The Square Game
Geometer’s Sketchpad
Number Theory
You will use Geometer’s Sketchpad to simulate “The Square Game”: a game where each player is given a rectangular piece of graph paper, and they must cut it into squares all the same size without any paper left over. The winner is the player who cuts the largest square pieces of paper. In this simulation, you will divide your rectangle grid into square pieces to make a quilt block design. Your goal is to find the largest square pieces (all the same size) that will cover the rectangular grid without any of the grid leftover.
Use the following directions to simulate the game:
1. Open the rectangular grid (18 by 30 Grid.gsp).
2. Make a 2 by 2 square as shown to the left using the following directions: a) Use the Point Tool to select the vertices of each square, b) construct each square by choosing Polygon Interior under the Construct menu, c) change the color of your square by choosing Color under the Display menu. (Once you have constructed your first square, you can use the translate function to create each new square to cover your grid.) Continue following the directions below to translate your square.
3. Select point A, and then, point B as labeled in the diagram.
4. While the points are highlighted, choose Mark Vector under the Transform menu.
5. Highlight your square using your Arrow tool, and select Translate under the Transform menu.
6. While the new square is still highlighted, change the color under the Display menu.
7. Continue translating your squares by keeping each new square highlighted and selecting Translate under the Transform menu. Then change the color to show alternating colors.
8. Once you have covered the bottom row of the grid and know how to use the Translate function, find the largest square pieces you could use to cover the entire grid without any of the grid leftover.
9. Use color pencils to color the grid on your worksheet showing the largest square piece you can use to cover the grid.
The Square Game
Geometer’s Sketchpad
Number Theory
What is the largest square piece you can use? Explain your answer. ______