Learn on PengienVision, Mathematics, Grade 5Chapter 2: Use Models and Strategies to Add and Subtract Decimals

Lesson 1: Mental Math

In this Grade 5 lesson from enVision Mathematics Chapter 2, students learn how to use mental math strategies — including the Commutative Property, Associative Property, and compensation — to add and subtract decimals. Students practice identifying compatible numbers and adjusting values to simplify calculations without paper or a calculator. The lesson builds fluency with decimal operations through real-world problems involving money and multi-addend expressions.

Section 1

Grouping Compatible Numbers Using Properties of Addition

Property

The Commutative Property lets you add numbers in any order: a+b=b+aa + b = b + a.
The Associative Property lets you change the grouping of numbers being added: (a+b)+c=a+(b+c)(a + b) + c = a + (b + c).
Together, these properties allow you to rearrange and group compatible numbers to simplify mental addition.

Examples

Section 2

Using Compensation for Addition

Property

To mentally calculate the sum a+ba + b, you can change one addend by an amount cc to make it an easier number to work with, and then adjust the sum by subtracting cc.

a+b=a+(b+c)−ca + b = a + (b + c) - c

Examples

Section 3

Using Compensation for Subtraction

Property

To mentally calculate a difference like a−ba - b, you can change the subtrahend (bb) to a nearby, easier number (cc). Then, subtract cc from aa and adjust the result by adding the difference between cc and bb.

a−b=(a−c)+(c−b)a - b = (a - c) + (c - b)

Examples

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Chapter 2: Use Models and Strategies to Add and Subtract Decimals

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    Lesson 1: Mental Math

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  2. Lesson 2

    Lesson 2: Estimate Sums and Differences of Decimals

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  3. Lesson 3

    Lesson 3: Use Models to Add and Subtract Decimals

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  4. Lesson 4

    Lesson 4: Use Strategies to Add Decimals

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  5. Lesson 5

    Lesson 5: Use Strategies to Subtract Decimals

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Lesson overview

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Section 1

Grouping Compatible Numbers Using Properties of Addition

Property

The Commutative Property lets you add numbers in any order: a+b=b+aa + b = b + a.
The Associative Property lets you change the grouping of numbers being added: (a+b)+c=a+(b+c)(a + b) + c = a + (b + c).
Together, these properties allow you to rearrange and group compatible numbers to simplify mental addition.

Examples

Section 2

Using Compensation for Addition

Property

To mentally calculate the sum a+ba + b, you can change one addend by an amount cc to make it an easier number to work with, and then adjust the sum by subtracting cc.

a+b=a+(b+c)−ca + b = a + (b + c) - c

Examples

Section 3

Using Compensation for Subtraction

Property

To mentally calculate a difference like a−ba - b, you can change the subtrahend (bb) to a nearby, easier number (cc). Then, subtract cc from aa and adjust the result by adding the difference between cc and bb.

a−b=(a−c)+(c−b)a - b = (a - c) + (c - b)

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 2: Use Models and Strategies to Add and Subtract Decimals

  1. Lesson 1Current

    Lesson 1: Mental Math

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  2. Lesson 2

    Lesson 2: Estimate Sums and Differences of Decimals

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  3. Lesson 3

    Lesson 3: Use Models to Add and Subtract Decimals

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  4. Lesson 4

    Lesson 4: Use Strategies to Add Decimals

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  5. Lesson 5

    Lesson 5: Use Strategies to Subtract Decimals

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