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

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

In this Grade 5 Eureka Math lesson from Chapter 8, students learn to connect area models and tape diagrams to partial products of the standard multiplication algorithm without renaming. Using the distributive property, students break multi-digit factors into expanded form to see how each partial product contributes to the final answer. The lesson builds on prior knowledge of area, unit form mental math, and place value to bridge visual representations with the written standard algorithm.

Section 1

Using the Distributive Property for Partial Products

Property

The distributive property allows us to multiply a sum by multiplying each addend separately and then adding the products.
When we decompose factors by place value, the results of these smaller multiplications are called partial products.

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

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 3Current

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

  4. Lesson 4

    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.

Expand

Section 1

Using the Distributive Property for Partial Products

Property

The distributive property allows us to multiply a sum by multiplying each addend separately and then adding the products.
When we decompose factors by place value, the results of these smaller multiplications are called partial products.

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

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 3Current

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

  4. Lesson 4

    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.