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Math Monday::Pentominoes!

{as an aside, let’s just all pretend that I actually write and post these on Monday, it would help keep the whole ‘math monday’ alliteration theme going…and help me keep my dignity…}

A few weeks ago, our Creative Math club met together and did even more things with the square inch pieces of paper that Sonja and I had cut out for the Square Numbers Math activities. I went to town with my paper cutter one night and ended up with about a bazillion squares before I realized it.


When the kids arrived, they just sat around the table and played with the squares for a little while. Then I focused it a little more and asked them to choose 5 squares, and see what kind of pictures or shapes they could make. Some were really pretty!


And finally, after a few minutes of that, I told them we were going to play a game, but that first we needed game pieces made from 5 squares. Each piece needed to have 5 squares connected–no more, no less. There would be a total of 12 game peices per person. Their job was to put the 5 squares together to see if it was a game peice…each piece had a specific rule to follow in order to use it to play the game with, but, I wasn’t going to tell them what the pieces looked like, I would only tell them yes or no if it was a piece as they showed me their ideas.


This is a technique I discovered works really well with visual spatial, right brain thinkers. Rather than tell them the rule, or explain how something works, I just give them the free reign to experience it for themselves and then tell me the rule or how it works. The rule for the game pieces is simply the definition for pentominoes…shapes that are formed by joining a series of 5 squares attached edge to edge (not edge to corner!). Or, another way of putting it: A pentomino is a polyomino composed of five (Greek πέντε / pente) congruent squares, connected orthogonally.

So, the kids would arrange 5 squares, then ask me if it was a game piece. Out of these 3 examples, only the two on the ends are pentominoes, because the middle one joins the squares at the corners.


If you’ve ever played Tetris, then you’ll recognize the pentomino shapes…even though Tetris only uses four block shapes.

Slowly they honed their skills, and it didn’t take long for them to figure out the characteristics of the pentomino shapes.

Picnik collage

Once they all had their 12 pieces glued to a sheet of construction paper, they cut them out and then I brought out my most favorite thing in the world….the laminator. It’s hard to express how much love I have for this thing, I’m totally addicted to laminating things. The kids were also totally addicted to watching their pentominoes go in with a thin sheet of plastic over them, and come out laminated and sturdy.


Now, they had their game pieces ready…but we’d run out of time. So, we’ll make the game boards next week and use the pentominoes in a very mathmatical and fun way. And then next math monday I’ll explain what games we played with them. In the meantime, here’s an Online Pentomino Gameand another online Pentomino Game.

To finish up our Math Club, we played Blokus, which is a family favorite in our household, and one that uses pentominoes and other shapes to create a simple and addicting game. This has been in heavy rotation around here for the past year, solid.


So, here’s a quick note about pentominoes, and why I love them. They are totally mathmatical, but totally non computational. Meaning, you don’t have to sit around with a calculator or worksheet. Pentominoes are meant to be played with, flipped around, discovered, explored, and used in a very hands on way. If you have a mathphobic kid, or are mathphobic yourself, I highly recommend getting a hold of some Pentominoes games and puzzles for a while. Math is fun! Just play with them! If you can’t resist a more ‘schooly’ way of dealing with them, there are lots of school standard type Fiction and Non Fiction books about Pentominoes.

More about Pentominoes here

Wikipedia article about pentominoes here.

Blokus game if you only have 2 players.

and then I just now saw this Blokus 3D Game, which looks pretty cool!

9 Responses

  1. Wow. Truly, you are my hero, and I’m dropping A off at your house when we get home. 😉 I really want to get to one of these math meetings, but that pesky school keeps getting in the way. 😉 Soon.

  2. do i really look like that!?

  3. Cool. But I think I will have to wait till the exams are over. Now for a month we are trying to keep ourselves oriented that way. 🙂 . But I am glad that this term it was real fun and I think two weeks for school world wouldn’t do much damage.

    Tiffany, Let me ask you one other thing. Now that I work in a completely different way with Swetha and when I see how nicely she responds my heart really goes out for Siva. I really wish I could have done it all with him. Even though I have tried every thing I could do to cover it I wonder will he ever able to forgive me. How is it for Naturalist . Did she get over it ?

  4. […] on December 8, 2009 by childsplay When I last left off our pentominoes investigation, the kids had made the pentomino shapes out of square pieces of paper and laminated them. The sheets of pentominoes looked like this, and then we cut them […]

  5. I came over from All Things Beautiful and I’m so glad I found your blog! We host Math Monday posts and it would be wonderful if you can link this up to our linky! This is fabulous! Thanks for sharing!

  6. I forgot to provide you with our math links…


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