Equivalent Fractions on Number Lines

Display the Show Equivalent Fractions Assessment Master. Ask students to take turns showing equivalent fractions:

1. The first student chooses a fraction, writes the fraction as a number, and shows it using one of the representations: pictures of circles, pictures of rectangles, or a number line.
2. The next student names a fraction equivalent to the first and uses the same model to explain why it is equivalent.
3. A third student shows both fractions but uses a different representation. He or she writes a number sentence and then shows why they are equivalent.

Here is an example of how one round of this activity might proceed:

• In Step 1, a student might choose 3/4 and the circle model. Figure 7 shows what he or she would show on the display.
• In Step 2, a different student chooses a fraction that is equivalent to 3/4 , for example 6/8. He or she uses the same representation to show this fraction, in this case the circle model. Figure 8 demonstrates what is shown on the display. The student explains that 3/4 is equivalent of 6/8 because the size of the shaded regions is the same.
• In Step 3, a third student uses a different model to show that 3/4 and 6/8 are equivalent, this time using number lines. Figure 9 shows what is on the display. The student writes 3/4 = 6/8 and explains that 3/4 and 6/8 are the same distance from 0.

Continue the activity until several fractions and equivalent fractions have been discussed.

Distribute copies of the Show Equivalent Fractions Assessment Master. Instruct students to do the following, just as they did in the Summarizing the Lesson activity, but independently:

1. Choose a fraction and write it as a number.
2. Show the fraction using one of the representations (e.g., number line).
3. Show an equivalent fraction using the same model (e.g., number line).
4. Show both fractions using a different representation (e.g., rectangles).
5. Write a number sentence.
6. Explain how they know the fractions are equivalent.