Learn on PengiEureka Math, Grade 5Chapter 8: The Standard Algorithm for Multi-Digit Whole Number Multiplication

Lesson 4: Fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to check for reasonableness of the product.

In this Grade 5 Eureka Math lesson, students connect area models and the distributive property to partial products of the standard algorithm with renaming. Using problems like 64 × 73, they decompose multi-digit factors, identify how each partial product from the area model corresponds to a step in the standard algorithm, and practice renaming tens and hundreds during multiplication. The lesson builds fluency with multi-digit whole number multiplication while reinforcing the relationship between visual models and symbolic procedures.

Section 1

Multiplying Mixed Numbers with an Area Model

Property

To multiply two numbers using an area model, decompose each factor into its place value components.
The total product is the sum of the partial products obtained by multiplying each component of the first factor by each component of the second factor.
For factors (a+b)(a+b) and (c+d)(c+d), the product is:

(a+b)×(c+d)=(a×c)+(a×d)+(b×c)+(b×d)(a+b) \times (c+d) = (a \times c) + (a \times d) + (b \times c) + (b \times d)

Examples

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Chapter 8: The Standard Algorithm for Multi-Digit Whole Number Multiplication

  1. Lesson 1

    Lesson 1: Write and interpret numerical expressions, and compare expressions using a visual model.

  2. Lesson 2

    Lesson 2: Convert numerical expressions into unit form as a mental strategy for multi-digit multiplication.

  3. Lesson 3

    Lesson 3: Connect visual models and the distributive property to partial products of the standard algorithm without renaming.

  4. Lesson 4Current

    Lesson 4: Fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to check for reasonableness of the product.

  5. Lesson 5

    Lesson 5: Fluently multiply multi-digit whole numbers using the standard algorithm to solve multi-step word problems.

  6. Lesson 6

    Lesson 6: Fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to check for reasonableness of the product.

  7. Lesson 7

    Lesson 7: Fluently multiply multi-digit whole numbers using the standard algorithm to solve multi-step word problems.

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Multiplying Mixed Numbers with an Area Model

Property

To multiply two numbers using an area model, decompose each factor into its place value components.
The total product is the sum of the partial products obtained by multiplying each component of the first factor by each component of the second factor.
For factors (a+b)(a+b) and (c+d)(c+d), the product is:

(a+b)×(c+d)=(a×c)+(a×d)+(b×c)+(b×d)(a+b) \times (c+d) = (a \times c) + (a \times d) + (b \times c) + (b \times d)

Examples

Book overview

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

Continue this chapter

Chapter 8: The Standard Algorithm for Multi-Digit Whole Number Multiplication

  1. Lesson 1

    Lesson 1: Write and interpret numerical expressions, and compare expressions using a visual model.

  2. Lesson 2

    Lesson 2: Convert numerical expressions into unit form as a mental strategy for multi-digit multiplication.

  3. Lesson 3

    Lesson 3: Connect visual models and the distributive property to partial products of the standard algorithm without renaming.

  4. Lesson 4Current

    Lesson 4: Fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to check for reasonableness of the product.

  5. Lesson 5

    Lesson 5: Fluently multiply multi-digit whole numbers using the standard algorithm to solve multi-step word problems.

  6. Lesson 6

    Lesson 6: Fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to check for reasonableness of the product.

  7. Lesson 7

    Lesson 7: Fluently multiply multi-digit whole numbers using the standard algorithm to solve multi-step word problems.