Measuring and the Number Line

Measuring with Paper Strips

Imagine a strip of paper representing 1 unit.

1. Fold it in half $\rightarrow$ Each part is $\frac{1}{2}$.
2. Fold it in half again $\rightarrow$ You now have 4 equal parts. Each is $\frac{1}{4}$.
3. Fold it again $\rightarrow$ You have 8 equal parts. Each is $\frac{1}{8}$.

We can collect these units:

• 2 times $\frac{1}{4} = \frac{2}{4}$
• 3 times $\frac{1}{4} = \frac{3}{4}$
• 4 times $\frac{1}{4} = \frac{4}{4} = 1$ (The whole strip)

Fractions on the Number Line

We place integers ($0, 1, 2, \dots$) on the number line. We can also place fractions between them. The distance between 0 and 1 is one unit.

If we divide this distance into 2 equal parts, the midpoint is $\frac{1}{2}$. If we divide it into 3 equal parts, the marks are at $\frac{1}{3}$ and $\frac{2}{3}$.