Locate Numbers on a Number Line. Display the following fractions.
Ask students to draw a number line similar to the Benchmark Number Line made and displayed in Lesson 9. See Figure 3 and Materials Preparation. Ask students to put the fractions in order on their Benchmark Number Line. Students should have available a set of fraction circle pieces and a Fraction Chart. Talk with students as they are working. When students have had a chance to put the fractions on the number line, ask them to think about what they did and how they did it.
- How did you use the numbers on the Benchmark Number Line to help you decide where to put each of the fractions? (I knew that all the fractions that were smaller than one-half were between 0 and 1/2 and those that are greater than one-half were between 1/2 and 1. I also knew that if a fraction was equal to one-half, it would go right under the 1/2 on the Benchmark Number Line.)
- When you thought about 2/3, did you use the fraction circle pieces or the Fraction Chart to help you decide where it goes on the number line, or did you have a picture in your head? What did you see in your head? (I thought about the fraction circle pieces. I knew two of the orange pieces were bigger than the pink piece, so I knew that 2/3 was bigger than 1/2.)
- How could you use the numerator and denominator to help you decide where to put 1/9 on your number line? (The numerators for 1/2 and 1/9 are both one, so I used the denominator to see that 1/9 was smaller than 1/2, because when you divide a whole into 9 pieces, the pieces will be smaller than if you divide it into 2 pieces.)
- How can you use your fraction chart to decide where to put 4/8 on the number line? (I found 4/8 on my chart and looked to see how it compared to 1/2. I saw that they are equal, so I put 4/8 right under 1/2 on my number line.)
- How can you use the numerator and denominator to decide where to put 4/8 on the number line? (I looked at the numerator and denominator and saw that if you divide both of them by 2 you get 1/2. That means that 4/8 and 1/2 are equivalent fractions.)
- Put the numbers in order from smallest to largest.
(1/9, 3/8, 4/8, 7/12, 2/3) What strategies did you use? (Possible response: I used fraction circles. I made each of the fractions with the circle pieces and compared them to see which was bigger. Another response: I used my chart. I found all the fractions and then looked to see which was the smallest. Then I put the rest of them in order. A third response: I used the numerators and denominators.
I knew that even though 12 was the smallest denominator, the numerator was 7. That means 7/12 was a little bigger than 1/2, so I knew 1/9 was the smallest fraction. Then I looked at 3/8 and 4/8 and I knew that 3/8 would be smaller than 4/8 because the numerator was smaller. Finally, I looked at 2/3 and 7/12. I found that 2/3is the same as 8/12 because if you multiply both the numerator and denominator by 4, you get 8/12. Since 8/12 is bigger than 7/12, I knew it was the biggest fraction.)
