The purpose of this What Do You Know about _____? is to invite students to share what they know and how they can represent the number 354. It gives the teacher an opportunity to hear how students think about representing a three-digit number by decomposing or renaming units. This will be helpful as students decompose units to subtract within 1,000 in future activities.
“Why might you need to represent 354 in different ways?” (You might want to show the value of each digit to compare numbers. You might want to decompose to subtract.)
Activity 1
Standards Alignment
Building On
Addressing
2.NBT.B.7
Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
The purpose of this activity is for students to subtract one-digit and two-digit numbers from a three-digit number, using the approaches that make sense to them. Each difference would require students to decompose a ten to subtract by place. However, the number choices are designed to elicit a variety of approaches and invite students to extend to subtracting within 1,000 the ways of decomposing a unit they showed when subtracting within 100.
Monitor for and select students with the following approaches to share how they found the value of in the Activity Synthesis:
Count back from 354 by ones and by tens, using a number line or other written method to keep track of the count.
Count on from 48 to 354 by ones and by hundreds, using a number line or other written method to keep track of the count.
Subtract tens from tens, and ones from ones, decomposing a ten, using base-ten blocks or a base-ten diagram.
The approaches are sequenced from those that rely on counting on by place to a strategy that explicitly shows decomposing a ten when subtracting by place. The goal of the discussion is to encourage students to continue to share the ways they used the relationships between the numbers to choose an approach, while also providing an opportunity to make sense of the ways students show decomposing a unit when subtracting within 1,000. They will continue to make sense of decomposing units (including hundreds) throughout the section. Aim to elicit both key mathematical ideas and a variety of student voices, especially those of students who haven't shared recently.
Engagement: Provide Access by Recruiting Interest. Optimize meaning and value. Invite students to share ideas of items to sell, such as cupcakes, sports cards, or video games, and use those as the contexts of the problems to solve. Discuss the action of selling to represent subtraction. Supports accessibility for: Attention, Conceptual Processing
Launch
Groups of 2
Give students access to base-ten blocks.
Activity
“Find the value of each expression in any way that makes sense to you. Explain or show your reasoning.”
3–4 minutes: independent work time
3–4 minutes: partner discussion
As you monitor for the approaches listed in the activity narrative, consider asking:
“What did you do first?”
“What did you notice about the numbers? How did that help you decide how to find the value of the difference?”
“How did you use what you know about hundreds, tens, and ones to find the value of the difference?”
Find the value of each expression in any way that makes sense to you. Explain your reasoning.
Activity Synthesis
Invite previously selected students to share in the given order. Record or display their work for all to see.
Connect students’ approaches by asking:
“What is the same and what is different about the ways we found the value of ?” (One way used a base-ten diagram and showed decomposing a ten. Another way showed a number line and counting back 36. They used the same numbers. They found the same difference.)
Connect students’ approaches to the learning goal by asking:
“Why did _____ decompose a ten when finding the value of ?” (They showed hundreds, tens, and ones, and wanted to subtract by place. There weren’t enough ones to subtract 8, so they needed to decompose a ten.)
Activity 2
Standards Alignment
Building On
Addressing
2.NBT.B.7
Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
The purpose of this activity is for students to practice decomposing a unit to subtract by place. In this activity, all students use base-ten blocks to find the value of each difference. Some students may be able to find the difference without blocks, but this is the first time they decompose a unit when subtracting beyond 100, so the blocks allow all students to see the work of decomposing a unit. This concrete experience will help students interpret other representations and anticipate when they may need to decompose units in future lessons. The blocks also provide a support for students as they create arguments for why they think they will decompose a unit, and explain how they find the difference (MP3).
As needed, ask students to decompose a tower of 10 connecting cubes into ones. Ask students how they would show the same decomposition with base-ten blocks.
Launch
Groups of 2
Give students base-ten blocks.
Activity
“Now we are all going to use base-ten blocks to subtract.”
“Work with your partner to find the value of each expression. One partner will start by reading the expression and representing the greater number, using blocks.”
“The next partner will decide if they think they will decompose any units to subtract. Then they will take away blocks to show the difference.”
“Discuss the difference and record it.”
As needed, demonstrate with .
10 minutes: partner work time
Work with your partner. Find the value of each expression.
Partner A: Read the expression. Represent the greater number, using blocks.
Partner B: Decide if you need to decompose a ten. Then subtract.
Discuss. Then write the difference.
Switch roles.
Student Response
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Advancing Student Thinking
If students add ones to their representation without taking away a ten when they show a decomposition, consider asking:
“Can you explain how you found the value of this difference?”
“Did you decompose a ten to subtract? How could you use the blocks to show that you decomposed a ten?”
Activity Synthesis
Invite a group to share how to use blocks to find the value of .
“What did _____ do to find the value of the difference?”
Invite a group to share how to use blocks to find the value of .
“What did _____ do to find the value of the difference?”
Lesson Synthesis
“Today we saw that we can subtract by place with greater numbers, and sometimes a ten is decomposed.”
“How did you know when a ten would be decomposed when you subtracted three-digit numbers?” (I could tell when I looked at the ones place and saw I didn't have enough ones to subtract ones from ones.)
“How was this the same as when you subtracted two-digit numbers? How was it different?” (It was just like when we subtracted two-digit numbers. It’s different because one of the numbers has hundreds.)
Standards Alignment
Building On
2.NBT.A.1
Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
