Lesson 16
Solve All Kinds of Compare Problems
Warmup: True or False: Multiples of 10 (10 minutes)
Narrative
The purpose of this True or False is to elicit strategies and understandings students have for composing a ten when adding within 100. This will be helpful in the lesson as students add within 100 to find unknown values in Compare problems. It also helps students develop fluency with addition within 100 and deepens their understanding of the properties of operations and structure of whole numbers (MP7).
Launch
 Display one statement.
 “Give me a signal when you know whether the statement is true and can explain how you know.”
 1 minute: quiet think time
Activity
 Share and record answers and strategy.
 Repeat with each statement.
Student Facing
Decide if each statement is true or false. Be prepared to explain your reasoning.
 \(18 + 5 = 18 + 2 + 3\)
 \(28 + 5 = 30 + 3\)
 \(38 + 4 = 40 + 3\)
Student Response
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Activity Synthesis
 "How could you change 28 + 5 to be 30 + 3?" (I could take 2 from 30 and add it to 3.)
Activity 1: A Trip to the Library (20 minutes)
Narrative
The purpose of this activity is for students to represent and solve Compare story problems. Students label a tape diagram based on the given information and represent the unknown with a question mark. When students connect the story problem and the diagram, they look for and make sense of the structure of the problem (MP2).
In the launch of the activity, it may be helpful to ask students to share what they know or have questions about in regards to a library to ensure each student has access into the context and understands books are checked out and returned.
Advances: Speaking, Conversing, Representing
Supports accessibility for: Attention, SocialEmotional Functioning
Launch
 Groups of 2
 Read the first part of the task statement.
 “Who returned more books?”
 1 minute: quiet think time
 Share responses.
 “How do you know?”
Activity
 “You’re going to keep working on this problem and solve another one like it. There is a diagram to use to represent each problem. You can choose to label the diagram first or answer the questions and then complete the diagram.”
 10 minutes: independent work time
 Monitor for students who started with the tape diagram on each problem to share during the synthesis.
 If students finish early, ask them if they can write their own problem that can be represented by a diagram.
Student Facing

Priya and Andre returned books to the library. Priya returned 29 books. Andre returned 8 more books than Priya.
 Who returned more books?
 Use the story problem to complete the diagram.
 How many books did Andre return?

Andre read 45 pages of his book last night. Priya read 20 fewer pages of her book than Andre.
 Who read more pages?
 Use the story problem to complete the diagram.
 How many pages did Priya read?
Student Response
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Advancing Student Thinking
If students identify which student has more, but the labels do not reflect this, consider asking, "Can you explain how you decided where each label should go?" "How do you know which quantity is bigger or smaller?" "How does this connect to the story?"
Activity Synthesis
 Display student work for the first problem.
 Students explain their work, describing how they used the tape diagram.
 “Does anyone have a question for _____ about their thinking or work?”
 “How did you know where to put the numbers and the question mark in this problem?”
 Repeat for second problem.
Activity 2: Solve Compare Problems (20 minutes)
Narrative
This activity begins with the use of the Three Reads Math Language Routine. This routine helps students practice a way to make sense of a problem and persevere in solving it (MP1). The purpose of this activity is for students to analyze and solve a variety of Compare problems. Students may use tape diagrams or any other method that makes sense to them to solve each story problem. Monitor for the different methods students use, including drawings other than tape diagrams and the use of equations. Also, monitor for how students compute and describe their computations when finding the unknown values. Listen for methods based on place value and making a ten.
Students begin the activity by looking at the first story problem displayed, rather than in their books. At the end of the launch, students open their books and work on the story problems. If students do not show their reasoning using a tape diagram and their equation does not match the story problem, ask them to describe the mathematics of the story problem by explaining what each quantity represents in the context of the story. As needed, draw an unlabeled tape diagram to support student thinking.
This activity uses MLR6 Three Reads. Advances: reading, listening, representing.
Launch
 Groups of 2
MLR6 Three Reads
 Display only the story problem stem for question 1, without revealing the question.
 “We are going to read this story problem 3 times.”
 1st read: "Jada read 10 fewer pages than Noah. Noah read 27 pages."
 “What is this story about?”
 1 minute: partner discussion.
 Listen for and clarify any questions about the context.
 2nd read: “Jada read 10 fewer pages than Noah. Noah read 27 pages.”
 “What are all the things we can count in
this story?” (We could count the pages Jada read, the books, the pages they read together.)  30 seconds: quiet think time
 2 minutes: partner discussion
 Share and record all quantities.
 Reveal the question(s)
 3rd read: Read the entire problem, including the question, aloud.
 “What are different ways we can solve this problem?” (We could make a tape diagram. We could write equations.)
 30 seconds: quiet think time
 1–2 minutes: partner discussion
Activity
 “Today, you’re going to solve problems with your partner. Show your thinking using drawings, numbers, words, or an equation.”
 “Remember to ask yourselves questions as you make sense of the problem and create representations.”
 12 minutes: partner work time
 As students work, monitor for different representations to share during the synthesis:
 tape diagrams
 equations
 other labeled drawings or diagrams.
Student Facing
 Jada read 10 fewer pages than Noah. Noah read 27 pages. How many pages did Jada read?
 Noah spent 25 minutes reading. Jada spent 30 more minutes reading than Noah. How many minutes did Jada spend reading?
 Jada read 47 pages of the book. Noah read 20 pages of the book. How many fewer pages did Noah read?
 Noah stacked 14 more books than Jada. Jada stacked 28 books. How many books did Noah stack?
Student Response
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Activity Synthesis
 Display student work that shows different ways to represent how many more minutes Jada spent reading.
 “What’s the same about their representations? What’s different?”
 1 minute: quiet think time
 1 minute: partner discussion
 “How did your representation help you decide whether to add or subtract?”
 If time, discuss computation strategies:
 adding and subtracting tens with tens (problems 2 and 3)
 decompose to make a ten (problem 4)
Lesson Synthesis
Lesson Synthesis
“Today we made sense of and solved many Compare problems. What did you do to figure out how to solve these problems?” (Read the problem carefully and several times to figure out who did more, who did less, and the difference. Made a diagram to show all of the information.)
Share and record strategies for all to see.
Cooldown: Compare the Pages (5 minutes)
CoolDown
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Student Section Summary
Student Facing
In this section of Unit 1, we learned how to represent and solve Compare problems. First, we used bar graphs to find the difference between two categories.
How many more students have cats than have rabbits? Show two ways to find the difference.
We learned about a new representation called a diagram. It helps us make sense of story problems. We can use diagrams to show which part of a comparison we need to find.
Jada read 47 pages of the book. Noah read 20 pages of the book. How many fewer pages did Noah read?
In this problem, we are finding the difference. We know how many pages Noah and Jada read, so the ? represents the difference.