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Pentasquares Puzzle

I’m really excited about this Pentasquares puzzle from Serhiy Grabarchuk. Pentasquares are five square shapes which fit inside a 3 x 3 dimension.

pentasquares puzzle serhiy grabarchuk

The goal of this puzzle is to put all six pentasquares inside a 6 x 6 square. You can rotate the pentasquares, but you may not overlap them or flip them over.

They will not form a perfect square,since 6 pentasquares X 5 squares = 30/36 possible squares. Instead, the goal is just to fit them within the square. There are multiple solutions.

pentasquares puzzle serhiy grabarchuk

To make it really clear which side of the pentasquares should be facing up, I added a dotted pattern to the front.

pentasquares puzzle serhiy grabarchuk

This puzzle is easy enough to leave out on a puzzle table for students to tackle on their own during spare class time. If you wanted to make it more of a full math lesson, I would have students discover the pentasquares for themselves first.

What is a pentasquare? Now, that you know what a pentasquare is, how many pentasquares are they?

As I said earlier, this pentasquares puzzle is by Serhiy Grabarchuk. I learned about it in Puzzle Box, Volume 2. This is one of a three-volume puzzle book set that is one of my go-to sources for excellent puzzles to use in the math classroom.

Digital Version of Pentasquares Puzzle

I created a digital version of the Pentasquares Puzzle in Mathigon’s Polypad.

Pentasquares puzzle on polypad.

Puzzle Solutions

I intentionally do not share solutions to the puzzles I feature on my website because I strive to provide learning experiences for my students that are not google-able. I would like other teachers to be able to use these puzzles in their classrooms as well without the solutions being easily found on the Internet.

However, I do recognize that us teachers are busy people and sometimes need to quickly reference an answer key to see if a student has solved a puzzle correctly or to see if they have interpreted the instructions properly.

If you are a teacher who is using these puzzles in your classroom, please send me an email at sarah@mathequalslove.net with information about what you teach and where you teach. I will be happy to forward an answer key to you.

john oberman

Friday 21st of May 2021

Sarah thank you for all of the wonderful things that you pass on. We usually played the pentominoes game on a board 12 *12 with two sets (different colors).Each pupil had one set and in turn, put them on the board. The player who can't put any more of his 12 pieces on the board loses. Best Wishes Johnny Oberman Israel

Sarah Carter

Wednesday 26th of May 2021

I like this! I've always wanted a Blokus game for my classroom. This is like that, but faster. Plus, there are so many other things you can do with pentominoes! Thanks for sharing!

Peter Horsch

Wednesday 19th of May 2021

Love this activity. We "created"? (I'm sure I got many of the ideas from somewhere else) a similar activity for our 9th graders last year (fall 2019)...we didn't do it this year, but now I'm wondering if we should break it out for the last day. https://drive.google.com/drive/folders/1pO3d8PIm1QS-VLalTcl1_UuTsaGL1ZFF?usp=sharing

Sarah Carter

Wednesday 26th of May 2021

Awesome! I always love seeing the different ways teachers use pentominoes! Thanks for sharing!