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Subtract

Your Way

Grade 2: Unit 2: Lesson 5

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Goals:

Subtract a one-digit number from a two-digit number in a way that makes sense to them.

Purpose:

The purpose of this lesson is for students to subtract a one-digit number from a two-digit number and describe decomposing a ten when subtracting by place.

Narrative:

In grade 1, students added within 100 using strategies based on place value and properties of operations. When using place value strategies to add, students learned that sometimes they need to compose a ten. To this point, when subtracting within 20, students used methods like counting on, decomposing a number to get to a ten, and using known addition facts, but did not explicitly decompose a ten.

In this lesson, students subtract a one-digit number from a two-digit number when a ten would need to be decomposed if they subtract by place. When subtracting a one-digit number from a two-digit number, students may count back to get to a ten and then count back from there. Although subtracting or counting back in this way is an effective method when subtracting a single-digit number, it is less practical when subtracting two-digit numbers. For this reason, students are encouraged to use cubes and base-ten blocks to help make decomposing a ten visible to all students and prepare students to consider decomposing the minuend in order to subtract by place. For example, 26= 10+16, so decomposing 26 into 1 ten and 16 ones will be helpful when representing subtraction using base-ten blocks later in this lesson.

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Number Talk:

Subtract a Little More

This Number Talk encourages students to think about subtraction with expressions that may require decomposing and to rely on using what they know about place value and counting up or back to mentally solve problems. The strategies elicited here will be helpful later in the lesson when students subtract one-digit numbers from two-digit numbers.

When students notice that they can use the value of previously found expressions to find new values, they look for and make use of structure (MP7). This Number Talk provides opportunities for students to notice they can subtract to get to a ten, then subtract the rest (17-8= 17-7-1=10-1=9).

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

Student work time:

Record answers and strategy.
Keep expressions and work displayed.
Repeat with each expression.

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17 - 7 =

17 - 8 =

26 - 6 =

26 - 8 =

Warm-Up

Find the value of each sum mentally.

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Activity 1:

How Do You Find the Value?

The purpose of this activity is for students to subtract in a way that makes sense to them. Students use a method of their choice and share their methods with one another. This can serve as a formative assessment of how students approach finding the value of a difference when a ten must be decomposed when subtracting by place. Although students may use many methods to subtract, including those based on counting or compensation, the synthesis focuses on connecting these methods to those based on place value where a ten is decomposed.

Monitor and select students with the following methods to share in the synthesis:

Uses connecting cubes to make 82 and removes 9 blocks. Counts back or counts all to find the difference.
Subtracts 2 from 82 to get to a ten, 80, and then subtracts 7 from 80 by counting back (with or without blocks).
Uses base-ten blocks to show 82 and decomposes a ten to get 12 ones. Subtracts 9 ones from 12 ones and counts the remaining blocks.

Gather:

Base-ten blocks
Connecting cubes

Launch:

Groups of 2
Give students access to connecting cubes and base-ten blocks.

Student Work Time:

“Find the difference for .”
“Show your thinking using drawings, numbers, or words.”
“Be prepared to share your thinking.”
As student work, consider asking: “What did you do first? Why?”
“What did you take away first? Why?”
“How did you show 82 at first? Did you have to make any changes to take away 9? Explain.”
“What tool did you use? Why?”

Activity Synthesis:

Ask selected students to share in the given order.

“Why did _____ need to change 82 to 7 tens and 12 ones to subtract ones from ones?”

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Activity 2:

Subtract with Base-ten Blocks

Diego started with 5 tens and 5 ones. Represent Diego’s blocks with the base-ten blocks.

Purpose:

The purpose of this activity is for students to subtract a one-digit number from a two-digit number. In the previous activity, students shared many ways to subtract including using connecting cubes or base-ten blocks to show decomposing a ten. They build on this understanding as they use base-ten blocks to represent the starting number and subtract an amount that requires them to decompose a ten.

Gather:

Base-ten blocks

Launch:

Groups of 2
Give each group access to base-ten blocks.

Student Work Time:

“Diego was representing numbers using base-ten blocks. Work with a partner to follow along and see what Diego discovered.”
“Use your blocks first to show what Diego does. Then answer any questions.”
8 minutes: partner work time
Monitor for students who talk about “exchanging” or “trading” a ten for ten ones.

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Activity 2:

Subtract with Base-ten Blocks

2. Diego took away 2 tens.

Draw a representation to show what happened to Diego’s blocks.

Write an equation to show how many Diego has now.

Purpose:

The purpose of this activity is for students to subtract a one-digit number from a two-digit number. In the previous activity, students shared many ways to subtract including using connecting cubes or base-ten blocks to show decomposing a ten. They build on this understanding as they use base-ten blocks to represent the starting number and subtract an amount that requires them to decompose a ten.

Gather:

Base-ten blocks

Launch:

Groups of 2
Give each group access to base-ten blocks.

Student Work Time:

“Diego was representing numbers using base-ten blocks. Work with a partner to follow along and see what Diego discovered.”
“Use your blocks first to show what Diego does. Then answer any questions.”
8 minutes: partner work time
Monitor for students who talk about “exchanging” or “trading” a ten for ten ones.

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Activity 2:

Subtract with Base-ten Blocks

3. Then, Diego took away 8 ones.

Draw a diagram to show what happened to Diego’s blocks.

Write an equation to show how many Diego has now. Be prepared to explain your reasoning.

Purpose:

The purpose of this activity is for students to subtract a one-digit number from a two-digit number. In the previous activity, students shared many ways to subtract including using connecting cubes or base-ten blocks to show decomposing a ten. They build on this understanding as they use base-ten blocks to represent the starting number and subtract an amount that requires them to decompose a ten.

Gather:

Base-ten blocks

Launch:

Groups of 2
Give each group access to base-ten blocks.

Student Work Time:

“Diego was representing numbers using base-ten blocks. Work with a partner to follow along and see what Diego discovered.”
“Use your blocks first to show what Diego does. Then answer any questions.”
8 minutes: partner work time
Monitor for students who talk about “exchanging” or “trading” a ten for ten ones.

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Activity 2: Centers…Choice Time!

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Lesson Synthesis

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Cool-Down: Find the Differences

Find the value of 75-9.

Show your thinking!

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Image Citations

https://pixabay.com/images/id-6305076/

https://pixabay.com/images/id-2768204/

https://pixabay.com/images/id-3181283/

https://pixabay.com/images/id-674828/

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