# Lesson 10

Addition and Subtraction with a Ten

## Warm-up: Number Talk: A Ten and Some Ones (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for addition and subtraction equations with 10 and some more. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to solve story problems with 10 and some more.

### 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.

• $$10 + 4$$
• $$14 - 4$$
• $$5 + 10$$
• $$15 - 5$$

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “How can you use problem one to help you find the difference in problem two?” (If $$10 + 4 = 14$$, then I know that $$14 - 4 = 10$$.)
• “Did anyone approach the problem in a different way?”

## Activity 1: Story Problems With a Ten (20 minutes)

### Narrative

The purpose of this activity is to elicit methods students have for solving story problems involving addition and subtraction with teen numbers. Students are presented with story problem types that are familiar to them to allow for discussion about methods they used to find the answer. Students solve the problems in any way that makes sense to them. They may build values and add-on or take-away, or use what they have learned about the $$10 + n$$ structure of teen numbers. Students write equations; they can write many different equations to represent the problem or how they solved it. It is important that students are able to relate their equations to the story problem and explain their work (MP2, MP4).

MLR6 Three Reads. Keep books or devices closed. To launch this activity, display only the problem stem, 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 are all the things we can count in this story?” Reveal the question. After the 3rd Read: “What are different ways we can solve this problem?”

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Give students access to double 10-frames and connecting cubes or two-color counters.
• “Many people have the hobby of collecting things. Do any of you collect something?”
• Share responses.
• “What are some things that you know people collect, or that you might like to collect?” (baseball cards, marbles, rocks)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.
• “Let’s solve some story problems about collections.”

### Activity

• “Write two equations to match each of these stories.”
• 6 minutes: independent work time
• 4 minutes: partner discussion
• Monitor for a student who wrote an addition equation and one who wrote a subtraction equation for the problem about Priya.

### Student Facing

1. Kiran has a collection of 5 baseball caps.

He gets some more baseball caps for his birthday.
Now he has 15 baseball caps all together.
How many baseball caps did he get?
Show your thinking using drawings, numbers, or words.

Equation: ________________________________

Equation: ________________________________

2. Priya has a comic book collection.
She gets 3 new comic books.
Now she has 13 comic books.
How many comic books did she have to start?
Show your thinking using drawings, numbers, or words.

Equation: ________________________________

Equation: ________________________________

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Invite previously identified students to share their equations for Priya’s problem.
• If no student writes a subtraction equation, display $$13 - 3 =\boxed{\phantom{10}}$$.
• “How do the equations match the story problem? How are they related to each other?” (They show that the total number of comic books is 13 and that 3 is one part and 10 is the other part. They all show that 10 is the missing number. The subtraction equations takes 3 away from the 13 to find the other part. The addition equation adds 3 to some number to get 13.)
• “Which equation makes more sense to you? Why?” (Addition, because I know that to get from 3 to 13, I have to add 10. Subtraction, because I know what number to start with and how many to take away. I don't know what numbers to use in the addition equation.)

## Activity 2: Related Equations (15 minutes)

### Narrative

The purpose of this activity is for students to discuss the relationship between addition and subtraction equations involving teen numbers. Students find the value that makes the addition and subtraction equations true with the unknown in all positions. Students may choose to use objects to represent the problems and find the value that makes the equation true (MP5).

Action and Expression: Internalize Executive Functions. Invite students to plan a method, including the tools they will use, for finding the missing value. If time allows, invite students to share their plan with a partner before they begin.
Supports accessibility for: Organization, Attention

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Give students access to double 10-frames and connecting cubes or two-color counters.
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.

### Activity

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

### Student Facing

Mai is finding the missing number in $$16 - 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$.

She says, “I can use what I know about 10 and some ones to help.”

What does Mai mean?

Find the number that makes each equation true.
Show your thinking using drawings, numbers, or words.

1. $$15 - 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
2. $$\boxed{\phantom{\frac{aaai}{aaai}}} = 13 - 3$$
3. $$8 = 18 -\boxed{\phantom{\frac{aaai}{aaai}}}$$
4. $$2 + \boxed{\phantom{\frac{aaai}{aaai}}} = 12$$

### Student Response

For access, consult one of our IM Certified Partners.

If students take away using drawings for each equation, consider asking:

• “How did you find the missing value?”
• “How could the double 10-frame help you find the missing value?”

### Activity Synthesis

• Share solutions for each problem.
• “How are $$\boxed{\phantom3} = 13 - 3$$ and $$2 + \boxed{\phantom 3} = 12$$ related?” (One is an addition problem and one is a subtraction problem, but you can use addition or subtraction for either one. For $$\boxed{\phantom 3} = 13 - 3$$ you can subtract or change it to $$3+ \boxed{\phantom3} = 13$$. For $$2 + \boxed{\phantom3} = 12$$ you can add or change it to $$12 - 2=\boxed{\phantom3}$$. Both have a missing value of 10.)

## Lesson Synthesis

### Lesson Synthesis

Display 17 on a double 10-frame.

Display $$\boxed{\phantom{17}} - 10 = 7$$. “Today we solved problems and completed equations with 10 and some more. We saw that sometimes we can use addition to help us with subtraction. How can using addition help you find the number that makes this equation true?” (I know that $$7 + 10 = 17$$ so the missing number is 17.)

Display $$10 + \boxed{\phantom{3}} = 17$$. “How can using subtraction help you find the number that makes this equation true?” (I see on the 10-frame that there’s 10 and 7 more. If I take away the 10, there’s 7 left.)

## Cool-down: What's Missing? (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.