Grade 1 Teacher Guide — Unit 2, Section C: Compare Story Problems

Section Overview

In this part of the unit, students learn to solve Compare, Difference Unknown story problems. These are problems where two amounts are described, but the difference between them—the part that tells "how many more" or "how many fewer"—is not given and must be figured out.

This kind of problem is tricky for a few reasons. First, like earlier "Put Together/Take Apart" problems, Compare problems describe a relationship between two amounts rather than an action like adding or taking away. Second, the difference between the two amounts isn't a real, physical thing you can point to—it has to be figured out. Third, the wording of these problems can be confusing, since words like "more" and "fewer" can be used in different ways.

Because of this, students start by returning to "are there enough?" problems from kindergarten, using the words "more" and "fewer" to compare amounts. Then they move on to "how many more?" and "how many fewer?" problems. These problems are designed to encourage matching strategies—lining up or pairing items from two groups to see what's left over.

For example:

There are 9 dry erase boards at the table.
There are 6 markers.
Are there more dry erase boards or more markers? How many more?

Matching strategies help students picture the relationship between the two amounts. Students learn to identify which amount is bigger and which is smaller, and they come to understand that the "difference" is the answer to "how many more?" or "how many fewer?"

Here's another example: "How many more cubes does Clare have than Andre?" To solve this, students might count the extra, unmatched cubes in Clare's tower. Some might add cubes to Andre's tower until it matches Clare's. Others might remove the matching cubes (say, 4) and count what's left in Clare's tower.

Students connect these strategies to the "missing addend" problems they solved earlier in the unit. After the teacher highlights key parts of the story, students look at how both an addition equation and a subtraction equation can represent the same problem. By comparing different ways to find the difference, students build a deeper understanding that subtraction can also be thought of as "finding a missing addend."

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Section C Checkpoint

Teacher Instructions: A full observation checklist for this Checkpoint Assessment is available in the unit's Assessments materials. Here is a summary of what is being checked:

Compare Story Problems

• Solve Compare, Difference Unknown problems by:
• Retelling the story in their own words
• Representing the story using objects or drawings
• Explaining how their representation matches the story
• Answering the question correctly
• Show an understanding of how addition and subtraction are related

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Practice Problems (7 Problems)

1. (from Lesson 11)
There are 7 dogs and 5 toys. Are there enough toys for each dog? Show your thinking using drawings, numbers, or words.
Answer: No.

2. (from Lesson 12)
There are 10 bats in the cave and 8 bats flying outside. Are there fewer bats in the cave or flying outside? How many fewer?
Answer: 2 fewer bats.

3. (from Lesson 13)
Tyler sees several colors of hot air balloons at a show.
a. How many more blue balloons does Tyler see than orange balloons?
b. How many fewer blue balloons does Tyler see than yellow balloons?
Answers: a. 3 more blue balloons. b. 2 fewer blue balloons (sample counting: "I counted 6... 7, 8.")

4. (from Lesson 14)
Jada's tower has 8 cubes. Mai's tower has 2 cubes. Show two ways to find how many more cubes Jada has.
Sample answers:

• Draw 6 more cubes onto Mai's tower until it matches Jada's, then count the cubes that were added.
• Draw Jada's tower of 8 cubes, cross off 2 to match Mai's tower, then count what's left.

5. (from Lesson 15)
There are 7 hedgehogs underground and 4 hedgehogs on the grass. How many fewer hedgehogs are on the grass?
Answer: 3 fewer hedgehogs. Sample responses:

• Draw a row of 7 shapes and a row of 4 shapes underneath, then count the shapes without a match.
• "I counted 4... 5, 6, 7. There are 3 more hedgehogs underground."

6. Exploration
There are 8 stuffed animals on the bed and 3 on the floor. Your teacher asks a question about this story, and the answer is 5. What could the question be?
Sample answer: "How many more stuffed animals are on the bed than on the floor?"

7. Exploration
Find two sets of objects at home or school. Write a story comparing them, solve your problem, and write an equation that matches the story.
Sample answer: "My sister has 8 pillows on her bed. I have 5 pillows on my bed. How many fewer pillows are on my bed than on my sister's bed? There are 3 fewer pillows on my bed."

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Lesson 11: Are There Enough?

Standards

• Building on: K.CC.B.4, K.CC.C.6
• Addressing: 1.OA.A.1
• Building toward: 1.OA.A.1

Instructional Routine

• Act It Out

Goals

• Describe out loud the difference between a bigger amount and a smaller amount using the phrases "1 more" or "1 fewer."
• Explain out loud different ways to represent an "are there enough?" problem.

Student-Facing Learning Goal

Let's figure out if there are enough.

Lesson Purpose

This lesson helps students represent and solve "are there enough?" problems in ways that make sense to them, and to compare objects using the phrases "1 more" or "1 fewer."

Narrative

In kindergarten, students learned to compare quantities and answer "are there enough?" questions, using the language "1 more" and "1 less" (or "1 fewer"). This lesson revisits that structure and language to help students get ready for the upcoming Compare, Difference Unknown problems.

Throughout the lesson, pay attention to how students describe the amounts in each story and how they explain the difference between them, using either everyday language or more formal math language.

Access for Students with Disabilities

• Engagement

Access for English Learners

• MLR8 (a support strategy for English learners)

Materials Needed

• 10-frames (grids used for counting): Activity 1
• Connecting cubes: Activity 1, Activity 2
• Two-color counters: Activity 1

Lesson Timeline

• Warm-up: 10 minutes
• Activity 1: 20 minutes
• Activity 2: 20 minutes
• Synthesis (wrap-up discussion): 10 minutes

Teacher Reflection Questions

In future lessons, students will represent and solve Compare, Difference Unknown story problems. How does the work in this lesson help students understand questions like "how many more?" and "how many fewer?" How do the matching strategies used in this lesson's stories help students understand the relationship between a bigger amount, a smaller amount, and the difference between them?

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Warm-up: Act It Out — Art Project (10 minutes)

Standards

• Building toward: 1.OA.A.1

Instructional Routine: Act It Out

This warm-up helps students connect everyday language to math representations—a skill they'll need later when solving story problems. Even though the Compare, Difference Unknown stories in later lessons don't involve an action (like handing something out), this "are there enough?" story is designed to get students matching items, which builds a helpful skill for finding differences later.

This warm-up also gives students a chance to practice making sense of problems (a math practice called MP1).

Student Task Statement:
Mai passes out crayons for an art project. There are 8 students waiting for crayons, and Mai has 7 packs of crayons. How can you act out this story?

Sample Student Responses:

• "We could have 8 students pretend to be the students waiting for crayons, and someone could pretend to be Mai and pass out 7 packs of crayons."
• "We could use counters to represent the 8 students waiting, and 7 blocks to be the packs of crayons."

Launch

• Put students in groups of 2.
• Display and read the story aloud.
• Ask: "What is the story about?"
• Give 30 seconds of quiet think time.
• Have students share their answers.
• Read the story again.
• Ask: "How can you act out this story?"
• Give 30 seconds of quiet think time.

Activity

• Have students discuss their thinking with a partner (1 minute).
• Share responses as a class.
• Choose one way to act out the story together.
• Read the story again as a class.

Wrap-Up Discussion

• Ask: "What are other ways we could represent this problem?" (Possible answers: using cubes or counters to act it out, or drawing a picture.)

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Activity 1: Are There Enough? (20 minutes)

Standards

• Building on: K.CC.C.6
• Building toward: 1.OA.A.1

This activity asks students to represent "are there enough?" story problems in ways that make sense to them, and to describe the relationships between the amounts in each story. The stories are designed on purpose to encourage matching strategies. As students work, watch how they show whether there are enough or not enough of something. Notice how they describe the bigger amount, the smaller amount, and the difference using their own words. During the wrap-up discussion, students will get a chance to describe these relationships using both "1 more" and "1 fewer."

Access for Students with Disabilities
Engagement: Build interest by connecting to real life. Invite students to share examples from their own lives when they had to figure out if there was "enough" of something.
This supports: thinking through concepts, and emotional/social comfort with the task.

Materials Needed

• 10-frames: Activity 1
• Connecting cubes: Activity 1
• Two-color counters: Activity 1

Student Task Statement

1. There are 9 markers in a bin and 4 caps for the markers. Are there enough caps for the markers? Show your thinking using drawings, numbers, or words.

1. There are 9 students at the table and 8 pencils. Are there enough pencils for every student? Show your thinking using drawings, numbers, or words.

1. There are 6 students and 8 chairs. Are there enough chairs for every student? Show your thinking using drawings, numbers, or words.

Sample Student Responses:

1. No. (Sample explanation: "9 is much more than 4.")

1. No. (Sample explanation continues in the next section of the guide.)