dr. Edwards is is a good math teacher. </span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">He is a good math teacher and he helps me with math. </span><br />
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<span style="background-color: white; font-family: 'trebuchet ms', sans-serif; font-size: 12.8000001907349px;">I like the way you teach. I like how at the end of the class you do the questions​ and the star bursts. </span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">Edwards is a gummy bear giving guy fun dude and the best math teacher.</span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">he is a asome teacher even tho the can be alitel stresfull but he is one of the best techers i ever had </span><br />
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<span style="background-color: white; color: #222222; font-family: tahoma, sans-serif; font-size: x-small;">I think that you are a really good math teacher and pushes us even though it gets hard. He is a really good person in general and helps people out no matter what. If he has to take up his time to help us he will just to make us better! </span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">I think Dr. Edwards is a great teacher he helps every one improve on the big tests he always has a plan and makes sure you do to so over all he is a great teacher and I would love to have him again</span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">hes the best math teacher and he teaches in his own ways that helps kids learn better </span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">That Dr. Edwards helps the students so much and helps them improve and is one of the beast teachers I had for helping me learn so much.</span><br />
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Amazing teacher guides us in the right path to learning more<br />
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<span style="background-color: white; color: blue; font-family: 'arial black', sans-serif; font-size: 12.8000001907349px;">He is nice teacher we have in the school.</span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">If we ask your students, what would they say about you? I would tell them that Dr Edwards is a really educated person that knows exactly what he wants you to do and exactly what time in an exact way. He knows how to get improvement out of kids.</span><br />
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<a href="https://www.youtube.com/watch?v=E-WHW-QNswE" style="background-color: white; color: #1155cc; font-family: arial, sans-serif; font-size: 12.8000001907349px;" target="_blank">https://www.youtube.com/watch?<wbr></wbr>v=E-WHW-QNswE</a><br />
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Basically says it all. Like... You let everyone work at there own pace. You have your entire website and we can do everything from home. YOU ARE A VIDEO GAMER. You're cool. Like. Really cool. Okay bye.</div>
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<span style="font-size: 12.8000001907349px;">That you try your best for every student to improve that you don't give up on anyone and you make sure every student is on task almost 100% of the time so that they do improve from the year before.</span></div>
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<span style="font-size: 12.8000001907349px;">Always trying to do the best for us. Focuses on getting us to do better and improve. Fun/Funny.</span></div>
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<span style="font-size: 12.8000001907349px;">I think your an awesome teacher</span></div>
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<span style="color: #9900ff; font-family: monospace, monospace; font-size: medium;">He is always willing to help. He lets you work together everyday. He helps you learn so much like I learned so much compared to last year.</span></div>
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<span style="font-size: 12.8000001907349px;">A really fun math teacher that cares about everyone. He has plans for everyone</span></div>
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<span style="color: blue; font-family: georgia, serif; font-size: medium;">Dr.Edwards is a very motivation person he pushes people with there work until they are done he doesn't just give you homework and say this is due Friday he will show you how to do it and make sure you do it. </span></div>
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<span style="color: #ff9900; font-family: 'arial narrow', sans-serif; font-size: medium;">I like how you let everyone work at heir own pace and that how you have a week to finish assngments and that you come to watch the play! Also how you always challenge us.</span></div>
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<span style="font-size: 12.8000001907349px;">I would have said that he was the best math teacher that I have ever had and that I am glad that he staying and he was awesome this year.</span></div>
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<span style="font-size: 12.8000001907349px;">I think E is amazing and a great friend and a amxing teacher evryone likes him and he pushed me to become a better math student.</span></div>
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<span style="color: #9900ff; font-family: arial, helvetica, sans-serif; font-size: x-small;">I think you would say that we love the way you make us laugh </span><img class="CToWUd" goomoji="364" src="https://mail.google.com/mail/e/364" style="color: #9900ff; font-family: arial, helvetica, sans-serif; font-size: small; margin: 0px 0.2ex; vertical-align: middle;" /></div>
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<span style="font-size: 12.8000001907349px;">That they think i am awesome (I is you)</span></div>
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<span style="font-size: 12.8000001907349px;">Best teacher to help me improve on math.</span></div>
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<span style="color: black; font-family: garamond, serif; font-size: medium;">he is a great teacher and I have never had such a good mach teacher</span></div>
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<b><u>7th Grade</u></b><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">I think Dr. Edwards is one of those teachers that if you need help he won't give you the answer he will help you, and he is one of those techers that treats his students like they are young adults.</span><br />
<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;"><br /></span>
<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">I think Dr. Edwards is flexible. Flexible because you are almost always available after school and before school just to help students. Thank you.</span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">He is the best teach with getting you and others improved. </span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">I think dr.edwards is fun and has a why of techie us a why most people don't do</span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">I would say that You care mostly about Improvment, and you take your job very seriously.</span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">I would say,</span><br />
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He's a good teacher and helps kids achieve the most they can achieve and has fun interactive activities.Overall he is a great teacher.</div>
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<span style="color: blue; font-family: 'comic sans ms', sans-serif; font-size: x-small;">Dr. Edwards is really helpful and he has simple ways of helping me out, and he doesn't let me give up. He just a really good teacher in general and i hope to have him again.</span></div>
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<span style="font-size: 12.8000001907349px;">CANDY/junk food addict</span><img class="CToWUd" goomoji="360" src="https://mail.google.com/mail/e/360" style="font-size: 12.8000001907349px; margin: 0px 0.2ex; vertical-align: middle;" /><img class="CToWUd" goomoji="360" src="https://mail.google.com/mail/e/360" style="font-size: 12.8000001907349px; margin: 0px 0.2ex; vertical-align: middle;" /><img class="CToWUd" goomoji="360" src="https://mail.google.com/mail/e/360" style="font-size: 12.8000001907349px; margin: 0px 0.2ex; vertical-align: middle;" /><img class="CToWUd" goomoji="360" src="https://mail.google.com/mail/e/360" style="font-size: 12.8000001907349px; margin: 0px 0.2ex; vertical-align: middle;" /><img class="CToWUd" goomoji="360" src="https://mail.google.com/mail/e/360" style="font-size: 12.8000001907349px; margin: 0px 0.2ex; vertical-align: middle;" /><img class="CToWUd" goomoji="360" src="https://mail.google.com/mail/e/360" style="font-size: 12.8000001907349px; margin: 0px 0.2ex; vertical-align: middle;" /><img class="CToWUd" goomoji="360" src="https://mail.google.com/mail/e/360" style="font-size: 12.8000001907349px; margin: 0px 0.2ex; vertical-align: middle;" /><img class="CToWUd" goomoji="360" src="https://mail.google.com/mail/e/360" style="font-size: 12.8000001907349px; margin: 0px 0.2ex; vertical-align: middle;" /><img class="CToWUd" goomoji="360" src="https://mail.google.com/mail/e/360" style="font-size: 12.8000001907349px; margin: 0px 0.2ex; vertical-align: middle;" /><img class="CToWUd" goomoji="360" src="https://mail.google.com/mail/e/360" style="font-size: 12.8000001907349px; margin: 0px 0.2ex; vertical-align: middle;" /><img class="CToWUd" goomoji="360" src="https://mail.google.com/mail/e/360" style="font-size: 12.8000001907349px; margin: 0px 0.2ex; vertical-align: middle;" /></div>
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<span style="color: #9900ff; font-family: garamond, serif; font-size: medium;">Dr.Edwards is a great teacher, he helps me a lot. More than any other teacher could.</span></div>
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<span style="font-family: 'comic sans ms', sans-serif; font-size: x-small;">I think that dr.edwards is a well liked teacher but when he gives me help, ususally he doesn't explain it very well</span></div>
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<span style="color: blue; font-family: garamond, serif; font-size: medium;">Dr. Edwards is my favorite teacher in the whole entire world.. and I hate teachers.</span></div>
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<span style="font-size: 12.8000001907349px;">I think Dr. Edwards is one of the best teachers I have had.</span></div>
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<span style="font-size: 12.8000001907349px;">On a scale of 1-10, answer being x, the equation would look like x*</span><wbr style="font-size: 12.8000001907349px;"></wbr><span style="font-size: 12.8000001907349px;">565576587657658765865765867578</span><wbr style="font-size: 12.8000001907349px;"></wbr><span style="font-size: 12.8000001907349px;">6576586587</span></div>
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<span style="font-family: 'arial narrow', sans-serif; font-size: 12.8000001907349px;">I would say "Doctor Edwards is pretty cool, he is a nice teacher, pushes us to work and improve, yet knows when to have a good time.</span></div>
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<span style="font-size: 12.8000001907349px;">What do you have to say about Dr. Edwards? I think that he is cool.</span></div>
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<span style="color: #ff9900; font-family: tahoma, sans-serif; font-size: 12.8000001907349px;">Dr.Edwards is very motivated for improvement.</span></div>
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<span style="font-size: 12.8000001907349px;">I think you are a type of teacher who gives me the best teaching for when it comes to improving. You compared to the 5th grade math teacher is huge. If you weren't my math teacher I probably wouldn't know what I know now and I probably wouldn't have the scores that I have now. I like how you teach your students. </span></div>
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<span style="color: #444444; font-family: 'arial black', sans-serif; font-size: medium;">He explains alot when you dont know what your doing and he has a unique was of teaching through videos.</span></div>
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<span style="font-family: 'trebuchet ms', sans-serif; font-size: medium;">He teaches efficiently </span></div>
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<span style="color: blue; font-family: 'courier new', monospace; font-size: x-small;">We would say he is a good teacher. And he helps the students learn better.</span></div>
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<span style="font-size: 12.8000001907349px;">Dr. Edwards makes sure we understand everything before we move on and he helps us understand it. </span></div>
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<span style="font-size: 12.8000001907349px;">He cares for his job and his students, he is very interested in our improvement makes sure we have a good year of math. Also he is really funny and good at sports...</span></div>
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<span style="font-size: 12.8000001907349px;">That you push us hard to improve, and get things done.</span></div>
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<span style="font-size: 12.8000001907349px;">I would say : That you are a great teacher that always strides for his students to improve.</span></div>
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<span style="color: black; font-family: garamond, serif; font-size: medium;">You usually give us enough time to complete assignments. </span></div>
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<span style="color: black; font-family: 'comic sans ms', sans-serif; font-size: medium;">I would say that he likes being here and that he likes his job. He is also always looking to make students better. </span></div>
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<span style="font-size: 12.8000001907349px;">I would saw that you take your student improvement very seriously </span></div>
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<span style="font-size: 12.8000001907349px;">is a math wizard and is very concerned about ur students being improved</span></div>
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<span style="color: black; font-family: 'arial black', sans-serif; font-size: medium;">I would say that I like how we never have to use textbooks and everything we do is actually fun not boring and he is very dedicated to his students and math</span></div>
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<span style="color: #222222; font-family: 'comic sans ms', sans-serif; font-size: x-small;">A person that dedicates a lot of time to math and cares a lot about his students improvement. ​</span></div>
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<span style="color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">I think you want everyone to improve and that is nice except when you get a little strict and that about it.</span></div>
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<span style="color: magenta; font-family: arial, sans-serif; font-size: x-large;">You should have answered that answer by saying you are a little too strict but we get stuff done in class.</span></div>
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<span style="color: #222222; font-family: arial, sans-serif; font-size: 12.8000001907349px;">your a great person and great teacher</span></div>
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<span style="line-height: 18.4799995422363px;"><a href="https://docs.google.com/document/d/1XGMMYabdD2ZJ3FrfcmpRZtLtJ3MAmCZ_vXHc821cm_8/edit?usp=sharing" style="color: #888888; text-decoration: none;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">What does a task look like in action?</span></a></span></div>
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<a href="https://docs.google.com/spreadsheets/d/1odw5amLUL77vBwOIt8bw72WRntZBWxwVHLAmeyMGAME/edit?usp=sharing" style="color: #888888; text-decoration: none;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Spreadsheet of Task I Have Used in the Classroom</span></a></div>
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<b><span style="font-family: Times, Times New Roman, serif;">Student Task Work Examples</span></b></div>
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<a href="http://pagingdoctormath.blogspot.com/2015/04/bubble-wrap-task.html" style="color: #888888; text-decoration: none;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Bubble Wrap Task</span></a></div>
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<a href="http://pagingdoctormath.blogspot.com/2015/05/hotel-snap.html" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Hotel Snap</span></a></div>
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<span style="font-family: Times, Times New Roman, serif;">Dr. Clayton M. Edwards</span></div>
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<span style="font-family: Times, Times New Roman, serif;">Ed. D. Curriculum and Instruction (UNI)</span></div>
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<a href="http://www.nctm.org/Publications/mathematics-teaching-in-middle-school/About-Mathematics-Teaching-in-the-Middle-School/" style="color: #1155cc;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">National Council of Teachers of Mathematics (NCTM) Middle School (MTMS) Editorial Panel</span></a></div>
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<a href="http://www.uni.edu/newsroom/uni-confers-yager-exemplary-teaching-recognition-awards-0" style="color: #1155cc;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Yager Exemplary Teaching Award 2014</span></a></div>
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<span style="font-family: Times, Times New Roman, serif;">Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa 2014</span></div>
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<span style="font-family: Times, Times New Roman, serif;">MA Middle Level Mathematics (UNI)</span></div>
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<span style="font-family: Times, Times New Roman, serif;">Middle School Mathematics Instructor</span></div>
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<span style="font-family: Times, Times New Roman, serif;">Grundy Center Middle School</span></div>
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<a href="mailto:cedwards@spartanpride.net" style="color: #1155cc;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">cedwards@spartanpride.net</span></a></div>
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<a href="http://twitter.com/Doctor_Math" style="color: #1155cc;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">@Doctor_Math (Twitter)</span></a></div>
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<span style="font-family: Times, Times New Roman, serif;"><a href="https://drive.google.com/file/d/0B13SidoEAHM3MUNzanhUcVlSOUE/view?usp=sharing" style="color: #1155cc;" target="_blank">Dr. Edwards' Curriculum Vita</a></span></div>
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<span style="font-family: Times, Times New Roman, serif;"><a href="http://tinyurl.com/edwardsbio" style="color: #1155cc;" target="_blank">About Dr. Edwards</a> </span></div>
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<a href="http://tinyurl.com/edwardspub" style="color: #1155cc;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Dr. Edwards' Publications</span></a></div>
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<a href="http://tinyurl.com/edwardsmath" style="color: #1155cc;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Dr. Edwards' Math Website</span></a></div>
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<a href="http://youtube.com/bucs2812" style="color: #1155cc;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Dr. Edwards' YouTube Channel</span></a></div>
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<a href="http://tinyurl.com/1to1math" style="color: #1155cc;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Dr. Edwards' 1:1 Math Philosophy</span></a></div>
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<span style="font-family: Times, Times New Roman, serif;"><a href="http://pagingdoctormath.blogspot.com/" style="color: #1155cc;" target="_blank">Dr. Edwards' Blog</a></span></div>
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<a href="http://tinyurl.com/mathematicstasks" style="color: #1155cc;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Dr. Edwards' Problem-Solving Task Spreadsheet</span></a></div>
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<a href="http://www.linkedin.com/in/doctoredwards" style="color: #1155cc;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Dr. Edwards' Linkedin</span></a></div>
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Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-78673148723452740392015-05-29T12:40:00.004-05:002015-05-29T12:40:31.095-05:00Hotel SnapAre you looking for a little good natured competition in your math classroom? Look no further than Hotel Snap created by <a href="https://twitter.com/fawnpnguyen" target="_blank">@fawnpnguyen</a> and <a href="https://twitter.com/mr_stadel" target="_blank">@mr_stadel</a>. In this task, students create hotels using blocks with the goal of making the most profit. From a mathematical standpoint this task does not provide a numerous amount of math concepts (small amounts of integers and percents), but rather a lot of thinking, communicating and planning as to what scenarios would garner the most profit, which is just as valuable. I was surprised at how many of my students did not understand the concept of making money and paying your debts leaving you with the remaining money. This task provides a small glance at financial literacy, a very important 21st century skill.<br />
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Here is the link to the original task:<br />
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<a href="http://fawnnguyen.com/hotel-snap/">http://fawnnguyen.com/hotel-snap/</a><br />
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Normally for these tasks I have the students start on their own as soon as they walk in by providing the directions and links on my television. This task has a lot of directions and rules that are worth going over ahead of time as a group first. I gave every student a copy of both of the price sheet and the tally sheet which are both provided on the above link. The students can write all over these and use them as a guide to help come up with their totals. I also printed off a copy of 3/4 inch grid paper to help the students see how many squares of land they are using (the blocks we used were approximately 3/4 inch cubes).<br />
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For these tasks I typically give a full day in class and then a week to complete before being due. I did the same here. I have done this twice now and presented it as a competition. The winner gets an A. If you are within 10% of the winner's cost you get an A, within 20% you get an A- and so on. The lowest you can get is a B- as long as you make a profit. My classroom is self-paced and we fix and correct everything we do for full credit so all of my students have As anyway, so I didn't feel bad about inserting the grade component into the competition. Those getting a B- weren't effected that much and I gave the students opportunities to keep modifying their idea as many times as they wanted. <br />
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I don't have the blocks that snap together in all directions so I feel that sometimes limits our designs, but the students get fairly creative with laying blocks across blocks to make something different. Each year I have students who go straight for the tower 50 blocks high to see if that would result in a high total. They always think about the tax last, which ends up being pretty funny to me because they go from the top of the world to depressed in the matter of 30 seconds.<br />
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When individuals or groups are finished, I have them take pictures of their hotels from all angles and send them to me. I also have them turn in their calculations. I use this information to check on accuracy. I hand it back if there are mistakes for correcting. Once everything has been approved, I put the numbers on a spreadsheet for the students to see. The spreadsheet looks like this...<br />
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One item that I don't ask them to fully flesh out and I should is a plan. They are given plenty of time to brainstorm, but in the future I would like to have the students write out a formal plan with explanations on why they feel this plan is the best choice for making the most profit. The plan doesn't have to be set in stone, but I would like something to have prior to the beginning of construction. All of my other tasks require so much explanation and understanding of the learning (as you can tell from all of the other student work posts) that I feel like this task needs more.<br />
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Below I have included a few examples of price plans as well as some designs. The students really enjoyed this task and many worked very hard to be at the top spot!<br />
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<span style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><a href="https://docs.google.com/document/d/1XGMMYabdD2ZJ3FrfcmpRZtLtJ3MAmCZ_vXHc821cm_8/edit?usp=sharing" style="color: #888888; text-decoration: none;" target="_blank">What does a task look like in action?</a></span></div>
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<a href="https://docs.google.com/spreadsheets/d/1odw5amLUL77vBwOIt8bw72WRntZBWxwVHLAmeyMGAME/edit?usp=sharing" style="color: #888888; text-decoration: none;" target="_blank">Spreadsheet of Task I Have Used in the Classroom</a></div>
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<b style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;">Other Posts with Tasks Containing Student Work</b><br /><br /><span style="font-family: Times, 'Times New Roman', serif;"><a href="http://pagingdoctormath.blogspot.com/2015/04/bubble-wrap-task.html" style="color: #888888; text-decoration: none;" target="_blank">Bubble Wrap Task</a></span></div>
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<a href="http://pagingdoctormath.blogspot.com/2015/04/flower-box-task.html" target="_blank">Flower Box Task</a></div>
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<a href="http://pagingdoctormath.blogspot.com/2015/04/doritos-roulette.html" style="color: #888888; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Doritos Roulette</span> </a><br style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;" /><div style="font-size: small; line-height: 18.2000007629395px;">
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<span style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif;"><a href="http://pagingdoctormath.blogspot.com/2015/02/jenga-task.html" style="color: #888888; text-decoration: none;" target="_blank">Jenga Task</a></span></span></div>
<b style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif;"><br /></span></b><span style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"></span><span style="font-family: Times, 'Times New Roman', serif; font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2015/02/shrinking-dollar-task.html" style="color: #888888; text-decoration: none;" target="_blank">Shrinking Dollar Task</a></span><br /><br style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;" /><span style="font-family: Times, 'Times New Roman', serif; font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2015/02/tile-floor-task.html" style="color: #888888; text-decoration: none;" target="_blank">Tile Floor Task</a><br style="line-height: 18.4799995422363px;" /><br style="line-height: 18.4799995422363px;" /><a href="http://pagingdoctormath.blogspot.com/2015/02/penny-cube-task.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank">Penny Cube Task</a></span></div>
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<span style="color: #888888; line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif; line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2014/12/are-thunder-playoff-bound.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank">Are the Thunder Playoff Bound?</a></span></span></div>
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<a href="http://pagingdoctormath.blogspot.com/2014/12/man-versus-squirrel.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Man Versus Squirrel </span></a></div>
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<span style="color: #888888; font-family: Times, 'Times New Roman', serif;"><a href="http://pagingdoctormath.blogspot.com/2015/01/in-n-out-burger-task.html" style="color: #888888; text-decoration: none;" target="_blank">In-N-Out Burger</a></span></div>
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<a href="http://pagingdoctormath.blogspot.com/2015/03/shower-versus-bath-task.html" style="color: #888888; text-decoration: none;" target="_blank">Shower Versus Bath</a></div>
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<a href="http://pagingdoctormath.blogspot.com/2015/03/cookie-cutter-task.html" style="color: #888888; text-decoration: none;" target="_blank">Cookie Cutter Task</a></div>
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<a href="http://pagingdoctormath.blogspot.com/2015/03/elevator-or-stairs-task.html" style="color: #888888; text-decoration: none;" target="_blank">Elevator or Stairs?</a></div>
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Dr. Clayton M. Edwards</div>
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Ed. D. Curriculum and Instruction (UNI)</div>
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<a href="http://www.nctm.org/Publications/mathematics-teaching-in-middle-school/About-Mathematics-Teaching-in-the-Middle-School/" style="color: #1155cc;" target="_blank">National Council of Teachers of Mathematics (NCTM) Middle School (MTMS) Editorial Panel</a></div>
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<a href="http://www.uni.edu/newsroom/uni-confers-yager-exemplary-teaching-recognition-awards-0" style="color: #1155cc;" target="_blank">Yager Exemplary Teaching Award 2014</a></div>
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Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa 2014</div>
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MA Middle Level Mathematics (UNI)</div>
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Middle School Mathematics Instructor</div>
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Grundy Center Middle School</div>
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<a href="mailto:cedwards@spartanpride.net" style="color: #1155cc;" target="_blank">cedwards@spartanpride.net</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://twitter.com/Doctor_Math" style="color: #1155cc;" target="_blank">@Doctor_Math (Twitter)</a></div>
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<a href="https://drive.google.com/file/d/0B13SidoEAHM3MUNzanhUcVlSOUE/view?usp=sharing" style="color: #1155cc; font-size: 12.8000001907349px;" target="_blank">Dr. Edwards' Curriculum Vita</a></div>
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<a href="http://tinyurl.com/edwardsbio" style="color: #1155cc;" target="_blank">About Dr. Edwards</a> </div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://tinyurl.com/edwardspub" style="color: #1155cc;" target="_blank">Dr. Edwards' Publications</a></div>
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<a href="http://tinyurl.com/edwardsmath" style="color: #1155cc;" target="_blank">Dr. Edwards' Math Website</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://youtube.com/bucs2812" style="color: #1155cc;" target="_blank">Dr. Edwards' YouTube Channel</a></div>
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<a href="http://tinyurl.com/1to1math" style="color: #1155cc;" target="_blank">Dr. Edwards' 1:1 Math Philosophy</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://pagingdoctormath.blogspot.com/" style="color: #1155cc;" target="_blank">Dr. Edwards' Blog</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://tinyurl.com/mathematicstasks" style="color: #1155cc;" target="_blank">Dr. Edwards' Problem-Solving Task Spreadsheet</a></div>
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<a href="http://www.linkedin.com/in/doctoredwards" style="color: #1155cc;" target="_blank">Dr. Edwards' Linkedin</a></div>
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Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-81169270194500431822015-05-15T16:41:00.000-05:002017-10-05T06:59:02.876-05:00Tasks and Standardized TestsIn the world of mathematics, what could be more opposite in the eyes of most than tasks and standardized tests? As an avid Twitter follower/poster (<a href="https://twitter.com/Doctor_Math" target="_blank">@doctor_math</a>) I normally see the two opposing view points clash. I realize this is an oversimplification and many educators could be in the middle, but for oversimplification's sake, you either love mathematical tasks and want to scrap testing (or are looking for a better type of test), or are more traditional and haven't met a set of 100 homework problems you didn't love to assign.<br />
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We are in the process of finishing our <a href="https://www.nwea.org/assessments/map/" target="_blank">NWEA MAP</a> testing, and I couldn't be happier with the results thus far as far as improvement shown. If you aren't familiar with the MAP, I would rate the test as much more strenuous than the Iowa Assessments, and a notch below Smarter Balanced. I don't necessarily love standardized testing, but my philosophy is that if we are going to test...we might as well do a good job with it. I've written a few MTMS blog postings that explain this a little more, so if interested, click below...<br />
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<a href="http://pagingdoctormath.blogspot.com/2014/10/standardized-mathematics-testing.html">http://pagingdoctormath.blogspot.com/2014/10/standardized-mathematics-testing.html</a><br />
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<a href="http://pagingdoctormath.blogspot.com/2014/11/standardized-mathematics-testing.html">http://pagingdoctormath.blogspot.com/2014/11/standardized-mathematics-testing.html</a><br />
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Many teachers I have met and talked with who are interested in making a change in philosophy are afraid to make the change because tests scores might drop. I can understand that this is a real concern to some, but from my experience, the moment I made the switch to mathematics for understanding (which includes tasks), my students saw improved standardized testing results almost immediately.<br />
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Aside from the obvious content advantages that mathematical tasks possess, many teachers don't think about the added bonuses that tasks provide. Tasks promote student to student and teacher to student interaction, which leads to mathematical discussions, which in turn leads to mathematical proof. This process ends with long-term mathematical understanding.<br />
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Tasks also promote student perseverance. Do you have students who will give up at the drop of hat? Try one of these<a href="https://docs.google.com/spreadsheets/d/1odw5amLUL77vBwOIt8bw72WRntZBWxwVHLAmeyMGAME/edit?usp=sharing" target="_blank"> tasks</a> each week. Students will gradually learn to fight through rough patches. I had a group of teachers visiting my room to see some of these problem-solving task. What were they most impressed with? It wasn't that my students are all Rhodes Scholars, but the fact that for 60 minutes, they never gave up. They kept discussing and overcoming obstacle after obstacle. That type of dedication isn't inherent in most students, it is something that is gained through gradual practice.<br />
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What does this have to do with standardized testing? It was very apparent while observing my students during testing that these hidden bonuses from tasks were out in full force. Many of my students worked for 10 to 15 minutes on one question. How may of your students try to finish one of these entire tests in 10 or 15 minutes? Mine used to 10 years ago. This is perseverance. It's hard to stay focused for 54 questions. My students do and that hasn't always been the case. This is perseverance. Take a look at my students' scratch paper (examples from a variety of students below). They write out and prove everything. That is directly linked to what they are asked to prove on these mathematical tasks. Bringing tasks into your classroom make all of these optimal math traits common practice.<br />
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Bottom line...if you want to improve your test scores, try implementing these tasks on a regular basis. Your students will become more adept at discussing and explaining, and the level of mathematical tenacity will rise considerably. All of these traits will serve your students a lot better on a standardized tests than trying to cram a week in advance.<br />
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<b>Student Task Work Examples</b></div>
<br />
<div class="p1" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; line-height: 18.4799995422363px;">
<span style="font-family: "times" , "times new roman" , serif;"><a href="http://pagingdoctormath.blogspot.com/2015/04/bubble-wrap-task.html" style="color: #888888; text-decoration: none;" target="_blank">Bubble Wrap Task</a></span></div>
<div class="p1" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; line-height: 18.4799995422363px;">
<span style="font-family: "times" , "times new roman" , serif;"><br /></span></div>
<div class="p1" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; line-height: 18.4799995422363px;">
<a href="http://pagingdoctormath.blogspot.com/2015/04/doritos-roulette.html" style="color: #888888; text-decoration: none;" target="_blank"><span style="font-family: "times" , "times new roman" , serif;">Doritos Roulette</span> </a><br />
<div style="font-size: small; line-height: 18.2000007629395px;">
<div class="separator" style="clear: both; line-height: 18.4799995422363px;">
<span style="line-height: 18.4799995422363px;"><br /></span></div>
<div class="separator" style="clear: both; line-height: 18.4799995422363px;">
<span style="line-height: 18.4799995422363px;"><span style="font-family: "times" , "times new roman" , serif;"><a href="http://pagingdoctormath.blogspot.com/2015/03/air-pump-task.html" style="color: #888888; text-decoration: none;" target="_blank">Air Pump Task</a></span></span></div>
<div class="separator" style="clear: both; font-size: 13.1999998092651px; line-height: 18.4799995422363px;">
<b style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></b></div>
<div class="separator" style="clear: both; font-size: 13.1999998092651px; line-height: 18.4799995422363px;">
<span style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><span style="font-family: "times" , "times new roman" , serif;"><a href="http://pagingdoctormath.blogspot.com/2015/02/jenga-task.html" style="color: #888888; text-decoration: none;" target="_blank">Jenga Task</a></span></span></div>
<b style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></b><span style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"></span><span style="font-family: "times" , "times new roman" , serif; font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2015/02/shrinking-dollar-task.html" style="color: #888888; text-decoration: none;" target="_blank">Shrinking Dollar Task</a></span><br />
<br style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;" />
<span style="font-family: "times" , "times new roman" , serif; font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2015/02/tile-floor-task.html" style="color: #888888; text-decoration: none;" target="_blank">Tile Floor Task</a><br style="line-height: 18.4799995422363px;" /><br style="line-height: 18.4799995422363px;" /><a href="http://pagingdoctormath.blogspot.com/2015/02/penny-cube-task.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank">Penny Cube Task</a></span></div>
<div style="font-size: small; line-height: 18.2000007629395px;">
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<span style="color: #888888; line-height: 18.4799995422363px;"><br /></span></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<span style="color: #888888; line-height: 18.4799995422363px;"><span style="font-family: "times" , "times new roman" , serif; line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2014/12/are-thunder-playoff-bound.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank">Are the Thunder Playoff Bound?</a></span></span></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<span style="font-family: "times" , "times new roman" , serif;"><br /></span></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<a href="http://pagingdoctormath.blogspot.com/2014/12/toothpick-task.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank"><span style="font-family: "times" , "times new roman" , serif;">Toothpick Task</span></a></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<span style="font-family: "times" , "times new roman" , serif;"><br /></span></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<a href="http://pagingdoctormath.blogspot.com/2014/12/man-versus-squirrel.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank"><span style="font-family: "times" , "times new roman" , serif;">Man Versus Squirrel </span></a></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<span style="font-family: "times" , "times new roman" , serif;"><br /></span></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<span style="color: #888888; font-family: "times" , "times new roman" , serif;"><a href="http://pagingdoctormath.blogspot.com/2015/01/in-n-out-burger-task.html" style="color: #888888; text-decoration: none;" target="_blank">In-N-Out Burger</a></span></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<br /></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<a href="http://pagingdoctormath.blogspot.com/2015/03/shower-versus-bath-task.html" style="color: #888888; text-decoration: none;" target="_blank">Shower Versus Bath</a></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<br /></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<a href="http://pagingdoctormath.blogspot.com/2015/03/cookie-cutter-task.html" style="color: #888888; text-decoration: none;" target="_blank">Cookie Cutter Task</a></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<br /></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<a href="http://pagingdoctormath.blogspot.com/2015/03/elevator-or-stairs-task.html" style="color: #888888; text-decoration: none;" target="_blank">Elevator or Stairs?</a></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<br /></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
Dr. Clayton M. Edwards</div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
Ed. D. Curriculum and Instruction (UNI)</div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://www.uni.edu/newsroom/uni-confers-yager-exemplary-teaching-recognition-awards-0" style="color: #1155cc; text-decoration: none;" target="_blank">Yager Exemplary Teaching Award 2014</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa 2014</div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
MA Middle Level Mathematics (UNI)</div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
Middle School Mathematics Instructor</div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
Grundy Center Middle School</div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="mailto:cedwards@spartanpride.net" style="color: #1155cc; text-decoration: none;" target="_blank">cedwards@spartanpride.net</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://twitter.com/Doctor_Math" style="color: #1155cc; text-decoration: none;" target="_blank">@Doctor_Math (Twitter)</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="https://drive.google.com/file/d/0B13SidoEAHM3MUNzanhUcVlSOUE/view?usp=sharing" style="color: #1155cc; font-size: 12.8000001907349px; text-decoration: none;" target="_blank">Dr. Edwards' Curriculum Vita</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://tinyurl.com/edwardsbio" style="color: #1155cc; text-decoration: none;" target="_blank">About Dr. Edwards</a> </div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://tinyurl.com/edwardspub" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Publications</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://tinyurl.com/edwardsmath" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Math Website</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://youtube.com/bucs2812" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' YouTube Channel</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://tinyurl.com/1to1math" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' 1:1 Math Philosophy</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://pagingdoctormath.blogspot.com/" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Blog</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://tinyurl.com/mathematicstasks" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Problem-Solving Task Spreadsheet</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://www.linkedin.com/in/doctoredwards" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Linkedin</a></div>
</div>
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Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-80583702381140632292015-04-27T19:49:00.001-05:002015-04-27T19:49:03.493-05:00Flower Box TaskNormally I start these posts off with who was responsible for this week's task...this week's task is courtesy of me, <a href="https://twitter.com/Doctor_Math" target="_blank">@doctor_math</a>. I normally don't make a lot of task...I usually don't have time and there are great educators out there who devote their time creating these resources. I'm not sure why I came up with this idea. I'm not much of a home improvement person nor am I much of a gardener. I did, however, feel this task was worthwhile for a few reasons. First, it gives a few situations using volume and surface area, and it forces the students to differentiate from the two. Probably more importantly though, it asks one question but forces students to be able to organize their data effectively to come to the solution. This is difficult for 6th graders with the vast amount of information being thrown at them, but no one gets better without being given the opportunity.<br />
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Here is the task the 6th graders saw on the television and their computers along with the standards being applied:<br />
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<a href="http://bit.ly/1ddiuIa" target="_blank">http://bit.ly/1ddiuIa</a><br />
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<a href="http://www.corestandards.org/Math/Content/6/G/A/2/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: Times, Times New Roman, serif;">6.G.A.2</span></span></a></div>
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<a href="http://www.corestandards.org/Math/Content/6/G/A/4/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: Times, Times New Roman, serif;">6.G.A.4</span></span></a></div>
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<a href="http://www.corestandards.org/Math/Content/6/RP/A/1/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: Times, Times New Roman, serif;">6.RP.A.1</span></span></a></div>
<span id="docs-internal-guid-5a18de72-f6d7-ef30-d9ea-8bf91276f1ab"><span style="color: #1155cc; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: Times, Times New Roman, serif;"><a href="http://www.corestandards.org/Math/Content/6/RP/A/3/" style="text-decoration: none;">6.RP.A.3</a></span></span></span><br />
<span><span style="color: #1155cc; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><br /></span></span>
<span style="white-space: pre-wrap;">It's interesting to see how each student or group chooses to go about this task. To me, it makes sense to find the totals for everything and not piece parts together. Take the soil for example. A student should be able to find how much soil is needed in total and then find the total bags. I had many students do that, but I also had students who found out that a little more than 5 boxes make up a bag and had to deal with the leftover in each bag, or students who find the total for each individual side of the house and add those totals together. None of those approaches are better or worse, but they are all a lot different. </span><br />
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<span style="white-space: pre-wrap;">This task is also an indication of how mathematics and reading are connected. I noticed that many of my students who are traditionally lower in reading struggled with this task. There are so many pieces of information to find and comprehend that missing something or not understanding something results in an incorrect final number. Not everything in math is going to be a simple numerical equation and nor should it be. Mathematics instructors...be nice to your reading and language counterparts!</span><br />
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<span style="white-space: pre-wrap;">Below are my student work examples and my discussion help sheet. I would swear that a few of my students were trying to one up me by writing their own versions of a dissertation. They worked together and managed to write a lot and both of their responses are unique and in their own words. For those of you worried that one student in a group will dominate the understanding and everyone else will follow along, here is a great example highlighting that if you want unique responses from group members, you will get it if that is the expectation. Enjoy!</span><br />
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<span style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><a href="https://docs.google.com/document/d/1XGMMYabdD2ZJ3FrfcmpRZtLtJ3MAmCZ_vXHc821cm_8/edit?usp=sharing" style="color: #888888; text-decoration: none;" target="_blank">What does a task look like in action?</a></span></div>
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<a href="https://docs.google.com/spreadsheets/d/1odw5amLUL77vBwOIt8bw72WRntZBWxwVHLAmeyMGAME/edit?usp=sharing" style="color: #888888; text-decoration: none;" target="_blank">Spreadsheet of Task I Have Used in the Classroom</a></div>
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<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; line-height: 18.4799995422363px;">Other Posts with Tasks Containing Student Work</b><br /><br /><span style="font-family: Times, Times New Roman, serif;"><a href="http://pagingdoctormath.blogspot.com/2015/04/bubble-wrap-task.html" target="_blank">Bubble Wrap Task</a></span></div>
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<a href="http://pagingdoctormath.blogspot.com/2015/04/doritos-roulette.html" style="text-decoration: none;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Doritos Roulette</span><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"> </span></a><br style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;" /><div style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: small; line-height: 18.2000007629395px;">
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<span style="line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif;"><a href="http://pagingdoctormath.blogspot.com/2015/03/air-pump-task.html" style="color: #888888; text-decoration: none;" target="_blank">Air Pump Task</a></span></span></div>
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<span style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif;"><a href="http://pagingdoctormath.blogspot.com/2015/02/jenga-task.html" style="color: #888888; text-decoration: none;" target="_blank">Jenga Task</a></span></span></div>
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<span style="color: #888888; font-family: Times, 'Times New Roman', serif;"><a href="http://pagingdoctormath.blogspot.com/2015/01/in-n-out-burger-task.html" style="color: #888888; text-decoration: none;" target="_blank">In-N-Out Burger</a></span></div>
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<a href="http://pagingdoctormath.blogspot.com/2015/03/shower-versus-bath-task.html" style="color: #888888; text-decoration: none;" target="_blank">Shower Versus Bath</a></div>
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<a href="http://pagingdoctormath.blogspot.com/2015/03/cookie-cutter-task.html" style="color: #888888; text-decoration: none;" target="_blank">Cookie Cutter Task</a></div>
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<a href="http://pagingdoctormath.blogspot.com/2015/03/elevator-or-stairs-task.html" style="color: #888888; text-decoration: none;" target="_blank">Elevator or Stairs?</a></div>
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Dr. Clayton M. Edwards</div>
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Ed. D. Curriculum and Instruction (UNI)</div>
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<a href="http://www.uni.edu/newsroom/uni-confers-yager-exemplary-teaching-recognition-awards-0" style="color: #1155cc; text-decoration: none;" target="_blank">Yager Exemplary Teaching Award 2014</a></div>
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Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa 2014</div>
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MA Middle Level Mathematics (UNI)</div>
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Middle School Mathematics Instructor</div>
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Grundy Center Middle School</div>
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<a href="mailto:cedwards@spartanpride.net" style="color: #1155cc; text-decoration: none;" target="_blank">cedwards@spartanpride.net</a></div>
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<a href="http://twitter.com/Doctor_Math" style="color: #1155cc; text-decoration: none;" target="_blank">@Doctor_Math (Twitter)</a></div>
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<a href="https://drive.google.com/file/d/0B13SidoEAHM3MUNzanhUcVlSOUE/view?usp=sharing" style="color: #1155cc; font-size: 12.8000001907349px; text-decoration: none;" target="_blank">Dr. Edwards' Curriculum Vita</a></div>
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<a href="http://tinyurl.com/edwardsbio" style="color: #1155cc; text-decoration: none;" target="_blank">About Dr. Edwards</a> </div>
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<a href="http://tinyurl.com/edwardspub" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Publications</a></div>
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<a href="http://tinyurl.com/edwardsmath" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Math Website</a></div>
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<a href="http://youtube.com/bucs2812" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' YouTube Channel</a></div>
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<a href="http://tinyurl.com/1to1math" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' 1:1 Math Philosophy</a></div>
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<a href="http://pagingdoctormath.blogspot.com/" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Blog</a></div>
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<a href="http://tinyurl.com/mathematicstasks" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Problem-Solving Task Spreadsheet</a></div>
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<a href="http://www.linkedin.com/in/doctoredwards" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Linkedin</a></div>
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Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-978235999709069922015-04-22T06:34:00.000-05:002015-04-22T06:34:14.693-05:00Bubble Wrap TaskOur 6th grade task for last week was <a href="https://twitter.com/ddmeyer" target="_blank">@ddmeyer</a>'s break for <a href="http://threeacts.mrmeyer.com/bubblewrap/" target="_blank">bubble wrap</a>. Most of my students are currently in our ratio unit, and this task was very valuable in solidifying their learning. I really enjoy this strand of mathematics because of the flexibility it brings. Each question basically had one answer, but most students went about that answer in a different manner.<br />
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Here is the modified task my students saw on my television as well as their computers...<br />
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<a href="http://bit.ly/1yh8gzO">http://bit.ly/1yh8gzO</a><br />
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I knew this would happen because I have done this task before, but right away I had many students thinking the answer to the first question was 10 minutes/15 minutes/20 minutes. This makes sense if you are thinking 5 minutes for every 4 inches, but as we discussed a little deeper, the students realized that more than just one side of the bubble wrap is being popped. We also had a discussion about what the area answer would mean in this case...square inches of bubble wrap of number of bubbles.<br />
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I enjoyed the layout of this task because it had one situation where you could get right to the number of square inches through repeated addition, and one where you had to find a reduced down version of the ratio first. This gave the students a few different viewpoints and for the most part didn't allow them to do the same thing twice.<br />
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I am a big fan of letting students discover shortcuts through actual mathematical understanding, and this task also allows for those types of transitions. I had one group who did a ratio table and went from 5 square inches in 2 minutes all the way up to 625 square inches. Sounds crazy? I don't think so. The students were able analyze their work and find quicker ways without me specifically telling them something. The understanding is owned by the student.<br />
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Question two was interesting after the students found the amount of square inches. Once 384 square inches was found and I asked them to find the side lengths of that square, many students put half of 384 or a quarter of 384 not really thinking what that answer would mean. This is a great situation to walk away as a teacher and make sure students get time to think about their decision.<br />
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Below is a list of the standards I tied to this task as well as student work and my discussion help sheet. Enjoy!<br />
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<a href="http://www.corestandards.org/Math/Content/6/RP/A/1/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">6.RP.A.1</span></a></div>
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<a href="http://www.corestandards.org/Math/Content/6/RP/A/2/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">6.RP.A.2</span></a></div>
<span id="docs-internal-guid-0b949d69-dbfb-1726-7854-ad95227520af"><a href="http://www.corestandards.org/Math/Content/6/RP/A/3/" style="text-decoration: none;"><span style="color: #1155cc; font-family: Arial; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">6.RP.A.3</span></a></span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiat2Ojq8oJXQVS5HMUz_AhGJdnTcwkWVB6GumyG0yhpknDY5iJ0XZyZNcHu6oK45LY4TB9-aGpBVfYpAEa6AAxd3BM9_EowAef0lFjcFnFtvICFGbC4M07hzFTURuz1BWVsYd4mxHCEyiZ/s1600/photo+(19).JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiat2Ojq8oJXQVS5HMUz_AhGJdnTcwkWVB6GumyG0yhpknDY5iJ0XZyZNcHu6oK45LY4TB9-aGpBVfYpAEa6AAxd3BM9_EowAef0lFjcFnFtvICFGbC4M07hzFTURuz1BWVsYd4mxHCEyiZ/s1600/photo+(19).JPG" height="640" width="478" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">My Discussion Help Sheet<br /><br /><div style="text-align: left;">
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</tbody></table>
<div class="p1" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; line-height: 18.4799995422363px;">
<span style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><a href="https://docs.google.com/document/d/1XGMMYabdD2ZJ3FrfcmpRZtLtJ3MAmCZ_vXHc821cm_8/edit?usp=sharing" style="color: #888888; text-decoration: none;" target="_blank">What does a task look like in action?</a></span></div>
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<a href="https://docs.google.com/spreadsheets/d/1odw5amLUL77vBwOIt8bw72WRntZBWxwVHLAmeyMGAME/edit?usp=sharing" style="color: #888888; text-decoration: none;" target="_blank">Spreadsheet of Task I Have Used in the Classroom</a></div>
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<b style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;">Other Posts with Tasks Containing Student Work</b><br /><br /><a href="http://pagingdoctormath.blogspot.com/2015/04/doritos-roulette.html" target="_blank">Doritos Roulette </a><br style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;" /><div style="font-size: small; line-height: 18.2000007629395px;">
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<span style="line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif;"><a href="http://pagingdoctormath.blogspot.com/2015/03/air-pump-task.html" style="color: #888888; text-decoration: none;" target="_blank">Air Pump Task</a></span></span></div>
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<span style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif;"><a href="http://pagingdoctormath.blogspot.com/2015/02/jenga-task.html" style="color: #888888; text-decoration: none;" target="_blank">Jenga Task</a></span></span></div>
<b style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif;"><br /></span></b><span style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"></span><span style="font-family: Times, 'Times New Roman', serif; font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2015/02/shrinking-dollar-task.html" style="color: #888888; text-decoration: none;" target="_blank">Shrinking Dollar Task</a></span><br /><br style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;" /><span style="font-family: Times, 'Times New Roman', serif; font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2015/02/tile-floor-task.html" style="color: #888888; text-decoration: none;" target="_blank">Tile Floor Task</a><br style="line-height: 18.4799995422363px;" /><br style="line-height: 18.4799995422363px;" /><a href="http://pagingdoctormath.blogspot.com/2015/02/penny-cube-task.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank">Penny Cube Task</a></span></div>
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<span style="color: #888888; line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif; line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2014/12/are-thunder-playoff-bound.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank">Are the Thunder Playoff Bound?</a></span></span></div>
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<span style="color: #888888; font-family: Times, 'Times New Roman', serif;"><a href="http://pagingdoctormath.blogspot.com/2015/01/in-n-out-burger-task.html" style="color: #888888; text-decoration: none;" target="_blank">In-N-Out Burger</a></span></div>
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<a href="http://pagingdoctormath.blogspot.com/2015/03/shower-versus-bath-task.html" style="color: #888888; text-decoration: none;" target="_blank">Shower Versus Bath</a></div>
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<a href="http://pagingdoctormath.blogspot.com/2015/03/cookie-cutter-task.html" style="color: #888888; text-decoration: none;" target="_blank">Cookie Cutter Task</a></div>
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<a href="http://pagingdoctormath.blogspot.com/2015/03/elevator-or-stairs-task.html" style="color: #888888; text-decoration: none;" target="_blank">Elevator or Stairs?</a></div>
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<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
Dr. Clayton M. Edwards</div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
Ed. D. Curriculum and Instruction (UNI)</div>
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<a href="http://www.uni.edu/newsroom/uni-confers-yager-exemplary-teaching-recognition-awards-0" style="color: #1155cc; text-decoration: none;" target="_blank">Yager Exemplary Teaching Award 2014</a></div>
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Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa 2014</div>
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MA Middle Level Mathematics (UNI)</div>
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Middle School Mathematics Instructor</div>
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Grundy Center Middle School</div>
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<a href="mailto:cedwards@spartanpride.net" style="color: #1155cc; text-decoration: none;" target="_blank">cedwards@spartanpride.net</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://twitter.com/Doctor_Math" style="color: #1155cc; text-decoration: none;" target="_blank">@Doctor_Math (Twitter)</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="https://drive.google.com/file/d/0B13SidoEAHM3MUNzanhUcVlSOUE/view?usp=sharing" style="color: #1155cc; font-size: 12.8000001907349px; text-decoration: none;" target="_blank">Dr. Edwards' Curriculum Vita</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://tinyurl.com/edwardsbio" style="color: #1155cc; text-decoration: none;" target="_blank">About Dr. Edwards</a> </div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://tinyurl.com/edwardspub" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Publications</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://tinyurl.com/edwardsmath" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Math Website</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://youtube.com/bucs2812" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' YouTube Channel</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://tinyurl.com/1to1math" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' 1:1 Math Philosophy</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://pagingdoctormath.blogspot.com/" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Blog</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://tinyurl.com/mathematicstasks" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Problem-Solving Task Spreadsheet</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://www.linkedin.com/in/doctoredwards" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Linkedin</a></div>
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</div>
</div>
Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-63093555062994071892015-04-17T07:28:00.002-05:002015-04-21T18:42:24.307-05:00Doritos RouletteThis task is why I am such a proponent of Twitter. Living in a small district you may be the only game in town when it comes to middle level mathematics (or whatever your subject is). It's difficult to hear about new ideas unless you take your own initiative to seek out said ideas. Through following a select number of mathematical experts on Twitter, I am able to find tasks to ensure my students have the best experience possible. This particular <a href="https://tapintoteenminds.com/3act-math/doritos-roulette-hot-or-not/" target="_blank">possibility</a> is courtesy of <a href="https://twitter.com/mathletepearce" target="_blank">@mathletepearce</a>. How else am I going to connect with a math professional from Canada without Twitter? We did a professional development dealing with Twitter the other day and while we have some outstanding teachers in our district, I was a little surprised that very few were taking advantage of Twitter as an educational tool. I was very pleased that out district is pushing this additional mode of personal professional development.<br />
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Here is the task with additional questions. This is what the students saw on my television and on their laptops when they walked in.<br />
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<span data-sheets-userformat="[null,null,707,[null,0],[null,2,16776960],null,null,null,null,1,1,null,0]" data-sheets-value="[null,2,"http://bit.ly/1F6zZ8X"]" style="color: #1155cc; font-family: arial,sans,sans-serif; font-size: 13px; text-align: center; text-decoration: underline;"><a class="in-cell-link" href="http://bit.ly/1F6zZ8X" target="_blank">http://bit.ly/1F6zZ8X</a></span><br />
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I like to make this as real as possible, so I bought a bag of these chips off of Amazon. It cost a pretty penny, but the students really enjoyed actually eating all of the chips and keeping track so we had some real data. <a href="https://twitter.com/mathletepearce" target="_blank">@mathletepearce</a> has a video on his link with data if you don't want to buy the chips, but again, I like to use the data that is relevant to my students upping the excitement level.<br />
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As we were collecting data (we did this at the conclusion of a few class periods...and by collect data I mean eat chips), I noticed a few inconsistencies. First, we had a lot of broken chips in our bag so it was hard to get an accurate total chip count. We ended up with way more than was supposedly in the bag. In addition to the broken chips, I feel some of my students might be on the wimpy end of the spectrum when it comes to properly identifying a "hot chip." In a bag where the chips are mixed, one would assume that there is a small amount of cross contamination involved. I felt like any small hint of spice resulted in my students tallying a hot chip when in reality it might have been a regular. In the grand scheme of things it didn't really matter because it brought more discussion into the theoretical and experimental probabilities.<br />
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One thing I noticed about this task was that it was a little ho hum as far as student answers sans the last question (and I didn't really like that one either as far as answers go, but we did have a nice post discussion). One theory I had was that the questions were not as high level as normal. That may have been it, but I actually think my students are just getting better at solving these tasks...more specifically figuring out what needs to be done. Up to this point many of my students had to spend a lot of time planning out what they needed to do to solve a question. I feel that through the use of these tasks through 6th and now 7th grade (I've had them for back to back years), students are able to dissect the different pieces of information faster leading to a quicker result.<br />
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Here are the standards I associated with this task. I have also included student work at the bottom along with my guide to help me quickly discuss with individual students or groups.<br />
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<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<a href="http://www.corestandards.org/Math/Content/7/SP/A/1/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">7.SP.A.1</span></a></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<a href="http://www.corestandards.org/Math/Content/7/SP/C/5/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">7.SP.C.5</span></a></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<a href="http://www.corestandards.org/Math/Content/7/SP/C/6/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">7.SP.C.6</span></a></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<a href="http://www.corestandards.org/Math/Content/7/SP/C/8/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">7.SP.C.8</span></a></div>
<span id="docs-internal-guid-ff474f55-bd11-e6f2-ffe6-d07e99508aed"><a href="http://www.corestandards.org/Math/Content/7/RP/A/3/" style="text-decoration: none;"><span style="color: #1155cc; font-family: Arial; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">7.RP.A.3</span></a></span><br />
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<tr><td class="tr-caption" style="text-align: center;">My Discussion Sheet</td></tr>
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<div class="p1" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; line-height: 18.4799995422363px;">
<span style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><a href="https://docs.google.com/document/d/1XGMMYabdD2ZJ3FrfcmpRZtLtJ3MAmCZ_vXHc821cm_8/edit?usp=sharing" style="color: #888888; text-decoration: none;" target="_blank">What does a task look like in action?</a></span></div>
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<a href="https://docs.google.com/spreadsheets/d/1odw5amLUL77vBwOIt8bw72WRntZBWxwVHLAmeyMGAME/edit?usp=sharing" target="_blank">Spreadsheet of Task I Have Used in the Classroom</a></div>
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<b style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;">Other Posts with Tasks Containing Student Work</b><br />
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<span style="line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif;"><a href="http://pagingdoctormath.blogspot.com/2015/03/air-pump-task.html" style="color: #888888; text-decoration: none;" target="_blank">Air Pump Task</a></span></span></div>
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<span style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif;"><a href="http://pagingdoctormath.blogspot.com/2015/02/jenga-task.html" style="color: #888888; text-decoration: none;" target="_blank">Jenga Task</a></span></span></div>
<b style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif;"><br /></span></b><span style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"></span><span style="font-family: Times, 'Times New Roman', serif; font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2015/02/shrinking-dollar-task.html" style="color: #888888; text-decoration: none;" target="_blank">Shrinking Dollar Task</a></span><br />
<br style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;" />
<span style="font-family: Times, 'Times New Roman', serif; font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2015/02/tile-floor-task.html" style="color: #888888; text-decoration: none;" target="_blank">Tile Floor Task</a><br style="line-height: 18.4799995422363px;" /><br style="line-height: 18.4799995422363px;" /><a href="http://pagingdoctormath.blogspot.com/2015/02/penny-cube-task.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank">Penny Cube Task</a></span></div>
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<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<span style="color: #888888; line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif; line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2014/12/are-thunder-playoff-bound.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank">Are the Thunder Playoff Bound?</a></span></span></div>
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<span style="font-family: Times, 'Times New Roman', serif;"><br /></span></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<a href="http://pagingdoctormath.blogspot.com/2014/12/toothpick-task.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Toothpick Task</span></a></div>
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<span style="font-family: Times, 'Times New Roman', serif;"><br /></span></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<a href="http://pagingdoctormath.blogspot.com/2014/12/man-versus-squirrel.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Man Versus Squirrel </span></a></div>
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<span style="font-family: Times, 'Times New Roman', serif;"><br /></span></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<span style="color: #888888; font-family: Times, 'Times New Roman', serif;"><a href="http://pagingdoctormath.blogspot.com/2015/01/in-n-out-burger-task.html" style="color: #888888; text-decoration: none;" target="_blank">In-N-Out Burger</a></span></div>
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<a href="http://pagingdoctormath.blogspot.com/2015/03/shower-versus-bath-task.html" style="color: #888888; text-decoration: none;" target="_blank">Shower Versus Bath</a></div>
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<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<a href="http://pagingdoctormath.blogspot.com/2015/03/cookie-cutter-task.html" style="color: #888888; text-decoration: none;" target="_blank">Cookie Cutter Task</a></div>
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<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<a href="http://pagingdoctormath.blogspot.com/2015/03/elevator-or-stairs-task.html" target="_blank">Elevator or Stairs?</a></div>
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<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
Dr. Clayton M. Edwards</div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
Ed. D. Curriculum and Instruction (UNI)</div>
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<a href="http://www.uni.edu/newsroom/uni-confers-yager-exemplary-teaching-recognition-awards-0" style="color: #1155cc;" target="_blank">Yager Exemplary Teaching Award 2014</a></div>
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MA Middle Level Mathematics (UNI)</div>
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Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-36790483325020643752015-03-31T16:37:00.002-05:002016-11-21T07:41:26.393-06:00Elevator or Stairs Task<br />
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This week's 6th grade task is brought to you courtesy of <a href="https://twitter.com/daneehlert"><span class="s1">@daneehlert</span></a> and deals with one of life's greatest dilemmas...do I wait forever for the elevator or just suck it up and take the stairs? I've been in this situation many times and it seems like I always make the wrong choice for some reason (similar to when I choose the wrong line to check-out at in Target). <br />
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My class is <a href="https://sites.google.com/a/spartanpride.net/technology-in-the-mathematics-classroom/" target="_blank">self-paced</a> for the most part, but at the current time most students are somewhere in our ratio unit. The task took longer for some students because they were at the very beginning of the unit and the task actually acted as both instruction and application. It was interesting to see the comparison between student's work who had already completed the ratio unit compared to those just starting. The only really difference was how long the task took...the learning was solid both ways.<br />
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Here is the original page for the task...<br />
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<a href="http://wmh3acts.weebly.com/elevator-or-stairs.html">http://wmh3acts.weebly.com/elevator-or-stairs.html</a><br />
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Here is the modified version the students were presented with...<br />
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<a href="https://docs.google.com/document/d/17qJNU_qvDe1Tx3wV0DA6bROrCUZiRmoZVCJ6VcaIZDI/edit?usp=sharing">https://docs.google.com/document/d/17qJNU_qvDe1Tx3wV0DA6bROrCUZiRmoZVCJ6VcaIZDI/edit?usp=sharing</a><br />
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I actually predicted this in a <a href="https://twitter.com/Doctor_Math/status/577814664232480768" target="_blank">Tweet</a> prior to the start of this task (which is more of a reason for teachers to plan obsessively to try to predict anything your students may come up with or struggle with so you are prepared...you won't, but try), but my students had a hard time grasping how if you were on the 4th floor, you really only had 3 flights of stairs to the 1st floor (same goes for the elevator).<br />
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Even though I push like crazy for as many labels and explanations as I can get, this concept is not as automatic with my 6th grade as I would like for a few select students. I noticed the two different sets of labels on the ratios were getting a little confusing to some. Seconds and stairs versus seconds and feet...this problem was most prevalent with those not using labels, so make sure to encourage labels and a key point of mathematical understanding.<br />
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The differences in methods were also interesting. When providing instruction with ratios, I always start with the ratio table. I feel like this makes the most sense to students, and also provides the base understanding needed to eventually shift to a quicker method. In the student work you will notice many students using the table, but other students who graduated to something else. I do not explicitly teach any shortcuts with ratios. I have found that this only skews the learning and prevents long-term understanding. When students are ready for the shortcuts, they will intuitively discover them.<br />
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Question two ended up being one of the most difficult questions the 6th grade had to encounter this year task-wise. I think most of this was due to the sheer amount of information each student had to keep track of. Again, having everything labeled really helps with the confusion. Students who were probably the most successful quickly figured out how many seconds it took to traverse one floor with the dueling modes of transportation, essentially creating their own usable ratio. Many students opted for a large scale chart which worked well but was time consuming.<br />
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We addressed many interesting questions like how the speed going down the stairs might change if you had a large number of flights, and what if you had to stop on the elevator to pick someone up? All of these are the unforeseen variables of life. Math is normally presented a lot cleaner than life. That is why I like these tasks so much. You can really dive into the all the variables at play and decide how much each one would change the outcome. Below is our student work, standards, as well as my help sheet for the task. Hopefully now you will be better prepared for when math and life collide!<br />
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<a href="http://www.corestandards.org/Math/Content/7/EE/B/4/a/" style="text-decoration: none;"><span style="color: #1155cc; font-family: "arial"; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">7.EE.B.4.A</span></a></div>
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<a href="http://www.corestandards.org/Math/Content/7/RP/A/1/" style="text-decoration: none;"><span style="color: #1155cc; font-family: "arial"; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">7.RP.A.1</span></a></div>
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<a href="http://www.corestandards.org/Math/Content/8/EE/C/8/c/" style="text-decoration: none;"><span style="color: #1155cc; font-family: "arial"; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">8.EE.C.8.C</span></a><br />
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<tr><td class="tr-caption" style="font-size: 12.8000001907349px;">My notes to help with the discussion<br />
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Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-63470820015466642732015-03-16T13:39:00.001-05:002015-03-16T13:39:33.914-05:00Cookie Cutter TaskWith Pi Day on the horizon (at the time), I decided to use a task that focused on the circle, which is a big introduction into the 7th grade curriculum. We started talking about circles about a month ago in more of a distributive practice fashion, measuring the diameter and circumference of various circles as well as a few other situations involving everyone's favorite horse <a href="https://youtu.be/y9DEWf-2do8" target="_blank">Prickly Pete</a> (apologies...low-quality video)<a href="http://illuminations.nctm.org/Activity.aspx?id=3547" target="_blank"> tied to a rope</a> (click on "problems" and yes I know it's a goat).<br />
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This task is courtesy of <a href="https://twitter.com/mathletepearce" target="_blank">@mathletepearce</a>. Here is the original situation...<br />
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<a href="https://tapintoteenminds.com/3act-math/cookie-cutter/">https://tapintoteenminds.com/3act-math/cookie-cutter/</a><br />
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This task is actually also accompanied by a video of my classroom that I decided to tape as an extra bonus...<br />
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<a href="https://docs.google.com/document/d/1XGMMYabdD2ZJ3FrfcmpRZtLtJ3MAmCZ_vXHc821cm_8/edit?usp=sharing" target="_blank">Classroom Video</a><br />
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Here is the information and questions I displayed for the students as they walked into the room...<br />
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<a href="http://bit.ly/1MhEopX">http://bit.ly/1MhEopX</a><br />
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This task ends up being a fairly straightforward subtracting out an area situation but the circle information is so new to the students that it adds an extra layer of thinking as to what exactly needs to be subtracted out. As we went through the task, a lot of interesting student ideas or missteps occurred (in no particular order):<br />
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*Do I use the circumference or area?<br />
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*How do I find the distance or the sides of the original dough?<br />
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*What does the decimal mean at the end of the first question when I found out there were three extra cookies? This was particularly interesting because many students thought this was the leftover dough at first when it is actually how much of a cookie is left.<br />
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*Could I just ignore the twelve original cookies and not subtract them out, instead just finding how many cookies could fit into the area of the original dough?<br />
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*What's a way to find the leftover dough after the 15 cookies? Take the area left after 12 cookies and subtract off the area of 3 cookies!<br />
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*Does circumference and diameter serve any purpose other than finding the area (actually just the diameter)?<br />
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*Do the little spaces of dough in between the cookies make that much of a difference?<br />
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*If there was about 2% of the dough unused, what percentage of the dough is needed to make a cookie?<br />
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*If there is no decimal left for the dough, does that mean there isn't any dough left?<br />
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*Should I find how many of the square cookies fit into each side of the dough or figure out how much space each of those cookies are and how many would fit?<br />
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*1/4 is 25% so 1/8 would be half that much?<br />
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*Oops I figured the square cookie as a circle...<br />
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There were a lot of big x-outs on student work this time around. I was really glad we did this task when we did because I think it did force the students to think deep past just the simple circle calculations into what was actually important...and there nothing wrong with students struggling, that is just part of the process. Below are the standards, student work, and my help sheet. Happy late Pi Day!<br />
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<a href="http://www.corestandards.org/Math/Content/7/G/B/4/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: Times, Times New Roman, serif;">7.G.B.4</span></span></a></div>
<b id="docs-internal-guid-b98a7902-2395-55df-0627-8530cd5c51af" style="font-weight: normal;"><span style="font-family: Times, Times New Roman, serif;"><br /></span></b>
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<a href="http://www.corestandards.org/Math/Content/7/G/B/6/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: Times, Times New Roman, serif;">7.G.B.6</span></span></a></div>
<span style="font-family: Times, Times New Roman, serif;"><br /><a href="http://www.corestandards.org/Math/Content/7/RP/A/3/" style="text-decoration: none;"><span style="color: #1155cc; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">7.RP.A.3</span></a></span><br />
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: large;">My discussion help sheet</span></td></tr>
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<b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; line-height: 18.4799995422363px;">Other Posts with Tasks Containing Student Work</b><br style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; line-height: 18.4799995422363px;" /></div>
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<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
Dr. Clayton M. Edwards</div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
Ed. D. Curriculum and Instruction (UNI)</div>
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<a href="http://www.uni.edu/newsroom/uni-confers-yager-exemplary-teaching-recognition-awards-0" style="color: #1155cc; text-decoration: none;" target="_blank">Yager Exemplary Teaching Award 2014</a></div>
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Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa 2014</div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
MA Middle Level Mathematics (UNI)</div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
Middle School Mathematics Instructor</div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
Grundy Center Middle School</div>
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<a href="mailto:cedwards@spartanpride.net" style="color: #1155cc; text-decoration: none;" target="_blank">cedwards@spartanpride.net</a></div>
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<a href="http://twitter.com/Doctor_Math" style="color: #1155cc; text-decoration: none;" target="_blank">@Doctor_Math (Twitter)</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="https://drive.google.com/file/d/0B13SidoEAHM3TkZjTUN4T0hpaDg/view?usp=sharing" style="color: #1155cc; font-size: 12.8000001907349px; text-decoration: none;" target="_blank">Dr. Edwards' Curriculum Vita</a></div>
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<a href="http://tinyurl.com/edwardsbio" style="color: #1155cc; text-decoration: none;" target="_blank">About Dr. Edwards</a> </div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://tinyurl.com/edwardspub" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Publications</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://tinyurl.com/edwardsmath" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Math Website</a></div>
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<a href="http://youtube.com/bucs2812" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' YouTube Channel</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://tinyurl.com/1to1math" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' 1:1 Math Philosophy</a></div>
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<a href="http://pagingdoctormath.blogspot.com/" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Blog</a></div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
<a href="http://tinyurl.com/mathematicstasks" style="color: #1155cc; text-decoration: none;">Dr. Edwards' Problem-Solving Task Spreadsheet</a></div>
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Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-87535048998462784772015-03-16T08:03:00.001-05:002015-03-16T08:05:13.853-05:00How I Implement Tasks in the Mathematics Classroom (With Classroom Video)Over the past few months I have featured the tasks of many mathematics experts on my blog. I credit these individuals for supplying my students with a premium experience for nothing. It is amazing to think about all the money that schools put into curricular materials when the best materials are usually free.<br />
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If you've found some of these tasks, then as a math teacher you have conquered half the battle. To get all the way there, it really depends on how effectively you use these tasks. This can be difficult because you must have a classroom culture where discussion and inquiry are the norm. The culture must also include students who are not afraid to falter (because they will falter). Transforming your classroom into this type of environment won't happen overnight. It takes days and weeks of modeling and discussion. I wrote a blog post for NCTM's MTMS Blogarithm on how to transform your classroom that can be found <a href="http://pagingdoctormath.blogspot.com/2014/11/written-and-verbal-mathematical.html" target="_blank">here (part one)</a> and <a href="http://pagingdoctormath.blogspot.com/2014/11/written-and-verbal-mathematical_28.html" target="_blank">here (part two)</a>.<br />
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Implementation of these tasks differs slightly depending on the teacher...but the goal is the same. Here is <a href="https://twitter.com/ddmeyer" target="_blank">@ddmeyer</a>'s <a href="http://blog.mrmeyer.com/2011/the-three-acts-of-a-mathematical-story/" target="_blank">approach</a>...and I took a lot of cues from this because I use a lot of his tasks and believe in his philosophy. Here is what I do...adapt as you see fit.<br />
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1. Students walk into my room and everything is ready to start. There is a timer set to know when class starts (we don't use bells), but the students always start before timer because they want to get started...they enjoy seeing what the task will be for the week. This particular week it happened to be about cookies...and who doesn't like cookies?<br />
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2. I have a big television in my room. All of the information for the students is front and center on the television so as soon as the students walk in, they know what is happening. The info would look like <a href="http://bit.ly/1MhEopX" target="_blank">this</a> minus the person who made the task and the standard numbers. My students all have their own laptops, and since my Google Doc they see on the television is already shared with them, they can go to their computers and have access to all the links and a closer look if they cannot see. I house all of these pages on my <a href="https://sites.google.com/a/spartanpride.net/edwards/Home/math-classroom-website" target="_blank">classroom website</a> towards the bottom. If your students do not have computers or tablets, you would just show this information to the whole class (like the informational video), but I like it this way because the students can go back at their own pace and view. <br />
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3. Some student like to be grouped together, some students like to stay by themselves, but either way I don't select the groups or who is by themselves. Some of these arrangements change from task to task and some stay the same. The students who are by themselves still talk with the other groups and me so they still have a large amount of communication happening.<br />
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4. I basically work the room for the whole period...walk around and listen to conversations, trying to help out without helping too much. I am good at walking away from students when my intention is to make sure they think about the situation for awhile. Middle school students are great at throwing out responses that have not been analyzed...and this helps. My 6th graders thought I was just rude at the beginning of the year but they figured it out. Students are going to struggle, but that is part of the process. When you first implement these tasks, students will struggle A LOT...especially if they have only been exposed to the traditional math class where discussion and collaboration can be lacking. Most of the discussion happens between groups or with me, but we will stop as a whole group if someone has discovered something noteworthy or if I can see everyone is struggling on the same idea and we need a classroom discussion.<br />
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5. Once a group or individual has finished a task, I will look it over. I may have also heard enough from the group that I just have them turn it in and I will look it over that night. What I am looking for from each student is a unique explanation so it is clear to me that they aren't just writing what a group member has, but that they actually understand. I will often hand back work and ask more clarifying questions to be able to gauge further if everything was understood. Ultimately I give the students an hour in class and then a week to finish the task before it is due. This fits nicely with my <a href="http://tinyurl.com/1to1math" target="_blank">self-paced</a> philosophy because some of these students need more think time than the hour.<br />
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I have included a link to a video of my 7th grade students participating in a <a href="http://bit.ly/1MhEopX" target="_blank">task</a>. The link will take you to a Google Doc with some information setting the stage, and the video is broken into four sections. Hopefully this post along with the video will give you ideas on how you can implement these tasks into your classroom.<br />
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<a href="https://docs.google.com/document/d/1XGMMYabdD2ZJ3FrfcmpRZtLtJ3MAmCZ_vXHc821cm_8/edit?usp=sharing" target="_blank">Problem-Solving Task Video</a><br />
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<b>Other Posts with Tasks Containing Student Work</b><br />
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<a href="http://pagingdoctormath.blogspot.com/2015/03/shower-versus-bath-task.html" target="_blank">Shower Versus Bath</a></div>
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<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
Dr. Clayton M. Edwards</div>
<div style="font-family: arial, sans-serif; font-size: small; line-height: normal;">
Ed. D. Curriculum and Instruction (UNI)</div>
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<a href="http://www.uni.edu/newsroom/uni-confers-yager-exemplary-teaching-recognition-awards-0" style="color: #1155cc;" target="_blank">Yager Exemplary Teaching Award 2014</a></div>
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Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa 2014</div>
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MA Middle Level Mathematics (UNI)</div>
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Middle School Mathematics Instructor</div>
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Grundy Center Middle School</div>
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<a href="mailto:cedwards@spartanpride.net" style="color: #1155cc;" target="_blank">cedwards@spartanpride.net</a></div>
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<a href="http://twitter.com/Doctor_Math" style="color: #1155cc;" target="_blank">@Doctor_Math (Twitter)</a></div>
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<a href="https://drive.google.com/file/d/0B13SidoEAHM3TkZjTUN4T0hpaDg/view?usp=sharing" style="color: #1155cc; font-size: 12.8000001907349px;" target="_blank">Dr. Edwards' Curriculum Vita</a></div>
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<a href="http://tinyurl.com/edwardsbio" style="color: #1155cc;" target="_blank">About Dr. Edwards</a> </div>
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<a href="http://tinyurl.com/edwardspub" style="color: #1155cc;" target="_blank">Dr. Edwards' Publications</a></div>
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<a href="http://tinyurl.com/edwardsmath" style="color: #1155cc;" target="_blank">Dr. Edwards' Math Website</a></div>
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<a href="http://youtube.com/bucs2812" style="color: #1155cc;" target="_blank">Dr. Edwards' YouTube Channel</a></div>
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<a href="http://tinyurl.com/1to1math" style="color: #1155cc;" target="_blank">Dr. Edwards' 1:1 Math Philosophy</a></div>
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<a href="http://pagingdoctormath.blogspot.com/" style="color: #1155cc;" target="_blank">Dr. Edwards' Blog</a></div>
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<a href="http://tinyurl.com/mathematicstasks" style="color: #1155cc;">Dr. Edwards' Problem-Solving Task Spreadsheet</a></div>
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Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-90015887229259508252015-03-11T06:58:00.001-05:002015-03-11T07:50:58.827-05:00Shower Versus Bath TaskLast week's 6th grade <a href="http://mrmeyer.com/threeacts/showervbath/" target="_blank">task</a> was courtesy of <a href="https://twitter.com/ddmeyer" target="_blank">@ddmeyer</a> and featured the price difference between taking a shower and taking a bath. This is a ratio heavy task and truthfully we have just started discussing ratios and proportions, so it was interesting to see how the students used what they already knew to come up with solutions.<br />
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Here is the modified task I displayed on my television before class for the students. As you will figure out from the student work, I changed the <a href="http://water.epa.gov/lawsregs/guidance/sdwa/upload/2009_08_28_sdwa_fs_30ann_dwsrf_web.pdf" target="_blank">cost per gallon of water to 1/5 of a cent</a> instead of the $0.19 I was using. I should have done some fact checking...<br />
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<a href="http://bit.ly/1A5Zcb7">http://bit.ly/1A5Zcb7</a><br />
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Many of my students got off to a good start, and there are many paths to get to a reasonable response, but about 1/4 of my students made the mistake in some way of not realizing that the times displayed were minutes and seconds. I should rephrase that...I think they knew the time was minutes and seconds, but since the time per gallon was in seconds, answers for total gallons were off which made for a good discussion piece. Some students tried to divide the time (2:23) by the 26 or 27 seconds for the gallon in the shower, which wasn't correct because 2:23 isn't 223 seconds. I also had students count up or count down by seconds in a chart type fashion which would have been fine, but some of those students did not realize that minutes are not out of 100 but 60. I also had to have discussions on how to change minutes and seconds into seconds...which should give you an idea of the various levels of students that coexist in my classroom (and I am sure all of yours).<br />
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While not explicitly discussed, I like the estimation aspect to these tasks. Many students realized quickly that the bath is going to use more water due to the combination of longer length and a shorter amount of time to use a gallon of water making more gallons. This seems pretty trivial, but I am excited that my students take the time to think about these idea ahead of time. Most of my students have a good idea of the outcome before they arrive at the solution which is an important skill to have in my book. <br />
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If you are a 6th grade teacher and have not started discussing ratios, this is a great way to get started. Seeing the simplicity of 10 seconds being 1 gallon and trying to arrive at an ending time provides a nice visual to get the students primed.<br />
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Below are the standards I felt this task involved, along with student work and my discussion sheet I planned out prior to the task.<br />
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<a href="http://www.corestandards.org/Math/Content/6/RP/A/1/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: Times, Times New Roman, serif;">6.RP.A.1</span></span></a></div>
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<a href="http://www.corestandards.org/Math/Content/6/RP/A/2/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: Times, Times New Roman, serif;">6.RP.A.2</span></span></a></div>
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<a href="http://www.corestandards.org/Math/Content/6/RP/A/3/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: Times, Times New Roman, serif;">6.RP.A.3</span></span></a></div>
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<a href="http://www.corestandards.org/Math/Content/6/EE/B/6/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: Times, Times New Roman, serif;">6.EE.B.6</span></span></a></div>
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<a href="http://www.corestandards.org/Math/Content/6/EE/B/7/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: Times, Times New Roman, serif;">6.EE.B.7</span></span></a></div>
<span id="docs-internal-guid-5c9d4955-03ac-c713-a517-360fab81dd73"><a href="http://www.corestandards.org/Math/Content/7/RP/A/3/" style="text-decoration: none;"><span style="color: #1155cc; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: Times, Times New Roman, serif;">7.RP.A.3</span></span></a></span><br />
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: large;">My Help Sheet I Prepared Prior to Task</span></td></tr>
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<b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: small; line-height: 18.4799995422363px; text-align: center;"><span style="font-family: Times, 'Times New Roman', serif;">Previous Posts with Student Work</span></b><br />
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<span style="line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif;"><a href="http://pagingdoctormath.blogspot.com/2015/03/air-pump-task.html" target="_blank">Air Pump Task</a></span></span></div>
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<span style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif;"><a href="http://pagingdoctormath.blogspot.com/2015/02/jenga-task.html" style="color: #888888; text-decoration: none;" target="_blank">Jenga Task</a></span></span></div>
<b style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif;"><br /></span></b><span style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"></span><span style="font-family: Times, 'Times New Roman', serif; font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2015/02/shrinking-dollar-task.html" style="color: #888888; text-decoration: none;" target="_blank">Shrinking Dollar Task</a></span><br />
<br style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;" />
<span style="font-family: Times, 'Times New Roman', serif; font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2015/02/tile-floor-task.html" style="color: #888888; text-decoration: none;" target="_blank">Tile Floor Task</a><br style="line-height: 18.4799995422363px;" /><br style="line-height: 18.4799995422363px;" /><a href="http://pagingdoctormath.blogspot.com/2015/02/penny-cube-task.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank">Penny Cube Task</a></span></div>
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<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<span style="color: #888888; line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2014/12/are-thunder-playoff-bound.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Are the Thunder Playoff Bound?</span></a></span></div>
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<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<a href="http://pagingdoctormath.blogspot.com/2014/12/toothpick-task.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Toothpick Task</span></a></div>
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<span style="font-family: Times, 'Times New Roman', serif;"><br /></span></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<a href="http://pagingdoctormath.blogspot.com/2014/12/man-versus-squirrel.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Man Versus Squirrel </span></a></div>
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<span style="font-family: Times, 'Times New Roman', serif;"><br /></span></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<span style="color: #888888; font-family: Times, 'Times New Roman', serif; text-decoration: none;"><a href="http://pagingdoctormath.blogspot.com/2015/01/in-n-out-burger-task.html" style="color: #888888; text-decoration: none;" target="_blank">In-N-Out Burger</a></span><br />
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<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<span style="font-family: Times, 'Times New Roman', serif;">Dr. Clayton M. Edwards</span></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<span style="font-family: Times, 'Times New Roman', serif;">Ed. D. Curriculum and Instruction (UNI)</span></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<a href="http://www.uni.edu/newsroom/uni-confers-yager-exemplary-teaching-recognition-awards-0" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Yager Exemplary Teaching Award 2014</span></a></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<span style="font-family: Times, 'Times New Roman', serif;">Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa 2014</span></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<span style="font-family: Times, 'Times New Roman', serif;">MA Middle Level Mathematics (UNI)</span></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<span style="font-family: Times, 'Times New Roman', serif;">Middle School Mathematics Instructor</span></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<span style="font-family: Times, 'Times New Roman', serif;">Grundy Center Middle School</span></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<a href="mailto:cedwards@spartanpride.net" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">cedwards@spartanpride.net</span></a></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<a href="http://twitter.com/Doctor_Math" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">@Doctor_Math (Twitter)</span></a></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<span style="font-family: Times, 'Times New Roman', serif;"><a href="http://tinyurl.com/edwardsbio" style="color: #1155cc; text-decoration: none;" target="_blank">About Dr. Edwards</a> </span></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<a href="http://tinyurl.com/edwardspub" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Dr. Edwards' Publications</span></a></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<a href="https://drive.google.com/file/d/0B13SidoEAHM3cVE3cjdQaTU1ckk/view?usp=sharing" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Dr. Edwards' Curriculum Vita</span></a></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<a href="http://tinyurl.com/edwardsmath" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Dr. Edwards' Math Website</span></a></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<a href="http://youtube.com/bucs2812" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Dr. Edwards' YouTube Channel</span></a></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<a href="http://tinyurl.com/1to1math" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Dr. Edwards' 1:1 Math Philosophy</span></a></div>
<div style="font-size: 13.1999998092651px; line-height: 14.7840003967285px;">
<span style="color: #1155cc;"><span style="font-family: Times, 'Times New Roman', serif;"><a href="http://pagingdoctormath.blogspot.com/" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Blog</a></span></span></div>
</div>
</div>
Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-8127299094729511042015-03-05T07:39:00.004-06:002015-03-05T07:39:54.715-06:00Air Pump TaskGenerally for these tasks, I give my students a full day to collaborate in class (one hour), and a week until the task is ultimately due. During that week they may or may not have time in class to work, but I try to be fair about the amount of time I give them. My 7th grade students participated in the Air Pump Task (thanks <a href="https://twitter.com/DaneEhlert" target="_blank">@daneehlert</a>) last week, but when only a handful of students finished within the hour, I knew this was going to be one of those weeks where we would need additional time.<br />
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Here is the modified version of the task I gave them...<br />
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<a href="http://bit.ly/1vXN8s7">http://bit.ly/1vXN8s7</a><br />
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I ended up giving them three full days in class to work (many only needed 2). During this time the students had plenty of other work to do, but I allowed the extra time so they would have myself and their peers handy to ask questions. These types of experiences where students struggle (and I am all for the struggle...that is what makes students better mathematically) more than they should causes myself to reflect on the concepts and how they have previously been presented. We have done a lot of work with 3-dimensional shapes, what surface area and volume literally mean (I have a whole wall with square shapes of all sizes and a corner with cubic shapes of their counterparts) and so on...but in reflecting, my ratio of working with 2-D shapes compared to 3-D shapes was not quite equal. I will work on that in the future, and this task served as a valuable learning tool for my students and their knowledge of 3-D shapes.<br />
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To my students' credit, they really worked hard to figure this task out. We've gotten to the point where all of my posing questions and walking away has paid off because I know I have a group of students with grit...not giving up when something isn't understood immediately. That is a big improvement from where we started at the first month of 6th grade. If you are new to these tasks, students usually have a lot of "give up" in them at first, so you as a teacher cannot give in to them...you are only doing your students a disservice if you do.<br />
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Once we reinforced the idea of a cubic shape, most students progressed nicely until the final two questions. The students who started out making the conversions right away were successful on most first attempts, but I had many students who found the volume of the shapes first, and then multiplied by the conversion amount once after the volume was found. We had a discussion on why we would have to multiply by the conversion rate three times instead of one if they did the conversion afterwards...again reinforcing that idea of a cubic shape.<br />
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While time consuming, this was a wonderful task that actually hit many topics at the same time. This task also caused me to reflect on my own practice, as well as being very proud of my students for their <span style="font-family: Times, 'Times New Roman', serif;">stick-to-itiveness</span><span style="color: #223645; font-family: Times, 'Times New Roman', serif;">. </span><br />
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<span style="font-family: Times, Times New Roman, serif; font-size: small;">Below are the standards we focused on, student work, and my task sheet I walk around with during the task to help question students...</span></div>
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<span style="font-family: Times, Times New Roman, serif; font-size: small;"><a href="http://www.corestandards.org/Math/Content/7/G/A/1/" target="_blank">7.GA.1</a></span></div>
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<span style="font-family: Times, Times New Roman, serif; font-size: small;"><a href="http://www.corestandards.org/Math/Content/7/G/B/6/" target="_blank">7.G.B.6</a></span></div>
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<span style="font-family: Times, Times New Roman, serif; font-size: small;"><a href="http://www.corestandards.org/Math/Content/6/RP/A/3/d/" target="_blank">6.RP.A.3.D</a></span></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-l2I5LRya1-L7VMExfQCruyuX4fxPLhGp1GpDLjrVYYchLMqRblGDGejep3gUWCEx6Pb94dTjEn6AiDNifao5zwaRseM7lw4HtWt2kf85LwmVnasvn7COBqn53XLFQrfK3M8hJQRSSX2d/s1600/photo+1+(19).JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-l2I5LRya1-L7VMExfQCruyuX4fxPLhGp1GpDLjrVYYchLMqRblGDGejep3gUWCEx6Pb94dTjEn6AiDNifao5zwaRseM7lw4HtWt2kf85LwmVnasvn7COBqn53XLFQrfK3M8hJQRSSX2d/s1600/photo+1+(19).JPG" height="640" width="478" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;"><b>My help sheet part one</b></span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhf26sP7fve-z2GYcE2JDmalLpAvzwGsyHLBuPqInO317i54VaRE9fGyPAJnpDTcIaEzBszbvKPqPu4_-BFfDkze1yug91w0OVK_5WTm2TRHKQYim5GQ7T90e6ZZCsoBox_Yn5xLrb-bJms/s1600/photo+2+(20).JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhf26sP7fve-z2GYcE2JDmalLpAvzwGsyHLBuPqInO317i54VaRE9fGyPAJnpDTcIaEzBszbvKPqPu4_-BFfDkze1yug91w0OVK_5WTm2TRHKQYim5GQ7T90e6ZZCsoBox_Yn5xLrb-bJms/s1600/photo+2+(20).JPG" height="640" width="478" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;"><b>Help sheet part two</b><br /><br /><div style="text-align: left;">
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<b style="line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif;">Previous Posts with Student Work</span></b></div>
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<b style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif;"><br /></span></b></div>
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<span style="font-size: 13.1999998092651px; line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif;"><a href="http://pagingdoctormath.blogspot.com/2015/02/jenga-task.html" target="_blank">Jenga Task</a></span></span></div>
<b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; font-weight: bold; line-height: 18.4799995422363px;"><span style="font-family: Times, 'Times New Roman', serif;"><br /></span></b><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; font-size: 13.1999998092651px; font-weight: normal; line-height: 18.4799995422363px; line-height: 18.4799995422363px;"></span><span style="background-color: white; color: #222222; font-family: Times, 'Times New Roman', serif; font-size: 13.1999998092651px; font-weight: normal; line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2015/02/shrinking-dollar-task.html" style="color: #888888; text-decoration: none;" target="_blank">Shrinking Dollar Task</a></span><br style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; font-weight: normal; line-height: 18.4799995422363px;" /><br style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; font-weight: normal; line-height: 18.4799995422363px;" /><span style="background-color: white; color: #222222; font-family: Times, 'Times New Roman', serif; font-size: 13.1999998092651px; font-weight: normal; line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2015/02/tile-floor-task.html" style="color: #888888; text-decoration: none;" target="_blank">Tile Floor Task</a><br style="line-height: 18.4799995422363px;" /><br style="line-height: 18.4799995422363px;" /><a href="http://pagingdoctormath.blogspot.com/2015/02/penny-cube-task.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank">Penny Cube Task</a></span></div>
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<span style="font-family: Times, Times New Roman, serif;"><br style="background-color: white; color: #222222; font-size: 13.1999998092651px; font-weight: normal; line-height: 18.4799995422363px;" /></span><div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; font-weight: normal; line-height: 14.7840003967285px;">
<span style="color: #888888; line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2014/12/are-thunder-playoff-bound.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Are the Thunder Playoff Bound?</span></a></span></div>
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<span style="font-family: Times, 'Times New Roman', serif;"><br /></span></div>
<div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; font-weight: normal; line-height: 14.7840003967285px;">
<a href="http://pagingdoctormath.blogspot.com/2014/12/toothpick-task.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Toothpick Task</span></a></div>
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<span style="font-family: Times, 'Times New Roman', serif;"><br /></span></div>
<div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; font-weight: normal; line-height: 14.7840003967285px;">
<a href="http://pagingdoctormath.blogspot.com/2014/12/man-versus-squirrel.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Man Versus Squirrel </span></a></div>
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<span style="font-family: Times, 'Times New Roman', serif;"><br /></span></div>
<div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; font-weight: normal; line-height: 14.7840003967285px;">
<a href="http://pagingdoctormath.blogspot.com/2015/01/in-n-out-burger-task.html" style="color: #888888; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">In-N-Out Burger</span></a></div>
<span style="background-color: white; color: #222222; font-family: Times, 'Times New Roman', serif; font-size: 13.1999998092651px; font-weight: normal; line-height: 18.4799995422363px;"><span style="line-height: 18.4799995422363px; text-align: center;"><br /></span><span style="line-height: 14.7840003967285px; text-align: center;"></span><span style="line-height: 18.4799995422363px;"></span></span><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; font-size: 13.1999998092651px; font-weight: normal; line-height: 18.4799995422363px; line-height: 18.4799995422363px;"></span><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; font-size: 13.1999998092651px; font-weight: normal; line-height: 18.4799995422363px; line-height: 18.4799995422363px;"></span><div class="separator" style="background-color: white; clear: both; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; font-weight: normal; line-height: 14.7840003967285px;">
<span style="font-family: Times, 'Times New Roman', serif;"><br /></span></div>
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<span style="font-family: Times, 'Times New Roman', serif;">Dr. Clayton M. Edwards</span></div>
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<span style="font-family: Times, 'Times New Roman', serif;">Ed. D. Curriculum and Instruction (UNI)</span></div>
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<a href="http://www.uni.edu/newsroom/uni-confers-yager-exemplary-teaching-recognition-awards-0" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Yager Exemplary Teaching Award 2014</span></a></div>
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<span style="font-family: Times, 'Times New Roman', serif;">Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa 2014</span></div>
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<span style="font-family: Times, 'Times New Roman', serif;">MA Middle Level Mathematics (UNI)</span></div>
<div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.1999998092651px; font-weight: normal; line-height: 14.7840003967285px;">
<span style="font-family: Times, 'Times New Roman', serif;">Middle School Mathematics Instructor</span></div>
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<span style="font-family: Times, 'Times New Roman', serif;">Grundy Center Middle School</span></div>
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<a href="mailto:cedwards@spartanpride.net" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">cedwards@spartanpride.net</span></a></div>
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<a href="http://twitter.com/Doctor_Math" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">@Doctor_Math (Twitter)</span></a></div>
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<span style="font-family: Times, 'Times New Roman', serif;"><a href="http://tinyurl.com/edwardsbio" style="color: #1155cc; text-decoration: none;" target="_blank">About Dr. Edwards</a> </span></div>
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<a href="http://tinyurl.com/edwardspub" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Dr. Edwards' Publications</span></a></div>
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<a href="https://drive.google.com/file/d/0B13SidoEAHM3cVE3cjdQaTU1ckk/view?usp=sharing" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Dr. Edwards' Curriculum Vita</span></a></div>
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<a href="http://tinyurl.com/edwardsmath" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Dr. Edwards' Math Website</span></a></div>
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<a href="http://youtube.com/bucs2812" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Dr. Edwards' YouTube Channel</span></a></div>
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<a href="http://tinyurl.com/1to1math" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, 'Times New Roman', serif;">Dr. Edwards' 1:1 Math Philosophy</span></a></div>
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<span style="color: #1155cc;"><span style="font-family: Times, 'Times New Roman', serif;"><a href="http://pagingdoctormath.blogspot.com/" style="color: #1155cc; text-decoration: none;" target="_blank">Dr. Edwards' Blog</a></span></span></div>
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<br />Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-2320748033851916622015-02-25T14:11:00.000-06:002016-11-21T07:40:24.773-06:00Jenga TaskI always like to make sure my students get as many quality tasks as possible, so when I came across the idea of this task, which is arguably more at a 6th grade level, I still wanted my 7th grade students to have the experience since we did not do this last year in 6th grade. You cannot have enough problem solving experiences in your classroom! I also gave this task to my current 6th grade students.<br />
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Here is the <a href="http://wmh3acts.weebly.com/life-size-jenga.html" target="_blank">original task</a> courtesy of <a href="https://twitter.com/DaneEhlert" target="_blank">@daneehlert</a>.<br />
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Here is my modified version of the task as the students viewed it...<br />
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<a href="http://bit.ly/19eFrJg">http://bit.ly/19eFrJg</a><br />
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While not a huge difference in question three, I decided to use the fraction 6 1/2 with the 6th grade students and 6 5/8 with my 7th graders. 6 5/8 is easier for my 7th grade because they are more fluid with fractions and decimals at this point. My 6th graders could have used 6 5/8, but I think the length of time the computation would have taken is not as important the problem-solving outcomes I am looking for.<br />
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We had a problem starting this task because all I gave them was the information on the modified task link. The students weren't sure how to read the label for the board that was $2.72. We stopped and had a discussion of what 2 by 4 by 96 meant. Once the students understood that the boards purchased at the store were 96 inches in length, they were able to begin.<br />
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I am all for calculator use as long as students explain their understanding, but I think the calculator actually became a hinderance for this problem...especially on question 3. When the students got 14.4 when they divided 96 by 6 5/8 or 14.7 when they divided 96 by 6 1/2, many thought this was the leftover inches but it was really how much of the extra board was left. This problem was personified from question 1 when students did 96/10 and got 9.6. Not only is .6 end up being 6/10 of a board which is 6 inches, but it is also the leftover amount of inches. This is one of those math occurrences where it just happens to work out that way. Students who draw a picture were much more successful, at least in the short term.<br />
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Question 2 was either very brief or fairly time consuming depending on how the students thought about it. Many students figured out that if you are using all 96 inches, you have 480 inches available which exactly matches the length of the boards in the life-size Jenga tower. Others took a more systematic approach, buying a board and saving the leftover until they could create another piece of the tower.<br />
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Finally, the terminology I used was fairly confusing from the standpoint of the 96 inch board and the 10 inch board. I needed to have a different word than "board" for both of these items to alleviate confusion.<br />
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Here are the standards I attached to this task, along with student work and the set-up page I created for the task. Overall, this was an enjoyable task and the students liked the concept of taking something like the Jenga game and the plausibility of actually making it life size.<br />
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<a href="http://www.corestandards.org/Math/Content/7/NS/A/3/" target="_blank">7.NS.A.3</a><br />
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<a href="http://www.corestandards.org/Math/Content/6/NS/A/1/" target="_blank">6.NS.A.1</a><br />
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<a href="http://www.corestandards.org/Math/Content/6/NS/B/2/" target="_blank">6.NS.B.2</a><br />
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Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0tag:blogger.com,1999:blog-5727328749190437216.post-16405874418921181072015-02-19T07:07:00.003-06:002015-02-19T07:07:16.872-06:00Shrinking Dollar TaskI find using these task very valuable as an assessment piece to make sure students can apply what they are doing within a unit, but even more worthwhile when the task comes much later than the unit was presented. If students can apply the information later down the road and can explain thinking in detail, chances are what you went through the first time around stuck. I also like using tasks to introduce new concepts, but that wasn't the case this time around.<br />
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For this week's 7th grade task, I found a <a href="https://twitter.com/ddmeyer" target="_blank">@ddmeyer</a> <a href="http://mrmeyer.com/threeacts/shrinkingdollar/" target="_blank">task</a> from his <a href="http://www.livebinders.com/play/play_or_edit?id=330579" target="_blank">spreadsheet</a> of tasks and added a few questions. I also took the answer video and put that at the beginning. The answer video did not have any numbers, but I thought it showed the students an excellent graphic of what this shrinking process would look like.<br />
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Here is what I presented to my students:<br />
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<a href="https://docs.google.com/document/d/1gkd4v2-ClRAmYW9e5E-O67vQSb5L0xqohqEFSLD8yxE/edit?usp=sharing" target="_blank">Modified Task</a><br />
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I think the biggest struggle for my students was the difference between percent growth/percent decrease, and the percentage remaining. To attempt to alleviate this problem, I emphasized that the growth or reduction should not include the original amount. We drew a few pictures to show this concept. I also related this to their own heights. We discussed what taking off an extra 100% would mean in this process as well. This wasn't prevalent with all my students, but it was the biggest problem.<br />
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I also had a few students confused with the wording of question six. If you can think of a better way to state that questions, please leave it in the comments. My goal was for them to see that while the sides decreased by 25%, the area actually decreased by 43% to 44% each time the dollar was shrunk on the copier.<br />
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As you will notice from the student work, most of my students use a ratio table method to work with all percent problems. I decided to present this as an option a few years ago because this method works for any proportion or percent situation, and the students understand what everything means. In the past I had student who would have to ask if they multiplied or divided in a percent scenario, but using this type of visual has alleviated that problem. Eventually, I have some students move on to other easier method that they figure out based on the ratio tables. In this task, I noticed a few students multiplied by .75 to find the 25% reduction. Other students spammed the divide 4 and multiply by 3 buttons on the calculator to simulate changing the whole to 25% and then 75% making the calculations quicker.<br />
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Here are the standards that I felt the task involved. I have also included the student work. One of the students commented that they saw a <a href="http://youtu.be/OmCxtWrRQJ8" target="_blank">Despicable Me where they scanned their butt on the copy machine</a> and could we try that next? I think we will stick with the dollar bills!<br />
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<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<a href="http://www.corestandards.org/Math/Content/7/RP/A/3/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: Times, Times New Roman, serif;">7.RP.A.3</span></span></a></div>
<b id="docs-internal-guid-62931582-9cb7-fa6e-b650-53832be67246" style="font-weight: normal;"><span style="font-family: Times, Times New Roman, serif;"><br /></span></b>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<a href="http://www.corestandards.org/Math/Content/7/EE/A/2/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: Times, Times New Roman, serif;">7.EE.A.2</span></span></a></div>
<span style="font-family: Times, Times New Roman, serif;"><br /><span style="color: #1155cc; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><a href="http://www.corestandards.org/Math/Content/7/EE/B/3/" style="text-decoration: none;">7.EE.B.3</a></span></span><br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_g90CNWdHMB_4iL33r-uUb4VYHfLdFguo63Cxrl_doMQ_6W40ZB1OwO8V1iWHKacl2Qif5rNMCzoJLX07whNvqMaZfocMH83mGI2cXMyIvliq2QfB9P2miUHRTM0_3W191CDMIoqQJ631/s1600/photo+(4).JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_g90CNWdHMB_4iL33r-uUb4VYHfLdFguo63Cxrl_doMQ_6W40ZB1OwO8V1iWHKacl2Qif5rNMCzoJLX07whNvqMaZfocMH83mGI2cXMyIvliq2QfB9P2miUHRTM0_3W191CDMIoqQJ631/s1600/photo+(4).JPG" height="640" width="478" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">My prep work I carry around on my iPad to help discussion with various groups and individuals...</span></td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoIfL27-Mdd6lRxhLeGYMtRe7bhmzu0EeHAHHAdaYJsJUNVuGKx1QFsWVGJPBhehjx2kDRQQydw6BKmDoD_CjozabuAL7yzALCFaej4xNt3B86rv6Adju8RLHGzrVgi_sBD0epU1iwjSe7/s1600/photo+(3).JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoIfL27-Mdd6lRxhLeGYMtRe7bhmzu0EeHAHHAdaYJsJUNVuGKx1QFsWVGJPBhehjx2kDRQQydw6BKmDoD_CjozabuAL7yzALCFaej4xNt3B86rv6Adju8RLHGzrVgi_sBD0epU1iwjSe7/s1600/photo+(3).JPG" height="640" width="478" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">I thought I would add this picture...a 7th grader trying to draw 5 millimeters with a meter stick...genius! This is why I love teaching middle school students...</span></td></tr>
</tbody></table>
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<b style="background-color: white; color: #222222; line-height: 18.4799995422363px;"><span style="font-family: Times, Times New Roman, serif;">Previous Posts with Student Work</span></b><br />
<b><span style="font-family: Times, Times New Roman, serif;"><br /></span></b>
<span style="font-family: Times, Times New Roman, serif;"><a href="http://pagingdoctormath.blogspot.com/2015/02/tile-floor-task.html" target="_blank">Tile Floor Task</a><br style="background-color: white; color: #222222; line-height: 18.4799995422363px;" /><br style="background-color: white; color: #222222; line-height: 18.4799995422363px;" /><a href="http://pagingdoctormath.blogspot.com/2015/02/penny-cube-task.html" style="background-color: white; color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank">Penny Cube Task</a><br style="background-color: white; color: #222222; line-height: 18.4799995422363px;" /></span><br />
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<span style="color: #888888; line-height: 18.4799995422363px;"><a href="http://pagingdoctormath.blogspot.com/2014/12/are-thunder-playoff-bound.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Are the Thunder Playoff Bound?</span></a></span></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<span style="font-family: Times, Times New Roman, serif;"><br /></span></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<a href="http://pagingdoctormath.blogspot.com/2014/12/toothpick-task.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Toothpick Task</span></a></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<span style="font-family: Times, Times New Roman, serif;"><br /></span></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<a href="http://pagingdoctormath.blogspot.com/2014/12/man-versus-squirrel.html" style="color: #888888; line-height: 18.4799995422363px; text-decoration: none;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Man Versus Squirrel </span></a></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<span style="font-family: Times, Times New Roman, serif;"><br /></span></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<a href="http://pagingdoctormath.blogspot.com/2015/01/in-n-out-burger-task.html" style="color: #888888; text-decoration: none;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">In-N-Out Burger</span></a></div>
<span style="font-family: Times, Times New Roman, serif;"><span style="background-color: white; color: #222222; line-height: 18.4799995422363px; text-align: center;"><br /></span><span style="background-color: white; color: #222222; line-height: 14.7840003967285px; text-align: center;"></span><span style="background-color: white; color: #222222; line-height: 18.4799995422363px;"></span></span>
<div class="separator" style="background-color: white; clear: both; color: #222222; line-height: 14.7840003967285px;">
<span style="font-family: Times, Times New Roman, serif;"><br /></span></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<span style="font-family: Times, Times New Roman, serif;">Dr. Clayton M. Edwards</span></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<span style="font-family: Times, Times New Roman, serif;">Ed. D. Curriculum and Instruction (UNI)</span></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<a href="http://www.uni.edu/newsroom/uni-confers-yager-exemplary-teaching-recognition-awards-0" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Yager Exemplary Teaching Award 2014</span></a></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<span style="font-family: Times, Times New Roman, serif;">Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa 2014</span></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<span style="font-family: Times, Times New Roman, serif;">MA Middle Level Mathematics (UNI)</span></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<span style="font-family: Times, Times New Roman, serif;">Middle School Mathematics Instructor</span></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<span style="font-family: Times, Times New Roman, serif;">Grundy Center Middle School</span></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<a href="mailto:cedwards@spartanpride.net" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">cedwards@spartanpride.net</span></a></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<a href="http://twitter.com/Doctor_Math" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">@Doctor_Math (Twitter)</span></a></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<span style="font-family: Times, Times New Roman, serif;"><a href="http://tinyurl.com/edwardsbio" style="color: #1155cc; text-decoration: none;" target="_blank">About Dr. Edwards</a> </span></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<a href="http://tinyurl.com/edwardspub" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Dr. Edwards' Publications</span></a></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<a href="https://drive.google.com/file/d/0B13SidoEAHM3cVE3cjdQaTU1ckk/view?usp=sharing" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Dr. Edwards' Curriculum Vita</span></a></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<a href="http://tinyurl.com/edwardsmath" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Dr. Edwards' Math Website</span></a></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<a href="http://youtube.com/bucs2812" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Dr. Edwards' YouTube Channel</span></a></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<a href="http://tinyurl.com/1to1math" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Dr. Edwards' 1:1 Math Philosophy</span></a></div>
<div style="background-color: white; color: #222222; line-height: 14.7840003967285px;">
<span style="color: #1155cc;"><a href="http://pagingdoctormath.blogspot.com/" style="color: #1155cc; text-decoration: none;" target="_blank"><span style="font-family: Times, Times New Roman, serif;">Dr. Edwards' Blog</span></a></span></div>
Clayton M. Edwardshttp://www.blogger.com/profile/12302173002285609690noreply@blogger.com0