# Lesson 16

Number Talk

## Warm-up: Number Talk: Division (10 minutes)

### Narrative

The purpose of this Number Talk is for students to demonstrate strategies and understandings they have for finding whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. These understandings help students develop fluency and will be helpful later in this lesson when students will develop their own number talk activity.

### Launch

• Display one problem.
• “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 problems and work displayed.
• Repeat with each problem.

### Student Facing

Find the value of each expression mentally.

• $$28\div14$$
• $$70\div14$$
• $$98\div14$$
• $$350\div14$$

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “What did the writer of this activity have to pay attention to when they designed this activity?” (The expressions need to be done mentally so they can't be too complex.)
• “Where do we see those things in how the expressions change during the Number Talk?” (The first problem helps to do the second one and the first 3 help to do the last one.)
• “Imagine this number talk continued with a fifth expression. How does $$700 \div 28$$ fit in with this number talk?” (It doubles the dividend and the divisor from the previous expression, which means the quotient is the same, 25.)

## Activity 1: Number Talk: Design 1 (15 minutes)

### Narrative

The purpose of this activity is for students to reason about strategies for finding whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Students add one expression to a partially-completed Number Talk activity. If there is time, students can facilitate their Number Talk with another group.

MLR8 Discussion Supports: Prior to solving the problems, invite students to make sense of the situations and take turns sharing their understanding with their partner. Listen for and clarify any questions about the context.
Advances: Reading, Representing
Engagement: Provide Access by Recruiting Interest. Synthesis: Optimize meaning and value. Invite students to share how they chose the last expression to complete the number talk with their favorite math teacher.
Supports accessibility for: Conceptual Processing, Language

### Launch

• Groups of 2 or 4
• “Now you will work with your group to complete a Number Talk activity. This activity has one expression missing. Decide on an expression that would complete the Number Talk and write it on the blank line.”

### Activity

• 10 minutes: small-group work time
• As students work, monitor for groups who discuss and design an expression based on some of the following:
• They keep the same divisor.
• They add the dividends, but keep the same divisor.
• They subtract the dividends and keep the same divisor.
• They make the dividend smaller to get $$15 \div 15$$ or $$3 \div 15$$.
• They use a combination of multiples, half, double, or triple the dividend and divisor to change both the dividend and divisor. For example, $$15 \div 60$$.

### Student Facing

Write an expression to complete the number talk. Be prepared to explain how you chose the last expression.

• $$30\div15$$
• $$45 \div15$$
• $$300\div15$$
• ___________

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Choose small groups to share who had different reasons for their fourth expression.
• Ask students to share their completed Number Talk and ask the class to share reasons for the last expression.
• As each group shares, continually ask others in the class if they agree or disagree and the reasons why.

## Activity 2: Number Talk: Design 2 (15 minutes)

### Narrative

The purpose of this activity is for students to reason about strategies for finding whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Students add two expressions to a partially-completed Number Talk activity. If there is time, students can facilitate their Number Talk with another group.

### Launch

• Groups of 2 or 4
• “Now you will work with your group to complete a Number Talk activity. This activity has two options that each have two expressions missing. Decide on expressions that would complete the Number Talk and write them in the blank lines.”

### Activity

• 10 minutes: small-group work time
• As students work, monitor for groups who discuss and design expressions based on some of the following:
• They adjust the dividend but keep the divisor.
• They adjust the divisor and keep the dividend.
• Use partial quotients either through addition or subtraction.
• Use multiplicative relationships such as halving and doubling and reason how that impacts the quotient.
• Use multiplicative relationships such as multiplying by 2 or 10 and dividing by 2 or 10 and reason how that impacts the quotient.

### Student Facing

Choose one of the number talks to complete. Be prepared to share your reasoning for the expressions you chose.

Option 1:

• $$220 \div 22$$
• $$66 \div 22$$
• ________________
• ________________

Option 2:

• $$260 \div 26$$
• $$260 \div 13$$
• ________________
• ________________

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Choose small groups to share that had different reasons for their expressions.
• Ask students to share their completed Number Talk and ask the class to share reasons for their expressions.
• As each group shares, continually ask others in the class if they agree or disagree and the reasons why.

## Activity 3: Number Talk: Design 3 (15 minutes)

### Narrative

The purpose of this activity is for students to reason about strategies for finding whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Students add three expressions to a partially-completed Number Talk activity. If there is time, students can facilitate their Number Talk with another group.

### Launch

• Groups of 2 or 4
• “Now you will work with your group to complete a Number Talk activity. This activity has three expressions missing. Decide on expressions that would complete the Number Talk and write them in the blank lines.”

### Activity

• 10 minutes: small-group work time
• As students work, monitor for groups who discuss and design expressions based on some of the following:
• They adjust the dividend but keep the divisor.
• They adjust the divisor and keep the dividend.
• Use partial quotients either through addition or subtraction.
• Use multiplicative relationships such as multiplying by 2 or 10 and dividing by 2 or 10 and reason how that impacts the quotient.

### Student Facing

Write expressions to complete the Number Talk. Be prepared to share your reasoning for the expressions.

• $$430 \div 43$$
• __________
• __________
• __________

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Choose small groups to share that had different reasons for their expressions.
• Ask students to share their completed Number Talk and ask the class to share reasons for their expressions.
• As each group shares, continually ask others in the class if they agree or disagree and the reasons why.

## Lesson Synthesis

### Lesson Synthesis

“What were the most important things about your expressions you had to consider as you created your Number Talk? Why were these things important?” (I needed to make sure my expressions could be evaluated mentally. I also needed to make sure my reasoning to connect the expressions was also visible to others.)

## Cool-down: Reflection (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.