Comparing Fractions with Different Bottoms

Grab these first

• paper
• pencil

1. 1

   Explain the idea

   Let's compare fractions that have different bottoms (denominators). The trick is to make the bottoms the same by finding a common denominator. Then we can see which fraction is bigger.

   First, compare 34 and 56.

   Find a common denominator. Both 4 and 6 go into 12.

   34 = 912

   56 = 1012

   Now that the bottoms match, compare the tops. 9 is less than 10, so 34 is less than 56.

   We can also mark them on a number line from 0 to 1 to see it clearly. Both fractions sit between 0 and 1. After changing them to twelfths, 912 lands closer to 1 than 1012 does? No, wait, 10 is bigger so 1012 is farther from 0 and closer to 1.

2. 2

   Sit with Theo at a table with paper and a pencil. Tell him today you will learn a cool way to compare fractions even when their bottoms look different. Ask him to think of two skateboarding tricks he knows, like an ollie and a kickflip, and which one feels harder. Say that just like comparing tricks, we can compare fractions by giving them the same bottom.

3. 3

   Read the concept explanation together out loud. Point out the worked examples. Have Theo copy the fractions and the changes on his own paper so he sees the steps.

4. 4

   Draw a number line from 0 to 1 on a fresh sheet of paper. Mark 0 and 1 clearly. Ask Theo to mark 34 and 56 on it by folding the paper or drawing tick marks. Talk about how the marks show which is closer to 1.

5. 5

   Give him two new pairs to try on the number line: 25 and 34, then 58 and 710. For each pair, first change them to equivalent fractions with the same bottom, then mark both on the line. Ask him to say which is larger and how he knows.

6. 6

   Wrap up by asking Theo what he noticed about using the number line. Tell him he just learned a skill that real mathematicians use all the time. Praise his work and let him know tomorrow's lesson will build right on this.

7. 7

   Do this together

   Make a quick comic strip with 4 boxes. In the first box draw a skateboarder at 0 on a number line. In the next two boxes show him jumping to 34 and to 56 (use the equivalent fractions you found). In the last box draw a speech bubble saying which jump went farther and why. This lets Theo use his love of drawing comics while practicing the math.