Wednesday, June 29, 2016

What to Expect From the Blog and Me in 2016-2017

It 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.

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.

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.

Here are a few of my previous posts to give you an idea...

In-N-Out Burger Task

Man Versus Squirrel

Doritos Roulette

I look forward to doing these tasks again, along with the many tasks on my spreadsheet I have tested...

Mathematical Task Spreadsheet

I found some new tasks as well that I know my students will enjoy...

Vroom Vroom

The Nardo Ring

Gas Station Ripoff

Marble Slide

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 #MTBoS and other math professionals on Twitter for consistently pumping out these tasks for my students to enjoy.

I will also be involved in a few professional development and speaking opportunities where I will be discussing 1:1 Mathematics, and Task-Based Mathematics.

Finally, I am in year two of being on NCTM's MTMS Editorial Panel. 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.

I look forward to blogging this year and hopefully helping you feel good about implementing tasks into your classrooms! Have a great summer!

Dr. Clayton M. Edwards
Grundy Center Middle School
Middle School Mathematics Instructor

National Council of Teachers of Mathematics Editorial Panel
Former Middle Level Coordinator (UNI)
Ed. D. Curriculum and Instruction (UNI)
MA Middle Level Mathematics (UNI) 

Yager Exemplary Teaching Award 2014
Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa 2014

Monday, January 4, 2016

Cube Net Task and the Excitement of Substitute Teaching

I 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.

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.

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.

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 robust problem-solving tasks, so I thought I would go that route.

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 tasks, 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.

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 6.G.A.4, 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 so much

Here are the directions for the task (note: this task comes from @NCTMillum):

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 Rick Wormeli at AMLE.

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.

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 @NCTMillum website so students had plenty of room to write, draw, and explain. 

Keep in mind that the order of the nets shifts around every time you start the online portion of the activity over, but it is easy to find which 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 discussion at the end. There are 11 nets that make cubes and 13 nets where something is incorrect (not enough faces, too many tops, etc). I did not tell them how many did or did not

This activity really takes 60+ minutes to do it right. I was there on an early out day with 40 minute classes, and by the time we did a few introductions and went over expectations/task objectives, we had about 30 minutes of student work time/discussion. 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 thinking...fat chance a 6th grader could hold onto a piece of paper for 2 could happen :-)
Right away, I could tell that some of the students were not strong with spatial thinking. 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 explaining that it made thinking about the cube easier if you picked out one of the faces to be the bottom before starting, and go 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. 

I enjoy using tasks from @jstevens009 and his site,, and I saw a lot of that argumentative spirit come out in these students when I am not sure they had ever thought about math this way before. Two boys were paired up, and they were not getting very far in making a decision on this net...


This seems pretty cut and dry to me, but from a 6th graders perspective who has been used to going with a gut feeling, I could see why he thought it was a cube. The conversation between these two boys was basically a yes it was, no it wasn't back and forth, which was going no where. 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 arguments, 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 changed positions. Both boys actually pictured the top/middle square as being the bottom and stated that there could never be a back side and the top would overlap. This is a great example of the power of individual think time before talking with a group. It arms everyone with ideas instead of just accepting what someone else has or denying someone's suggestions just because a gut feeling told you so.

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.

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.

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.

(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 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).

Dr. Clayton M. Edwards
Assistant Professor of Curriculum and Instruction 
Middle Level Program Coordinator
University of Northern Iowa
Curriculum Vita
Mathematical Tasks Spreadsheet
1:1 Mathematical Philosophy

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 ~ 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
Mathematical Tasks Spreadsheet
1:1 Mathematical Philosophy

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, 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
Middle Level Major Requirements
National Council of Teachers of Mathematics Editorial Panel
Curriculum Vita
Mathematical Tasks Spreadsheet
1:1 Mathematical Philosophy

Student Task Work Examples

Doritos Roulette 

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
Mathematical Tasks Spreadsheet
1:1 Mathematical Philosophy

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. 

Student Task Work Examples