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

Lesson 2: Estimate Sums and Differences of Decimals

In this Grade 5 enVision Mathematics lesson from Chapter 2, students learn how to estimate sums and differences of decimals using two key strategies: rounding to a given place value and substituting compatible numbers. The lesson guides students through applying these techniques to both addition and subtraction problems with decimals in real-world contexts. Practice problems reinforce when to choose estimation over exact calculation and how to evaluate the reasonableness of an estimate.

Section 1

Estimating Sums and Differences by Rounding

Property

To estimate a sum or difference, first round each number to a specified place value, then perform the addition or subtraction on the rounded numbers. The result is an approximation, denoted by the ≈\approx symbol. For numbers AA and BB, an estimated sum is round(A)+round(B)\text{round}(A) + \text{round}(B) and an estimated difference is round(A)−round(B)\text{round}(A) - \text{round}(B).

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Section 2

Determine if an Estimate is an Overestimate or Underestimate

Property

To determine if an estimate is an overestimate (greater than the actual answer) or an underestimate (less than the actual answer), analyze how each number was rounded.

  • Addition: If both numbers are rounded up, the sum is an overestimate. If both are rounded down, the sum is an underestimate.
  • Subtraction (A−BA - B): If AA is rounded up and BB is rounded down, the difference is an overestimate. If AA is rounded down and BB is rounded up, the difference is an underestimate.

Examples

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

  1. Lesson 1

    Lesson 1: Mental Math

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  2. Lesson 2Current

    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

Estimating Sums and Differences by Rounding

Property

To estimate a sum or difference, first round each number to a specified place value, then perform the addition or subtraction on the rounded numbers. The result is an approximation, denoted by the ≈\approx symbol. For numbers AA and BB, an estimated sum is round(A)+round(B)\text{round}(A) + \text{round}(B) and an estimated difference is round(A)−round(B)\text{round}(A) - \text{round}(B).

Examples

Section 2

Determine if an Estimate is an Overestimate or Underestimate

Property

To determine if an estimate is an overestimate (greater than the actual answer) or an underestimate (less than the actual answer), analyze how each number was rounded.

  • Addition: If both numbers are rounded up, the sum is an overestimate. If both are rounded down, the sum is an underestimate.
  • Subtraction (A−BA - B): If AA is rounded up and BB is rounded down, the difference is an overestimate. If AA is rounded down and BB is rounded up, the difference is an underestimate.

Examples

Book overview

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

  1. Lesson 1

    Lesson 1: Mental Math

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  2. Lesson 2Current

    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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