In this activity, students reinforce their understanding of equivalent fractions and decimals by sorting a set of cards by their value. This sorting task gives students opportunities to analyze fractions, decimals, and diagrams closely and make connections (MP7).

• “What do you mean when you say these numbers are not the same?”
• “How would you represent each number on a square grid? What is the same about the amounts and what is not the same?”

• Invite previously selected groups to share each set of sorted cards and explain how they knew the representations belong together.
• “How did you know what fraction and decimal to write for the diagram without any matches?”
• Invite a student to share their response to the last problem. Highlight the equivalence of 0.2 and 0.20 as shown in the Student Responses.

In this activity, students apply their understanding of equivalent fractions and decimals more formally, by analyzing equations and correcting the ones that are false. The last question refers to decimals on a number line and sets the stage for the next lesson where the primary representation is the number line.

As students discuss and justify their decisions about the claim in the last question, they critically analyze student reasoning (MP3).

• “Share your response to the last question 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.”
• 3–4 minutes: structured partner discussion.
• Repeat with 1–2 new partners.
• “Revise your initial draft based on the feedback you got from your partners.”
• 2–3 minutes: independent work time