# Lesson 15

Decompose a Ten and a Hundred to Subtract

## Warm-up: Choral Count: Hundreds and Tens (10 minutes)

### Narrative

The purpose of this Choral Count is for students to practice counting back by 10 and notice patterns in the count. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to decompose hundreds.

### Launch

• “Count back by 10, starting at 590.”
• Record as students count.
• Stop counting and recording at 390.

### Activity

• “What patterns do you see?”
• 1–2 minutes: quiet think time
• Record responses.

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “What comes after 390 if we keep counting back by 10? What comes after 300?”

## Activity 1: Elena’s Thinking (15 minutes)

### Narrative

The purpose of this activity is for students to use their knowledge of base-ten diagrams and place value to make sense of a written method. They describe how numbers, words, and equations can be used to represent the steps they have used with other representations (MP2). Students will explore other ways to use equations, including the standard algorithm, in future grades. Although some grade 2 students may begin to use recording methods like the standard algorithm, it is important to encourage students use the methods that make the most sense to them.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Display Elena’s work.
• “Take a minute to make sense of Elena’s subtraction.”
• 1–2 minutes: quiet think time
• “Discuss Elena’s work with your partner.”
• 1–2 minutes: partner discussion
• Share and record responses. Highlight responses that describe the numbers Elena is subtracting and how Elena shows decomposing units.

### Activity

• “Elena is finding the value of $$726-558$$. Use base-ten blocks or a base-ten diagram to show Elena’s steps. Then finish Elena’s work. If you have time, work together to show a different way Elena could use numbers or equations to show her steps.”
• 7 minutes: partner work time
• Monitor for student examples that record in a way similar to Elena, but use numbers to show the value of each place.

### Student Facing

Elena’s thinking:

Step 1:

Step 2:

Step 3:

1. Use base-ten blocks or a base-ten diagram to show Elena’s steps.

2. Finish Elena’s work to find the value of $$726-558$$.
3. What is another way you could use numbers or equations to show subtracting by place to find the value of $$726-558$$?

### Student Response

For access, consult one of our IM Certified Partners.

If students rely on one way to show subtracting by place with numbers or equations, consider asking:
• “How did Elena represent the value of each digit in 726 and 558?”
• “What is another way you could represent the value of the digits and show subtracting by place?”

### Activity Synthesis

• Display a student representation of Elena’s steps with a base-ten diagram and 1–2 other representations that use numbers and equations.
• “How are these representations the same? How are they different?” (They all show decomposing a hundred and a ten before you subtract. They all show subtracting hundreds from hundreds, tens from tens, and ones from ones. They use different ways to represent each unit. One uses base-ten diagrams, one uses numbers and words, and one just represents the value of each place.)

## Activity 2: Walk About and Subtract (20 minutes)

### Narrative

The purpose of this activity is for students to practice subtracting within 1,000. Each student starts with a card with a three-digit number on it. Students walk around the room and find a student with a different number. They find the difference between their numbers and write an equation to represent the difference. As time allows, students find a new partners. The numbers on the cards were chosen so any pair of numbers would require decomposing a hundred and a ten when subtracting by place. However, in addition to monitoring for ways students try written methods for subtracting by place, monitor for the ways students use what they know about the relationship between the numbers to choose a method. For example, if students are finding the value of $$733-198$$, they may choose to add on 2 to 198 and count on by place instead of decomposing a hundred and a ten.

MLR8 Discussion Supports. Invite students to take turns sharing how they subtracted and how they showed their thinking. Ask students to restate what they heard using precise mathematical language and their own words. Display the sentence frame: “I heard you say . . .” Original speakers can agree or clarify for their partner.
Engagement: Provide Access by Recruiting Interest. Invite students to generate a list of contexts that represent subtraction. Choose one of the contexts that connect to their personal backgrounds and interests to use when subtracting. Refer back to the context while students work.
Supports accessibility for: Attention, Conceptual Processing

### Required Materials

Materials to Gather

Materials to Copy

• Walk About and Subtract Cards

### Required Preparation

• Create a set of cards from the blackline master so that each student will receive 1 card.

### Launch

• Groups of 2
• Give each student a card.

### Activity

• “We are going to create our own subtraction expressions and find their values. You will walk around and find someone who has a different number than you. Create an expression and find the difference between your numbers. Show your thinking.”
• “Trade cards and find a new partner.”
• 12 minutes: partner work time
• Monitor for students who represent subtracting by place with:
• a base-ten diagram
• numbers, words, or equations

### Student Facing

• Find someone with a different number than you.
• Find the difference between your numbers.

• Trade cards and find a new partner.
1. Partner 1:
2. Partner 2:
3. Partner 3:

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Invite previously identified students to describe the steps they used to find the difference for one of their expressions.
• “What questions do you have for _____ about their steps or their representation?”
• “How did you use a similar representation? How were your steps the same? How were they different?”

## Lesson Synthesis

### Lesson Synthesis

Keep student work samples that were shared in Activity 2 synthesis displayed.

“How are these representations the same? How are they different?” (They show different expressions. Some use base-ten diagrams and some only use numbers and equations. They each show subtracting hundreds from hundreds, tens from tens, and ones from ones. They each show decomposing units.)

“Which methods did you try today? Which methods do you prefer?”

## Cool-down: Find the Error (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.