Lesson 11
How Long Are Our Shoes?
Warmup: Notice and Wonder: Length of a Shoe (10 minutes)
Narrative
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?
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.
Required Materials
Materials to Gather
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
 an addition equation
 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.
Solve these problems about the length of your group’s shoes.
Show your thinking using drawings, numbers, words, or equations.
 What is the length of your shoe and your partner’s shoe together?

Whose shoe is longer, yours or your partner’s?
How much longer?

Whose shoe is shorter, your teacher’s shoe or your shoe?
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.
Advances: Reading, Representing
Supports accessibility for: Language, SocialEmotional Functioning
Required Materials
Materials to Gather
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
 Read the task statement.
 6 minutes: independent work time
 “Discuss your work with your partner.”
 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.

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? 
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? 
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? 
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.
Advancing Student Thinking
 “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.
 Consider asking:
 “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.)
Cooldown: Measure Shoes (5 minutes)
CoolDown
For access, consult one of our IM Certified Partners.