Section C: Compare Story Problems

Standards

Building On: K.CC.B.4, K.CC.C.6

Addressing: 1.MD.C.4, 1.OA.A.1, 1.OA.C.5, 1.OA.C.6

Building Towards: 1.OA.A.1, 1.OA.C.5, 1.OA.C.6, 1.OA.D.7

Goals

• Show how addition and subtraction are connected.
• Solve "Compare, Difference Unknown" story problems (word problems where two amounts are compared and students must find the difference, or gap, between them).

Narrative

In this section, students solve Compare, Difference Unknown story problems. This work strengthens their understanding of how addition and subtraction relate to each other.

Like "Put Together/Take Apart" problems from earlier lessons, Compare problems describe a relationship between two quantities rather than an action like adding to or taking away from a group. That makes them harder to picture. Another challenge is that one part of the relationship — the difference — isn't a physical group students can point to. On top of that, the wording of these problems can be tricky and open to more than one interpretation.

Because of these challenges, students start this section by revisiting the "are there enough?" problems they first saw in kindergarten. This gives them practice comparing quantities using the words "more" and "fewer." Next, students tackle "how many more?" and "how many fewer?" problems set in situations that naturally lead them to use matching strategies — that is, lining up or pairing items from each group to see what's left over. Students learn to identify which quantity is "more" and which is "fewer," and to figure out exactly how many more or fewer.

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 these relationships clearly. They learn to identify the bigger amount and the smaller amount, and to understand that the difference between them answers the question "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 cubes in Clare's tower that don't have a matching cube in Andre's tower. Some might physically add cubes to Andre's tower until it's the same height as Clare's. Others might remove the matched cubes — say, 4 of them — and simply count what's left in Clare's tower.

Students connect these strategies to the "unknown addend" problems (problems where you know the total and one part, and must find the missing part) they solved in the previous section. After the teacher records student thinking, students study both an addition equation and a subtraction equation that can represent the same problem. By comparing different ways to find the difference, students build a deeper understanding of subtraction as a way of finding a missing addend.

Section C Checkpoint

Teacher Instructions

For this Checkpoint Assessment, a full observation checklist is available in the Assessments for this unit. The content being assessed is listed below for reference.

Compare Story Problems

• Solve Compare, Difference Unknown problems:
• Retell the story in their own words.
• Represent the story using objects or drawings.
• Explain how their representation matches the story.
• Answer the question correctly.
• Show how addition and subtraction are related.

Practice Problems

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.

Solution: No. (Sample response shown with drawings.)

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.

Solution: 2 fewer bats. (Sample response shown with drawings.)

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.

Solution:
a. 3 more blue balloons.
b. 2 fewer blue balloons. Sample reasoning: "I counted 6... 7, 8."

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.

Solution: Sample response:

• Draw 6 more cubes added onto a tower of 2 cubes, then count the added cubes.
• Draw a tower of 8 cubes, cross off 2 cubes, then count the cubes that remain.

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.

Solution: 3 fewer hedgehogs. Sample responses:

• Draw a row of 7 shapes and a row of 4 shapes underneath, then count the shapes that don't have a match.
• "I counted 4... 5, 6, 7. There are 3 more hedgehogs underground."

6. Exploration. 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?

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

7. Exploration. 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.

Solution: Sample response: "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)

---

Unit 2, Lesson 11: Are There Enough?

Standards

Building On: K.CC.B.4, K.CC.C.6

Addressing: 1.OA.A.1

Building Towards: 1.OA.A.1

Instructional Routines: Act It Out

Goals

• Describe out loud the difference between a larger quantity and a smaller quantity using the phrases "1 more" or "1 fewer."
• Explain out loud different methods for representing an "are there enough?" problem.

Student-Facing Learning Goal

Let's figure out if there are enough.

Lesson Purpose

The purpose of this lesson is for students to represent and solve "are there enough?" problems in whatever way makes sense to them, and to use the phrases "1 more" or "1 fewer" to compare groups of objects.

Narrative

In kindergarten, students compared quantities and answered "are there enough?" questions, using the language "1 more" and "1 less" (or "1 fewer"). In this lesson, students return to this type of problem and its language to get ready for solving Compare, Difference Unknown problems in upcoming lessons.

Throughout the lesson, pay attention to the different ways students describe the quantities in the story problems and activities, and how they describe the difference using both everyday language and more formal math language.

Access for Students with Disabilities

Engagement

Access for English Learners

MLR8

Required Materials

Materials to Gather:

• 10-frames: 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: 10 minutes (estimate)

Teacher Reflection Questions

In upcoming lessons, students will represent and solve Compare, Difference Unknown story problems. How will the work in this lesson help prepare students to make sense of questions like "how many more?" and "how many fewer?" How will the matching strategies that come up in this lesson's problems help students understand the relationship between a bigger quantity, a smaller quantity, and the difference between them?

Warm-up: Act It Out — Art Project

10 minutes

Standards — Building Towards: 1.OA.A.1

Instructional Routines: Act It Out

The purpose of this warm-up is to let students connect everyday language to a mathematical representation — a skill they'll need when they represent and solve story problems later in the lesson. Although the Compare, Difference Unknown problems students will solve in future lessons don't describe an action taking place, the "are there enough?" context in this problem naturally encourages matching strategies that will help students understand and discuss the difference between two quantities.

This warm-up gives students a chance to practice making sense of problems.

Student Task Statement

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?

Student Response

Sample responses:

• "We could have 8 students pretend to be the students waiting for crayons. We could have someone 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

• Groups of 2.
• Display and read the story aloud.
• Ask: "What is the story about?"
• Give 30 seconds of quiet think time.
• Share responses.
• Read the story again.
• Ask: "How can you act out this story?"
• Give 30 seconds of quiet think time.

Activity

• Say: "Discuss your thinking with your partner."
• Give 1 minute for partner discussion.
• Share responses as a class.
• Choose one way to represent the story together.
• Read the story together as a class.

Activity Synthesis

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

Activity 1: Are There Enough?

20 minutes

Standards — Building On: K.CC.C.6
Building Towards: 1.OA.A.1

The purpose of this activity is for students to represent "are there enough?" story problems in whatever way makes sense to them, and to describe the relationships between the quantities involved. The situations in this activity are designed on purpose to encourage matching strategies. Watch for the different ways students show whether there are or aren't enough of something. Listen for — and highlight — the ways students describe the bigger quantity, the smaller quantity, and the difference between them using everyday language. During the Synthesis discussion, students will get a chance to describe the relationship between the bigger and smaller quantities using both "1 more" and "1 fewer."

Access for Students with Disabilities

Engagement: Provide Access by Recruiting Interest. Invite students to share examples from their own lives of times they had to figure out if there were enough of something.

Supports accessibility for: Conceptual Processing, Social-Emotional Functioning

Required Materials

Materials to Gather:

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

Student Task Statement

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.

Student Response

1. No. Sample responses: (drawings shown); "9 is much more than 4."

1. No