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Launch

Groups of 2
Display the image.
“What is an estimate that’s too high? Too low? About right?”
1 minute: quiet think time

Activity

“Discuss your thinking with your partner.”
1 minute: partner discussion
Record responses.

What is the area of the shaded region?

Diagram. Square, length and width, 1. Rectangle with length of about 1 half and width of about 3 fifths shaded.

Record an estimate that is:

too low	about right	too high

Student Response

to access Student Response.

Advancing Student Thinking

Activity 1

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

None

Activity Narrative

The purpose of this activity is for students to write expressions for and find the area of shaded regions whose side lengths are a unit fraction and a non-unit fraction. Students look at a series of diagrams with an increasingly large shaded region so they can look for and make use of structure (MP7).

It is important to relate the work here to what students have already learned about the product of a unit fraction and a unit fraction. This is the goal of the Activity Synthesis. For example, students have seen that . Since is six s, the product will be six s or .

MLR8 Discussion Supports. Prior to solving the problems, invite students to make sense of the situations and take turns sharing their understanding with their partner. Listen for and clarify any questions about the context.
Advances: Listening, Conversing

Launch

Groups of 2
Display Diagram A from the student book.
“What is a multiplication expression that represents the shaded region?”(, )
“How does the diagram represent your expression?”(There is of the first row shaded and that row is of the square. There are 2 shaded pieces and each is of the whole square.)

Activity Synthesis

Ask previously selected students to share the patterns they noticed in the table.
Display the expression from the last problem: .
“How does the diagram show ?” (The first row of pieces in a square is of the square.)
“How does the diagram show ?” (There are 6 pieces shaded and each one is of the row.)
“How does the diagram show ?” (There is of a row shaded and that row is of a square unit.)

Activity 2

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

None

Activity Narrative

The purpose of this activity is for students to write multiplication expressions to estimate the area of a shaded region. This builds on the Warm-up and the Activity Launches by asking students to write an expression for the shaded region in the image they considered in the Warm-up.

This work in this activity combines the skill of estimation with an understanding that the area of a rectangle relates to its length and width. So far, students have only calculated these areas as products of fractions when at least one side length is a unit fraction. Students may write products of two non-unit fractions. While they have not yet learned how to calculate these products and relate them to areas, these answers are valid when the estimates are reasonable and students will learn in the next lesson how to find the value of these expressions.

Action and Expression: Internalize Executive Functions. Synthesis: Invite students to plan a strategy, including the tools they will use, for estimating the area of the shaded rectangle. If time allows, invite students to share their plan with a partner before they begin.
Supports accessibility for: Conceptual Processing, Language

Launch

Groups of 2
Display the image from the Warm-up: “What multiplication expression might represent the area of the shaded region?” (, )
“Why do those expressions make sense?” (We can see that the shaded region is a fraction of . It is more than .)
“We are going to look at more diagrams and write multiplication expressions that might represent the area of the shaded regions in each one.”

Activity

3–5 minutes: independent work time
3–5 minutes: partner discussion
Monitor for students who:
- Use a unit fraction to help them determine reasonable expressions.
- Reason about the size of the shaded region before writing an expression.
- Draw lines to partition the squares.

Represent the area of the shaded region. Write a multiplication expression.

Square, length and width, 1. Rectangle portion shaded, about 3 fourths of the length and 1 half of the width. — 1.

Square. Length and width, 1. Rectangle with width of about 2 thirds and length of about 1 fourth shaded. — 2.

Square, length and width, 1. Rectangle portion shaded, about 3 fourths of the length and 1 third of the width. — 3.

Diagram. Rectangle. Length, 2. Width, 1. Rectangle of length about 3 halves and width about 1 fifth shaded. — 4.

Student Response

to access Student Response.

Advancing Student Thinking

Activity Synthesis

Ask previously selected students to share their solutions.
Display the first diagram.
“How does thinking about help us estimate the area of the shaded region?” (We know the area is less than because only part of is shaded.)
“About what fraction of is shaded?” (More than of . Maybe of or of .)

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Lesson 5

Multiply a Unit Fraction by a Non-Unit Fraction

Warm-up

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 1

Standards Alignment

Building On

Addressing

5.NF.B.4.b

Building Toward

Instructional Routines

Materials

Activity Narrative

Launch

Activity Synthesis

Activity 2

Standards Alignment

Building On

Addressing

5.NF.B.4.b

Building Toward

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Lesson Synthesis

Standards Alignment

Building On

Addressing

5.NF.B.4.b

Building Toward

Activity

Student Response

Advancing Student Thinking