Learn on PengienVision, Mathematics, Grade 5Chapter 5: Use Models and Strategies to Divide Whole Numbers

Lesson 3: Use Models and Properties to Divide With 2-Digit Divisors

In this Grade 5 lesson from enVision Mathematics, students learn how to divide whole numbers by 2-digit divisors using area models and the Distributive Property. They practice breaking dividends into partial products, applying place value to find quotients step by step. Real-world problems, such as finding garden dimensions and arranging rows of chairs, help students connect division concepts to practical situations.

Section 1

Calculate Area Using an Area Model

Property

An area model is a rectangle with its side lengths labeled. The area of the rectangle is the product of its length and width.

Area = length \times width

Examples

Section 2

Write a Related Multiplication Equation

Property

A division equation can be written as a related multiplication equation with an unknown factor. If $a \div b = c$ , then it is also true that $b \times c = a$ .

Examples

The division problem $360 \div 20 = w$ can be written as the multiplication equation $20 \times w = 360$ .
The division problem $729 \div 27 = n$ can be written as the multiplication equation $27 \times n = 729$ .
The division problem $1,250 \div 50 = p$ can be written as the multiplication equation $50 \times p = 1,250$ .

Explanation

Division and multiplication are inverse operations, meaning they undo each other. You can use this relationship to solve division problems by thinking about them in terms of multiplication. This is helpful when using an area model, where the dividend is the area, the divisor is a known side, and the quotient is the unknown side you need to find.

Section 3

Use an Area Model to Divide

Property

To divide a dividend by a divisor, you can use an area model. The dividend is the total area of a rectangle, and the divisor is one of the side lengths. The quotient is the unknown side length. You can break the dividend into smaller parts that are easier to divide, find the partial quotient for each part, and then add the partial quotients together to find the final answer. This uses the idea that $(a+b) \div c = (a \div c) + (b \div c)$ .

Examples

To solve $368 \div 16$ , we can break the dividend $368$ into $320 + 48$ . We find the partial quotients: $320 \div 16 = 20$ and $48 \div 16 = 3$ . The final quotient is the sum of the partial quotients: $20 + 3 = 23$ .
To solve $504 \div 21$ , we can break the dividend $504$ into $420 + 84$ . We find the partial quotients: $420 \div 21 = 20$ and $84 \div 21 = 4$ . The final quotient is the sum of the partial quotients: $20 + 4 = 24$ .

Explanation

Using an area model helps visualize the division process. You represent the dividend as the total area inside a rectangle and the divisor as one of its side lengths. By breaking the total area into smaller, more manageable sections, you can use basic multiplication facts and estimation to find partial quotients. Adding these partial quotients gives you the total unknown side length, which is the final answer to the division problem.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Calculate Area Using an Area Model

Property

An area model is a rectangle with its side lengths labeled. The area of the rectangle is the product of its length and width.

Area = length \times width

Examples

Section 2

Write a Related Multiplication Equation

Property

A division equation can be written as a related multiplication equation with an unknown factor. If $a \div b = c$ , then it is also true that $b \times c = a$ .

Examples

The division problem $360 \div 20 = w$ can be written as the multiplication equation $20 \times w = 360$ .
The division problem $729 \div 27 = n$ can be written as the multiplication equation $27 \times n = 729$ .
The division problem $1,250 \div 50 = p$ can be written as the multiplication equation $50 \times p = 1,250$ .

Explanation

Section 3

Use an Area Model to Divide

Property

Examples

To solve $368 \div 16$ , we can break the dividend $368$ into $320 + 48$ . We find the partial quotients: $320 \div 16 = 20$ and $48 \div 16 = 3$ . The final quotient is the sum of the partial quotients: $20 + 3 = 23$ .
To solve $504 \div 21$ , we can break the dividend $504$ into $420 + 84$ . We find the partial quotients: $420 \div 21 = 20$ and $84 \div 21 = 4$ . The final quotient is the sum of the partial quotients: $20 + 4 = 24$ .

Explanation

Overview

Lesson overview

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

Overview

Section 1

Calculate Area Using an Area Model

Property

An area model is a rectangle with its side lengths labeled. The area of the rectangle is the product of its length and width.

Area = length \times width

Examples

Section 2

Write a Related Multiplication Equation

Property

A division equation can be written as a related multiplication equation with an unknown factor. If $a \div b = c$ , then it is also true that $b \times c = a$ .

Examples

The division problem $360 \div 20 = w$ can be written as the multiplication equation $20 \times w = 360$ .
The division problem $729 \div 27 = n$ can be written as the multiplication equation $27 \times n = 729$ .
The division problem $1,250 \div 50 = p$ can be written as the multiplication equation $50 \times p = 1,250$ .

Explanation

Section 3

Use an Area Model to Divide

Property

Examples

To solve $368 \div 16$ , we can break the dividend $368$ into $320 + 48$ . We find the partial quotients: $320 \div 16 = 20$ and $48 \div 16 = 3$ . The final quotient is the sum of the partial quotients: $20 + 3 = 23$ .
To solve $504 \div 21$ , we can break the dividend $504$ into $420 + 84$ . We find the partial quotients: $420 \div 21 = 20$ and $84 \div 21 = 4$ . The final quotient is the sum of the partial quotients: $20 + 4 = 24$ .