# Lesson 4

Add and Subtract Three-digit Numbers in Different Ways

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

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for counting back by place as a strategy for subtraction. These understandings help students develop fluency with subtracting multiples of 10 and 100 from three-digit numbers. As students share, represent their thinking on an open number line.

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

### Student Facing

Find the value of each expression mentally.

• $$586 - 100$$
• $$486 - 20$$
• $$457 - 200$$
• $$257 - 30$$

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Display $$457 - 230$$.
• “How can the last 2 expressions help us think about this problem?” (Even though it is 230 being taken away, we can still subtract the hundreds and then the tens.)
• “Today we will see how we can use counting methods to help us subtract bigger numbers.”

## Activity 1: Zero Tens and Zero Ones (20 minutes)

### Narrative

The purpose of this activity is for students to use the relationship between addition and subtraction to make sense of different counting methods for subtracting three-digit numbers. Students analyze 2 different methods for a given problem where a number is being subtracted from a multiple of 100. They consider how thinking about a subtraction expression as an unknown addend equation can be helpful and discuss how counting on can be a useful method for subtraction. The number line can support this method, so they have the opportunity to make connections between counting on a number line and adding on or subtracting by place using equations.

Action and Expression: Develop Expression and Communication. Identify connections between the strategies that Mai and Lin use alongside a number line representation. The strategies result in the same outcomes but use differing approaches. The number line is less abstract. Add the context of an animal jumping (frog, rabbit, grasshopper, etc.) to enhance the conceptual model as well.
Supports accessibility for: Conceptual Processing, Organization

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• “Mai and Lin were asked to find the value of $$500 - 387$$. Here is their work.”
• Display the images of Mai and Lin’s work.
• “What is the same and different about the methods they used to find the difference?” (They both represented it with equations, but Mai also used a number line. Mai showed it as addition with a missing addend. They both broke apart the second number. They both got 113 as the answer.)
• 30 seconds: quiet think time
• “Discuss with a partner.”
• 2 minutes: partner discussion
• If it doesn’t come up, ask, “Where do you see the answer in Mai’s representation?” (How far she jumped shows the difference.)
• “Why do you think Lin started with $$387 = 300 + 80 + 7$$?” (That way she could see each part that she needed to take away.)

### Activity

• “Now try Mai’s way and Lin’s way.”
• 10 minutes: independent work time

### Student Facing

Mai and Lin were asked to find the value of $$500 - 387$$.

Here is their work.

Mai's Work

$$387 + {?} = 500$$

$$387 + 100 = 487$$

$$487 + 10 = 497$$

$$497 + 3 = 500$$

$$100 + 10 + 3 = 113$$

Lin's Work

$$387 = 300 + 80 + 7$$

$$500 - 300 = 200$$

$$200 - 80 = 120$$

$$120 - 7 = 113$$

Find the value of each expression.

1. Try Mai’s way to find the value of $$600 - 476$$.

2. Try Lin’s way to find the value of $$400 - 134$$.

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “Which method do you prefer? Explain.” (I prefer counting on because you count until you get to the number. When you count on, you can do it in parts so you can make each part something that is easy for you and get to a ten. The number line helped me. I prefer the equations because it helps me see the parts as they are taken away.)

## Activity 2: Add or Subtract with Expanded Form (15 minutes)

### Narrative

The purpose of this activity is for students to use their understanding of expanded form, place value, and properties of operations to reason about adding and subtracting by place (MP7). Students analyze different methods and representations that show adding hundreds and hundreds, tens and tens, and ones and ones. Students notice that hundreds, tens, and ones can be added in any order. In the next section, the focus will be on strategies based on place value and will include composing and decomposing tens and hundreds. In the synthesis, there are discussions that honor all methods while connecting each strategy to place value in preparation for the work of the upcoming lessons.

MLR7 Compare and Connect. Synthesis: After all strategies have been presented, lead a discussion comparing, contrasting, and connecting the different approaches. Ask, “Did anyone solve the problem the same way, but would explain it differently?”

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• “We have used base-ten blocks, diagrams, and equations to add and subtract numbers using what we know about place value.”
• “Andre and Diego showed their thinking in different ways. What is the same and what is different about their work?” (They both grouped the same places together. Andre used a different equation to show adding each place. Diego put each number in expanded form and put the places on top of one another.)
• 1 minute: quiet think time
• 3 minutes: partner discussion
• Record responses.
• “Where do you see each number in their work?” (Diego shows the place value in expanded form, but Andre adds 1 place at a time. In Andre’s I see the numbers up and down, but in Diego’s I see the numbers across.)
• 30 seconds: quiet think time
• Share responses
• “Try Andre’s way and Diego’s way.”
• 8 minutes: independent work time
• “Compare with a partner”
• 2 minutes: partner discussion
• Monitor for students who use Andre’s way, but add by place value in different orders.

### Student Facing

1. Andre and Diego showed their thinking with equations to find the value of $$427 + 351$$.

Andre's Work

Diego's Work

What is the same or different about their work?

2. Try Andre’s way to find the value of $$725 + 243$$.

3. Try Diego’s way to find the value of $$863 - 432$$.

4. Choose your own way to find the value of $$163 + 326$$. Show your thinking.

5. Choose your own way to find the value of $$692 - 571$$. Show your thinking.

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Invite 12 students to share how they used each way.
• “Which way did you prefer? Why?” (I prefer Diego’s way because I can see how things are grouped and I write fewer equations OR I prefer Andre’s way because it helps me remember to add ones and ones, tens and tens, and hundreds and hundreds.)
• “How was it the same or different when finding the sum versus finding the difference?” (It worked either way. I liked Diego’s way of finding the difference because it was lined up by place, so the answer is across the bottom when you are done.)

## Lesson Synthesis

### Lesson Synthesis

“Today you shared different ways to represent adding and subtracting numbers. You also talked about how thinking about place value and expanded form can help you find the value of expressions.”

“What was most helpful to you when finding the difference?”

“What is something that you learned from comparing with a partner when adding or subtracting three-digit numbers by place value?”

## Cool-down: Find the Sum, Find the Difference (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.

## Student Section Summary

### Student Facing

In this section of the unit, we compared three-digit numbers and looked at how addition can be used to find the difference, especially when numbers are close together. We added and subtracted by counting on or back by place and used expanded form to think about adding or subtracting using place value based strategies.