# Lesson 1

Times as Many

## Warm-up: Notice and Wonder: Compare Cubes (10 minutes)

### Narrative

The purpose of this warm-up is to elicit comparison language from students, which will be useful when students represent situations that involve “_____ times as many” later in the lesson. While students may notice and wonder many things about the cube images, the language used to compare the two sets of images is most important for discussion. Consider using actual connecting cubes rather than the display image.

### Launch

• Groups of 2
• Display the image.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time

### Activity

• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

### Student Facing

What do you notice? What do you wonder?

### Activity Synthesis

• “How are the images alike?” (Both show Andre has 3 cubes and Han and Mai have more cubes.)
• “How are they different?” (Sample responses:
• Han has cubes in four colors and 3 cubes of each color. Mai has two different colors of cubes—3 cubes in one color and 4 cubes in another color.
• Han has 9 more cubes than Andre. Mai has 4 more cubes than Andre.)

## Activity 1: Twice as Many (10 minutes)

### Narrative

The purpose of this activity is for students to build on what they know about the language of “twice” and “twice as many” to represent comparison situations.

In this activity, students are encouraged to represent the situation in a way that makes sense to them, though discrete representations (cubes or drawings) are the focus of the activity synthesis. The representations used in this activity serve as a foundation for the more abstract tape diagrams that will be used later in the section.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Read first part of task statement aloud.
• “What does it mean for Han to have twice as many cubes as Andre?” (It means he has double. It means he has 2 times as many.)
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share and record responses.
• Read the entire task statement aloud.

### Activity

• 3 minutes: independent work time
• “Share your work with your partner. Explain how you know Han has twice as many cubes as Andre has.”
• “If you have time, work with your partner to come up with another amount of cubes for Andre and Han.”
• 4 minutes: partner discussion
• Monitor for students who organize their cubes (or drawings) into groups to show Andre’s cubes “twice” for Han.

### Student Facing

Andre has some cubes. Han has twice as many cubes as Andre.

Use cubes, pictures, or other diagrams to show how many cubes Andre could have and how many cubes Han could have.

Be prepared to explain how your representation shows that Han has twice as many cubes.

### Advancing Student Thinking

Students may represent “2 more than” and not “2 times as many” in this task. If so, consider asking “Show with cubes how 2 more and twice as many are different.”

### Activity Synthesis

• Select 3–4 different student examples (a mix of cubes and drawings).
• “How does each representation show that Han has twice as many as Andre?” (In each set, Andre’s number of cubes is repeated 2 times.)
• “Another way of saying twice as many is 2 times as many.”
• “How do you know that Andre’s number of cubes is ‘2 times’ in Han’s amount?” (Andre’s number of cubes is repeated twice. Sometimes they are stuck together in one stick and other times they are separate.)

## Activity 2: Times as Many (20 minutes)

### Narrative

The purpose of this activity is to extend the intuitive idea of representing “twice as many” to represent “4, 6, and 8 times as many.” Although students are prompted to draw to represent each situation, keep the connecting cubes accessible for students to use as needed.

MLR8 Discussion Supports. Synthesis: During group presentations, invite the student(s) who are not speaking to follow along and point to the corresponding parts of the display.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• “Think about how you might use the connecting cubes or drawings to solve each problem.”
• 2 minutes: quiet think time

### Activity

• 5 minutes: partner work time
• Monitor for students who:
• organize their cubes or drawings to visualize the comparison.
• reason using multiplication expressions or equations.

### Student Facing

Draw a picture to show the number of cubes the students have in each situation. Be prepared to explain your reasoning.

1. Andre has the following cubes and Han has 4 times as many.

2. Priya has the following cubes and Jada has 6 times as many.

3. Tyler has the following cubes and Mai has 8 times as many.

4. What number represents “8 times as many as 2”? Show your reasoning.

### Advancing Student Thinking

Students may write expressions to reason about the number of cubes in each problem. If students write addition expressions, ask them what multiplication expressions they could write. Then, ask what each number represents.

### Activity Synthesis

• Invite selected students to share their representations and their reasoning.
• For each question, ask, “Where do you see _____ times as many in _____’s representation?”
• “What does it mean to have ‘_____ times as many’?” (It means we have that many groups of the original number of cubes.)
• For students who reason using multiplication expressions or equations, ask, “How does this equation show ‘times as many’? What does each number represent?” (In the example of Priya and Jada, the equation $$6 \times 3 = 18$$ represents 6 times as many as 3. The 3 is the number of cubes Priya has, 18 represents the number of cubes that Jada has, which is 6 times as many as Priya.)

## Activity 3: Make $n$ Times as Many [OPTIONAL] (15 minutes)

### Narrative

The purpose of this optional activity is for students to practice representing “$$n$$ times as many” with cubes and diagrams. Students may not have enough cubes to build each comparison. This gives students an opportunity to make sense of each quantity and how it relates to their corresponding cubes or diagram (MP2). Encourage them to draw a diagram to represent the cubes.

Action and Expression: Develop Expression and Communication. Provide access to a pre-formatted page that says, “Show _____ times as many as _____.” Invite Partner A to place their connecting cubes in the second blank and Partner B to place the number cube in the first blank.
Supports accessibility for: Language, Organization, Attention

### Required Materials

Materials to Gather

Materials to Copy

• Times as Many Recording Mat

### Required Preparation

• Each group of 2 needs 40 connecting cubes.

### Launch

• Groups of 2
• Demonstrate the activity with a student as your partner.
• Give each group a copy of the recording mat from the blackline master, a number cube, and connecting cubes.

### Activity

• “What questions do you have about the activity?”
• 8 minutes: partner work time

### Student Facing

Work with a partner on this activity.

1. Partner A: Create a set of connecting cubes between 2–6 and show Partner B.

Partner B: Roll a number cube. Let’s call the number rolled $$n$$.

2. Partner A: Use the connecting cubes or a diagram to show $$n$$ times as many as the original set of cubes. Show your reasoning.

Partner B: Check your partner’s work and discuss any disagreements.

3. Switch roles and repeat.

### Activity Synthesis

• “What was your method for representing the $$n$$ times as many?” (Sample responses: I built that many groups of the original group size. I multiplied the original number by the number rolled and counted out that many cubes.)

## Lesson Synthesis

### Lesson Synthesis

“Today, we learned how to represent ‘___ times as many.’”

Display the images from the warm-up.

“Which of these pictures shows 4 times as many? How do you know?” (Han has 4 times as many cubes as Andre. He has 4 groups of 3 and Andre has 1 group of 3.)

“How many cubes would I have if I have 6 times as many cubes as Andre? 8 times?”