Composition Exploration

Objective: Understand the effect of two reflections done in sequence.

Materials

• Scissors.
• Two printed copies of the "FLIP ME" disk.

Procedure

Performing one operation followed by another is called a composition of the two operations.

1. Print the disk and cut it out.
2. Lay the disk flat, face up in front of you. Flip over along the horizontal line, then flip over along the vertical line. What angle rotation resulted? What angle was formed by the two flip lines?
3. Return the disk its starting position. Now flip over along the horizontal line, then flip over along the 45° line running southwest to northeast. What angle rotation resulted? What angle was formed by the two flip lines?
4. Return the disk to its starting position. Reverse the flips in question 2. That is, first flip along the 45° line then flip along the horizontal line. How did the results differ from question 2?
5. Try flipping along the horizontal line and another line at about a 30° angle. How much rotation results?
6. Can you guess a general pattern?

Handin: A sheet with answers to all questions.