Skill: Partition shapes into smaller shapes

To partition a shape, divide the whole shape into equal-area parts. The parts must fit together with no gaps or overlaps.

Example: Partition a rectangle into fourths.

1. Imagine the rectangle is $8$ squares long and $4$ squares wide.
2. Divide the long side into $4$ equal sections. Each section is $2$ squares long.
3. Draw a line from top to bottom at each section mark.

Now the rectangle is divided into $4$ smaller rectangles:

$$8 \times 4 = 32 \text{ square units}$$

Each smaller rectangle has area:

$$2 \times 4 = 8 \text{ square units}$$

All $4$ parts have the same area, and together they cover the whole rectangle. Therefore, each part is called one-fourth, or $\frac14$, of the rectangle.