# Lesson 12

## Warm-up: Number Talk: Make a Ten (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for adding within 100. These understandings help students develop fluency and will be helpful later in this lesson when students add 2 two-digit numbers, with composing a ten, using methods based on place value and the properties of operations.

In this activity, students have an opportunity to look for and make use of structure (MP7) because they decompose addends to make a new ten.

### 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.

• $$7 + 3$$
• $$37 + 3$$
• $$7 + 8$$
• $$57 + 8$$

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “How could $$7 + 3$$ help you solve $$37 + 3$$?” (I know 37 is 3 more tens than 7. Since I know $$3 + 7$$ is 10, I need to add $$30 +10$$.)
• “How could $$7 + 3$$ help you solve $$7 + 8$$?” ($$7 + 3 = 10$$. So far I have added 3 of the 8 and have 5 left. $$10 + 5 = 15$$.)
• “How could $$7 + 8$$ help you solve $$57 + 8$$?” (Since I know $$7 + 8 = 15$$, I can add $$50 + 15 = 65$$)

## Activity 1: Add Two-digit Numbers Within 100 (15 minutes)

### Narrative

The purpose of this activity is for students to add 2 two-digit numbers within 100 and show their thinking with equations. Although some students may write each step of their thinking with equations, it is not required that they do so. Students can write one equation that shows the sum and represent their solution pathway in their drawings. In the activity synthesis, students present their method verbally to a new partner.

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

### Launch

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.
• “We have been learning about different ways to add within 100. You are going to find sums using a method that makes most sense to you for each problem. Record equations to show your thinking.”

### Activity

• 5 minutes: independent work time
• “Compare your work with your partner’s. Did you use the same method? Did you represent your method in the same way? How is your work the same? How is it different?"
• 5 minutes: partner work time
• Monitor for a student who wrote equations related to making ten and one who wrote equations related to adding by place.

### Student Facing

Find the value of each sum using any method that you want.
Show your thinking using drawings, numbers, or words.
Write equations to represent your thinking.

1. $$48 + 15$$

2. $$57 + 36$$

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

MLR8 Discussion Supports:
• Display sentence frames to support students when they explain their method as equations:
• “First, I _____ because . . .”
• “I noticed _____ so I . . .”
• “You are going to explain your method to another student in the class. Practice what you will say with your partner. Use these sentence starters to help you.”
• 3 minutes: partner discussion
• “Find a new partner and explain your method.”
• 2 minutes: partner discussion

### Narrative

The purpose of this activity is for students to use what they know about the base-ten structure of numbers to create different expressions. Students use place value reasoning to create expressions with the smallest and largest values and expressions that may or may not require composing a ten when adding using methods based on place value (MP7). In the synthesis, students explain how they reasoned about whether or not a new ten could be composed just by looking at the addends (MP3). Although some students may complete the activity without finding any sums, others may need to find partial sums or complete sums in order to explain what happens when adding.

MLR8 Discussion Supports. Synthesis: For each method that is shared, invite students to turn to a partner and restate what they heard using precise mathematical language.
Representation: Access for Perception. Some students may benefit from hearing the instructions read aloud more than once.
Supports accessibility for: Attention, Language, Memory

### Launch

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.
• “Now we are going to use what we know about numbers and addition to think about what will happen when we add different numbers together. You may add the numbers if it is helpful, but you don’t have to.”

### Activity

• 8 minutes: partner work time
• Monitor for students who write expressions without finding the value of the sums and can explain their reasoning.

### Student Facing

37

22

18

56

41

Choose 2 numbers from above and write an addition expression to make each statement true.

• This sum has the smallest possible value.

Expression:_______________________

• This sum has the largest possible value.

Expression:_______________________

• You do not need to make a new ten to find the value of this sum.

Expression:_______________________

• If you make a new ten to find the value of this sum, you will still have some more ones.

Expression:_______________________

• If you make a new ten to find the value of this sum, you will have no more ones.

Expression:_______________________

Be ready to explain your thinking in a way that others will understand.

If you have time: Choose 2 numbers from above and write an addition expression where the value is closest to 95.
How do you know the value is closest to 95?

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Invite a previously identified student to share their expression that does not require making a new ten.
• “Are there other numbers you could use? How do you know?"
• Invite a student who found two numbers that make a ten without finding the sums to share.
• “Are there other numbers you could use? How do you know?"

## Activity 3: Ways We Volunteer [OPTIONAL] (20 minutes)

### Narrative

The purpose of this activity is for students to relate adding within 100 to real-world contexts. In previous lessons and activities, students have used different methods to add within 100. In this activity, students solve problems that help them see when this type of addition is used in people’s lives. This activity is optional because it is an opportunity for extra practice that not all classes may need.

When students connect the quantities in the story problem to an equation, they reason abstractly and quantitatively (MP2).

### Launch

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.
• “We recently discussed a story problem about a class that volunteered to clean up their local park. What are some other ways you can volunteer to help in your community?” (You can volunteer at an animal shelter. You can help by donating food or clothes.)
• 30 seconds: quiet think time
• Share responses.
• “We are going to solve some more problems about people volunteering in different ways.”

### Activity

• 5 minutes: independent work time
• 5 minutes: partner discussion

### Student Facing

1. Mai’s school is having a book drive.
They collect 48 children’s books.
How many books do they collect all together?
Show your thinking using drawings, numbers, or words.

2. The community soup kitchen has lots of volunteers who help serve food.
They have 35 volunteers during the week and 56 volunteers on the weekend.
How many volunteers do they have all together?
Show your thinking using drawings, numbers, or words.

3. Elena and her mother volunteer to plant a community garden in their neighborhood.
They plant 18 strawberry plants and 24 cucumber plants.
How many plants did they plant all together?
Show your thinking using drawings, numbers, or words.

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Invite students to share the methods used for each problem. Record equations to match each method.

## Lesson Synthesis

### Lesson Synthesis

“During this unit you learned how to add within 100. What are some things that you learned?” (I can add tens and tens and ones and ones. I can make ten when adding by breaking apart the ones.)

“What are you most proud of learning? What do you still need to work on?”

## Cool-down: Add Within 100 (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.

## Student Section Summary

### Student Facing

We learned to add any 2 two-digit numbers within 100 and write equations to represent our methods.

We added tens and tens and ones and ones.

$$37 + 26$$
$$30 + 20 = 50$$
$$7 + 6 = 13$$
$$50 + 13 = 63$$
$$37 + 26$$
$$37 + 3 + 3 = 43$$
$$43 + 20 = 63$$