# Lesson 16

Add Three Numbers

## Warm-up: Number Talk: Related Expressions (10 minutes)

### Narrative

### 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 strategy.
- Keep expressions and work displayed.
- Repeat with each expression.

### Student Facing

Find the value of each expression mentally.

- \(7 + 10\)
- \(7 + 2 + 8\)
- \(10 + 9\)
- \(4 + 9 + 6\)

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

- “Why did some of the expressions have the same value?”

## Activity 1: Match Expressions (15 minutes)

### Narrative

*MLR2 Collect and Display.*Circulate, listen for, and collect the language students use as they work with partners. On a visible display, record words and phrases such as: equivalent, expression, the same, different, sum. Invite students to borrow language from the display as needed, and update it throughout the lesson.

*Advances: Conversing, Speaking*

*Representation: Develop Language and Symbols.*Synthesis: Make connections between representations visible. Ask students to identify the correspondences between concrete representations (10-frames or connecting cubes) and expressions.

*Supports accessibility for: Conceptual Processing, Visual-Spatial Processing*

### Required Materials

Materials to Gather

### Launch

- Groups of 2
- Give students access to double 10-frames and connecting cubes or two-color counters.

### Activity

- Read the task statement.
- 8 minutes: partner work time

### Student Facing

Draw a line to match expressions with the same value.

expressions with 3 numbers

\(10 + \boxed{\phantom{3}}\) expression

- \(4 + 6 + 8\)
- \(3 + 6 + 7\)
- \(9 + 1 + 1\)
- \(8 + 4 + 2\)
- \(5 + 5 + 9\)
- \(7 + 3 + 3\)
- \(5 + 10 + 5\)
- \(4 + 7 + 6\)
- \(9 + 5 + 1\)
- \(1+ 10 + 1\)

\(10 + 1\)

\(10 + 2\)

\(10 + 3\)

\(10 + 4\)

\(10 + 5\)

\(10 + 6\)

\(10 + 7\)

\(10 + 8\)

\(10 + 9\)

\(10 + 10\)

If you have time: Write another expression with 3 numbers. 2 of the numbers should make 10.

Ask your partner to think of the matching \(10 + \boxed{\phantom{\frac{aaai}{aaai}}}\) expression.

### Student Response

For access, consult one of our IM Certified Partners.

### Advancing Student Thinking

If students find the value of each three addend expression, rather than making a ten first, consider asking:

- “Can you explain how you know these expressions match?”
- “How can we use the numbers in this expression to make 10? After we make 10, what number is left to add? What expression does that match?”

### Activity Synthesis

- “How did you know which expressions have the same value?” (I looked for ways to make 10 and the amount left to add.)
- “What patterns did you notice?” (They are all teen numbers. They are all 10 + facts.)

## Activity 2: Is the Equation True? (10 minutes)

### Narrative

The purpose of this activity is for students to determine whether equations with an expression on each side of the equal sign are true. Each equation has an expression with three addends on one side and a 10 +n expression on the other. Students do not need to find the value of each expression in order to determine if the equation is true, but some students may do so. In this activity, students have an opportunity to look for and make use of structure (MP7) because they apply the associative property and \(10 + n\) pattern to determine whether equations are true.

### Required Materials

Materials to Gather

### Launch

- Groups of 2
- Give students access to double 10-frames and connecting cubes or two-color counters.

### Activity

- Read the task statement.
- 4 minutes: independent work time
- 3 minutes: partner discussion
- Monitor for a student who uses 10-frames and counters or drawings to show \(3 + 7 + 8\) as \(10 + 8\) and a student who uses reasoning that \(3 + 7 = 10\) and \(10 + 8 = 8 + 10\).

### Student Facing

Determine whether each equation is true or false.

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

- \(7 + 3 + 4 = 10 + 4\)
- \(6 + 5 + 4 = 15 + 10\)
- \(9 + 10 = 9 + 10 + 1\)
- \(3 + 7 + 8 = 8 + 10\)
- \(5 + 10 + 5 = 10 + 10\)

If you have time:

- Make any false equations true.
- Write 1 equation that is true and 1 that is false.

Switch with your partner.

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

- Invite previously identified students to share.
- “Does their reasoning prove whether the equation is true? Why or why not?” (Yes, we can see that it is \(10 + 8\) on the 10-frame. Yes, we see that \(3 + 7\) is 10 and then there are 8 left. That is the same as \(8 + 10\).)

## Activity 3: Write Expressions (10 minutes)

### Narrative

The purpose of this activity is for students to write a \(10 + n\) expression that is equal to a given expression. Each expression given has three addends, two of which make a ten.

### Required Materials

Materials to Gather

### Launch

- Groups of 2
- Give students access to double 10-frames and connecting cubes or two-color counters.
- “Now you will write a \(10 + n\) expression with the same value as each of the given expressions.”

### Activity

- 5 minutes: independent work time
- 3 minutes: partner discussion

### Student Facing

Write a \(10 + \boxed{\phantom{3}}\) expression that has the same value as each expression.

- \(5 + 7 + 5\)
- \(3 + 7 + 6\)
- \(1 + 9 + 9\)
- \(4 + 8 + 6\)
- \(8 + 10 + 2\)

If you have time, write as many expressions as you can with 3 numbers that are equal to \(10 + 5\).

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

- Display each \(10 + n\) expression.
- “In order to make adding three numbers easier, we can rewrite each expression as a \(10 + \boxed{\phantom{3}}\) expression.”
- Invite students to say the value of each \(10 + n\) expression together.

## Lesson Synthesis

### Lesson Synthesis

Give students access to double 10-frames and connecting cubes or two-color counters.

Display \(2 + 6 + 8 = 7 + 3 + 6\).

“Today we worked with expression with three numbers and expressions with 10. Is this equation true or false? How do you know?” (True. \(2 + 8 = 10\), \(10 + 6 = 16\). \(7 + 3 = 10\). \(10 + 6 = 16\).)

If needed, “Did anyone determine whether it is true or false without adding all the numbers?” (Yes. Both sides have a 6, so I looked to see if the other numbers made 10. \(2 + 8 = 10\) and \(7 + 3 = 10\), so both sides of the equation are equal to \(10 + 6\).)

## Cool-down: Add Them Up (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.