# Let’s Make Squares Activity

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Several years ago, I heard about the Let’s Make Squares activity from an OKMath Newsletter sent out by Christine Koerner. She recommended Let’s Make Squares as a great activity for the first week of school.

I had already decided that I was going to do the 2s to 9s Challenge as my first day of school activity, but I was intrigued by the square activity. I wrote a note in my Google Keep to investigate this activity, but I never did anything with it until the other day.

It turns out the Let’s Make Squares activity was from a book that I already had on my shelf – Cooperative Learning by Dr. Spencer Kagan. I actually have an older edition of the book (1994 edition). Newer versions of the book appear to have more copy-friendly blackline masters. Since my edition didn’t, I decided to type up my own set of directions to give my students.

For the Let’s Make Squares Activity, students will need to be in groups of 4. Each group member needs three pieces (I used jumbo popsicle sticks) in a unique color from the rest of the group. If you don’t have access to colored popsicle sticks, you can also use strips of colored paper.

Groups must work together to use all 12 sticks/strips to form various numbers of squares. Each teammate is only allowed to touch/move their color of sticks/strips. This encourages groups to work together and communicate as a group as they work through the various levels of the puzzle.

Pieces must lay flat on the table. They cannot be folded, bent, torn, or broken in any way. This is one of the reasons I chose to use colored popsicle sticks instead of colored paper.

I included a diagram of what moves are allowed/not allowed in the process of making squares.

Sticks are always allowed to cross. They are never allowed to be stacked on top of one another or be arranged so sticks are touching one another along the long edge.

The hardest rule for students to follow is that “extras” are not allowed. This means that every stick must contribute to the making of squares.

Each group gets a bag of popsicle sticks (or colored paper strips), a set of instructions, and a recording sheet.

The recording sheet is my own addition to this activity. I decided I wanted a way for students to record their solutions as they found them instead of having to wait for me to check each of their solutions before moving on.

Plus, it gives students a way to keep track of which numbers of squares they have found and which ones they still need to find.

All twelve puzzles have a solution!

I cut some 11 inch strips from some colored cardstock to make a set of demonstration pieces to use with students on my dry erase board.

I added disc magnets to the back of each piece.

I show them that sticks are allowed to cross.

I also demonstrate the actions that are not allowed.

Stacking

Touching

Extras. For example, this would not count as one square since all 12 pieces are not contributing to the square.

Still not sure what I mean about making squares? Check out some action shots I took when I tested this activity with my senior statistics students during the last bit of the school year.

There was much debate over whether this next picture contained 4 or 5 squares! When students decided that it was actually 5 squares, this opened up an entire new window of possibilities for them.

Realizing that they could also overlap squares was another huge realization.

This Let’s Make Squares activity resulted in some great communication and collaboration. There were many exciting lightbulb moments to witness! I’m excited to use it as a first week of school activity with my students this coming year!

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1. Anita Sahai says:

Hi Sarah. Thank you for this!! My students are LOVING it. Do you have the solutions to all 12 squares? I would love to see how you figured out 8, 9.

Anitasahai@gmail.com

2. DeeDee says:

Could I have the solution for 8, 9, and 12 squares?

1. Casey says:

Could I get the answer key as well?

3. Caroline M Van Ness says:

LOVED this activity! Team building, geometry, problem solving, we couldn’t get enough. Can you please email me the solutions? vannessc09@gmail.com I have student pictures if you would like to post.

4. Kristen says:

Thank you for the wonderful resource. Would you mind emailing me the answer key as well?

5. Carla Fitzgerald says:

Could I please get your solutions? We are baffled by a few of them. Thanks!

.

6. Shelby says:

Hi Sarah. Am I able to also get the solutions? Thank you!

7. Chloe says:

Thank you for this! Would it be possible to get the answers? My email address is: chloeyazdani28@gmail.com

8. Linda says:

Yikes I would really appreciate the solutions sheet. Great activity – thank you.

Thanks for your Mahi (Maori word for work). Love the ideas. 1a.m. in Auckland NZ. we in lockdown but will use this when we get back to school. Can’t think right now. Can I get solutions please?

1. Emailing them to you! Hope you are out of lockdown soon!

10. Casey says:

Also, wondering if the outer most square counts as one square when dividing the square up.

1. Yes, all the squares count, no matter the size.

11. Michelle says:

Could I get solutions to 8, 9, and 12? Thank you!

12. Michele C says:

Hi Sarah
Can you send the answer key to me? Can’t wait to have the middle school students give this a try.
Thank you

13. Lindsay Papio says:

Can we get a solutions page? We are struggling with 9.

14. korinna says:

hi! my kids are struggling with some of these; could I see possible solutions? the kids are LOVING this though!!

1. Emailing you. I have also posted the solutions as one of the downloads.

15. Christopher says:

Hi Sarah, I am also unable to come up with the 8, 9, 12 solutions for this puzzle.