# Lesson 16

Solve All Kinds of Compare Problems

## Warm-up: 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.

• $$18 + 5 = 18 + 2 + 3$$
• $$28 + 5 = 30 + 3$$
• $$38 + 4 = 40 + 3$$

### 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.

MLR8 Discussion Supports. Synthesis: Give students 2–3 minutes to plan what they will say and practice with a partner before they present to the class. Encourage them to ask each other questions by using sentence frames such as, “Can you say more about . . .?” and, “Why did you . . . ?”
Engagement: Provide Access by Recruiting Interest. Provide choice. Invite students to decide in which order to complete the problems. Allow the students to choose where to start.
Supports accessibility for: Attention, Social-Emotional Functioning

### Launch

• Groups of 2
• “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

1. Priya and Andre returned books to the library. Priya returned 29 books. Andre returned 8 more books than Priya.

1. Who returned more books?
2. Use the story problem to complete the diagram.
3. How many books did Andre return?
2. Andre read 45 pages of his book last night. Priya read 20 fewer pages of her book than Andre.

2. Use the story problem to complete the diagram.
3. How many pages did Priya read?

### Student Response

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.

### Launch

• Groups of 2

• Display only the story problem stem for question 1, without revealing the question.
• “We are going to read this story problem 3 times.”
• “What is this story about?”
• 1 minute: partner discussion.
•  Listen for and clarify any questions about the context.
• “What are all the things we can count in
• 30 seconds: quiet think time
• 2 minutes: partner discussion
• Share and record all quantities.
• Reveal the question(s)
• “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

4. Noah stacked 14 more books than Jada. Jada stacked 28 books. How many books did Noah stack?

### 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
• 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.

## 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.