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Activity 1

Standards Alignment

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Addressing

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Materials

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Activity Narrative

The purpose of this activity is for students to think of different ways of using multiplication expressions to represent a non-unit fraction. Students informally use the associative property as they work toward generalizing that .

Action and Expression: Develop Expression and Communication. Provide access to fraction strips or pre-formatted tape diagrams, including sevenths, fifths, and tenths.
Supports accessibility for: Visual-Spatial Processing, Fine Motor Skills

Launch

Groups of 2

Activity

“Work with your partner to complete the first problem. Talk about how you know what numbers make the equations true.”
3 minutes: partner work time
Monitor for students who use the factors of 12 to complete the equations.
“Now take a few minutes to complete the rest of the problems independently. Afterward, share your responses with your partner.”
7 minutes: independent work time
3 minutes: partner discussion
“Did you choose the same numbers as your partner? If not, are both equations correct?”

Find the number that makes each equation true. Draw a diagram if it is helpful.
Here are two sets of numbers:

Set A:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11

Set B:
1. Choose a number from Set A and a number from Set B to complete this equation and make it true:
2. Choose a different number from Set A and from Set B to complete the equation to make it true.
Explain or show how you know that the two equations you wrote are both true.

Activity Synthesis

“How did you know what fractions to use to complete each equation in the first problem?” (We looked for the numbers to multiply to get . The denominator stays the same, so we find the whole number and the numerator by knowing the factor pairs of 12.)
Select 2–3 partners to share the following equations from the second problem:
“Why are all these equations true?” (To get , we can multiply the whole number by the numerator and then keep the denominator the same. In all of these, multiplying the whole number and the numerator gives 6. There are different ways to multiply to get 6 as a numerator: , , , and .)

Activity 2

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

None

Activity Narrative

In this activity, students analyze multiplication expressions, match each to one of a given set of fractions, and explain how they know that certain expressions represent the same fraction (MP7).

MLR8 Discussion Supports. Students should take turns finding a match and explaining their reasoning to their partner. Display the following sentence frame for all to see: “I noticed ____ , so I matched . . . .” Encourage students to challenge each other when they disagree.
Advances: Speaking, Conversing

Launch

Groups of 2

Activity

“Match the expressions to a fraction that shows its value. Be prepared to explain how you know which expressions match which fraction.”
“Each fraction may not have the same number of matching expressions.”
5–7 minutes: partner work time
Pause for a discussion before students continue to the second half of the activity.
Select students to share their matches and their explanations.
“Are there any expressions without a match? How do you know?” (Yes, Expressions G and I. Their values are and .)
“You've seen that multiple expressions can represent the same fraction. Some of the expressions have two factors, some have three. All of them show unit fractions.”
“Now complete each equation in the second problem with two factors that would make the equation true. See if you can use factors that are not unit fractions.”
5 minutes: independent work time

Here is a set of expressions:

Match each expression to one of the following fractions, if possible. Record your matches.
Complete each equation to make it true. Try to complete the equation, without using unit fractions.

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Lesson 5

Equivalent Multiplication Expressions

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.4.b

4.NF.4.c

Building Toward

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Activity Synthesis

Activity 2

Standards Alignment

Building On

Addressing

4.NF.4.b

4.NF.4.c

Building Toward

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Lesson Synthesis

Standards Alignment

Building On

Addressing

4.NF.4.b

Building Toward

Student Response

Advancing Student Thinking