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Let’s Make Squares Activity

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1 Free Download of Let’s Make Squares Activity
2 More Fun Activities for the First Week of School

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.

let's make squares activity on student desk.

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.

Let's Make Squares Activity Rules.

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.

Handouts for Let's Make Squares Activity.

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.

Popsicle Sticks and paper Strips for Let's Make Squares Activity.

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.

jumbo colored craft sticks

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.

let's make squares activity rules for what is always allowed and never allowed.

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

Popsicle sticks bagged up for let's make squares activity.

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!

let's make squares activity recording sheet.

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.

cutting paper strips for let's make squares activity.

I added disc magnets to the back of each piece.

paper strips with magnets on them for let's make squares activity.

I show them that sticks are allowed to cross.

example of sticks crossing in let's make squares activity.

I also demonstrate the actions that are not allowed.

Stacking

example of sticks overlapping in let's make squares activity.

Touching

example of sticks touching in let's make squares activity.

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

paper strips on dry erase board to illustrate let's make squares activity.

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.

student work on let's make squares activity
student work on let's make squares activity
student work on let's make squares activity
student recording sheet for let's make squares activity.

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.

student work on let's make squares activity
student work on let's make squares activity
student work on let's make squares activity

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

student work on let's make squares activity
student work on let's make squares activity

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!

More Fun Activities for the First Week of School

Sarah Carter teaches high school math in her hometown of Coweta, Oklahoma. She currently teaches AP Precalculus, AP Calculus AB, and Statistics. She is passionate about sharing creative and hands-on teaching ideas with math teachers around the world through her blog, Math = Love.

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117 Comments

  1. OK…Just making sure if they are all possible? If yes I will keep on brainstorming with the popsicle sticks

  2. Hi Sarah,
    I am planning on doing this during week 1 this year. About how long do you estimate it would take for 7th graders?

  3. Thank you for this! I’m a new teacher and I very much want to use this activity with my students next week. A burning question I always have, with this and other activities: What if my class isn’t divisible by 4? In my class of 27, I would need to have one group of 3; I’m thinking that in that case it would be better to use just 3 colors of popsicle sticks and give each student 4 of the same color?

    1. That’s exactly what I would do. Thankfully, the 12 sticks are divisible by 2, 3, and 4.

      Wouldn’t it be perfect if our class sizes were always perfectly divisible and no one was every absent?!?

  4. This sounds like a great activity. Are all 12 sets possible? Do your students generally find all 12?

  5. Thanks for posting this great activity! My kiddos loved it. We are having a hard time to find 8 squares with those sticks. Has anyone got it in your class?

      1. I’m having a hard time finding some of the answers, can you send me the answers so I’m prepared for my students.

  7. 9! Holy cow. This exercise was exactly what my quiet classes needed to learn to work together… 9 and 10th grade geometry. We are all baffled by 9. Any solutions out there?

  8. Say my students make a “window” made out of a 2 x 2 square with the a vertical and horizontal divider in the middle. Do you count this as 4 squares or 5? I let me students decide and then said that rule must stay the same for all of their pictures. If they count the larger square window and the smaller 4 panes, then they must always include the larger square if they make other squares. How do you do it? Have you had anyone be successful with 12?

  9. Hi do you have an answer sheet? I cannot for the life of me figure out 9 squares ha ha. Thanks in advanced.

  11. We are struggling to find solutions for 8, 9, 11, and 12. Anyone willing to share their solutions?

  13. I tried to make the 8-9-11-12 square but I was not able to do it. Do you have a solution for these square?

          1. Hi- I love this activity! Thank you for sharing! Would you mind sending me your solutions? There are a couple I’m stuck on. 🙂

          3. I am so excited to use this with my students next week! Could I get a copy of the solutions emailed to me please?

  14. Hi and thank you for this activity. Any chance you can provide the solutions? Thank you.

  16. Hi Sarah, would you be able to email the solutions?

    Thanks, I.m excited to use this with my classes

  17. This is such a great activity! I am definitely hoping to try it during our first week. If possible, could you email me the solutions? I am gathering up the materials to try it out myself, but there are a few I am not sure how to. Thank you for your help and for sharing this fun, hands on activity!

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