Object:
Earn the most points by collecting by collecting ladybugs.

Set-Up:
The game board is a coordinate grid. At all times, the board is populated by ladybugs and fireflies. To the left are the transformation tokens used to move the triangle around the board and collect bugs. In the center is the action bar used to build your transformations.

Play:
Begin the game by customizing your triangle. The triangle is your game piece, used to collect bugs from various parts of the game board. Drag any vertex to adjust the shape of the triangle. Drag the triangle interior to move the triangle on the grid. When you are finished, click Submit Triangle.

On your turn, build your transformation to move your triangle. Your goal is to capture as many bugs as you can. The fireflies dilate your triangle, making the triangle bigger for every firefly collected. The ladybugs earn points when captured. Each ladybug is initially worth 100 points. With each dilation of the triangle, the point value of the ladybugs doubles. For example, after two fireflies, the triangle dilates twice, so the ladybugs are worth 400 points each.

Each transformation token in your bank performs a single transformation. The choices are as follows:

• x-Translate: Translate (slide) your triangle right or left by some number of units.
• y-Translate: Translate your triangle up or down by some number of units.
• Rotate: Rotate (turn) your triangle some degrees clockwise (CW) or counterclockwise (CCW) about a point.
• Reflect: Reflect (flip) your triangle over a line.

Drag the token for the transformation you want to the action bar in the middle. A settings window will automatically open to set the parameters of your transformation. You can add as many as four transformations in a single turn. If you want to change the settings of a token after its been added, click on that token to reopen the settings window. You can also remove transformations from the action bar by dragging the tokens back to your bank. When you have finished building your transformation, click Go! to perform the transformation(s).

Play alternates as players transform their triangles and collect bugs. Once a token is used in an action, it is removed from your bank. The game ends either when one player has used all the tokens in the players bank or when both players have had 5 turns.

Winning the Game:
At the end of the game, the player with more points wins.

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.