# Lesson 19

Methods for Addition Within 20

## Warm-up: Number Talk: Related Expressions (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for the structure of adding within 20. These understandings help students develop fluency and will be helpful later in this lesson when students use relationships between addends to make equivalent expressions to find sums.

### Launch

- Display one expression.
- “Give me a signal when you have an answer and can explain how you got it.”
- 1 minute: quiet think time

### Activity

- Record answers and strategy.
- Keep expressions and work displayed.
- Repeat with each expression.

### Student Facing

Find the value of each expression mentally.

- \(5 + 8\)
- \(6 + 7\)
- \(8 + 7\)
- \(6 + 9\)

### Student Response

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### Activity Synthesis

- “Who can restate _____'s reasoning in a different way?”

## Activity 1: Lin, Han, and Kiran Add (20 minutes)

### Narrative

The purpose of this activity is for students to analyze three different methods for solving \(7 + 8\), two of which involve decomposing an addend to make a known fact. The third method involves adding 1 to make a known fact then taking 1 away from the sum.

Throughout this activity, students must justify and explain the work of the given characters. Students share their thinking and have opportunities to listen to and critique the reasoning of their peers (MP3).

This activity uses *MLR8 Discussion Supports. Advances: listening, speaking, representing*

### Required Materials

Materials to Gather

### Launch

- Groups of 2
- Give students access to double 10-frames and connecting cubes or two-color counters.

### Activity

- Read the task statement.
- “Use double 10-frames and counters to determine how each method works. Show your thinking in a way that others will understand.”
- 10 minutes: partner work time
- 3 minutes: partner discussion
- Monitor for students who can explain each method using 10-frames.

### Student Facing

Lin, Han, and Kiran are finding the value of \(8 + 7\).

Lin thinks about \(8 + 2 + 5\) .

Han thinks about \(7 + 7 + 1\).

Kiran thinks about \(8 + 8 - 1\).

Explain how each student’s method works.

Show your thinking using drawings, numbers, or words.

### Student Response

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### Activity Synthesis

- Invite previously identified students to share their explanations.

**MLR8 Discussion Supports**

- “Who can restate what _____ shared in their own words?”
- 30 seconds: quiet think time
- Consider providing students time to restate what they heard to a partner before selecting one or two students to share with the class.

## Activity 2: How Did You Add? (20 minutes)

### Narrative

The purpose of this activity is for students to find sums within 20, using addition methods flexibly based on the numbers in a given problem. Students may use any method they choose. For example, for a sum such as \(9 + 2\), students may choose to count on. For \(7 + 9\), students may apply the commutative and associative properties, and think \(9 + 7 = 10 + 6\). Students may use known facts and adjust addends as needed. Students first work independently to find each sum and then explain their method to their partner. During the activity synthesis, the teacher records student methods as equations.

*MLR8 Discussion Supports.*Synthesis: Display sentence frames to support whole-class discussion: “My favorite equation is _____ because. . . .,” “First, I _____ because . . . .,” and “My approach and _____’s approach are alike because . . . .”

*Advances: Speaking, Conversing*

*Action and Expression: Internalize Executive Functions.*Check for understanding by inviting students to rephrase directions in their own words.

*Supports accessibility for: Memory, Organization*

### Required Materials

Materials to Gather

### Required Preparation

- Each group needs a set of the Compare Stage 2 Addition Cards cards from the previous lesson.

### Launch

- Groups of 2
- Give each group a set of addition cards from the previous lesson and access to double 10-frames and connecting cubes or two-color counters.
- Display card \(5 + 6\).
- “What is the sum? How do you know?” (11. I can count on from 6. It’s the same as \(10 + 1\). It’s \(5 + 5 + 1\).)
- 1 minute: quiet think time
- 30 seconds: partner discussion
- Record responses.
- “You have learned a lot of different ways to find sums, and now you are going choose the best way for you to solve each problem.”

### Activity

- Read the task statement.
- 5 minutes: partner work time
- “Choose your favorite equation. Show how you found the value using drawings, numbers, or words.”
- 2 minutes: independent work time

### Student Facing

- Choose an addition card.
- Each partner finds the value independently.
- Each partner gives a signal when they are ready to explain their thinking.
- Each partner shares their thinking.
- Each partner writes the equation.

Choose your favorite equation.

Show how you found the value using drawings, numbers, or words.

### Student Response

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### Advancing Student Thinking

If students count all to find the sum, consider asking,

- “How did you find the sum?”
- “How could you find the sum without counting all of the circles?”

### Activity Synthesis

- “What is your favorite equation? Explain how you found the sum.”
- “Did someone find that sum in a different way?”
- Share two or three equations and methods, as time allows.

## Lesson Synthesis

### Lesson Synthesis

Give students access to 10-frames and two-color counters.

“Today, we used different methods to find sums.”

Display \(7 + 6\).

“I saw some different ways students thought about this problem.”

Display: \(6 + 6 + 1\) \(7 + 3 + 3\) \(3 + 4 + 6\)

“Pick one of those ways and explain to your partner what the student did.” (In the first one, they thought about \(6 + 6 = 12\) and then added 1 more. In the second one, they broke the 6 into a 3 and a 3 so they could combine a 3 with a 7 to make 10. In the last one, they broke the 7 into a 3 and a 4 so that they could combine 6 and 4 to make 10.)

## Cool-down: Unit 3, Section C Checkpoint (0 minutes)

### Cool-Down

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