# Lesson 7

Does it Make a New Ten?

## Warm-up: Which One Doesn’t Belong: Expressions (10 minutes)

### Narrative

This warm-up prompts students to compare four expressions. It gives the teacher an opportunity to hear how students talk about the characteristics of addends and use terminology related to the digits, the values of the addends, and the value of the sum.

### Launch

• Groups of 2
• Display the image.
• “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

### Activity

• 2–3 minutes: partner discussion
• Share and record responses.

### Student Facing

Which one doesn’t belong?

### Activity Synthesis

• “Let’s find at least one reason why each one doesn’t belong.”

## Activity 1: A Ten or Not a Ten? (15 minutes)

### Narrative

The purpose of this activity is for students to use place value reasoning and properties of operations to determine whether they would compose a ten when adding a two-digit and a one-digit number.

Students write equations to show how they solved such as:

$$9 + 63$$
$$63 + 7 = 70$$
$$70 + 2 = 72$$

$$9 + 63$$
$$9 + 3 = 12$$
$$12 + 60 = 72$$

It is not important that students write their equations in this way, but it is important that they can relate each part of the equation to how they found the sum.

Students may write $$63 + 7 = 70 + 2 = 72$$. Since this equation is not true, it is important to remind students that the equal sign means “the same amount as” and that it is necessary to use two separate equations.

Action and Expression: Develop Expression and Communication. Provide students with alternatives to writing their explanations on paper: students can share their learning orally or using double 10-frames, two-color counters, and connecting cubes in towers of 10 and singles.
Supports accessibility for: Language, Conceptual Processing

### Launch

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.

### Activity

• 5 minutes: independent work time
• 3 minutes: partner discussion
• Monitor for students who:
• can explain why the expression does or doesn’t make a new ten, without finding the sum.
• use connecting cubes to show why there are or are not enough ones to make a new ten without representing the entire sum.

### Student Facing

Jada likes to look for ways to make a new ten when she adds. Would she be able to a make a new ten when she adds to find the value of these sums?
If Jada could make a new ten, circle “Yes.”
If Jada could not make a new ten, circle “No.”

1. Does the expression make a new ten?

$$45 + 5$$

Yes

No

Explain how you know.

Find the value.

Write equations to show how you found the value of the sum.

2. Does the expression make a new ten?

$$9 + 63$$

Yes

No

Explain how you know.

Find the value.

Write equations to show how you found the value of the sum.

3. Does the expression make a new ten?

$$26 + 3$$

Yes

No

Explain how you know.

Find the value.

Write equations to show how you found the value of the sum.

4. Does the expression make a new ten?

$$8 + 47$$

Yes

No

Explain how you know.

Find the value.

Write equations to show how you found the value of the sum.

### Student Response

If students write equations that do not match their method for finding the sum, consider asking:

• “How did you find the sum?”
• “What equation could we write to represent your first step? Next step?”

### Activity Synthesis

• Invite previously identified students to share.
• “Let’s think some more about how we know whether or not we will make a new ten.”

## Activity 2: Missing Numbers (20 minutes)

### Narrative

The purpose of this activity is for students to deepen their understanding of place value and properties of operations when adding one-digit numbers and two-digit numbers. Students find an unknown addend that fits a specific rule for each expression. Some expressions have more than one number that fits the rule. As students complete each expression, they look for and make use of structure (MP7) as they think about whether or not the ones in the two numbers will combine to make a new 10.

During the activity synthesis, students look at different one-digit numbers that would make or not make a new ten when added to 16. In the lesson synthesis, students share their answers to the last problem in the task which encourages them to make generalizations (MP8).

MLR6 Three Reads. Keep books or devices closed. To launch this activity, display only the problem stem for the first problem, without revealing the question. “We are going to read this story problem three times.” After the 1st Read: “Tell your partner what happened in the story.” After the 2nd Read: “What question might we be asked to solve?” Reveal the question. After the 3rd Read: “What are different ways we can solve this problem?”

### Launch

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.
• Display:
• “Lin wrote a one-digit number where the smudge is. She said you can not make a new ten when you find the value of the sum. What number could she have written?” (0, 1, 2, 3, 4, or 5)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• “Are there other numbers she could have written?”
• Record responses.

### Activity

• 5 minutes: independent work time
• 5 minutes: partner discussion
• Monitor for students with a range of responses for the last two questions.

### Student Facing

Lin’s brother spilled water on her math work!
Figure out what number Lin wrote before it got smudged.

1. Lin wrote a one-digit number with which you can make a new ten when you find the value of the sum.

What could Lin’s number be?
Write equations to show your thinking.

2. Lin wrote a one-digit number with which you can not make a new ten when you find the value of the sum.

What could Lin’s number be?
Write equations to show your thinking.

3. Lin wrote a two-digit number with which you can make a new ten when you find the value of the sum.

What could Lin’s number be?
Write equations to show your thinking.

4. Lin wrote a two-digit number with which you can not make a new ten when you find the value of the sum.

What could Lin’s number be?
Write equations to show your thinking.

5. How do you know whether or not you can make a new ten when you are finding the value of a sum?

### Student Response

If students choose numbers that do not follow Lin's rule or show they believe that only one number could follow the rule for a problem, consider asking:

• “What needs to be true about Lin's number for this sum?”
• “How do you know your number works? How could you prove your thinking with the connecting cubes?”
• “Are there other numbers Lin could have written? How could you prove it with the connecting cubes or a drawing?”

### Activity Synthesis

• Display
• “What two-digit numbers can she add that will make a new ten?” (12, 35, 49)
• “What two-digit numbers can she add that will not make a new ten?” (11, 30, 41)
• “What do you notice about each list of numbers?” (If she doesn't make a new ten, the number can only have 0 or 1 in the ones place, but it can have any number in the tens place. If she does make a new ten, the number can have 2, 3, 4, 5, 6, 7, 8, or 9 in the ones place.)

## Lesson Synthesis

### Lesson Synthesis

“Today we looked at addition expressions and determined if you could make a new ten or not. How does knowing that you might have to make a new ten help you decide what method to use?” (If I know I have to make a new ten, I do that first. Then I add the rest of the ones. I add the ones and ones then the tens either way so it doesn’t change my method.)

## Student Section Summary

### Student Facing

We added one-digit numbers and two-digit numbers.
We used different methods to add.
We learned you can think of counting on to make a new ten.

$$45 + 8$$
$$45 + 5 + 3 = \boxed{53}$$

We also saw you can think of adding all the ones and then the tens.
Sometimes when you add the ones you might be able to make a new ten.

$$5 + 8 = 13$$
$$40 + 13 = 53$$