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Activity 1

Standards Alignment

Building On

Instructional Routines

None

Materials

To Gather

Straightedges

Activity Narrative

This activity serves two main goals: to revisit the idea of equivalence from grade 3, and to represent non-unit fractions with denominators 10 and 12. Students use diagrams of fraction strips, which allow them to see and reason about fractions that are the same size. In the next activity, students will apply a similar process of partitioning to represent these fractional parts on number lines.

Engagement: Provide Access by Recruiting Interest. Provide choice and autonomy. Provide access to colored pencils students can use to label each rectangle.
Supports accessibility for: Attention, Organization

Launch

Groups of 2
Give each student a straightedge.
“Here is a diagram of fraction strips you saw before, with two new rows added.”
“How can we show tenths and twelfths in the two rows? Think quietly for a minute.”
1 minute: quiet think time

Activity

“Work on the first two questions on your own. Afterward, discuss your responses with your partner.”
“Use a straightedge when drawing your diagram.”
5–6 minutes: independent work time
2–3 minutes: partner discussion
Monitor for students who found the size of tenths and twelfths as noted in Student Responses.
Pause for a brief discussion. Select students who used different strategies to find tenths and twelfths to share.
After each student shares, ask if others in the class did it the same way or if they have anything to add to the explanation.
“Look at your completed diagram. What can you say about the relationship between and ?” (There are two s in every . One fifth is twice one tenth. One fifth is the same size as 2 tenths.)
“What can you say about the relationship between and ?” (There are two s in every . One sixth is twice one twelfth. One sixth is the same size as 2 twelfths.)
“Take 2 minutes to answer the last question.”
2 minutes: independent or group work time

Here’s a diagram of fraction strips, with two blank strips added.

Use one blank strip to show tenths. Label the parts. How did you partition the strip?
Use the other blank strip to show twelfths. Label the parts. How did you partition the strip?
Jada says, “I notice that 1 of the parts is the same size as 2 of the parts and 3 of the parts. So, , , and must be equivalent fractions.” Jada’s reasoning is correct.

Find a fraction in the diagram that is equivalent to each of the following fractions. Be prepared to explain your reasoning.

Student Response

to access Student Response.

Advancing Student Thinking

Activity Synthesis

Invite students to share their response to the last question and explain how they found equivalent fractions.
Highlight the idea that two fractions that are the same size are equivalent, even if they have different numbers for the numerators and denominators.
If needed, ask: “How many fractions that are equivalent to do you see on the diagram?” (Every strip on the diagram shows a fraction equivalent to .)

Activity 2

Standards Alignment

Building On

Instructional Routines

MLR5 Co-Craft Questions

Materials

None

Activity Narrative

The purpose of this activity is to remind students of their work in grade 3 using number lines as a way to reason about fractions. Students see that they can partition number lines in a similar way as they partitioned fraction strips and diagrams.

This activity gives students another opportunity to notice the relationship between two fractions where one denominator is a multiple or a factor of the other, and then use this relationship to locate fractions on a number line. In doing so, students practice looking for and making use of structure (MP7).

The work prepares students to use number lines to think about equivalent fractions in the next lesson.

Launch

Groups of 2

MLR5 Co-craft Questions

“Keep your books closed.”
Display only the four number lines without revealing the question(s).
“Write a list of mathematical questions that could be asked about these number lines.”
2 minutes: independent work time
2–3 minutes: partner discussion
Invite several students to share one question with the class. Record responses.
“What do these questions have in common? How are they different?”
Reveal the task (students open books), and invite additional connections.

Activity

“Take 5 minutes to complete the first two questions.”
5 minutes: independent work time
“Discuss your work with a partner. Make sure you and your partner agree on the labels for the number lines and can explain how you know before moving on to the last question.”
2 minutes: partner discussion
Monitor for students who use the tick marks for , , and on the given number lines to locate , , and .

The point on this number line shows the fraction .

Label the tick marks on each number line.
You will locate , , and on one of the number lines.
1. Which number line would you use for each fraction? Be prepared to explain your reasoning.
2. Locate and label each fraction (, , and ) on a different number line.
Locate and label each fraction on one of the number lines.

Student Response

to access Student Response.

Advancing Student Thinking

If students place the labels between the tick marks on the number line, rather than at or below the tick marks, consider asking:

“How did you decide to label the tick marks on each line?”
“How can you use the number line that shows to help you label the tick marks on the other number lines?”

Activity Synthesis

Select 1–2 students to share their completed number lines for the second problem.
“How did you know which number line to choose for , , and ?” (We could locate , for example, on any of the number lines. But since we know that , we can split each part in the number line that shows thirds into 2 equal parts to make 6 equal parts. Having 6 equal parts makes it easiest to locate .)

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Lesson 4

Same Size, Related Sizes

Warm-up

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 1

Standards Alignment

Building On

3.NF.A.3.b

Instructional Routines

Materials

To Gather

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 2

Standards Alignment

Building On

3.NF.A.2.a

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Lesson Synthesis

Standards Alignment

Building On

3.NF.A.2

Addressing

Building Toward

4.NF.A.1

Addressing

4.NF.A.1

Building Toward

Addressing

Building Toward

4.NF.A.1