Lesson 6
Compare Methods for Subtraction
Warmup: True or False: How many Tens? How many Ones? (10 minutes)
Narrative
Launch
 Display one statement.
 “Give me a signal when you know whether the statement is true and can explain how you know.”
 1 minute: quiet think time
Activity
 Share and record answers and strategy.
 Repeat with each statement.
Student Facing
Decide if each statement is true or false. Be prepared to explain your reasoning.
 \(64 = 60 + 4\)
 \(64 = 50 + 14\)
 \(64 = 30 + 24\)
Student Response
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Activity Synthesis
 “What pattern did you notice?” (When the first addend went down by 10, the second addend went up by ten, so the sum stayed the same.)
 Consider asking, “How could the second problem help you think about the third one?” (30 is 20 less than 50, but 24 is only 10 more than 14 so the sum had to be different from the second problem.)
Activity 1: Different Ways to Decompose (15 minutes)
Narrative
The purpose of this activity is for students to interpret and compare representations that show decomposing a ten to subtract by place. One student shows decomposing a ten by crossing off a ten and drawing 10 ones. The other representation shows a student who begins their drawing with a ten decomposed into 10 ones. Students compare and make connections between the representations and a set of equations that also shows how to find the value of the difference (MP3).
This activity uses MLR2 Collect and Display. Advances: conversing, reading, writing
Supports accessibility for: Attention, Memory
Required Materials
Materials to Gather
Launch
 Groups of 2
 Give students access to baseten blocks.
Activity
 “Diego and Elena drew baseten diagrams to find the value of \(829\).”
 “Think about what is the same or different on your own. Then, discuss your ideas with your partner.”
 1 minute: quiet think time
 2–3 minutes: partner discussion
MLR2 Collect and Display
 Circulate, listen for, and collect the language students use to describe the diagrams and how the ten is decomposed. Listen for: break apart a ten, decompose, tens, need more ones.
 Record students’ words and phrases on a visual display and update it throughout the lesson.
 Share responses. Consider asking:
 “Did Diego and Elena find the same value for \(829\)? How do you know?”
 “What is the difference between their diagrams?”
 “Tyler found the value by using equations. Diego says Tyler’s equations match his diagram. Elena says the equations match her diagram. Who do you agree with?”
 2 minutes: independent work time
 4 minutes: partner discussion
 Monitor for students who agree with Diego, Elena, or both and can explain their reasoning with connections to the diagrams.
Student Facing
Diego and Elena drew baseten diagrams to find the value of \(829\).
Diego
Elena

Compare Deigo’s work to Elena’s.
 What is the same?
 What is different?

Tyler used equations to show his thinking.
\(82  9\)
\(82 = 70 + 12\)
\(12  9 = 3\)
\(70 + 3 = 73\)Diego says Tyler’s work matches his diagram.
Elena says Tyler’s work matches her diagram.Who do you agree with? Explain.
Student Response
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Advancing Student Thinking
 “What was the value of Elena’s blocks before she started subtracting? Explain.”
 “How could you make 82 with baseten blocks if you only had 7 tens?” Allow students to share how they could represent 82 with 7 tens and 12 ones.
Activity Synthesis
 Invite previously identified students to share.
 “Diego, Elena, and Tyler saw they needed more ones before they could subtract ones from ones. They showed decomposing a ten in different ways.”
 Display the list of words and phrases recorded during the activity.
 “Here are some of the words we used to describe subtracting by place.”
 “Are there any other words or phrases that are important to include on our display?”
 As students share responses, update the display, by adding (or replacing) language, diagrams, or annotations.
 Remind students to borrow language from the display as needed.
Activity 2: Introduce Target Numbers, Subtract Tens or Ones (20 minutes)
Narrative
Required Materials
Materials to Gather
Materials to Copy
 Target Numbers Stage 4 Recording Sheet
Required Preparation
 Remove 0 and 10 from each set of cards (or prompt students to remove them) before the activity.
Launch
 Groups of 2
 Give each student a copy of the recording sheet and a set of the number cards.
 “We are going to learn a new way to play Target Numbers. You and your partner will start with 99 and race to see who can get closest to 0.”
 “First, represent 99 with baseten blocks. When it’s your turn, draw a card. Decide whether you want to subtract that many tens or that many ones. Then show the subtraction with your blocks and write an equation on your recording sheet.”
 “Take turns drawing a card and subtracting until you play 6 rounds or one player reaches 0. After 6 rounds, whoever is closest to 0 is the winner.”
 As needed, demonstrate a round with a student volunteer.
Activity
 10–15 minutes: partner work
 Monitor for examples when students draw cards that require them to decompose a ten to subtract by place.
Activity Synthesis
 Invite 2–3 previously identified students to share how they decomposed a ten to subtract by place.
 As needed, record the student examples using baseten diagrams.
 Keep the diagrams displayed.
 “What is the same and what is different about how the ten was decomposed in each of these examples?”
 Consider asking:
 “Why did you choose to subtract _____ ones instead of _____ tens?”
 “Why did you have to decompose a ten?”
 “What equation did you write to show your subtraction?”
 “How can you tell by looking at the equation that you would need to decompose a ten?”
Lesson Synthesis
Lesson Synthesis
“Today we compared methods for subtracting and representations for showing our thinking when subtracting.”
“What are different methods you could use to find the value of \(507\)?” (I could use baseten blocks to show 4 tens and 10 ones and take away 7 ones. I could draw 5 tens and then decompose 1 ten.)
Cooldown: Mai’s Method (5 minutes)
CoolDown
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