Students may work on this project individually, in groups of two, or in groups of three. Depending on their skill, this project may take from one to three periods.

  Tools and materials:

1 ruler 1 compass 1 protractor 1 a simple calculator such as a TI-108 (3) three colored index cards 5 inches by 8 inches transparent Scotch tape.

Task:
From these three cards students make 6 pyramids (with open bases) whose bases are regular polygons with 3, 4, 5, 6, 7, and 8 sides (equilateral triangle, square, and regular pentagon, hexagon, heptagon, and octagon).

General method:
From the first card students cut out a regular 7-gon, inscribed in a circle with a 5 inch diameter. They divide it into two parts; one contains 3 sections of the 7-gon, and the other contains the remaining 4 sections. They fold the first section to form three faces of a pyramid with a triangular base, and fasten them with Scotch tape. They fold the second part, forming four faces of a pyramid with a square base, and fasten them with Scotch tape.

From the second card students cut out a regular 11-gon, inscribed in a circle with a 5 inch diameter. They divide it into two parts; one contains 5 sections of the 11-gon, and the other contains the remaining 6 sections. They make two pyramids, one with a pentagonal base and the other with a hexagonal base.

From the third card students cut out a regular 15-gon, inscribed in a circle with a 5 inch diameter. They divide it into two parts; one contains 7 sections of the 11-gon, and the other contains the remaining 8 sections. They make the last two pyramids.

Detailed description of the first part of the task.

1. Find the center of the card as the crossing of its two diagonals.
   


2. Draw a circle with a 2.5 inch radius.
   
3. Draw one radius (or one diagonal) to align the 0-line of a protractor.
4. Use a calculator to divide the circle into 7 equal parts

5. Draw all radii, making a "spoked" wheel.
   
6. Score each radius with the sharp point of a compass (use a ruler to keep the line straight) to make future creasing easy.
7. Draw the 7 sides of the polygon.

7 sided polygon

11 sided polygon

15 sided polygon



8. Cut out the polygon.
9. Cut it into two parts, one having 3 sections, and the other 4 sections.
   
10. Crease each part to form a pyramid and fasten it with Scotch tape.

Remarks: - Parts two and three are done in the same way. Drawing a 15-gon is the hardest, but the calculations do not require rounding (360/15 = 24). - The task naturally divides into three parts: drawing, computing, and cutting out. So working in groups of three is reasonable, if each student does all three parts. (For example, one student cuts the first two pyramids, draws the second two, and operates the calculator in the third part of the task). - The six pyramids have similar volumes, surface areas, heights, and overall shapes. But each one is different. Their differences and similarities are a good topic for a class discussion.