 # Multiply using Partial Products

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Lesson Plans and Worksheets for Grade 4
Lesson Plans and Worksheets for all Grades

Examples, solutions, and videos to help Grade 4 students learn how to multiply two-digit by two-digit numbers using four partial products.

Common Core Standards: 4.NBT.5, 4.OA.3, 4.MD.3

### New York State Common Core Math Grade 4, Module 3, Lesson 36

The following diagram shows examples of partial products multiplication for 2-digit multiplier and 2-digit multiplier. Scroll down the page for more examples and solutions on multiplication using partial products. ### NYS Math Grade 4, Module 3, Lesson 36 Application Problem

Mr. Goggins set up 30 rows of chairs in the gymnasium. If each row had 35 chairs, how many chairs did Mr. Goggins set up? Draw an area model to represent and to help solve this problem.
Problem 1
Use the distributive property to represent and solve two-digit by two-digit multiplication.
Problem 2
Find the product of 23 and 31 using an area model and partial products to solve.
Problem 3
Find the product of 26 and 34 using partial products. Verify partial products using the area model.
Problem 4
Find the product of 26 and 34 without using an area model. Record the partial products to solve.

### NYS Math Grade 4, Module 3, Lesson 36 Concept Development

Problem 2
Find the product of 23 and 31 using an area model and partial products to solve.
Problem 4
Find the product of 26 and 34 without using an area model. Record the partial products to solve.

### NYS Math Module 3 Grade 4 Lesson 36 Problem Set

1. a. In each of the two models pictured below, write the expressions that determine the area of each of the four smaller rectangles.
b. Using the distributive property, rewrite the area of the large rectangle as the sum of the areas of the four smaller rectangles. Express first in number form and then read in unit form.
14 × 12 = (4 × __ ) + (4 × __ ) + (10 × __ ) + (10 × __ )

### NYS Math Grade 4, Module 3, Lesson 36 Problem Set

2. Use an area model to represent the following expressions. Record the partial products and solve.
a. 14 × 22

Draw an area model to represent the following expressions. Record the partial products vertically and solve.
3. 25 × 32
4. 35 × 42 2. Use an area model to represent the following expressions. Record the partial products and solve.
a. 14 × 22

### NYS Math Grade 4, Module 3, Lesson 36 Homework

1. a. In each of the two models pictured below, write the expressions that determine the area of each of the four smaller rectangles.
b. Using the distributive property, rewrite the area of the large rectangle as the sum of the areas of the four smaller rectangles. Express first in number form and then read in unit form.

Use an area model to represent the following expressions. Record the partial products and solve.
2. 17 × 34

Draw an area model to represent the following expressions. Record the partial products vertically and solve.
3. 45 × 18
4. 45 × 19

Visualize the area model and solve the following numerically using four partial products. (You may sketch an area model if it helps.)
5. 12 × 47
6. 23 × 93
7. 23 × 11
8. 23 × 22

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