The purpose of this activity is to prompt students to reason about the relative sizes of two fractions with the same numerator and articulate how they know which one is greater. Students have done similar reasoning work (and used similar tools to support their reasoning) in grade 3, but here the fractions include those with denominators 5 and 10. When students observe that 5 equal parts are greater than 3 of the same equal part, regardless of the size of those parts, they see regularity in repeated reasoning (MP8).

To add movement to this activity and if time permits, assign each group a pair of fractions in the second question and ask them to create a visual display showing their reasoning. Then allow a few minutes for a Gallery Walk. Ask students to identify any patterns they notice on the displays.

• “What do you notice about each pair of fractions in the second question?” (They all have 3 and 5 for the numerators, and each pair has the same denominator.)
• “What does it mean when two fractions, say and , have the same denominator?” (They are made up of the same fractional part—eighths in this case.)
• “How can we tell which fraction is greater when they have the same denominator?” (Because the fractional parts are the same size, we can compare the numerators. The fraction with the greater numerator is greater because it has more parts.)

The purpose of this activity is for students to reason about the relative sizes of two fractions with the same numerator. As before, a diagram of fraction strips can be used to help students visualize the sizes of various fractional parts. When students discuss and improve their explanation for why is greater than they develop their mathematical communication skills (MP3).

This activity uses MLR1 Stronger and Clearer Each Time. Advances: Reading, Writing.

• Select students to share their responses to the first two questions. 
• “In the set of fractions you saw, why are the fractions with 3 for the denominator always greater than fractions with 5 for the denominator?” (A third is always greater than a fifth, so some number of thirds will always be greater than the same number of fifths.)

MLR1 Stronger and Clearer Each Time

• “Share your response to the third question with your partner. Take turns being the speaker and the listener. If you are the speaker, share your explanation. If you are the listener, ask questions and give feedback to help your partner improve their explanation.”
• 3–5 minutes: structured partner discussion 
• Repeat with 2–3 different partners.
• “Revise your initial explanation based on the feedback from your partners.”
• 2–3 minutes: independent work time