# Area Model and Long Division

Examples, solutions, and videos to help Grade 4 students learn how to explain the connection of the area model of division to the long division algorithm for three- and four-digit dividends.

Common Core Standards: 4.OA.3, 4.NBT.6, 4.NBT.1

### NYS Math Module 3 Grade 4 Lesson 33 Concept Development

Problem 1
672 ÷ 3 and 1,344 ÷ 6
Draw a rectangle with an area of 672 square inches and a width of 3 inches.
Problem 2
1,216 ÷ 4

### NYS Math Module 3 Grade 4 Lesson 33 Problem Set

1. Ursula solved the following division problem by drawing an area model.
a. What division problem did she solve?
b. Show a number bond to represent Ursula’s area model and represent the total length using the distributive property.
2. a. Solve 960 ÷ 4 using the area model. There is no remainder in this problem.
b. Draw a number bond and use the long division algorithm to record your work from (a).
3. a. Draw an area model to solve 774 ÷ 3.
b. Draw a number bond to represent this problem.
c. Record your work using the long division algorithm.
4. a. Draw an area model to solve 1,584 ÷ 2.
b. Draw a number bond to represent this problem.
c. Record your work using the long division algorithm.

### NYS Math Module 3 Grade 4 Lesson 33 Application Problem

Write an equation to find the unknown length of each rectangle. Then find the sum of the two unknown lengths.

### NYS Math Module 3 Grade 4 Lesson 33 Homework

1. Arabelle solved the following division problem by drawing an area model. a. What division problem did she solve?
b. Show a number bond to represent Arabelle’s area model and represent the total length using the distributive property.
2. a. Solve 816 ÷ 4 using the area model. There is no remainder in this problem.
b. Draw a number bond and use a written method to record your work from (a).
3. a. Draw an area model to solve 549 ÷ 3.
b. Draw a number bond to represent this problem.
c. Record your work using the long division algorithm.
4. a. Draw an area model to solve 2,762 ÷ 2.
b. Draw a number bond to represent this problem.
c. Record your work using the long division algorithm.

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