GRADE 1

Teacher Guide

UNIT 2

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Section C: Compare Story Problems

Standards

Standards are the skills students should learn. This section builds on skills from Kindergarten (called K.CC.B.4 and K.CC.C.6). It teaches new skills for Grade 1 (called 1.MD.C.4, 1.OA.A.1, 1.OA.C.5, and 1.OA.C.6). It also helps students get ready for more new skills later (1.OA.A.1, 1.OA.C.5, 1.OA.C.6, and 1.OA.D.7).

Goals

• See how adding and subtracting are connected.
• Solve "Compare" story problems where you need to find the difference (how many more or how many fewer).

What This Section Is About

In this section, kids solve story problems that compare two groups. These problems show how adding and subtracting are connected.

Compare problems are tricky. They are not about something happening, like giving away toys. They are about a relationship between two groups. Also, one part of the problem — the difference — is not something you can see or hold. The words in these problems can also be confusing.

Because of this, kids start by remembering "are there enough?" problems from Kindergarten. They practice using the words "more" and "fewer" to compare groups. Then they solve "how many more?" and "how many fewer?" problems. These problems help kids line up, or match, items from each group to compare them. Kids find out which group has more or fewer, and by how many.

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 things up helps kids see the relationship between the two groups. They find the bigger group and the smaller group. The difference is the answer to "how many more?" or "how many fewer?"

Another Example:

"How many more cubes does Clare have than Andre?"

Kids might count the cubes in Clare's tower that don't have a match in Andre's tower. Some kids might add cubes to Andre's tower until it's the same size as Clare's. Other kids might take away the matching cubes (4 of them) and count what's left in Clare's tower.

Kids connect these ways of finding the difference to problems they solved before, where one number in an addition problem was missing. The teacher writes down, or "annotates," both kinds of number sentences (called equations) that can describe the same problem — one for adding and one for subtracting. By comparing these, kids understand better how subtracting can also mean finding a missing part in addition.

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Section C Checkpoint

Teacher Instructions

For this check-in, teachers can use a checklist found in the Assessments section of this unit. Here is what is being checked:

Compare Story Problems

• Solve Compare problems where the difference is missing.
• Tell the story back in your own words.
• Show the story using objects or drawings.
• Explain how your drawing matches the story.
• Give the right answer.
• Show how adding and subtracting are connected.

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Practice Problems

7 Problems

Problem 1 — from Unit 2, 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. Sample: A drawing showing 7 dogs and only 5 toys, with 2 dogs having no toy.

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Problem 2 — from Unit 2, 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. Sample: A drawing matching up bats from each group and counting the extra ones.

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Problem 3 — from Unit 2, 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: "I counted 6... 7, 8."

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Problem 4 — from Unit 2, 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 of 2, then count the new cubes added.
• Draw Jada's tower of 8 cubes, cross out 2, then count what's left.

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Problem 5 — from Unit 2, 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 ways:

• Draw a row of 7 shapes and a row of 4 shapes under it. Count the shapes with no match.
• "I counted 4... 5, 6, 7. There are 3 more hedgehogs underground."

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Exploration Problem

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?

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

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Exploration Problem

Find 2 groups of objects at home or at school. Write a story comparing them.

Solve your problem. Write an equation (a number sentence) that matches the story.

Answer: Sample: "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. 5 + 3 = 8."

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Unit 2, Lesson 11

Are There Enough?

Standards

This lesson builds on Kindergarten skills (K.CC.B.4, K.CC.C.6) and works toward a new Grade 1 skill (1.OA.A.1).

Instructional Routine

• Act It Out — kids act out the story to understand it better.

Goals

• Talk out loud about the difference between a bigger group and a smaller group, using the words "1 more" or "1 fewer."
• Talk out loud about ways to show an "are there enough?" problem.

What Students Will Learn

Let's figure out if there are enough.

Why This Lesson Matters

This lesson helps kids show and solve "are there enough?" problems in their own way. They use the words "1 more" or "1 fewer" to compare objects.

Background

In Kindergarten, kids compared groups and answered "are there enough?" questions. They compared numbers using "1 more" and "1 less" (or "1 fewer"). In this lesson, kids remember these ideas and words. This gets them ready to solve Compare problems (finding the difference) in future lessons.

During the lesson, notice how kids describe the groups and the difference between them, using both everyday words and math words.

Support for Students with Disabilities

• Engagement: Help kids stay interested and involved.

Support for English Learners

• MLR8 — a teaching method to help kids learn English while learning math.

Materials Needed

• 10-frames (a tool with 10 boxes 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
• Wrap-up (Synthesis): 10 minutes

Questions for Teachers to Think About

In upcoming lessons, kids will solve Compare problems where the difference is missing. How does this lesson help kids understand "how many more?" and "how many fewer?" questions? How does matching things up in this lesson help kids understand the bigger group, the smaller group, and the difference between them?

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Warm-up: Act It Out — Art Project

10 minutes

Standards

This works toward skill 1.OA.A.1.

Instructional Routine

• Act It Out

This warm-up helps kids connect words to math ideas. This will help later when kids show and solve story problems. The Compare problems kids solve in later lessons don't involve action — but this "are there enough?" story does. Acting it out helps kids practice matching things up, which will help them understand the difference later.

This warm-up also helps kids practice making 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. Someone could pretend to be Mai and pass out 7 packs of crayons.
• We could use counters for the 8 students waiting and blocks for the 7 packs of crayons.

How to Start

• Put students in pairs.
• Show and read the story out loud.
• Ask: "What is the story about?"
• Give 30 seconds of quiet thinking time.
• Have kids share their ideas.
• Read the story again.
• Ask: "How can you act out this story?"
• Give 30 seconds of quiet thinking time.

The Activity

• Have kids talk with their partner about their thinking.
• Give 1 minute for partner talk.
• Have kids share their ideas.
• Pick one way to act out the story as a class.
• Read the story together.

Wrap-up Questions

• Ask: "What are other ways we could show this problem?" (Some ide