Let’s Learn!
How do you partition a number line to record fractions?
Goal:
Goal:
This is a section of Caleb’s newest gingerbread house. He has decorated \({ \frac{2}{3} }\) of this square. \({ \frac{2}{3} }\) is a fraction of a whole. A fraction names a certain number of parts out of the total number of parts of a whole. Let’s record \({ \frac{2}{3} }\) on a number line!
Draw an empty rectangle.
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 \({ \frac{2}{3} }\).
Let’s look at more fractions! Click on each fraction below to see it recorded on a number line.
\({ \frac{1}{2} }\)
Rectangle partitioned into 2 parts with 1 part filled in. Number line from 0 to 1 with markers for each part. Markers are labeled \({ \frac{0}{2} }\), \({ \frac{1}{2} }\), \({ \frac{2}{2} }\).
\({ \frac{1}{3} }\)
Rectangle partitioned into 3 parts with 1 part filled in. Number line from 0 to 1 with markers for each part. Markers are labeled \({ \frac{0}{3} }\), \({ \frac{1}{3} }\), \({ \frac{2}{3} }\), \({ \frac{3}{3} }\).
\({ \frac{1}{4} }\)
Rectangle partitioned into 4 parts with 1 part filled in. Number line from 0 to 1 with markers for each part. Markers are labeled \({ \frac{0}{4} }\), \({ \frac{1}{4} }\), \({ \frac{2}{4} }\), \({ \frac{3}{4} }\), \({ \frac{4}{4} }\).
\({ \frac{1}{6} }\)
Rectangle partitioned into 6 parts with 1 part filled in. Number line from 0 to 1 with markers for each part. Markers are labeled \({ \frac{0}{6} }\), \({ \frac{1}{6} }\), \({ \frac{2}{6} }\), \({ \frac{3}{6} }\), \({ \frac{4}{6} }\), \({ \frac{5}{6} }\), \({ \frac{6}{6} }\).
\({ \frac{1}{8} }\)
Rectangle partitioned into 8 parts with 1 part filled in. Number line from 0 to 1 with markers for each part. Markers are labeled \({ \frac{0}{8} }\), \({ \frac{1}{8} }\), \({ \frac{2}{8} }\), \({ \frac{3}{8} }\), \({ \frac{4}{8} }\), \({ \frac{5}{8} }\), \({ \frac{6}{8} }\), \({ \frac{7}{8} }\), \({ \frac{8}{8} }\).