# Area Model Multiplication – Definition With Examples

Updated on January 8, 2024

At Brighterly, our mission is to make learning math engaging and enjoyable for children. One of the best ways to do that is by introducing them to the area model method of multiplication. This versatile and powerful tool provides a visual representation of multiplication and division, making it easier for students to grasp the underlying concepts and build confidence in their math skills.

That’s why we’ve designed a unique approach to teaching area model multiplication that incorporates engaging visuals, real-world examples, and hands-on activities. Our lessons guide students step by step through the process of using the area model, providing clear explanations and plenty of opportunities for practice.

By incorporating the area model into our curriculum, we aim to help students develop a solid foundation in multiplication and division, enabling them to tackle a wide range of problems involving whole numbers, fractions, and decimals. Our goal is to help students master these essential skills and become confident, lifelong learners.

## What Is Area?

Area is a fundamental concept in geometry and mathematics, representing the amount of space occupied by a two-dimensional shape. It is typically measured in square units, such as square inches, square feet, or square meters. Understanding area is essential for many real-world applications, including calculating the size of a room, determining how much paint or wallpaper is needed for a wall, and even designing a garden. Various formulas are used to find the area of different shapes, such as rectangles, triangles, and circles.

## Area Model of Fractions

Fractions represent parts of a whole, and the area model provides a visual way to understand and manipulate fractions. With the area model, a shape (often a rectangle or square) is divided into equal parts, and each part represents a fraction of the whole. For example, a rectangle divided into four equal parts represents the fractions 1/4, 2/4, 3/4, and 4/4. This model helps children grasp the meaning of fractions and provides a foundation for learning fraction addition, subtraction, multiplication, and division.

## What Is an Area Model of Multiplication and Division?

The area model is a visual approach to teaching multiplication and division, particularly helpful for children learning these operations. It breaks down numbers into their place values and uses rectangles to represent the products or quotients. The area model makes complex multiplication and division problems more manageable by showing how to multiply or divide numbers step by step, using partial products or partial quotients. This method promotes a deep understanding of the underlying concepts and helps students build confidence in their math skills.

## Area Model of Multiplication of Whole Numbers

When using the area model to multiply whole numbers, start by breaking down the numbers into their place values. Then, draw a rectangle to represent the product and divide it into smaller rectangles based on the place values. Finally, find the area of each smaller rectangle and add them together to get the product. This method can be applied to a variety of multiplication problems involving one-digit, two-digit, and three-digit numbers.

## Multiplication of Two-digit Number by One-digit Number

To multiply a two-digit number by a one-digit number using the area model, follow these steps:

- Break down the two-digit number into its tens and ones place values.
- Draw a rectangle and divide it into two smaller rectangles based on the place values.
- Multiply the one-digit number by the tens and ones place values separately.
- Find the area of each smaller rectangle and add them together to get the product.

## Multiplication of Two-Digit Number by Two-Digit Number

The area model can also be used to multiply two-digit numbers together. To do this:

- Break down both two-digit numbers into their tens and ones place values.
- Draw a large rectangle and divide it into four smaller rectangles based on the place values.
- Multiply the tens and ones place values of both numbers separately.
- Find the area of each smaller rectangle and add them together to get the product.

For a comprehensive guide on multiplying two-digit numbers using the area model, visit Brighterly.

## Multiplication of Three-Digit Number by Two-Digit Number

When multiplying a three-digit number by a two-digit number using the area model, follow these steps:

- Break down the three-digit number into its hundreds, tens, and ones place values, and the two-digit number into its tens and ones place values.
- Draw a rectangle and divide it into six smaller rectangles based on the place values.
- Multiply the place values of both numbers separately.
- Find the area of each smaller rectangle and add them together to get the product.

For more examples and explanations on this method, check out Brighterly.

## Area Model of Multiplying the Fractions

The area model can also be used to multiply fractions. To do this:

- Draw a rectangle and divide it into equal parts based on the denominators of the fractions.
- Shade the parts that represent the numerators of both fractions.
- Find the overlapping shaded region and determine its fraction of the whole.
- Simplify the resulting fraction, if necessary.

## Area Model for Multiplying the Decimals

To multiply decimals using the area model, follow these steps:

- Convert the decimals to fractions or whole numbers.
- Use the area model to multiply the fractions or whole numbers.
- Convert the resulting product back to a decimal.

## Area Model of Division of Whole Numbers

The area model can also be used for division of whole numbers. To do this:

- Break down the dividend into its place values.
- Draw a rectangle and divide it into smaller rectangles based on the divisor and the place values.
- Determine the quotient by counting the number of times the divisor can fit into the dividend.

## Conclusion

The area model is an invaluable tool for teaching and learning multiplication and division, and at Brighterly, we’re committed to helping children master this method. By providing a visual representation of the underlying concepts, the area model helps students develop a deeper understanding of math and boosts their confidence in solving complex problems.

With practice and mastery of the area model, students can tackle a wide range of multiplication and division problems involving whole numbers, fractions, and decimals. Our unique approach to teaching the area model, combined with our engaging and interactive lessons, ensures that learning math is a positive and enjoyable experience for children.

At Brighterly, we’re passionate about helping children reach their full potential and discover the joy of learning. By incorporating the area model into our curriculum, we’re giving students the tools they need to succeed in math and beyond.

## Frequently Asked Questions on Area Model Multiplication

### What is the area model?

The area model is a visual approach to teaching multiplication and division that uses rectangles to represent the products or quotients. It breaks down numbers into their place values and promotes a deep understanding of the underlying concepts.

### How does the area model help with multiplication and division?

The area model makes complex multiplication and division problems more manageable by showing how to multiply or divide numbers step by step, using partial products or partial quotients. This method helps students build confidence in their math skills.

### Can the area model be used for fractions and decimals?

Yes, the area model can be used to multiply and divide fractions and decimals by converting them to whole numbers or fractions and following the steps outlined in this article.