# Lesson 6

Compare Methods for Subtraction

## Warm-up: True or False: How many Tens? How many Ones? (10 minutes)

### Narrative

The purpose of this True or False is to elicit the ways students notice and explain why the value of an expression doesn’t change when the total number of tens and ones stays the same (MP8). Student reasoning here helps deepen their understanding of the base-ten structure of numbers and the properties of operations (MP7). It will also be helpful later when students decompose a ten when subtracting by place.

### 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.

• $$64 = 60 + 4$$
• $$64 = 50 + 14$$
• $$64 = 30 + 24$$

### 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).

Representation: Internalize Comprehension. Invite students to identify which details were most useful from each strategy to solve the problem. Display the sentence frame, “The next time I have a subtraction task, I will look for . . . .“ Encourage decomposition, drawing pictures or using manipulatives as the main strategies.
Supports accessibility for: Attention, Memory

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• “Diego and Elena drew base-ten diagrams to find the value of $$82-9$$.”
• 1 minute: quiet think time
• 23 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.
• “Did Diego and Elena find the same value for $$82-9$$? 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 base-ten diagrams to find the value of $$82-9$$.

Diego

Elena

1. Compare Deigo’s work to Elena’s.

1. What is the same?
2. What is different?
2. 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

Some students may only recognize 82 as 8 tens and 2 ones. Consider asking:
• “What was the value of Elena’s blocks before she started subtracting? Explain.”
• “How could you make 82 with base-ten 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

The purpose of this activity is for students to subtract numbers within 100 with and without decomposing a ten. Students learn stage 4 of the Target Numbers center, which was introduced in grade 1. For the introduction of this stage, have students start at 99 and subtract tens or ones to get as close to 0 as possible. Students start by representing 99 with base-ten blocks and then take turns flipping a number card and choosing whether to subtract that number of tens or ones and write an equation. The value of the difference becomes the first number in the next equation. The player who gets closest to 0 in 6 rounds, without going below 0, is the winner.

### 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 base-ten 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

• 1015 minutes: partner work
• Monitor for examples when students draw cards that require them to decompose a ten to subtract by place.

### Activity Synthesis

• Invite 23 previously identified students to share how they decomposed a ten to subtract by place.
• As needed, record the student examples using base-ten diagrams.
• Keep the diagrams displayed.
• “What is the same and what is different about how the ten was decomposed in each of these examples?”
• “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 $$50-7$$?” (I could use base-ten blocks to show 4 tens and 10 ones and take away 7 ones. I could draw 5 tens and then decompose 1 ten.)