Section C: Compare Story Problems

What This Section Is About

In this section, students learn to solve a special kind of math story problem called "Compare, Difference Unknown." These problems help students understand how addition and subtraction are connected.

Compare problems are tricky because they aren't about someone doing an action, like adding items to a pile. Instead, they ask us to think about how two groups relate to each other. Another tricky part is that one number in the problem — the difference, or how much more or less one group has — is not shown directly. Students have to figure it out. On top of that, the wording in these problems can be confusing.

Because of this, students start by remembering "are there enough?" problems from kindergarten. This helps them practice comparing groups using the words "more" and "fewer." Next, students solve "how many more?" and "how many fewer?" problems. These problems help students figure out which group has more, which has fewer, and exactly how many more or fewer.

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?

To solve problems like this, students often use "matching" strategies. This means they match up items from each group to see what's left over. This helps them picture the bigger group, the smaller group, and the difference between them — which is the answer to "how many more?" or "how many fewer?"

Another example: "How many more cubes does Clare have than Andre?"
Students might count the extra cubes in Clare's tower that don't have a match in Andre's tower. Some students might add cubes to Andre's tower until it's the same size as Clare's. Others might take away the matching cubes and count what's left in Clare's tower.

Students connect these strategies to what they learned before about finding a missing addend (the missing number in an addition problem). By comparing addition and subtraction equations that describe the same problem, students understand subtraction even better — as finding a missing addend.

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Section C Checkpoint

What Students Should Be Able to Do:

• Solve Compare, Difference Unknown problems by:
• Retelling the story in their own words
• Showing the story using objects or drawings
• Explaining how their drawing matches the story
• Getting the correct answer
• Show how addition and subtraction are connected

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Practice Problems

1. From Lesson 11
There are 7 dogs.
There are 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.
There are 8 bats flying outside.
Are there fewer bats in the cave or flying outside?
How many fewer?
Show your thinking with drawings, numbers, or words.

Answer: 2 fewer bats are flying outside.

3. From Lesson 13
Here are the colors of some hot air balloons that Tyler sees at a show.

a. How many more blue balloons does Tyler see than orange balloons?
Show your thinking using drawings, numbers, or words.

b. How many fewer blue balloons does Tyler see than yellow balloons?
Show your thinking using drawings, numbers, or words.

Answer:
a. 3 more blue balloons.
b. 2 fewer blue balloons. (Sample thinking: counting up from 6 to 8.)

4. From Lesson 14
Jada's tower has 8 cubes.
Mai's tower has 2 cubes.
Show 2 ways to find how many more cubes Jada has.
Show your thinking using objects, drawings, numbers, or words.

Answer (sample ways):

• Draw 6 more cubes onto Mai's tower to match Jada's, then count the cubes you added.
• Draw Jada's tower of 8 cubes, cross out 2 of them, and count what's left.

5. From Lesson 15
7 hedgehogs are underground.
4 hedgehogs are on the grass.
How many fewer hedgehogs are on the grass?
Show your thinking using drawings, numbers, or words.

Answer: 3 fewer hedgehogs. (Sample thinking: draw a row of 7 shapes and a row of 4 shapes below it, then count the shapes without a match. Or count up from 4 to 7.)

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Exploration Problems

6.
8 stuffed animals are on the bed.
3 stuffed animals are on the floor.
Your teacher asks a question about this story problem.
The answer to the question is 5.
What could the question be?

Sample answer: "How many more stuffed animals are on the bed than on the floor?"

7.
Find 2 sets of objects at home or at school. Write a story comparing them.
Solve your problem. 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. (8 − 5 = 3)

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Lesson 11: Are There Enough?

What Students Will Learn

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

Learning Goal for Students

"Let's figure out if there are enough."

Purpose of This Lesson

This lesson helps students show and solve "are there enough?" problems in ways that make sense to them. Students also practice using "1 more" or "1 fewer" to compare objects.

Background

In kindergarten, students compared groups and answered "are there enough?" questions using words like "1 more" and "1 less" or "1 fewer." This lesson brings back that thinking to help students get ready for solving Compare, Difference Unknown problems in the next few lessons.

Throughout the lesson, teachers should notice the different ways students talk about the groups in the problems, and how they describe the difference using both everyday words and math words.

Materials Needed

• 10-frames (grids used for counting)
• Connecting cubes
• Two-color counters

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

This warm-up helps students connect words to math pictures or actions, which will help them later when they solve story problems. Even though this story doesn't involve the same kind of comparing they'll do later, the "are there enough?" setup encourages matching strategies that will help students understand difference problems soon.

This activity gives students a chance to make sense of problems.

The Story:
Mai passes out crayons for an art project.
There are 8 students waiting for crayons.
Mai has 7 packs of crayons.
How can you act out this story?

Sample Answers:

• We could have 8 students pretend to be the students waiting for crayons, and one student pretend to be Mai passing out 7 packs of crayons.
• We could use counters for the 8 students waiting and blocks for the 7 packs of crayons.

How to Teach It:

• Put students in pairs.
• Show and read the story aloud.
• Ask: "What is the story about?"
• Give 30 seconds of quiet thinking time.
• Have students share their ideas.
• Read the story again.
• Ask: "How can you act out this story?"
• Give 30 seconds of quiet thinking time.
• Have partners discuss their ideas for 1 minute.
• Share ideas as a class.
• Pick one way to act out the story together.
• Read the story together as a class.

Wrap-Up Question:
"What are other ways we could show this problem?" (Ideas: use cubes or counters to act it out, or draw a picture.)

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Activity 1: Are There Enough? (20 minutes)

This activity asks students to show "are there enough?" story problems in ways that make sense to them, and to describe how the groups in the problem relate to each other. The stories in this activity are designed to get students to use matching strategies. Watch for how students show whether there are enough or not enough of something. Listen for how they describe the bigger group, the smaller group, and the difference using their own words. Afterward, help students describe the relationship using both "1 more" and "1 fewer."

Materials Needed:

• 10-frames
• Connecting cubes
• Two-color counters

Problems:

1. There are 9 markers in a bin.

There are 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.

There are 8 pencils.
Are there enough pencils for every student?
Show your thinking using drawings, numbers, or words.

1. There are 6 students.

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

Sample Answers:

1. No. (9 is a lot more than 4.)
2. No.