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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.
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.
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