We included HMH Into Math Grade 4 Answer Key PDF Module 8 Lesson 3 Relate Area Models and Partial Products to make students experts in learning maths.
HMH Into Math Grade 4 Module 8 Lesson 3 Answer Key Relate Area Models and Partial Products
I Can use area models and partial products to multiply two 2-digit numbers.
Spark Your Learning
A stained glass artist explains that the purpose of stained glass windows is to control light or tell a story. They contain pieces of colorful glass arranged in patterns or pictures held together in the form by strips of lead. How many different multiplication problems can you write using the measures of these glass pieces?
Answer:
From the figure,
( 10 x 10 ) + ( 10 x 3 ) + ( 3 x 10 ) + (3 x 3 )
( 100 ) + ( 30 ) + ( 30 ) + ( 9 ) = 169
Therefore, there are 169 different multiplication problems can you write using the measures of these glass pieces
Turn and Talk How did you decide on the factors for each multiplication problem?
Build Understanding
1. In Dr. Brewer’s art class, students will be making 15 rag rugs. Each rug uses 14 yards of fabric. How many yards of fabric will be needed to make all of the rag rugs?
A. How can you find the number of yards of fabric needed?
_____________________________
_____________________________
Answer:
Given,
In Dr. Brewer’s art class, students will be making 15 rag rugs.
Each rug uses 14 yards of fabric.
number of yards = 15 x 14 = 210
Therefore, the number of yards of fabric needed is 210.
B. Show how you can use an area model to represent the problem.
Answer:
C. How can you write multiplication equations to find the partial products? Record the equations above.
Answer:
10 x 10 = 100
4 x 10 = 40
10 x 5 = 50
4 x 5 = 20.
D. How can you use the partial products to find the whole product?
Answer:
So, 100 + 40 + 50 + 20 = 210.
E. __________ yards of fabric will be needed to make the rag rugs.
Answer:
Therefore, 210 yards of fabric will be needed to make the rag rugs.
Turn and Talk How does the area model make it easier to find the product?
Step It Out
In the storage closet, there are 17 different types of paint brushes with 23 of each type. How many paint brushes are there?
A. Break apart each factor into tens and ones.
17 = __ + ___
23 = ____ + ___
Answer:
17 = 10 + 7
23 = 20 + 3
Total number of brushes = 17 x 23 = 391
B. Label the area model with the factors.
Answer:
C. Use the Distributive Property to find the partial products.
Answer:
D. Add the partial products to find the whole product.
Answer:
200 + 30 + 140 + 21 = 391.
Turn and Talk How does the area model show that the sum of the partial products is the product?
Check Understanding Math Board
Complete the area model. Find the product.
Question 1.
13 × 16 = ___
Answer:
Product = 13 x 16 = ( 100 + 30 + 60 + 18 ) = 208.
On Your Own
Question 2.
Model with Mathematics Complete the area model. Write and solve an equation for the area model.
___ × __ = ___
Answer:
The area of the model is
( 20 x 20 ) + ( 20 x 8 ) + ( 6 x 20 ) + ( 6 x 8 )
( 400 ) + ( 160 ) + ( 120 ) + ( 480 ) = 728
Therefore, product is 728.
Question 3.
Reason There are 22 students in Mrs. Taylor’s fourth grade class. Each student is asked to bring in 15 pencils at the beginning of the school year. How can you determine how many pencils the class will have as the new school year begins?
_____________________________
_____________________________
Answer:
Given,
There are 22 students in Mrs. Taylor’s fourth-grade class.
Each student is asked to bring in 15 pencils at the beginning of the school year.
the Total number of pencils = Number of students x Number of pencils with each student.
So, 22 x 15 =
( 10 x 20 ) + ( 10 x 2 ) + ( 5 x 20 ) + ( 5 x 2 )
( 200 ) + ( 20 ) + ( 100 ) + ( 10 ) = 330
Therefore, number of pencils = 330.
Draw an area model to represent the product. Then record the product.
Question 14.
17 × 13 = ___
Answer:
Therefore, product of 17 x 13 = 221
Question 5.
14 × 21 = ___
Answer:
Therefore, product of 14 x 21 = 294
I’m in a Learning Mindset!
How did practice help me master area models and partial products?
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Answer:
While practicing, we can improve our problem-solving skills and we can rectify our mistakes which helps us to master area models and partial products.