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 \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 \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

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Multiplying with an Area Model

Property

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

Examples

Section 2

Calculate Partial Products

Property

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

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Multiplying with an Area Model

Property

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

Examples

Section 2

Calculate Partial Products

Property

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.