Lesson 1
Compare, Count on, and Count Back
Warmup: Number Talk: Count Back (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 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
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Activity Synthesis
 “Even though there were threedigit 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 twodigit numbers to add and subtract with threedigit numbers.”
Activity 1: Notice the Difference (20 minutes)
Narrative
The purpose of this activity is for students to compare threedigit numbers and find the value of their difference. Students used the number line to compare threedigit numbers in an earlier unit. They build on this understanding as they find the difference between 2 threedigit 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).
Supports accessibility for: Conceptual Processing, Attention
Launch
 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 threedigit 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
\(\begin{align} 8170 &=11 \\ 119&= 2 \\ \end{align} \)
Elena
\(81  79 = 2\)
What do you notice? What do you wonder?

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.

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.

Locate and label 501 and 499 on the number line.
Find the value of \(501  499\). Show your thinking.

Find the value of \(400  396\). Show your thinking.
Student Response
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Advancing Student Thinking
 “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 warmup to find the difference?”
 “How could you think about this difference as an unknown addend equation?”
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.
Advances: Conversing
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

Fill in the missing numbers.
Does this number line show counting on by 10 or counting on by 100?

Fill in the missing numbers.
Does this number line show counting on by 10 or counting on by 100?

Fill in the missing numbers.
Does this number line show counting on by 10 or counting on by 100?

Fill in the missing numbers to show counting on by 10.
739, 749, __________, 769, __________

Explain how you can tell your numbers show counting on by 10 and not counting on by 100.
Student Response
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Advancing Student Thinking
 “What digit is changing? Is it going up or down?”
 “How can that help you figure out the count?”
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 threedigit 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.)
Cooldown: Subtract and Count (5 minutes)
CoolDown
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