Let’s Learn!

Partition the rectangle, and color it in to represent ${ \frac{2}{3} }$. That means the rectangle should be partitioned into 3 equal parts with 2 of the parts colored in.

Create the number line. A number line is a straight line with arrows at both ends and numbers equally spaced out. Draw a horizontal line right underneath your rectangle with arrows at both ends of the line, just like this:

Label the number line. ${ \frac{2}{3} }$ is between 0 and 1, because we can see that the full rectangle is not shaded. That means the number line will begin at 0 and end at 1.

Label the number line with fractions. First, draw a line segment where each partition of the rectangle meets the number line.

The rectangle is partitioned into 3 equal parts, so the denominator is 3. Next, label each segment with the denominator, even where the 0 and 1 are.

Rectangle partitioned into 3 equal parts. With 2 parts filled in. Number line underneath from 0 to 1. Markers for each partition. Number line is labeled ${ \frac{}{3} }$ for each marker.

Finally, label the numerators. Remember to start at ${ \frac{0}{3} }$, or 0, and end at ${ \frac{3}{3} }$, or 1.

Rectangle partitioned into 3 equal parts. With 2 parts filled in. Number line underneath from 0 to 1. Markers for each partition. Number line is labeled ${ \frac{0}{3} }$, ${ \frac{1}{3} }$, ${ \frac{2}{3} }$, ${ \frac{3}{3} }$, ${ \frac{4}{3} }$.

Caleb needs to record ${ \frac{2}{3} }$ on the number line. We record this fraction by drawing a dot above ${ \frac{2}{3} }$.

Rectangle partitioned into 3 equal parts. With 2 parts filled in. Number line underneath from 0 to 1. Markers for each partition. Number line is labeled ${ \frac{0}{3} }$, ${ \frac{1}{3} }$, ${ \frac{2}{3} }$, ${ \frac{3}{3} }$, ${ \frac{4}{3} }$. Dot on ${ \frac{2}{3} }$.

Great job! We can remove the rectangle so we can see just the number line. This is ${ \frac{2}{3} }$ on a number line!

Number line is labeled ${ \frac{0}{3} }$, ${ \frac{1}{3} }$, ${ \frac{2}{3} }$, ${ \frac{3}{3} }$, ${ \frac{4}{3} }$. Dot on ${ \frac{2}{3} }$.