Making a Wreath and a Pinwheel

Materials: Eight paper squares, same size (two colors)

Do the following to each square:

• Fold the square to create four creases: vertical in center, horizontal in center, two diagonals.
• Fold the top corners down to make the roof of a house.
• Fold the house in half such that the flaps are on the inside.
• Hold the half-house by the acute angle at the bottom left.
• Push in the bottom right corner to form a parallelogram.

Making the wreath:

• Position one piece with the folded edge to the left, and the acute angle at the bottom left.
• Position the next piece with the folded edge at the top and the acute angle at the upper left.
• Slide the acute angle on the right piece into the fold pocket of the left piece.
• Fold down the tips of the left piece into the valley of the right piece.
• Attach the remaining pieces.
• Connect the last piece to the first piece.

Making the pinwheel:

Gently slide the sides of the wreath toward the center.

Questions regarding symmetry:

1. Describe the reflectional and rotational symmetries of the following:

• Square
• House
• Half-house
• Parallelogram
• Wreath
• Pinwheel

2. Slide the pinwheel to the wreath. Push on a pair of opposite sides to get a pinwheel with only two wings. What are the reflectional and rotational symmetries of this figure?

3. Slide the pinwheel to the wreath. Push on opposite sides to produce other shapes. What shapes can you create in the center opening?

Reference:

Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (1998). Connected mathematics: Kaleidoscopes, hubcaps, and mirrors. La Porte, IN: Prentice Hall, Dale Seymour Publications.