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Activity 1

Standards Alignment

Building On

Addressing

Instructional Routines

Card Sort

Materials

To Copy (from Blackline Masters)

Card Sort Diagrams of Fractions and Decimals

Activity Narrative

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).

Representation: Access for Perception. Synthesis: Display a 10-by-10 grid, as well as a square of the exact same size, but with only the columns shown (representing just tenths). Shade 20 hundredths on the 10-by-10 grid and write 0.20 (twenty hundredths) above it. Shade 2 tenths on the other square and write 0.2 (2 tenths) above it. Invite students to discuss how these diagrams demonstrate equivalence of the two numbers.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing

Launch

Groups of 2–4
Give each group a set of cards.

Activity

“This set of cards includes fractions, decimals, and diagrams. Sort the cards by their value. Work with your group to explain your reasoning.”
“One diagram has no matching cards. Write the fraction and decimal it represents.”
6–7 minutes: group work on the first two problems
Monitor for the ways students sort the cards and the features of the representations to which they attend.
“Work on the last problem independently.”
2–3 minutes: independent work on the last problem

Your teacher will give you a set of cards. Each large square on the cards represents 1.

Sort the cards into groups so that the representations in each group have the same value. Be ready to explain your reasoning.
One of the diagrams has no matching number card. What number does it represent? Write that number as a fraction and in decimal notation.
Are 0.20 and 0.2 equivalent? Use fractions and a diagram to explain your reasoning.

Student Response

to access Student Response.

Advancing Student Thinking

If students respond that 0.20 and 0.2 are not “the same,” consider asking:

“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?”

Activity Synthesis

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.

Activity 2

Standards Alignment

Building On

Addressing

Instructional Routines

MLR1 Stronger and Clearer Each Time

Materials

None

Activity Narrative

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).

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

Launch

Groups of 2
“Earlier, we saw some equations with fractions on both sides of the equal sign. Now let’s look at some equations that include fractions and decimals or just decimals.”

Activity

“Take a few minutes to complete the activity independently. Then share your thinking with your partner.”
6–7 minutes: independent work time
“For each equation in the first problem, take turns explaining to your partner how you know whether it is true or false.”
3–4 minutes: partner discussion

Decide whether each statement is true or false. For each statement that is false, replace one of the numbers to make it true. A different number should be shown on either side of the equal sign.
Jada says if you locate the numbers 0.05, 0.5, and 0.50 on the number line, you should have only 2 points. Do you agree? Explain your reasoning.

Student Response

to access Student Response.

Advancing Student Thinking

Activity Synthesis

MLR1 Stronger and Clearer Each Time

“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

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Lesson 2

Equivalent Decimals

Warm-up

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 1

Standards Alignment

Building On

Addressing

4.NF.C.6

Instructional Routines

Materials

To Copy (from Blackline Masters)

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 2

Standards Alignment

Building On

Addressing

4.NF.C.6

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Lesson Synthesis

Standards Alignment

Building On

Addressing

4.NF.C.5

Building Toward

Building Toward

4.NF.C.7

Building Toward