Lesson 3
Count on or Count Back to Subtract
Warmup: Number Talk: Tens and Hundreds (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 students’ thinking on an open number line and with equations.
 Keep expressions and work displayed.
 Repeat with each expression.
Student Facing
Find the value of each expression mentally.
 \(120 + 20\)
 \(120 + 200\)
 \(124 + 30\)
 \(124 + 300\)
Student Response
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Activity Synthesis
 “What patterns did you notice with these expressions?” (We added numbers that changed the tens place and numbers that changed the hundreds place. Only the number in the tens place or hundreds place changed depending on the number.)
Activity 1: Jump Back, Back, Back (20 minutes)
Narrative
Required Materials
Materials to Gather
Launch
 Groups of 2
 Give students access to baseten blocks.
 Display the images for Jada's work and Andre's work.
 “Jada and Andre both found the value of \(375  24\), but thought about it a little differently.”
 “Take a minute to look at their work. What do you notice? What do you wonder?”
 1–2 minutes: quiet think time
 2 minutes: partner discussion
 Share responses.
 As needed:
 “What did you notice about the representations?” (Jada used a baseten diagram and Andre used a number line and equations. They showed subtraction with jumps and by crossing out.)
 “Where in her representation can you see Jada subtracting 4 ones?” (She subtracts 4 by crossing out 4 ones.)
 “Where in his representation can you see Andre subtracting 4 ones?” (He jumped 20 and then 4. So his second jump shows subtracting 4.)
 “We have been using baseten blocks and baseten diagrams to find differences.”
 “When we use these representations, we subtract by place, taking ones from ones and tens from tens.”
 “Another way we can find the difference is by counting back. We can use what we know about place value to count back in parts to make it easier.”
Activity
 “Now, try using Andre’s way to find the value of \(189  73\). Then, find the value of \(647  46\) your own way.”
 8 minutes: independent work time
 “Compare your work with a partner.”
 2 minutes: partner discussion
 Monitor for students who:
 represent their thinking using baseten diagrams
 represent their thinking using a number line
 represent their thinking using equations
Student Facing
Jada and Andre found the value of \(375  24\).
Here is their work.
Jada's Work
\(375  24 = 351\)
Andre's Work
\(375  20 = 355\\ 355  4 = 351\\ 375  24 = 351\)
What do you notice? What do you wonder?

Try Andre’s way to find the value of \(189  73\).
Show your thinking. Use a number line if it helps.

Find the value of \(647  46\) in your own way.
Show your thinking. Use a number line if it helps.
Student Response
For access, consult one of our IM Certified Partners.
Advancing Student Thinking
If students use baseten diagrams without making the connection to counting on the number line, show jumps of 10 instead of a multiple of 10. For example, show 70 as 7 jumps of 10. Consider asking:
 “Where do you see the 7 tens on this number line representation?”
 “How does this connect to your baseten representation?”
Activity Synthesis
 Invite previously identified students to share for each expression.
 Consider sharing work from students who use baseten diagrams and students who use number lines or equations to make connections and show reasoning about place value.
 “What is the same and what is different between _____’s representation and _____’s representation?”
 Highlight connections based on place value across representations.
Activity 2: Who Spilled Paint? (15 minutes)
Narrative
The purpose of this activity is for students to analyze equations to determine the unknown value. Students use their understanding of place value and counting within 1,000 to find the value that makes each equation true. Students are given equations with an unknown addend and a sum that is a multiple of 100 or equations with a number that is subtracted from a multiple of 100. They use any method that works for them to find the numbers that make each equation true. Monitor for ways students use what they know about sums of 10 and 100 and counting on or back by place. They may also use an open number line or baseten diagrams as needed to make sense of each equation or show their thinking. If they do use baseten diagrams, look for ways they consider composing or decomposing units. All students will make sense of this method in upcoming lessons.
Advances: Speaking, Conversing, Representing
Supports accessibility for: Attention, Organization, Language
Launch
 Groups of 2
 Display the image for Diego’s equation.
 “Oh no! Diego spilled paint on his paper and now he can’t see all the numbers.”
 “What number do you think got smudged? How do you know?” (460 because \(540 + 60 = 600\) and \(600 + 400 = 1,\!000\))
 30 seconds: quiet think time
 1 minute: partner discussion
 Share responses.
Activity
 “Now you are going to work on a few more equations where Diego made a mess.”
 “How can sums of 10 help you think about these equations?” (\(3 + 7 = 10\) and \(30 + 70 = 100\))
 “You’ll work on your own first and then have time to share with a partner.”
 4 minutes: independent work time
 “I know you may not have finished all of the problems. That is okay.”
 “Compare with a partner and solve the rest together if you’d like.”
 6 minutes: partner work
 Monitor for students who find \(900  370 = 530\) by:
 counting on by hundreds then tens
 counting on by tens then hundreds
 counting back by hundreds then tens
 using a number line to keep track of their method
Student Facing
Oh no! Diego spilled paint on his paper and now he can’t see all the numbers. Find the number hidden by the paint.
Find the number that makes each equation true.

__________

__________

__________

__________

__________
Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis
 Invite previously identified students to share how they found the value of \(900  370\).
 Display \(370 + {?} = 900\).
 “How could this expression help us think about this problem?” (You can start at 370 and count up to 900 to find the difference.)
Lesson Synthesis
Lesson Synthesis
“Today you used the relationship between addition and subtraction to find the value of differences and numbers that make equations true.”
“Think about all of the ways you saw used to find the value of differences and unknown addends. Tell your partner about one that you feel really confident about using and why.”
Share responses.
Cooldown: Mystery Number (5 minutes)
CoolDown
For access, consult one of our IM Certified Partners.