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Let’s Learn!

Did you know a shape can be partitioned in different ways?

Goal:

Goal:

fraction fox

Think About It!

Goal: Understand that a shape can be partitioned into a given number of equal parts in a variety of ways.

Both Madelyn and her cousin partitioned their bike lanes into 4 equal parts, but they did it in different ways. Madelyn used vertical lines, and her cousin used horizontal lines. Because both of their drawings made 4 equal parts, each bike lane represents \(\Large\frac{1}{4}\) of the total lanes.

Let’s look at how the same shape can be partitioned in different ways. Click through the tabs below to see how each shape can be partitioned.

Squares

Squares can be partitioned in a variety of ways. Just make sure each part is the same size as each of the others. Let’s partition these squares into 4 equal parts. Each equal part will represent \(\Large\frac{1}{4}\) of the square.

A square

Vertical lines

A square partitioned with 3 vertical lines making 4 equal parts.

Vertical lines

A square

Horizontal lines

A square partitioned with a horizontal and vertical line crossing in the center creating 4 equal parts.

Horizontal lines

A square

Vertical and horizontal lines

A square partitioned with a vertical and horizontal line making 4 equal parts.

Vertical and horizontal lines

A square

Diagonal lines

A square partitioned with 2 Diagonal lines making 4 equal parts.

Diagonal lines

Rectangles

Rectangles can also be partitioned in a variety of ways. Just make sure each part is the same size as each of the others. Let’s partition these rectangles into 6 equal parts. Each equal part of the rectangle will represent \(\Large\frac{1}{6}\) of the rectangle.

A rectangle

Vertical lines

A rectangle partitioned with 3 vertical lines making 4 equal parts.

Vertical lines

A rectangle

Horizontal lines

A rectangle partitioned with 3 horizontal lines making 4 equal parts.

Horizontal lines

A rectangle

Vertical and Horizontal lines

A rectangle partitioned with 2 vertical lines and 1 horizontal line making 6 equal parts.

Vertical and Horizontal lines

Circles

When you partition circles, each line must pass through the middle of the circle. Here are a few examples of how circles can be partitioned.

10 circles. A circle. A circle with partitioned into 2 equal parts with 1 line. A circle with partitioned into 3 equal parts. A circle with partitioned into 4 equal parts. A circle with partitioned into 5 equal parts. A circle with partitioned into 6 equal parts. A circle with partitioned into 7 equal parts. A circle with partitioned into 8 equal parts. A circle with partitioned into 9 equal parts. A circle with partitioned into 10 equal parts.

In each circle, all the parts of the circle are equal.

When you partition a circle, you cannot use more than 1 vertical and 1 horizontal line. If you try using more horizontal or vertical lines, you will not make equal parts. Look at the examples below.

A circled partitioned with a vertical and horizontal line dividing the circle into 4 equal parts. A circle divided by 3 vertical lines without equal parts. A circled partitioned horizontally without equal parts.