# Lesson 14

Compare with Addition and Subtraction

## Warm-up: True or False: Equal Sign (10 minutes)

### Narrative

The purpose of this True or False is to continue to develop and deepen student understanding of the equal sign. These understandings will be helpful when students work with equations with expressions on both sides of the equal sign in a later unit.
This is the second time students will do this instructional routine. The teacher should read aloud each equation. When students are more familiar with equations, they do not need to be read by the teacher.

### 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 equation.

### Student Facing

Decide if each statement is true or false.
Be prepared to explain your reasoning.

• $$7 + 3 = 10$$
• $$10 = 7 + 3$$
• $$10 = 3 + 6$$

### Activity Synthesis

• “How is 10 the same amount as $$7 + 3$$?” (When I add 7 and 3, the total is 10.)
• “If $$7 + 3 = 10$$, and $$10 = 7 + 3$$, would $$10 = 3 + 7$$?” (Yes, because 7 + 3 is the same amount as 10, and 10 is the same amount as $$3 + 7$$.)

## Activity 1: Is It Addition or Subtraction? (15 minutes)

### Narrative

The purpose of this activity is for students to explore the relationship between addition and subtraction through a Compare, Difference Unknown story problems. They analyze two equations, one addition and one subtraction, that match the same problem and discuss the relationship between the two equations and the story problem. Students should notice that both equations can be used to describe how they solve the problem. This also helps them relate addition and subtraction and see that often either operation can be used to solve a problem (MP7).

### Launch

• Groups of 2
• Give students access to connecting cubes or two-color counters.
• Display the image in the student book.
• 1 minute: quiet think time
• 2 minutes: partner discussion
• Share responses.

### Activity

• 5 minutes: partner work time
• Encourage students to use the representation to make sense of both equations.
• Monitor for a group who uses the representation to explain the addition equation and one who explains the subtraction equation.

### Student Facing

There are 8 glue sticks and 3 scissors at the art station.
How many fewer scissors are there than glue sticks?

Mai created a picture.

She is not sure which equation she should use to find the difference.

$$8 - 3 = \boxed{5}$$
$$3 + \boxed{5} = 8$$

Help her decide.
Show your thinking using drawings, numbers, or words.

### Advancing Student Thinking

If students find the difference using only one operation, consider asking:

• "Can you explain how you found the difference between the number of glue sticks and scissors?"
• "Where in your drawing (objects) do you see the difference? How could you find that part of the representation by adding (subtracting)?"

### Activity Synthesis

• “What are we trying to find out in this story problem?” (How many fewer scissors there are than glue sticks. The difference between the number of scissors and glue sticks.)
• Invite previously identified groups to share.
• “What is the same? What is different?” (3, 5, and 8 are in each equation. The numbers represent the same things in both. The 5 is boxed in both. One uses addition and the other uses subtraction. The boxed number is in a different place.)

## Activity 2: Which Equation? (10 minutes)

### Narrative

The purpose of this activity is for students to identify addition and subtraction equations that match Compare, Difference Unknown story problems. Students may not initially choose more than one equation for each problem, so this is the emphasis of the activity synthesis. Students continue to build their language of Compare problems and solidify the relationship between addition and subtraction.

MLR2 Collect and Display. Collect the language students use to explain their thinking. Display words and phrases such as: more, fewer, equation, drawings, words. During the synthesis, invite students to suggest ways to update the display: “What are some other words or phrases we should include?”, etc. Invite students to borrow language from the display as needed.
Engagement: Internalize Self-Regulation. Synthesis: Provide students an opportunity to self-assess and reflect on their own progress. For example, ask students to check over their work to make sure they used drawings, numbers, or words to show their thinking, and also included at least one equation to show how they solved the problem.
Supports accessibility for: Conceptual Processing, Attention

### Launch

• Groups of 2
• Give students access to connecting cubes or two-color counters.

### Activity

• 3 minutes: independent work time
• 2 minutes: partner discussion
• Monitor for a student who can show and explain how they chose which equation matches.

### Student Facing

1. There are 5 red pillows and 3 blue pillows on the reading rug.
How many more red pillows are there than blue pillows?
Show your thinking using drawings, numbers, or words.

Circle the equation that matches the problem.

$$5 + 3 = \boxed{\phantom{8}}$$

$$5 - 3 = \boxed{\phantom{2}}$$

$$5 + \boxed{\phantom{2}} = 3$$

$$3 + \boxed{\phantom{2}} = 5$$

2. There are 7 calculators on the table.
There are 8 math books.
How many more math books are there than calculators?
Show your thinking using drawings, numbers, or words.

Circle the equation that matches the problem.

$$7 + \boxed{\phantom{1}} = 8$$

$$8 - 7 = \boxed{\phantom{1}}$$

$$7 - 8 = \boxed{\phantom{0}}$$

$$8 + \boxed{\phantom{1}} = 7$$

3. In Mr. Green’s class, 3 students have purple backpacks and 7 students have black backpacks.
How many more students have black backpacks than purple backpacks?
Show your thinking using drawings, numbers, or words.

Circle the equation that matches the problem.

$$3 + 7 = \boxed{\phantom{10}}$$

$$3 + \boxed{\phantom{4}} = 7$$

$$7 - \boxed{\phantom{4}} = 3$$

$$7 + \boxed{\phantom{1}} = 3$$

### Activity Synthesis

• “How did you know which equation matched the problem about backpacks?" (I made a tower of 3 cubes to show the purple backpacks, and a tower of 7 cubes to show the black backpacks. Then I broke off the difference, which is 4. This matches 7 - __ = 3 because the 4 shows the difference.)
• “Are there any other equations that represent this problem?” (Yes, 3 + ___ = 7 also matches. I started with 3 cubes, and added cubes until I got to 7. The amount I added was 4.)
• "There were two equations that match this problem. Check the other problems to see if there are any other equations that match."

## Activity 3: Centers: Choice Time (15 minutes)

### Narrative

The purpose of this activity is for students to choose from activities that offer practice telling and solving story problems and adding and subtracting within 10. Students choose from any stage of previously introduced centers.

• Capture Squares
• Math Stories
• Shake and Spill

### Required Materials

Materials to Gather

### Required Preparation

• Gather materials from previous centers:
• Capture Squares, Stage 1
• Math Stories, Stage 4
• Shake and Spill, Stages 3 and 4

### Launch

• Groups of 2
• “Now you are going to choose from centers we have already learned.”
• Display the center choices in the student book.
• “Think about what you would like to do.”
• 30 seconds: quiet think time

### Activity

• Invite students to work at the center of their choice.
• 10 minutes: center work time

Choose a center.

Capture Squares

Math Stories

Shake and Spill

### Activity Synthesis

• “Tell your partner one thing they did that helped you during center time today.”

## Lesson Synthesis

### Lesson Synthesis

Display: In Mr. Green's class, 3 students have purple backpacks and 7 students have black backpacks. How many more students have black backpacks than purple backpacks?

​​$$3 + \boxed{4} = 7$$ and $$7 - 3 = \boxed{4}$$.

“Today we explained how different equations can match the same story. These are the equations that match this story. Why does the position of the answer change?” (Because one equation is addition and one is subtraction, because they used different methods to solve the problem, so the answer came in different places.)

“What does each number represent?”