Are there any rules or guidelines for partitioning shapes?

• All parts have to be the same size. You can’t partition a shape into multiple parts if they’re not equal in size.

What tools or techniques can I use to partition shapes accurately?

• There are many techniques that require the use of a compass and/or a protractor.
• For the instructions below, all you’ll need is a pencil and some patience.

PARTITIONING CIRCLES:

Remember: When partitioning circles, make sure your lines go straight through the center of the circle. You can find the center by folding the circle in half twice. Where your folds cross is the center.

2 or 4 parts
If you draw a straight line from one side of the circle to the other (through the center) you’ll have partitioned the circle into two equal parts. Cut each half in half, and you’ll have four equal parts.

8, 16, or 32 parts
If you continue cutting your parts in half you’ll end up with 8 equal parts, then 16 equal parts, and 32 equal parts. Will you ever need to cut a circle into 32 equal parts? Probably not, but if you do you’ll know how!

3 parts
Cutting a circle into 3 equal parts seems tricky if you don’t have a protractor or compass, but here’s a trick. Start by finding the center of the circle, then draw a line from the top to the bottom, through the center. Fold the bottom of the circle up to the center. Unfold the paper. Draw a line connecting the center of the circle to each point where your fold crosses your circle. Erase the bottom half of your original line, and voila. Thirds.

6, 12, or 24 parts
Start by cutting the circle into three equal parts, then extend your lines through to the other side of the circle. That will make sixths. From there, cut each sixth in half, and you’ll end up with 12 equal parts. Cut them in half again to get 24 equal parts.

5 parts
There are tricks for cutting a circle into 5 equal parts, but they aren’t as easy as cutting a circle into three parts (see above). Here’s a fairly simple way to partition a circle into fifth by eye-balling it. First, find the center of the circle. Then, draw a line from the center to the top. Draw an upside down ‘V’ (from the center to the edge of the circle) to partition off 1/5. Cut each of the two remaining sections in half. If all of your pieces aren’t the same size, adjust.

10 or 20 parts
Start by cutting the circle into five equal parts, then extend your lines through to the other side of the circle. That will create tenths. From there, cut each tenth in half, and you’ll create 20 equal parts.

7 parts
Find the center of the circle. Then, draw a line from the center to the top. Draw an upside down ‘V’ (from the center to the edge of the circle) to partition off 1/7. Cut each of the two remaining sections into thirds. If all of your pieces aren’t the same size, adjust.

9 parts
Find the center of the circle. Then, draw a line from the center to the top. Draw an upside down ‘V’ (from the center to the edge of the circle) to partition off 1/9. Cut each of the two remaining sections in half. Then cut each of those halves in half again. If all of your pieces aren’t the same size, adjust.