# Lesson 11

How Long Are Our Shoes?

## Warm-up: Notice and Wonder: Length of a Shoe (10 minutes)

### Narrative

The purpose of this warm-up is to elicit the idea of measuring length with connecting cubes, which prepares students to measure their own shoes and solve story problems about their measurements in the next activity.

### 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?

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “Now you are going to get a chance to measure the length of your own shoe.”

## Activity 1: The Length of Our Shoes (20 minutes)

### Narrative

The purpose of this activity is for students to measure the length of their shoe using connecting cubes and solve a Put Together, Result Unknown problem and a Compare, Difference Unknown problem about their measurements. To solve the Put Together problem, students may put the connecting cube towers together and count all, count on, use known facts, or use methods such as making a ten. To solve the Compare problems, students may draw a diagram directly comparing the lengths then count up or count back or use known facts to determine the difference. When students find sums and distances using their measurements they reason abstractly and quantitatively (MP2).

It is likely that students’ shoes will not be the length of an exact number of connecting cubes. Encourage students to write the closest number of whole units. There is no need to check students’ measuring techniques in this activity because the focus of the activity is solving story problems.

### Launch

• Groups of 2
• Give each group connecting cubes in towers of 10 and singles and paper.
• “A few days ago we measured the length of the biggest foot in the world. Today we are each going to measure the length of our own shoe and solve some problems using the length. First we will trace our shoe on a piece of paper and then use connecting cubes to measure the length of our shoe.”
• Demonstrate tracing or have a student trace your shoe and measure the length.
• “Record the length of my shoe in your book.”
• “Now your partner will trace your shoe on a piece of paper and then you will use connecting cubes to measure the length of your own shoe. Measure from the tip of the toe to the back of the heel. Your shoe might not line up with the end of a connecting cube. Find the closest number of cubes to the length of your shoe. Record the length of your shoe and your partner’s shoe.”
• 5 minutes: partner work time

### Activity

• “Solve the problems using your measurements.”
• 3 minutes: independent work time
• 2 minutes: partner discussion
• Monitor for a student who represents the third problem with:
• two towers of cubes, one to represent the length of their shoe and one to represent the length of the teacher’s shoe
• a drawing that directly compares shoe lengths
• a subtraction equation

### Student Facing

My teacher's shoe is ____________ connecting cubes long.

My shoe is ____________ connecting cubes long.

My partner’s shoe is ____________ connecting cubes long.

Show your thinking using drawings, numbers, words, or equations.

1. What is the length of your shoe and your partner’s shoe together?
2. Whose shoe is longer, yours or your partner’s?

How much longer?

How much shorter?

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Invite previously identified students to share.
• “What is the same about these representations? What is different?” (The first two show the length of the shoes but the others just use numbers. They all find the difference between the length of the shoes.)

## Activity 2: Shoe Stories (15 minutes)

### Narrative

The purpose of this activity is for students to solve familiar story problem types in a measurement context. Students represent their thinking using drawings, numbers, words, or equations (MP2). Students may use the cubes or drawings to make sense of the problems if they choose. The activity synthesis focuses on a problem that can be represented as either addition or subtraction.

MLR6 Three Reads. Keep books or devices closed. To launch this activity, display only the first problem stem, without revealing the question. “We are going to read this story problem three times.” After the 1st Read: “Tell your partner what happened in the story.” After the 2nd Read: “What are all the things we can count in this story?” Reveal the question. After the 3rd Read: “What are different ways we can solve this problem?”
Representation: Access for Perception. Provide appropriate reading accommodations and supports to ensure student access to all the word problems.
Supports accessibility for: Language, Social-Emotional Functioning

### Launch

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.
• "Let's solve more problems about the length of different shoes."

### Activity

• 6 minutes: independent work time
• 3 minutes: partner discussion
• Monitor for a student who uses addition, and another who uses subtraction, for the story about Diego and his father.

### Student Facing

Show your thinking using drawings, numbers, words, or equations.

1. Clare’s shoe is 9 cubes long.
Han’s shoe is 7 cubes long.
How many cubes long are Clare’s and Han’s shoes together?

2. Kiran’s shoe is 7 cubes long.
His older brother's shoe is 9 cubes long.
His younger brother's shoe is 4 cubes long.
What is the total length of their shoes?

3. Diego's shoe is 8 cubes long.
His father's shoe is 13 cubes long.
How many cubes longer is his father's shoe than his shoe?

4. Jada's shoe is 8 cubes long.
She put her shoe together with Elena’s shoe.
Together the shoes are 17 cubes long.
How long is Elena's shoe?

### Student Response

For access, consult one of our IM Certified Partners.

If students find the sum of the lengths in the problems about Diego and Jada, consider asking:
• “What does the story problem ask you to find?”
• “How does your representations match the story?”
• “How could you use your tools or a diagram to solve the problem?”

### Activity Synthesis

• Invite previously identified students to share.
• “How do both methods show the length of Diego's shoe, his father’s shoe, and the difference between the two shoes?”
• “How are the methods the same? How are they different?”

## Lesson Synthesis

### Lesson Synthesis

Display the story problem and equations:

Jada’s shoe is 8 cubes long.
She put her shoe together with Elena’s shoe.
Together the shoes are 17 cubes long.
How long is Elena’s shoe?

$$8 + \boxed{9} = 17$$ and $$17 - 8 = \boxed{9}$$

“Today we solved story problems about measurement. Some problems were solved using addition or subtraction. What do the numbers in these equations represent?” (8 is the length of Jada's shoe. 17 is the length of their shoes together. 9 is the length of Elena’s shoe.)

## Cool-down: Measure Shoes (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.