# Lesson 1

Compare, Count on, and Count Back

## Warm-up: Number Talk: Count Back (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for counting back as a strategy for finding the value of differences. These understandings help students develop fluency and will be helpful later in this lesson when students subtract within 1,000. As students share their thinking, represent it on an open number line to help them make connections.

### 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 strategies on an open number line.
• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Find the value of each expression mentally.

• $$586 - 6$$
• $$586 - 8$$
• $$434 - 5$$
• $$352 - 4$$

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “Even though there were three-digit numbers, I noticed that some of you used the same strategies you’ve used before. Why does that work?” (If you are subtracting a small amount, you can count back by ones to find the answer.)
• “Today we are going to look at other ways we can use strategies we've used for adding and subtracting two-digit numbers to add and subtract with three-digit numbers.”

## Activity 1: Notice the Difference (20 minutes)

### Narrative

The purpose of this activity is for students to compare three-digit numbers and find the value of their difference. Students used the number line to compare three-digit numbers in an earlier unit. They build on this understanding as they find the difference between 2 three-digit numbers that are within 10 of one another. Students notice that when the numbers in a subtraction expression are close together, they can count on or count back to find the value of the difference (MP7, MP8).

Engagement: Provide Access by Recruiting Interest. Optimize meaning and value. Invite students to represent the jumps/movement on the number line using an animal (frog, rabbit, grasshopper, etc.). Focus on the minimal jumping the animal does when the numbers are close on the number line.
Supports accessibility for: Conceptual Processing, Attention

• Groups of 2

### Activity

• “Tyler and Elena were asked to find $$81 - 79$$. This is their work.”
• “What do you notice? What do you wonder?” (The numbers are really close on the number line. Tyler drew out all the tens and ones for 81 and subtracted almost all the tens and ones. Why did Elena put a point on 79 and count up instead of subtracting 79?)
• “You have learned in an earlier lesson that you can subtract by taking an amount away. You also learned you can count on or count back from one number to the other to find the difference between the 2 numbers.”
• “This works with three-digit numbers too.”
• “Do the next few problems on your own, and then compare your thinking with a partner.”
• 8 minutes: independent work time
• 4 minutes: partner discussion
• Monitor for students who count on or count back.

### Student Facing

Tyler and Elena were asked to find the value of $$81 - 79$$.
Their work is shown.

Tyler

\begin{align} 81-70 &=11 \\ 11-9&= 2 \\ \end{align}

Elena

$$81 - 79 = 2$$

What do you notice? What do you wonder?

1. Locate and label 203 and 198 on the number line.

Compare using >, <, or =.

$$\underline{\hspace{1.5cm}} \quad\boxed{\phantom{\huge00}} \quad \underline{\hspace{1.5cm}}$$

Find the value of $$203 - 198$$. Show your thinking.

2. Locate and label 673 and 680 on the number line.

Compare using >, <, or =.

$$\underline{\hspace{1.5cm}} \quad\boxed{\phantom{\huge00}} \quad \underline{\hspace{1.5cm}}$$

Find the value of $$680 - 673$$. Show your thinking.

3. Locate and label 501 and 499 on the number line.

Find the value of $$501 - 499$$. Show your thinking.

4. Find the value of $$400 - 396$$. Show your thinking.

### Student Response

For access, consult one of our IM Certified Partners.

If students find the difference by subtracting the second number from the first using base-ten blocks or base-ten diagrams, consider asking:
• “What did you notice when you located the numbers on the number line? How could that help you think about finding the difference without a number line?”
• “How could you use one of the strategies we shared in the warm-up to find the difference?”

### Activity Synthesis

• Invite previously identified students to share how they found the value of $$400 - 396$$.
• As time permits, invite students to share their comparisons and how they found the value of each difference.
• “What did you notice about the numbers when you located them on the number line?” (They were close together. It was easy to see a way to just count from one number to the other.)

## Activity 2: What’s the Big Difference? (15 minutes)

### Narrative

The purpose of this activity is for students to use what they know about counting within 1,000 to make sense of number lines that show counting on or counting back by 10 or 100. This work helps build fluency with counting within 1,000 and connects to an upcoming lesson where students add and subtract multiples of 10 or 100 using equations.

MLR8 Discussion Supports. Invite students to begin partner interactions by repeating the question, “What pattern do you notice?” This gives both students an opportunity to produce language.

### Launch

• Groups of 2
• Display the number line with jumps of 100.
• “On this number line there are 5 tick marks, but only 3 are labeled. What are the missing numbers and how do you know?” (534 and 634 because the jumps are the same length and they must be jumps of 100. The hundreds place is increasing by 1, but the other places are not changing.)
• 30 seconds: quiet think time
• 30 seconds: partner discussion
• Share and record responses.
• “You recognized that the length between each tick mark must represent 100. The tick marks and arrows show counting on by 100 on the number line.”

### Activity

• “For each of the problems, use what you know about counting, representing numbers on the number line, and place value to find the missing numbers.”
• 10 minutes: partner work time
• Monitor for a student to share their reasoning for _____, _____, 332, 342, 352

### Student Facing

1. Fill in the missing numbers.

Does this number line show counting on by 10 or counting on by 100?

2. Fill in the missing numbers.

Does this number line show counting on by 10 or counting on by 100?

3. Fill in the missing numbers.

Does this number line show counting on by 10 or counting on by 100?

4. Fill in the missing numbers to show counting on by 10.

739, 749, __________, 769, __________

5. Explain how you can tell your numbers show counting on by 10 and not counting on by 100.

### Student Response

For access, consult one of our IM Certified Partners.

If students find the missing numbers by counting by 1 instead of using patterns increasing by 10 or 100, consider asking:
• “What digit is changing? Is it going up or down?”

### Activity Synthesis

• Invite a student to share their reasoning for _____, _____, 332, 342, 352.
• “How did you figure out the starting number?” (I saw that it was going up by 10, so I knew I had to count back by 10 to find the starting numbers.)
• Record responses with an open number line and equations.

## Lesson Synthesis

### Lesson Synthesis

“Today you compared three-digit numbers and found the difference between them.”

“You also made sense of counting on and counting back by 10 or 100 on the number line.”

“How can this help you think about $$234 + 200$$?” (It is like 2 jumps of 100 on the number line, so it would be 434.)

## Cool-down: Subtract and Count (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.