# Lesson 6

Make a Ten and Make Sense of Equations

## Warm-up: Number Talk: Add Within 20 (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for making a ten when adding within 20. The numbers chosen lend themselves to making a ten to find the value of the sum. These understandings help students develop fluency and will be helpful later in this lesson when students make a ten when adding one-digit numbers and two-digit numbers.

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

### Student Facing

Find the value of each expression mentally.

• $$8 + 2$$
• $$8 + 5$$
• $$9 + 8$$
• $$7 + 6$$

### Activity Synthesis

• “How could $$8 + 2$$ help you to find the value of $$8 + 5$$?” (I can add 2 to 8 to get to 10, and then I have 3 more to add. $$10 + 3$$ is 13.)

## Activity 1: How Many to the Next Ten? (10 minutes)

### Narrative

The purpose of this activity is for students to determine the unknown addend in equations with sums that are multiples of 10. The first two problems are represented using both ten-frames and equations to encourage students to visualize the unknown addend. Students may initially find the unknown addend using fingers or math tools, then see that they can use known facts to combine the ones to make ten.

During the synthesis, the teacher records equations to show how the student decomposed the two-digit addend and used a known fact to make ten. For example, to solve $$24 + \boxed{\phantom{3}}= 30$$, the teacher records:

$$24 + \boxed{\phantom{3}} = 30$$

$$20 + 4 + \boxed{6} = 30$$

This notation and the discussion that follows can help students transition from counting on to the next ten to using the facts they know within 10 to help them add within 100. This also prepares them for the next activity where they describe making a ten using place value understanding.

Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk.
Supports accessibility for: Attention, Social-Emotional Functioning

### Launch

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.
• Display the first image in the student workbook.
• “What number makes this equation true? How do you know?” (5. I see 4 tens 5 ones and 5 more would fill up the 10-frame.)
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share responses.

### Activity

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

### Student Facing

Find the number that makes each equation true.

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

1.

$$45 + \boxed{\phantom{\frac{aaai}{aaai}}} = 50$$

2.

$$38 + \boxed{\phantom{\frac{aaai}{aaai}}} = 40$$

3. $$63 + \boxed{\phantom{\frac{aaai}{aaai}}} = 70$$
4. $$24 + \boxed{\phantom{\frac{aaai}{aaai}}} = 30$$
5. $$42 + \boxed{\phantom{\frac{aaai}{aaai}}} = 50$$
6. $$57 + \boxed{\phantom{\frac{aaai}{aaai}}} = 60$$
7. $$71 + \boxed{\phantom{\frac{aaai}{aaai}}} = 80$$
8. $$89 + \boxed{\phantom{\frac{aaai}{aaai}}} = 90$$
9. What did you notice about the unknown number in each equation?

### Activity Synthesis

• Display $$42 + \boxed{\phantom{3}} = 50$$
• Invite students to share their thinking.
• After the first student shares, record $$40 + 2 + \boxed{8} = 50$$
• “How does this equation match how they thought about the problem?” (42 can be broken apart into 40 and 2. To get to the next ten, which is 50, they can think about what can be added to 2 to get 10. $$2 + 8 = 10$$ and $$40 + 10 = 50$$.)
• If needed, ask:
• “Where is 42 in this equation?”
• “Where is 10 in this equation?”

## Activity 2: Elena and Andre Add (15 minutes)

### Narrative

The purpose of this activity is for students to add one-digit and two-digit numbers with composing a ten and deepen their understanding of place value. In this activity, students make sense of two different addition methods where an addend is decomposed to make a ten. Students then determine the next step needed to find the value of the original sum. Invite students to use different representations to make sense of these methods including connecting cubes and base-ten drawings. Completing the start of a calculation as students do here requires critically analyzing, understanding, and expressing different strategies (MP3).

Students then have an opportunity to add using one of these methods and the representations that make sense to them. Monitor for students who show composing a new unit of ten using connecting cubes or base-ten diagrams. Students use appropriate tools strategically as they choose which tools help them add (MP5). As selected students share their thinking during the activity synthesis, record their thinking as drawings and equations so that students can connect the method to the concept of making a new unit of ten from 10 ones.

For example,

$$68 + 6 = \boxed{\phantom{3}}$$

$$68 + 2 + 4 \\60+10+4= \boxed{74}$$

MLR7 Compare and Connect. Synthesis: After all representations have been presented, lead a discussion comparing, contrasting, and connecting the different representations. Ask, “How can you see Elena’s method in the drawings, numbers, and words that were shared?” and “How are the drawings, numbers, and words similar? How are they different?”

### Launch

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.
• Display $$34 + 9$$.
• “Elena and Andre found the value of $$34 + 9$$. Elena showed her first step by writing $$34 + 6 = 40$$. What do you notice about her first step?” (She only added 6. Maybe she wanted to make the next ten. She wanted to make a ten with $$4+6$$.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• “What does she need to do to finish her work?” (She needs to add 9 in all. She added 6, now she needs to add 3 more to 40.)
• 2 minutes: independent work time
• 1 minute: partner discussion
• Record student thinking as equations ($$34 + 6 + 3 = \boxed{43}$$).
• “Where do you see 9 in this equation?” ($$6 + 3$$)

### Activity

• Display and read Andre’s first step.
• “Now decide what Andre needs to do next. Then find the value of $$6 + 68$$ using any method that makes sense to you. Show your thinking with drawings, numbers or words.”
• 4 minutes: independent work time
• 3 minutes: partner work time
• Monitor for students who represent composing a ten in different ways, including with connecting cubes and with different equations.

### Student Facing

Elena and Andre found the value of $$34 + 9$$.

1. Elena started with $$34 + 6 = 40$$.
What does Elena need to do next?
Show your thinking using drawings, numbers, or words.

2. Andre started with $$9 + 1 = 10$$.
What does Andre need to do next?
Show your thinking with drawings, numbers, or words.

3. Find the value of $$6 + 68$$. Show your thinking using drawings, numbers, or words.

### Activity Synthesis

• “How are Elena and Andre’s methods the same? How are they different?” (They are the same because they both made a ten. They are different because Elena showed making a ten with the 4 ones from 34 and 6 ones from the 9. Andre made a ten with the 9 ones and one of the ones from 34.)
• Invite previously identified students to share their representations for $$6 + 68$$. Consider beginning with students who used connecting cubes to show composing a ten before students who use only equations.
• If needed, record student thinking with base-ten drawings and equations (see activity narrative for an example).
• “How does this equation match the representation?” (They drew 6 tens and 8 ones for 68 and 6 ones for the 6. They showed they combined the 8 ones with 2 ones to make a ten. That matches the part of the equation that shows $$8 + 2$$. They showed they counted 60, 70, and 4 more to get to 74. That matches where they wrote $$60 + 10 + 4 = 74$$.)

## Activity 3: Introduce Target Numbers, Add Ones (15 minutes)

### Narrative

The purpose of this activity is for students to learn a new center called Target Numbers. Students add a one-digit number to a two-digit number with composing a ten in order to get as close to 95 as possible. Students start their first equation with 55 and turn over a number card and add it to their starting number for the round. The sum becomes the first addend in the next round. The player who gets closest to 95 in 6 rounds, without going over, is the winner. Students may use any method they want to find the value of each sum, but should be encouraged to think about how they can decompose the one-digit number in order to compose a new ten. Students write an equation to represent each round. During the activity synthesis, the teacher records equations that match student thinking and encourages students to make connections between the equation and how the student found the sum.

### Required Materials

Materials to Gather

Materials to Copy

• Target Numbers Stage 1 Recording Sheet

### Launch

• Groups of 2
• Give each group a set of number cards, two recording sheets, and access to connecting cubes in towers of 10 and singles.
• “Remove the cards that show 0 or 10.”
• “We are going to learn a new center called Target Numbers. Let’s play a round together. First, mix up your number cards.”
• 30 seconds: partner work time
• “We start at 55, pick a number card, and find the sum of the numbers.”
• Demonstrate picking a card and thinking aloud as you find the sum of 55 and the number on the card, highlighting making a new ten if appropriate.
• “Check with your partner to make sure they agree on the sum. If your partner agrees, then you record an equation to represent the round.”
• Demonstrate writing the equation.
• “After you write your equation, the sum becomes your starting number for the next round, so you write it in as the first number in the next equation.”
• If needed, play another round with the class.
• “Play six rounds. The player who gets closest to 95 without going over is the winner.”

### Activity

• 10 minutes: partner work time
• Monitor for two students who find the sum in different ways.

### Activity Synthesis

• Invite previously identified students to share.
• Record student thinking using equations.

## Lesson Synthesis

### Lesson Synthesis

“Today we added two-digit and one-digit numbers and wrote equations. Choose one of your favorite equations from the game we played. Explain to a partner how you found the sum. You may use connecting cubes or drawings to help you explain your method.”

Display the sentence frame: “I heard you say . . . .”

“After your partner shares, restate what you heard. Then, ask your partner if you restated their thinking accurately.”

Repeat as time allows.