Perimeter Jumble

You’ve seen this problem before.

I was discussing this problem with a co-worker a week or so ago and they suggested I change the scenario to a fence around a skate park….”to make it more relatable to students.” I wasn’t sure that particular fix was going to make my students want to solve it more (more on that from Dan here, here, and here). Instead, “I want to make it more curious than that…and get my students to do most of the heavy lifting”.

The textbook and many teachers will tell you to break out the geoboards and bands. But I still feel like that is telling them what to explore. I wanted them to ask the question before we do the exploring. How can we make this topic more curious?

Here is my attempt at making this more curious:

Show them this and ask for what do you notice? What do you wonder?

Today, my students noticed: “The number of pieces stayed the same,” Different rectangles, squares were made,” “The rectangles were blue,”

Today, my students wondered: “What would the perimeter be?” “How big were the rectangles?” “Were they all the same area?” “Why are we doing this” “Which shape would be the biggest?” “How long was each piece?”

I circled the wonder: Which shape is the biggest? But I extended it…. I confirmed some of their other wonderings like…yes the number of lines didn’t change. How many did you see? Did you guess 24?


Draw one of those rectangles you saw on your whiteboard. Write the dimensions. Determine the area.

I asked each student what dimensions they had and the area. Who has the biggest? I extended the idea….”I wonder what would happen if we had a different number of lines, a different perimeter to work with?”

The rest of the lesson would flow much like all of those geoboards lesson (get their hands/minds working — the less I talk the more they learn).

I assigned each pair of students a piece of chart paper with a new perimeter to work with. Draw rectangles with your set perimeter. Record the dimensions and the perimeter.


The recorded on the sheet:


I showed some pics of student graphs on the TV and we concluded together that squares were making the largest area!

The groups then turned to doing some practice problems of “Here is a perimeter…what dimensions will produce the max area” and the backwards questions…”If the largest rectangle has an area of ___ what would the perimeter be?” Some groups were given the problem where we only use 3 sides to enclose an area. What now will make the largest area?

Stripping this problem of context didn’t make them want to investigate less……in this case my students were engaged as much as I’ve seen them lately.

I wasn’t pushing them to memorize that it’s a square that will give the max area….I feel like the big idea here for us was taking our own wonderings and investigating them systematically to discover a relationship. For me that is the bigger take away for these grade 9 students.



Fav & Fix – Dec 1

For the Favourite & Fix series I’m posting one idea from my lessons that week that was my favourite and one topic that I need help on. Something I hope to fix. I’m hoping that in the comments or on Twitter (#Fav&Fix) you amazing readers can help me out with some hints, tips, and suggestions.

Favourite: The Cheating Quiz

This week I gave a quiz to my grade 9 applied students. It consisted of 4 questions – Two on linear relations and two on reading distance-time graphs. After the quiz was over I said “It’s time to do a little cheating.” Each student is to find another student they were comfortable sharing their work with. I said, “For question 2 only, share your work with each other. Discuss what you notice about each other’s solution. Do you have the same? If you have different solutions who is more right? After you discussion go back and adjust your solution if you need to. Hand in after.

I really enjoyed listening to them share. It was interesting to see how they defended (or didn’t defend) their answers. After reviewing their new work on that question it not only gave me insight into that one students thinking, it gave me some insight into what their partner was thinking too. For the student below I can see some really good thinking about how the linear relation changes. But now I know for both of these students we need to have a discussion how the increase of 100 every 5 people affects the equation. Looking at each students paper in the room now tells me a lot more about my class’ understanding compared to not having a “cheating quiz”


Fix (just a comment)

My MEL3E class is coming off a two week themed activity where we designed, built and launched rockets. Today we were completing the Sugar sugar Desmos Activity and a student says to me: “When are we going to do something fun?” I relply, “Fun?”….he says, “yeah, like watch a movie.”

I’m not one to show movies in class. 

Why do students always equate fun in class with movie watching? How does the student who just smiled through two weeks of math class, built and launched rockets, helped me fix the launcher numerous times, and today, yes today, defended his choice on which sugary cereal was the best choice not know he was having fun?

I guess enjoying class does not equal “having fun”.

Math class doesn’t have to be fun…just worth it. 

Really Big Lights – A math problem

Here’s a really big problem you can work on with your students this holiday season.

Act 1:
Show them this video and ask: What do you notice? What do you wonder?

After allowing them to voice their noticing and wonderings guide them to wonder: How big is that new light? How many times bigger is the big light compared to the old light? How many Really Big Lights would you have to put up to cover the same length as last year?

Act 2: Here are some images to help make some conclusions:

Guess: How long is the big light? How many times longer is the big light than the small light?




Guess: How many small lights are in one string that stretches 15 feet?




Work together to determine how many Really Big Lights would replace the string of 50 lights? What assumptions will you make?

Act 3: Reveal


Why might your calculated answer be different from the answer shown?

If you had 50 Really Big lights how long would could they reach? How many cars could you put in that garage?

Grab all files for this activity

You can see more info about the lights over at

One Favourite, Two Fixes: Nov 5

I need help! Every time I go through a lesson there is aways something I want to fix. Something that can be improved upon. Something that can get my students to think a little deeper about the math or something that can make my organization better, or class management better. Sometimes I can think of how to fix it, sometimes I know there is a fix out there and I can’t see it. That’s where you come in.

Each week I’m going to post one idea from my lessons that was my favourite and two topics that I need help on. Two topics I hope to fix. I’m hoping that in the comments or on Twitter you amazing readers can help me out with some hints, tips, and suggestions.


For the last two weeks one of my class’s atmosphere seemed poisoned (see below).  My favourite this week though helped restore (for a short time) that atmosphere back to where we have spent most of the year. Warm-ups to the rescue! Our warm-ups dive into our Everyday Math curriculum like nobody’s business. Sometimes they take 10 minutes, sometimes 20….and I’m ok with that. Each one has my class engaged for that time. This week my favourite was Dan Meyer’s Dueling Discounts.

The kids each had a copy of a $20 off coupon and a 20% off coupon. For each item I showed, I had them hold up their choice of coupon to use. I was loving that all students were actively engaged and WANTED to know which was the better deal. It was so nice to see this with my kids again.

First Fix

Like I said above, my class’ atmosphere has seemed poisoned for the last two weeks. Before that we had an amazing atmosphere…..all kids worked well together. They sat in random pairs everyday, they were engaged! Then a few things happened.

  • Outside of class somebody was texting things they shouldn’t to somebody else….VP said they are not to work together.
  • A new student was added and talks a lot
  • Two others can’t work together because of a fight they were in last week.

So now we don’t have the awesome —we all can work together and build off each other atmosphere I love and had. I’m looking for tips to try so we can re-create our atmosphere we started with. Any ideas?

Second Fix

In my grade 9 mfm1p class this week we worked on solving proportions through the Smart Car Smash activity. screen-shot-2016-11-06-at-9-22-20-am

After going through super gross lesson and seeing the kids smile and cringe at the same time it was time to practice our strategies. I gave out this sheet below.


This is where all the excitement for math was lost….”ah man, a worksheet”. Most students solved the problems. Some kids who were actively engaged with the first problem now were shut down. How can I keep the practice portion that I need but keep engagement up?

Thanks for reading. I would love your help. Share your suggestions on Twitter or below in the comments.

Helpful Fixes from Readers: