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This visually challenging game helps students understand congruence through translation (slides), rotations (turns), or reflections (flips). At the beginning, when the board is completely open and no squares have been filled in the game doesn’t appear to be too difficult. After all, we’re just filling in patterns of squares, right? Well, as players keep filling in the board, it’s more and more challenging to find ways to slide, turn, and flip the available shapes to fit the remaining blank squares. Some of the most mind-bending are the rotations. They’re not obvious at all and it sometimes takes quite a bit of mental gymnastics to figure out if something really will fit.
Don’t rearrange the four different patterns! You can slide them, flip them, or turn them but you’re not allowed to take them apart. Another way to play this game is to give each player a color pencil and when the game board is as filled in with shapes as possible the player with the most individual squares filled in wins.
Another way to play this game is to use color construction paper or tiles. Just because a player has placed a tile on a square doesn’t mean a second player couldn’t place a different-colored tile there as well. For this game, every move that’s made has to cover at least one blank square that has not been covered before. Remaining squares for that particular move can be covered more than once. This extends game play and it can be quite interesting to see which squares are covered numerous times.
It might also be interesting to pose some other questions to students when using this in a classroom setting. Can they see any way to fill the entire board so that there are no white squares left at all? How many of each of the patterns are used on the board? In other words, how many of #1, #2, #3, and #4 have been used? It might be fun to compare different finished games as well to see if there are any patterns from game to game or let two teams of two players each compete to see who can fill in the boards the fastest.
There are so many fun ways to play this game. Students will understand simple transformations better than ever after practicing with
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Common Core Mathematical Standards
8.G.1 Verify experimentally the properties of rotations, reflections, and translations.
8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
“I see this as an excellent source for higher-order thinking. I will be using this during an Observation knowing it will be the “hook” my students need to engage in their understanding of new knowledge! Thank you! Great idea!” – CATHERINE P.
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“This game is pretty fabulous!” – Celestine Van Rensselaer
“Your 5 minute filler games are great for end of term maths to do stations with. Kids love them and so do I – Thank-you so much!!” – Anne G.
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this game would be incredible as an iOS app.
each game starts with the grid you designed, except one instance of each of the four “tetris” shapes is placed randomly on the grid. players begin from there with the same rules you have specified. if the pieces don’t start on the game board (as you specified), isn’t everything a translation?
for more advanced students, you could have them “proof” the transformation by specifying algebraically what transformation they performed (ex: for a translation of left 4 and up 2, the player would write (x,y)->(x-4,y+2). Opponents can challenge if they think they see a mistake.
this could be played with manipulatives as well?
thanks for getting my mathgame brain going!