# Lesson 10

## Warm-up: Number Talk: Use Sums to Find Sums (10 minutes)

### Narrative

This Number Talk encourages students to think about the relationship between addends in an expression and to rely on what they know about making the next ten or next hundred to mentally solve problems. These understandings help students develop fluency and will be helpful later in this lesson when students are asked to choose methods that make sense to them and explain their choices. As students share their thinking, consider recording on an open number line.

### 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

• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Find the value of each expression mentally.

• $$199 + 23$$
• $$198 + 24$$
• $$297 + 25$$
• $$395 + 27$$

### Activity Synthesis

• “When finding $$199 + 23$$, we could think about adding by place and composing a ten and a hundred.”
• “Some people thought about counting on to get to the next hundred and then added what was left. Why is that a useful method?” (199 is really close to a new hundred. It’s easier for me to add $$200 + 22$$ in my head than try to add by place in my head.)

## Activity 1: Card Sort: Three-digit Sums (20 minutes)

### Narrative

The purpose of this activity is for students to sort addition expressions based on their perceived difficulty. They find the values of expressions they feel are less challenging and expressions they feel are more challenging. Then they compare the methods they use for the expressions they solve with their peers. When sharing, students have opportunities to ask questions about the methods and representations their peers use and suggest methods or representations for expressions that peers may feel are difficult to solve (MP3).

When students sort the expressions they look for place value structure to see how they would find the sums (MP7).

Action and Expression: Internalize Executive Functions. Check for understanding by inviting students to rephrase directions in their own words. Allow students to check off each task as it is completed.
Supports accessibility for: Memory, Organization

### Required Materials

Materials to Gather

Materials to Copy

• How Did You Do That? Addition Card Sort

### Required Preparation

• Create a set of cards from the blackline master for each group of 2.

### Launch

• Groups of 2
• Give each group a set of cards.

### Activity

• “This set of cards includes different expressions. Sort the cards by thinking about whether it would be less challenging or more challenging to find the value of the sum.”
• “Make 1 group of sums that you both agree would be less challenging. Make another group of sums that you agree would be more challenging.”
• “If you cannot agree on where to place a card, keep it separate from the other groups.”
MLR8 Discussion Supports
• Display sentence frames to support students when they share their reasoning:
• “I think this value is less difficult to find because …”
• “I think this value is more difficult to find because …”
• “I agree because …”
• “I disagree because …”
• “Choose one expression from each category and find the value of the sum. Show your thinking using diagrams, symbols, or other representations.”
• 6 minutes: partner work time
• “If you have not started finding the value of the sums, please do so.”
• 5 minutes: independent work
• 4 minutes: partner discussion
• Monitor for students who choose sums that are:
• less difficult because they do not involve making new units
• less difficult because they can use the relationships between the numbers to find the sum mentally
• more difficult based on the number of compositions required
• more difficult based on the size of the numbers or digits

### Student Facing

1. Sort the cards into 2 groups with your partner.

• Make a group of expressions that you agree the value is less challenging to find.
• Make another group of expressions that you agree the value is more challenging to find.
• Keep any expressions together that you and your partner disagree on.
2. Choose an expression that you feel is less challenging.

Find the value of the sum. Show your thinking.

3. Choose an expression that you feel is more challenging.

Find the value of the sum. Show your thinking.

4. Discuss one card you and your partner disagreed on. If you felt the expression was more challenging, explain why. If you felt the expression was less challenging, explain your method.

### Student Response

If students sort most or all of their cards into the “more challenging” group, consider asking:
• “How could you arrange your expressions in order of ‘least challenging’ to ‘most challenging’?”

### Activity Synthesis

• Invite a previously identified student to share how they found the value they felt was less challenging to find.
• “What questions do you have for _____ about their method?”
MLR8 Discussion Supports
• Display question starters:
• “Why did you …?”
• “Can you say more about …?”
• “Did you think about trying …?”
• 1 minute: quiet think time
• Invite 2–3 students to ask questions.
• Repeat with a previously identified student to share a value they felt was more challenging to find.
• If time, continue to select students to share strategies for expressions that they felt were less or more challenging.

## Activity 2: Find the Unknown Value (15 minutes)

### Narrative

The purpose of this activity is for students find an unknown addend in sums that have a value of 1,000. They may use what they know about counting by 5, 10, and 100 or use what they know about composing larger units. Although students do not need to know that a thousand is a unit made up of 10 hundreds in grade 2, listen for students who generalize their understanding of place value to make this conjecture to share in the synthesis.

### Required Materials

Materials to Gather

### Launch

• Groups of 2.
• Display the image that shows 900 + __0 = 1,000.
• “Oh no! Diego spilled paint on his paper and now he can’t see the whole number. What three-digit number do you think is covered up? How do you know?” (100. Because it's like counting to 1,000 by 100. It would be 900, 1,000.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.

### Activity

• “Now you are going to make sense of a couple more equations where Diego made a mess. Each equation has a part of the three-digit number that is covered up by paint. You’ll work on your own at first, and then have time to share with a partner.”
• 5 minutes: independent work time
• 5 minutes: partner work time
• Monitor for students who added $$615 + 85$$ to find the unknown value for _85 + 615 = 1,000.

### Student Facing

Oh no! Diego spilled paint on his paper and now he can’t see all the digits in each of his equations.
1. What three-digit number makes the equation true? Show your thinking.
2. What three-digit number makes the equation true? Show your thinking.

### Activity Synthesis

• Invite previously identified students to share their work.
• “How did _____ find the unknown number?” (They started by adding the 85 to the 615 to get 700. Then they knew they needed 3 more hundreds to get to 1,000.)
• Share responses and record with equations and on an open number line.

## Lesson Synthesis

### Lesson Synthesis

“Today you added with three-digit numbers using methods that made sense to you. You shared ways to think about the addends in an expression to choose a method for finding the value of a sum.”

Display $$429 + 387$$ and $$498 + 387$$.

“Which of these expressions might be more challenging? Why?” (In both expressions, a ten and a hundred will be composed, but since 498 is very close to 500, it would be easier to me.)

## Student Section Summary

### Student Facing

In this section of the unit, we learned many different ways to add three-digit numbers using what we know about place value. We used base-ten blocks, diagrams, and equations to show adding hundreds to hundreds, tens to tens, and ones to ones. We learned that when you add by place, you may need to compose a ten, a hundred, or both.

Base-ten Diagram
$$358+67$$

Unit Form and Equations
$$358+67$$

3 hundreds + 11 tens + 15 ones
11 tens = 110
15 ones = 15

$$300 + 110 + 15 = 425$$

$$267 + 338$$
$$200 + 300 = 500$$
$$60 + 30 = 90$$
$$7 + 8 = 15$$
$$500 + 90 + 15$$
$$500 + 90 + 10 + 5$$
$$500 + 100 + 5 = 605$$