Math Concepts: Transformations, Congruence, Similarity

What You Can Do: This game focuses on the topic of transformations, how figures move around space without changing shape. In the game, players translate (slide), rotate (turn), and reflect (flip) their triangles on a coordinate grid, but triangles and other shapes can be translated anywhere. Artwork and graphics frequently use transformations in their design. Try looking at common product logos and see what examples of transformations you can find.

As another exercise, a student can create unique images using transformations, perhaps a design for a t-shirt. Discuss how the shapes were manipulated to create the most appealing result. The game has players compose transformations by performing several transformations in sequence. Do your students designs compose any transformations? Do any of the logos you looked at? If resources are available, you can even print the design on a t-shirt.

Math in the Game: Transformations can touch on many areas of geometry. In translating, rotating, and reflecting the triangle, students never change the shape, the pre-image and image (before and after) are congruent. Capturing fireflies dilated the triangles. Dilation is unique because the image is not congruent to the pre-image, but it is still similar. The game encourages composition because performing several transformations makes it easier to capture bugs. Composition of transformation can be a higher level topic by discussing the order in which to perform the transformation. Different orders can result in different results.

Lastly, the opening step of creating a triangle addresses triangle concepts specifically. The given triangle has an area of 10 square units, and the game only allows certain changes so the area doesnt change. Each vertex can only be moved along a line parallel to the opposite side. The distance from the point to the line is always the same, and therefore the height is always the same. If the base and height are equal in two triangles, the areas are equal.

Related Resources:

*Transformations and Frieze Patterns*

Students identify and create patterns using transformations to identify various classes of patterns.

*Paper Quilts*

Using translation, reflection, rotation, and line of symmetry to make four-part quilt squares.

*Flip-n-Slide: Exploring Transformations through Modeling and Computer Games*