Pentasquares Puzzle
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I’m really excited about this Pentasquares puzzle from Serhiy Grabarchuk. Pentasquares are five square shapes which fit inside a 3 x 3 dimension.
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.
To make it really clear which side of the pentasquares should be facing up, I added a dotted pattern to the front.
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.
Free Download of Pentasquares Puzzle
Click here to Download
Pentasquares (PDF)
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Pentasquares (Editable Publisher File ZIP)
2344 downloads – 126.73 KB
Want more puzzles? Check out my puzzles page!
Puzzle Solutions
Puzzle solutions are available on a password-protected solution page. I do not openly post the puzzle answer keys because one of my goals as a resource creator is to craft learning experiences for students that are non-google-able. I want teachers to be able to use these puzzles in their classrooms without the solutions being found easily on the Internet.
Please email me at sarah@mathequalslove.net for the password to the answer key database featuring all of my printable puzzles and math worksheets. I frequently have students emailing me for the answer key, so please specify in your email what school you teach at and what subjects you teach. If you do not provide these details, I will not be able to send you the password.
Not a teacher? Go ahead and send me an email as well. Just let me know what you are using the puzzles for. I am continually in awe of how many people are using these puzzles with scouting groups, with senior adults battling dementia, or as fun activities in their workplace. Just give me enough details so I know you are not a student looking for answers to the puzzle that was assigned as their homework!
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
Awesome! I always love seeing the different ways teachers use pentominoes! Thanks for sharing!
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
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!