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Let’s Learn!

How do you partition a shape into equal parts?

Goal:

Goal:

fraction fox.

Think About It!

Goal: Partition a shape into equal parts.

Caleb drew a rectangle and partitioned it into 18 equal parts to keep track of the racers’ times. Let’s look at how we can partition shapes into equal parts. Click through the tabs below to see how to partition shapes into equal parts.

Halves

To partition a shape into halves, or 2 equal parts, draw a straight line across the middle of the shape. You can use a vertical line, a horizontal line, and sometimes a diagonal line. Let’s partition these shapes into 2 equal parts.

A square
A square partitioned diagonally into 2 equal parts

diagonal line

A rectangle
A rectangle vertically into 2 equal parts

vertical line

A circle
A circle partitioned horizontally into 2 equal parts

horizontal line

Thirds

To partition a shape like a square or rectangle into thirds, or 3 equal parts, draw 2 straight lines across the shape, either vertically or horizontally. Remember to space your lines so that each part is equal in size. For a circle, draw 3 lines that meet in the center of the circle. Let’s partition some shapes into thirds.

A square
A square partitioned horizontally into 3 equal parts
A rectangle
A rectangle partitioned vertically into 3 equal parts
A circle
A circle partitioned into 3 equal parts

Fourths

To partition a shape like a square or rectangle into fourths, or 4 equal parts, draw 3 straight lines across the shape, either vertically or horizontally. Remember to space your lines so that each part is equal in size. You can also draw 1 vertical line down the middle and 1 horizontal line across the middle to make 4 equal parts. This also works for circles. Let’s partition some shapes into fourths.

A square
A square partitioned horizontally into 4 equal parts
A rectangle
A rectangle partitioned vertically into 4 equal parts
A circle
A circle partitioned into 4 equal parts

Squares and Rectangles

In general, when you need to partition a square or rectangle into a given number of equal parts, draw 1 less line than the number of equal parts. For example, if you need to partition a rectangle into 6 equal parts, draw 5 equally spaced lines. Below are a couple of examples.

A square
A square partitioned horizontally into 5 equal parts. There are four partition lines each line is labelled 1,2,3,4.
A rectangle
A rectangle partitioned vertically into 6 equal parts. There are five partition lines. Each line is labelled 1,2,3,4,5.

Circles

When you partition a circle into equal parts, all the lines will meet in the center of the circle. When the number of equal parts is odd, you will draw the same number of lines as equal parts. For example, if you need 5 equal parts, you will draw 5 lines. When the number of equal parts is even, you can draw half as many lines that go from one side of the circle to the other that meet in the middle. For example, if you need 6 equal parts, you can draw 3 lines that go from one side of the circle to the other and cross in the middle. Below are a couple examples.

A circle

Partition the circle into 5 equal parts

A circle partitioned into 5 equal parts. There are five partition lines each line is labelled 1,2,3,4.

Draw 5 lines that meet in the center.

A circle

Partition the circle into 6 equal parts

A circle partitioned into 6 equal parts with three partition lines. Each line is labelled 1,2,3.

Draw 3 lines that go from one side of the circle to the other and that cross in the middle.

Doubles

You can use both vertical and horizontal lines in squares and rectangles to make doubles. For example, if you needed 6 equal parts, you could make 3 equal parts using vertical lines and then draw a horizontal line across the middle changing the 3 equal parts to 6 equal parts. Here are some examples.

Partition the square into 6 equal parts.

A square, A square with 3 equal parts partitioned with 2 horizontal lines. A square with A square with 6 equal parts partitioned with 2 horizontal lines and 1 vertical line.

Partition the rectangle into 10 equal parts.

A rectangle, the rectangle has an arrow pointing to A rectangle with 5 equal parts partitioned with 4 vertical lines. This is pointing too. A rectangle with 10 equal parts partitioned with 4 vertical lines and 1 horizontal line.