The purpose of this activity is for students to locate 1 on a number line, given the location of a non-unit fraction less than 1 or greater than 1. In either case, it is likely students will reason about unit fractions to locate 1.

In the first problem, students may use the size of thirds to locate 1. In the second problem, they reinforce their knowledge that the denominator of a fraction tells the number of equal parts in a whole and the size of a unit fraction, and that the numerator gives the number of those parts (MP6). Students typically use the denominator to partition a number line, but here they need to use the numerator.

This activity uses MLR1 Stronger and Clearer Each Time. Advances: reading, writing.

• “What do we know about this fraction?”
• “How could that help us find 1?”

MLR1 Stronger and Clearer Each Time

• “Share your written reasoning for one of the number lines with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
• 3–5 minutes: structured partner discussion
• Repeat with 2 or 3 different partners.
• “Revise your initial draft, based on the feedback you got from your partners.”
• 2–3 minutes: independent work time
• Invite students to share their revised explanations of how they located 1 on the number lines.

The purpose of this activity is for students to use the location of a unit fraction to find another fraction, with a different denominator, on the number line. Students can use their knowledge from the previous activity to place 1 on the number line, and then use that to partition the interval from 0 to 1 to find other numbers. Because students have located only fractions with the same denominator on a single number line, they may want to use more than one number line in this activity. They may or may not label the points they find along the way to . Encourage them to use whatever strategy makes sense to them.

This activity is optional because it goes beyond the depth of understanding required to address grade 3 standards.

• Ask the two selected students to display their work side by side for all to see.
• “What do these strategies have in common? How are these representations different?” (Both located 1 before locating . In the first strategy, the thirds are on one number line and used to find 1. Then the 1 is on the second number line and used to find . In the second strategy, the thirds and fourths are marked on the same number line.)
• Consider asking: “What questions do you have about these representations?”