Tuesday, December 8, 2015

The 12 Math Tasks of Christmas...

I have a lot to be thankful for this holiday season:
  • A new daughter
  • 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
  • A group of math professionals scattered around the web that pump out mathematical task after mathematical task for classroom use TASK SPREADSHEET
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!

Day One ~ You can feed your leftover fruitcake to this giant squirrel...

Courtesy of @emergentmath and also adapted by @daneehlert

Man Versus Squirrel Blog Post With Student Work

Man Versus Squirrel Student Directions 

Day Two ~ Mmmmm...holiday cookies (use your imagination)

Courtesy of @mathletepearce

Cookie Cutter Task Blog Post With Student Work

Cookie Cutter Task Student Directions

Day Three ~ Instead of serving ham for the holidays, try this big stack of beef...

Courtesy of @robertkaplinsky 

In-N-Out Burger Task Blog Post With Student Work 

In-N-Out Burger Task Student Directions

Day Four ~ It would be nice if I could print money to buy presents for the holidays...

Courtesy of @ddmeyer

Shrinking Dollar Task Blog Post With Student Work 

Shrinking Dollar Task Student Directions   

Day Five ~ Buying presents can be expensive, especially if your budget consists of only pennies in a cube 6 inch cube...

Courtesy of @mikewiernicki 

Penny Cube Task Blog Post With Student Work

Penny Cube Task Student Directions

Day Six ~ The ultimate holiday party game...Giant Jenga!

Courtesy of @daneehlert

Jenga Task Blog Post With Student Work

Jenga Task Student Directions

Day Seven ~ The weather has been so nice in Iowa that I might have to mow in December...

Courtesy of @mathletepearce

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 :-)

Part One of Student Work

Part Two of Student Work 

Lawn Mowing Task Student Directions

Day Eight ~  Inflatable Holiday Decorations...How Long to Inflate?

Courtesy of @daneehlert

Air Pump Task Blog Post With Student Work

Air Pump Task Student Directions

Day Nine ~  Laying some new tile? I don't know what that has to do with the holidays, but it was a great task...

Courtesy of Santa??? I am not really sure where this came from, but I would like to know.

Tile Floor Task Blog Post With Student Work

Tile Floor Task Student Directions

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! 

Day Eleven ~ These toothpicks make a festive tree for the holiday season...

Courtesy of @ddmeyer

Toothpick Task Blog Post With Student Work

Toothpick Task Student Directions

 Day Twelve ~ These blocks might be a popular holiday gift...

 Courtesy of @fawnpnguyen and @mr_stadel

Hotel Snap Task Blog Post With Student Work

Hotel Snap Directions

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!

 Here are some other relatable posts if interested:

 Tasks and Standardized Testing

How to Implement a Mathematical Task

How to Get Your Students Talking and Writing One

How to Get Your Students Talking and Writing Two

Dr. Clayton M. Edwards
Assistant Professor of Curriculum and Instruction 
University of Northern Iowa
Curriculum Vita
@doctor_math
Mathematical Tasks Spreadsheet
1:1 Mathematical Philosophy
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Friday, October 23, 2015

Animal Crossing Amiibo Cards...Can You Collect All 100?

I recently collected all 100 of the series one Animal Crossing Amiibo Cards. Here is a look at my haul (Timmy is probably my favorite)...



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.

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).

The cards are also readily available on eBay in exchange for various amounts of money. Some of the dealers sell individuals and some make you choose multiple amounts at a time. Either could be better depending on what you need.

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 (here are my doubles if anyone is interested...each red box is one card). 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.

My grand total was $282. I did not plan out this experience, but it got me thinking...what would be the cheapest way to get all 100 cards?

$5.99 per pack + tax gets you 1 of cards 1 through 15 and 5 of cards 16 through 100

Most cards 16 through 100 can be had on eBay for $2 per card

Most cards 1 through 15 can be purchased on eBay for $4 per card

Lucky for me, I will get to experience this card buying process again when series two 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).

I thought about this problem mathematically from a few perspectives, and I think your students would have a good time with this as well.

If I had purchased the entire first series on eBay...

15 specials * about $4 per card = $60

85 regulars * about $2 per card = $170

Total eBay amount = $230

Clearly I did not get a good deal in spending $282.

Although pretty much impossible, I thought about the fewest number of packs I would need to buy to get all 100:

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).

17 pack * $5.99 * 1.07 = about $109

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.

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.

I am specifically thinking about those always difficult 6th grade statistics and probability standards 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.

If you go to random.org/integers, we can set up a simulation.

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

You will get a list similar to this:

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.











You'll end up with something like this:


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.

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.

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.

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.

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!

Dr. Clayton M. Edwards
Assistant Professor of Curriculum and Instruction 
University of Northern Iowa
Schindler Education Center/Nielsen Field House
clayton.edwards@uni.edu
Middle Level Major Requirements
National Council of Teachers of Mathematics Editorial Panel
Curriculum Vita
@doctor_math
Mathematical Tasks Spreadsheet
1:1 Mathematical Philosophy

What does a task look like in action?

Spreadsheet of Task I Have Used in the Classroom

Student Task Work Examples

Bubble Wrap Task

Doritos Roulette 









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Thursday, August 6, 2015

Estimation via Splatoon

I am a huge fan the website Estimation 180 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 @Estimation180 Twitter feed for others to enjoy.

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 Splatoon by Nintendo. 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 game footage to give you an idea...

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.

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!


 
Dr. Clayton M. Edwards
Assistant Professor of Curriculum and Instruction 
University of Northern Iowa
Schindler Education Center/Nielsen Field House
National Council of Teachers of Mathematics Editorial Panel
Curriculum Vita
@doctor_math
Mathematical Tasks Spreadsheet
1:1 Mathematical Philosophy
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Monday, June 22, 2015

Sticky Note Task

Since 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 @mr_stadel. 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:



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 Estimation 180 (created by the same @mr_stadel) has put them in this mindset, which isn't a bad thing. 

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 Tile Floor Task, 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. 

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. 

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. 

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. 




































What does a task look like in action?

Spreadsheet of Task I Have Used in the Classroom

Student Task Work Examples

Bubble Wrap Task

Doritos Roulette 








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Monday, June 1, 2015

What 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.

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.

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.

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:

"but when he gives me help, usually he doesn't explain it very well"

 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?

I didn't know I was so funny. Maybe the students mean funny looking. It didn't work for Joey in Full House when he was a substitute, 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.

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.

I even got a Rocky reference from a kid who I doubt has seen any of those movies...

https://www.youtube.com/watch?v=E-WHW-QNswE

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:

"Dr. Edwards is my favorite teacher in the whole entire world.. and I hate teachers."

6th Grade

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. 

 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. 

 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...

 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

 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! 

 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.

 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.

 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!

 grate teacher

 nice funny I learn a lot from you and is my favorite teacher.  

 Persistant because he wants you to improve.

 He is helpful funny and a motivator 

 That you are the best teacher and you make the day way better 

 I would say that you are the best math teacher ever.

 i would say he is an awesome math teacher, he is really nice, and he cares about improvement

 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.

 Dr. Edwards is is a good math teacher. 

 He is a good math teacher and he helps me with math. 

 I like the way you teach. I like how at the end of the class you do the questions​ and the star bursts. 

 Edwards is a gummy bear giving guy fun dude and the best math teacher.

 he is a asome teacher even tho the can be alitel stresfull but he is one of  the best techers i ever had 

 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! 

 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

 hes the best math teacher and he teaches in his own ways that helps kids learn better   

 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.

 Amazing teacher guides us in the right path to learning more

He is nice teacher we have in the school.

 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.

 https://www.youtube.com/watch?v=E-WHW-QNswE

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.

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.

Always trying to do the best for us. Focuses on getting us to do better and improve. Fun/Funny.

I think your an awesome teacher

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.

A really fun math teacher that cares about everyone. He has plans for everyone

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. 

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.

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.

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.

I think you would say that we love the way you make us laugh 

That they think i am awesome (I is you)

Best teacher to help me improve on math.

he is a great teacher and I have never had such a good mach teacher


7th Grade

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.

 I think Dr. Edwards is flexible. Flexible because you are almost always available after school and before school just to help students. Thank you.

 He is the best teach with getting you and others improved. 

 I think dr.edwards is fun and has a why of techie us a why most people don't do

 I would say that You care mostly about Improvment, and you take your job very seriously.

 I would say,
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.

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.

CANDY/junk food addict

Dr.Edwards is a great teacher, he helps me a lot. More than any other teacher could.

I think that dr.edwards is a well liked teacher but when he gives me help, ususally he doesn't explain it very well

Dr. Edwards is my favorite teacher in the whole entire world.. and I hate teachers.

I think Dr. Edwards is one of the best teachers I have had.

On a scale of 1-10, answer being x, the equation would look like x*5655765876576587658657658675786576586587

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.

What do you have to say about Dr. Edwards? I think that he is cool.

Dr.Edwards is very motivated for improvement.

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. 

He explains alot when you dont know what your doing and he has a unique was of teaching through videos.

He teaches efficiently    

We would say he is a good teacher. And he helps the students learn better.

Dr. Edwards makes sure we understand everything before we move on and he helps us understand it. 

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...

That you push us hard to improve, and get things done.

I would say : That you are a great teacher that always strides for his students to improve.

You usually give us enough time to complete assignments. 

I would say that he likes being here and that he likes his job. He is also always looking to make students better. 

I would saw that you take your student improvement very seriously 

is a math wizard and is very concerned about ur students being improved

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

A person that dedicates a lot of time to math and cares a lot about his students improvement. ​

I think you want everyone to improve and that is nice except when you get a little strict and that about it.

You should have answered that answer by saying you are a little too strict but we get stuff done in class.

your a great person and great teacher

__________________________________

What does a task look like in action?

Spreadsheet of Task I Have Used in the Classroom

Student Task Work Examples

Bubble Wrap Task

Doritos Roulette 








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