# Lesson 9

Measure to Find the Area

## Warm-up: Notice and Wonder: Groups and Arrays (10 minutes)

### Narrative

In this warm-up, students observe two dot images that show the same number of dots in groups of 3 but arranged in different ways. The purpose is to elicit observations about the similarities in their structure (5 groups of 3 dots, plus 1 more group of 3 dots) and to prepare students to make sense of expressions with a similar structure in an upcoming lesson.

When students notice that there is an additional group of 3 in the equal groups diagram and the array, they are looking for and making use of structure (MP7).

### Launch

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

### Activity

• 1 minute: partner discussion
• Share and record responses.

### Student Facing

What do you notice? What do you wonder?

### Activity Synthesis

• “How do you see the extra equal group of 3 in each diagram?” (In the equal groups diagram it’s an extra group that is separate from the 5 groups of 3. In the array the extra group of 3 is the column of dots that is a different color.)

## Activity 1: Measure to Find Area (15 minutes)

### Narrative

The purpose of this activity is for students to measure the side lengths of a rectangle and multiply them to find the area. Students may use the ruler to create tick marks along the sides of the rectangle to help them visualize square units or multiply the side lengths. Either strategy is fine as students work towards finding the area of rectangles with labeled side lengths.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Display or sketch two rectangles, one with tick marks on two sides and one without.

• “How could we use a ruler to find the area of the rectangle without marks on the sides?” (We could measure to see how long each side is. The ruler would help us see the marks so we know what numbers to multiply.)
• 30 seconds: quiet think time
• Share responses.
• “We are going to measure some rectangles in centimeters to help us calculate the area. First, look at all of them and predict which one has the greatest area.”
• 30 seconds: quiet think time
• “Circle the letter of the rectangle that you think has the greatest area.”
• Give each student a centimeter ruler.

### Activity

• “Use your ruler to measure the rectangles in centimeters. Find the area of each rectangle, and include the units.”
• 8–12 minutes: partner work

### Student Facing

Use a ruler to measure the rectangles. Then, calculate the area of the rectangles in square centimeters.

### Student Response

If students say they need to see the squares before they can multiply to find the area of the rectangle, consider asking:

• “What have you tried so far to find the area?”
• “Could you use the ruler to make tick marks to help you picture the squares?”

### Activity Synthesis

• “How does measuring with a ruler help you find the area?” (Measuring with the ruler gives the side lengths, which we can multiply.)

## Activity 2: Create a Rectangle (20 minutes)

### Narrative

The purpose of this activity is for students to create a rectangle with a given area. Students use what they know about area and the structure of rectangles to decide on the side lengths of the rectangle. Students use tape (painter's or masking) to create the rectangles. They should have enough tape to create square feet within the rectangle, but should be encouraged to mark the 1 foot intervals to help them visualize the square feet inside the rectangle, if needed.

In the synthesis, each group shares strategies for creating a rectangle and how they know the area is the given number of square feet.

When students think about the structure of a rectangle and use it to create a rectangle with a given area they are looking for and making use of structure (MP7).

MLR8 Discussion Supports. Synthesis: At the appropriate time, give students 2–3 minutes to make sure that everyone in their group can explain their approach. Invite groups to rehearse what they will say when they share with the whole class.
Engagement: Develop Effort and Persistence: Check in and provide each group with feedback that encourages collaboration and community. For example, make sure all students are participating. Elicit from each group such things as what is your strategy, what is your first step, how do you know your rectangle is correct.
Supports accessibility for: Social-Emotional Functioning

### Required Materials

Materials to Gather

### Required Preparation

• Each group of 4 will need one roll of either painter's tape or masking tape.

### Launch

• Groups of 4
• Give students painter's or masking tape.
• Assign each group an area.

### Activity

• “Work together to create a rectangle that has the area your group is assigned.”
• 7–10 minutes: small-group work time

### Student Facing

Your teacher will give you some tape. Use it to create a rectangle with your assigned area.

• Area 1: 4 square feet
• Area 2: 6 square feet
• Area 3: 9 square feet
• Area 4: 10 square feet
• Area 5: 12 square feet
• Area 6: 16 square feet

### Student Response

If students don’t create a rectangle with the given area, consider asking:

• “How did you build your rectangle?”
• “How could you build the rectangle if you started with 1 square foot?”

### Activity Synthesis

• Select each group to share the rectangle they created and how they know it has the given area.
• “Are there any other side lengths that would give us a rectangle with an area of ___ square feet?”
• “How do we know this rectangle has an area of ___ square feet?”

## Lesson Synthesis

### Lesson Synthesis

Display a fully gridded rectangle, a partially gridded rectangle, and a rectangle with only labeled side lengths.

“Over the last few lessons, we’ve solved area problems where the square units are less and less visible, and in this lesson you couldn’t see them at all.”

“How has the way you solve area problems changed as the grid has gone away?” (I’ve drawn the grid to help me count the squares. I’ve pictured the squares even though they’re not there. I’ve measured and multiplied the side lengths because it’s the same as the number of unit squares as if I count them.)