Learn on PengienVision, Mathematics, Grade 4Chapter 3: Use Strategies and Properties to Multiply by 1-Digit Numbers

Lesson 4: Use Area Models and Partial Products to Multiply

Property.

Section 1

Multiplying with an Area Model

Property

To multiply using an area model, decompose one factor by place value to determine the dimensions of the partitioned rectangle.
The total product is the sum of the partial products (the areas of the smaller sections).
This visually represents the distributive property:

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

Examples

Section 2

Calculate Partial Products

Property

The partial products algorithm uses the distributive property to solve multiplication.
A multi-digit number is broken into the sum of its place values (expanded form), and each part is multiplied separately before adding the results.

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

This can be visualized using an area model, where each partial product represents the area of a rectangle, and the total product is the sum of these areas.

Examples

Book overview

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Chapter 3: Use Strategies and Properties to Multiply by 1-Digit Numbers

  1. Lesson 1

    Lesson 1: Multiply by Multiples of 10, 100, and 1,000

  2. Lesson 2

    Lesson 2: Estimate Products

  3. Lesson 3

    Lesson 3: Use Arrays and Partial Products to Multiply

  4. Lesson 4Current

    Lesson 4: Use Area Models and Partial Products to Multiply

  5. Lesson 5

    Lesson 5: More Use Area Models and Partial Products to Multiply

  6. Lesson 6

    Lesson 6: Mental Math Strategies for Multiplication

  7. Lesson 7

    Lesson 7: Choose a Strategy to Multiply

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Multiplying with an Area Model

Property

To multiply using an area model, decompose one factor by place value to determine the dimensions of the partitioned rectangle.
The total product is the sum of the partial products (the areas of the smaller sections).
This visually represents the distributive property:

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

Examples

Section 2

Calculate Partial Products

Property

The partial products algorithm uses the distributive property to solve multiplication.
A multi-digit number is broken into the sum of its place values (expanded form), and each part is multiplied separately before adding the results.

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

This can be visualized using an area model, where each partial product represents the area of a rectangle, and the total product is the sum of these areas.

Examples

Book overview

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

Continue this chapter

Chapter 3: Use Strategies and Properties to Multiply by 1-Digit Numbers

  1. Lesson 1

    Lesson 1: Multiply by Multiples of 10, 100, and 1,000

  2. Lesson 2

    Lesson 2: Estimate Products

  3. Lesson 3

    Lesson 3: Use Arrays and Partial Products to Multiply

  4. Lesson 4Current

    Lesson 4: Use Area Models and Partial Products to Multiply

  5. Lesson 5

    Lesson 5: More Use Area Models and Partial Products to Multiply

  6. Lesson 6

    Lesson 6: Mental Math Strategies for Multiplication

  7. Lesson 7

    Lesson 7: Choose a Strategy to Multiply