# Lesson 7

Meters and Centimeters

## Warm-up: Notice and Wonder: Big Bug, Little Bug (10 minutes)

### Narrative

The purpose of this warm-up is to elicit what students know about length measurement and about units of measurement. While no unit is specified for the ruler in the image, students are likely to bring up centimeters (given the way each 1 unit is partitioned into 10 smaller parts, as seen on centimeter rulers). The work here prepares students to think about the relationship between meters and centimeters later in the lesson.

### 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

• Consider sharing that the large insect is a stick insect. (The longest species ever found measured more than 60 cm.) The small insect is a green potato bug.
• “If each unit in the ruler is 1 centimeter, about how long is the potato bug?” (1 cm) “What about the stick insect?” (About 16 cm with the antennae, about 12 cm otherwise.)

## Activity 1: How Long is One Meter? (25 minutes)

### Narrative

The purpose of this activity is for students to develop an intuition of 1 meter as 100 times as long as 1 centimeter. Students build a 1-meter long strip out of centimeter grid paper. They use this tool to identify objects or distances that are about 1 meter long.

MLR8 Discussion Supports. Synthesis: At the appropriate time, give groups 2–3 minutes to plan what they will say when they present to the class. “Practice what you will say when you share your predictions and results with the class. Talk about what is important to say, and decide who will speak and who will share each part.”

### Required Materials

Materials to Gather

Materials to Copy

• Centimeter Grid Paper - Standard

### Launch

• Groups of 3–4
• Give each group 2–3 sheets of centimeter grid paper, 2–3 pairs of scissors, and some tape.
• “Each grid on the paper is 1 centimeter long.”
• “Work with your group to cut the centimeter grid paper into strips and then join them to make a strip of paper that is exactly 1 meter long.”

### Activity

• “After your 1-meter-long strip is made, identify some objects in the classroom or some distances you think are about 1 meter long. Then, use your tool to check your predictions.”
• 15 minutes: group work on the first two problems
• 2–3 minutes: independent work on the last problem

### Student Facing

1. Use the centimeter paper to build a strip that is 100 centimeters long. You will need scissors and tape.

If you do it precisely, your paper strip will be 1 meter long.

2. List 5 items in the classroom that you think are about 1 meter long.

Then, use your paper strip to check how close your prediction is to 1 meter.

3. Decide whether each of the following is more than 1 meter, less than 1 meter, or about 1 meter.

1. The stick insect in the warm-up activity
2. The step you make when walking
3. The step you make when running

Be prepared to explain how you know.

### Student Response

Students may make a counting error and put together a strip that is shorter or longer than 1 meter. Consider asking:

• “How did you organize and count the centimeter pieces?”
• “How can you make sure there are 100 centimeter pieces? Can grouping the pieces help?”

### Activity Synthesis

• Invite groups to share their predictions and the results of their measurement.
• Select students to share their responses to the last problem. If time permits, allow students to measure the arm span or step length of a few students.
• “How many 1 centimeter grid squares did you put together to make 1 meter?”

## Activity 2: In and Around the School (10 minutes)

### Narrative

In this activity, students analyze student work converting meters to centimeters to develop the understanding that a meter is “100 times as long” as a centimeter. They correct errors in reasoning centering around place value (MP3).

Representation: Access for Perception. Begin by demonstrating how to measure the height of the classroom door with a meter stick (or a student’s meter strip from the previous activity) to support understanding of the context. Pause after measuring each meter to ask students, “How many centimeters have we measured?” As students begin working independently, invite them to imagine using their meter strip to find each measurement.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing

### Launch

• Groups of 2
• Read the opening paragraph as a class. Ask 1–2 students to reframe the context in their own words.

### Activity

• “Take 5 quiet minutes to spot and correct Priya’s errors and find the missing measurement. Then, share your thinking with your partner.”
• 5 minutes: independent work time
• 3–4 minutes: partner discussion
• Monitor for students who place zeros for the measurement in centimeters and those who explicitly reason in terms of 100 times the value in meters.

### Student Facing

Priya took some measurements in meters and recorded them in the table, but she made some errors when converting them to centimeters. She also left out one measurement.

measurement in meters measurement in centimeter
a. height of door 2 200
b. height of hallway 3 30
c. width of hallway 5 500
d. length of gym 18 180
e. length of hallway 27 2,700
f. length of playground 50
1. Find and correct Priya’s conversion errors. Be prepared to explain how you know.
2. Fill in the length of the playground in centimeters. Write an equation to represent your thinking.

### Student Response

If students place zeros for the measurement in centimeters, ask them to explain their rationale and check if they do so as a result of observing a pattern (for instance, “I noticed that every time we convert from meters to centimeters, the number in centimeters ends in two zeros”) or because they have internalized the value in centimeters as 100 times as much as that in meters.

### Activity Synthesis

• See lesson synthesis.

## Lesson Synthesis

### Lesson Synthesis

“Today we looked at centimeters and meters and related them to our multiplication work.”

“Write one sentence to describe the relationship between the two units. Be as specific and precise as you can in your word choice.”

While students’ statements may emphasize the equivalence of 1 meter and 100 centimeters (“one meter is 100 centimeters”), highlight explanations that articulate the multiplicative relationship of the two units (“1 meter is 100 times as long as 1 centimeter”).

Display the table showing Priya’s measurements. Invite students to share their responses to the last activity.

Reiterate the multiplicative relationship of the values in the two columns, revoicing students’ responses as needed. (For instance, “If 1 meter is 100 times 1 centimeter, then 3 meters must be $$3 \times 100$$ centimeters or 300 centimeters, rather than 30 centimeters.”)