In this activity, students look closely at the relationships between fractions with denominators 5, 10, and 100. Students use their observations and understanding to identify equivalent fractions and to explain why two fractions are or are not equivalent. When students analyze and criticize the reasoning presented in the activity statements and when they discuss their work with classmates, they are critiquing the reasoning of others and improving their arguments (MP3).

MLR1 Stronger and Clearer Each Time

• “Compartan su razonamiento y sus rectas numéricas con su compañero. Por turnos, uno habla y el otro escucha. Si es su turno de hablar, compartan sus ideas y lo que han escrito hasta ese momento. Si es su turno de escuchar, hagan preguntas y comentarios que ayuden a su compañero a mejorar su trabajo” // “Share your reasoning and 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 2–3 different partners.
• “Ajusten su borrador inicial basándose en los comentarios que les hicieron sus compañeros” // “Revise your initial draft based on the feedback you got from your partners.”
• 2–3 minutes: independent work time

This activity gives students opportunities to practice explaining or showing whether two fractions are equivalent. Students may do so using a visual representation, by reasoning about the number and size of the fractional parts in each fraction, or by thinking about multiplicative relationships between the numbers in the given fractions. 

Students participate in a Gallery Walk in which they generate equivalent fractions for the numbers on the posters. Students visit at least two of six posters (or as many as time permits). At least one poster should have two fractions (Cards A–C), and at least one should have three fractions (Cards D–F).

For the posters with two fractions (A–C), students need to generate an equivalent fraction that hasn’t already been written by others. This makes generating equivalent fractions more difficult as the activity goes on. Consider using this fact to differentiate for students who may need an additional challenge: start them at the posters with three fractions (D–F).

Select groups to share their responses and reasoning for each poster.

Highlight visual diagrams or verbal explanations that clearly show how the number and size of the parts of two fractions can differ even though the fractions are the same size.

When students explain their work on Posters D–F, ask about the non-equivalent fraction. For instance: “¿Cómo supieron que  y  son equivalentes, pero que  no es equivalente a ellas?” // “How did you know that  and  are equivalent, but is not equivalent to them?”