Area Model Multiplication

Core Concepts

Use boxes (area models) to visually organize and solve multi-digit multiplication problems.

Area Model Multiplication

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What are the partial products for \(5 \times 146\) using an area model?

An area model diagram for 5 times 146, showing a rectangle with a height of 5 divided into three columns of widths 100, 40, and 6, containing the partial products 500, 200, and 30.

\(5 \times 100 = 500\) \(5 \times 40 = 200\) \(5 \times 6 = 30\)

After finding the partial products \(500\), \(200\), and \(30\) for \(5 \times 146\), what is the final step?

An area model displaying partial products 500, 200, and 30, with an addition equation below showing their sum circled as the final product of 730.

Add the partial products together to find the final product: \(500 + 200 + 30 = 730\).

Find the partial products for \(8 \times 57\) using an area model.

An area model rectangle divided into two sections showing the partial products 400 and 56, representing the decomposed multiplication of 8 times 50 and 8 times 7.

\(8 \times 50 = 400\) \(8 \times 7 = 56\)

What is the final product of \(8 \times 57\)?

An area model with a height of 8 containing partial products 400 and 56, followed by the addition equation 400 plus 56 equals 456 to find the final product.

Add the partial products: \(400 + 56 = 456\).

Set up the area model for \(4 \times 2,315\).

Draw a rectangle split into four parts. Label a side with \(4\). Label the top with the expanded form: \(2000\), \(300\), \(10\), and \(5\).

Find the partial products for \(4 \times 2,315\).

The partial products are: \(4 \times 2000 = 8000\) \(4 \times 300 = 1200\) \(4 \times 10 = 40\) \(4 \times 5 = 20\)

What is the final product of \(4 \times 2,315\)?

Add the partial products: \(8000 + 1200 + 40 + 20 = 9260\).

How does the area model relate to the distributive property?

The area model is a visual representation of the distributive property. Breaking the number into expanded form on the model is the same as breaking it into a sum, and finding the partial products is the same as distributing the other factor.

What is an advantage of using the area model for multiplication?

It helps organize the problem and makes sure you multiply all the parts correctly. It is very visual and clearly shows the partial products based on place value.

To solve \(5 \times 146\) with an area model, how would you draw the box and label the sides?

An area model rectangle with a left side labeled 5, divided vertically into three sections with the top edge labeled 100, 40, and 6 to represent the expanded form of 146.

Draw a rectangle. Label one side with the single-digit factor, \(5\). Split the rectangle into \(3\) parts and label the top with the expanded form of \(146\), which is \(100\), \(40\), and \(6\).

In an area model for \(5 \times 146\), what three multiplication problems do you solve inside the boxes?

An area model rectangle divided into three sections representing the partial products for multiplying 5 by 146, labeled from left to right as 5 times 100, 5 times 40, and 5 times 6.

You solve for the area of each smaller rectangle: 1. \(5 \times 100\) 2. \(5 \times 40\) 3. \(5 \times 6\)

Set up the area model for the problem \(8 \times 57\).

An area model setup for 8 times 57, showing a rectangle divided into two parts with a left height of 8 and top segments labeled 50 and 7.

Draw a rectangle split into two parts. Label the side with \(8\). Label the top with the expanded form of \(57\), which is \(50\) and \(7\).

Area Model Multiplication

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