Distributive Property
Name
7.4 ?
Number and Operations—3.4.E, 3.4.K Algebraic Reasoning— 3.5.B Also 3.4.D, 3.5.D MATHEMATICAL PROCESSES 3.1.C, 3.1.D, 3.1.E
Distributive Property
ALGEBRA
Essential Question
How can you use the Distributive Property to find products?
Unlock Unlock the the Problem Problem Mark bought 6 new fish for his aquarium. He paid $7 for each fish. How much did he spend in all?
• Describe the groups in this problem. • Circle the numbers you will use to
Find 6 × $7.
solve the problem.
You can use the Distributive Property to solve the problem. The Distributive Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
Activity
Materials ■ square tiles
Make an array with tiles to show 6 rows of 7.
© Houghton Mifflin Harcourt Publishing Company
6×7=
Remember sum—the answer to an addition problem addends—the numbers being added Hands On
Break apart the array to make two smaller arrays for facts you know.
■
6×5
6×7=■ 6 × 7 = 6 × (5 + 2) Think: 7 = 5 + 2 6 × 7 = (6 × 5) + (6 × 2) Multiply each addend by 6. 6×7=_+_
Add the products.
6×7=_
6×2
Math Talk Mathematical Processes
What other ways could you break apart the 6 × 7 array?
So, Mark spent $ _ for his new fish. Module 7
229
Share Share and and Show Show Draw a line to show how you could break apart this 6 × 8 array into two smaller arrays for facts you know.
1.
• What numbers do you multiply? _ and _
_ and _ • What numbers do you add? _ + _ 6 × 8 = 6 × (_ + _)
Math Talk Mathematical Processes
6 × 8 = (_ × _) + (_ × _) 6×8=_+_ 6×8=_
Why do you have to add to find the total product when you use the Distributive Property?
Write one way to break apart the array. Then find the product. 2.
3.
Problem Problem Solving Solving
230
Shade tiles to make an array that shows a fact with 7, 8, or 9 as a factor. Write the fact. Explain how you found the product. © Houghton Mifflin Harcourt Publishing Company
4.
Name
Problem Problem Solving Solving 5.
Sense or Nonsense? Robin says, “I can find 8 × 7 by multiplying 3 × 7 and doubling it.“ Does her statement make sense? Justify your answer.
6.
Multi-Step Brandon needs 8 boxes of spinners for his fishing club. The cost of each box is $9. How much will Brandon pay? 8 × $9 = ■
Look at how Brandon solved the problem. Find and describe his error.
8 × 9 = (4 × 9) + (5 × 9) 8 × 9 = 36 + 45 8 × 9 = 81
Use the array to help solve the problem and correct Brandon’s error.
8 × 9 = (4 + 4) × 9
© Houghton Mifflin Harcourt Publishing Company
8 × 9 = (_ × _) + (_ × _) 8×9=_+_ 8×9=_
So, Brandon will pay $ _ for the spinners.
Module 7 • Lesson 4 231
Mathematical Processes M Model ¥ Reason ¥ Communicate M
Daily Daily Assessment Assessment Task Task Fill in the bubble for the correct answer choice. You may use models or strategies to solve. 7.
8.
9.
Use Diagrams Maurice planted 8 rows of popcorn plants. There are 6 plants in each row. The array shows Maurice’s garden. How many popcorn plants does Maurice have? A
36
C
48
B
42
D
64
At a grocery store, the cans of nuts are arranged in 9 rows. There are 6 cans in each row. Which shows one way to find the total number of cans of nuts? A
(5 + 4) × 6
B
(3 + 3) × 6
C
(5 + 5) × 6
D
(5 + 3) × 6
Multi-Step Jillian bought 6 books for $7 each. She paid with $50. How much change should Jillian receive? A
$37
C
$43
B
$18
D
$8
TEXAS Test Prep
232
Representation Which number sentence below is an example of the Distributive Property? A
6 × 8 = 40 + 8
B
(8 × 2) × 3 = 8 × (2 × 3)
C
6×8=8×6
D
6 × 8 = (6 × 2) + (6 × 6)
© Houghton Mifflin Harcourt Publishing Company
10.
H o mewo rk and Practice
7.4
Number and Operations—3.4.E, 3.4.K Algebraic Reasoning—3.5.B Also 3.4.D, 3.5.D MATHEMATICAL PROCESSES 3.1.C, 3.1.D, 3.1.E
Name
Distributive Property
ALGEBRA
Write one way to break apart the array. Then find the product. 1.
3.
2.
Shade tiles to make an array that shows a fact with 5, 6, or 7 as a factor. Explain how you found the product.
Problem Problem Solving Solving
© Houghton Mifflin Harcourt Publishing Company
4.
Shawn makes a tile design by using 7 rows of 8 tiles. Explain how Shawn can break apart his design to find how many tiles he used.
Module 7 • Lesson 4 233
TEXAS Test Prep
Lesson Lesson Check Check Fill in the bubble completely to show your answer.
7.
9.
234
There are 8 tables in the art class. Five students sit at each table. How many students are in the art class?
6.
Seven large trucks are in a parking lot. Each truck has 6 wheels. How many wheels are there in all?
A
13
A
67
B
40
B
40
C
45
C
42
D
85
D
13
Jonas buys 6 packages of corn. Each package has 8 ears of corn. Which way can Jonas use to show how many ears of corn he buys?
8.
A store sells bags of 9 apples. Mr. Hyon buys 5 bags of apples to make pies. Which way can Mr. Hyon use to show how many apples he buys?
A
(4 + 2) × 8
B
(3 + 2) × 8
A
(4 × 9) + (5 × 9)
C
(6 + 6) × 8
B
(3 × 5) + (6 × 5)
D
(4 + 4) × 6
C
(4 × 5) + (5 × 9)
D
(3 × 5) + (9 × 5)
Multi-Step Minka buys 8 CDs for $6 each. She pays with three $20 bills. How much change should Minka receive?
10.
Multi-Step Kent buys 5 bags of potatoes that cost $7 each. He gives the clerk $40. How much change should Kent receive?
A
$48
A
$35
B
$12
B
$12
C
$34
C
$5
D
$68
D
$52
© Houghton Mifflin Harcourt Publishing Company
5.
Name
Module 7 Assessment Vocabulary Vocabulary
Vocabulary Commutative Property
Choose the best term from the box to complete the sentence.
of Multiplication
1.
A ___ of 4 is any product that has 4 as one of its factors. (p. 217)
2.
This is an example of the ___ Property.
Distributive Property multiple
3 × 8 = (3 × 6) + (3 × 2) This property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. (p. 229)
Concepts Concepts and and Skills Skills Write one way to break apart the array. Then find the product. q TEKS 3.4.E, 3.4.K 3.
4.
© Houghton Mifflin Harcourt Publishing Company
Find the product. 5.
3×1=_
9.
2 ×1 _
q TEKS 3.4.E, 3.4.K
6.
10.
5×6=_
6 ×6 _
11.
7.
6 ×7 _
4×7=_ 12.
6 ×3 _
8.
2 × 10 = _ 13.
3 ×8 _
Module 7
235
TEXAS Test Prep
Fill in the bubble for the correct answer choice. You may use models to solve. 14. Lori saw 6 lightning bugs. They each had 6 legs. How many legs did the lightning bugs have in all? q TEKS 3.4.E, 3.4.K
A
36
B
6
C 12 D 24 15.
Zach gave his dog 1 dog biscuit each day, for 5 days. Then he gave his dog 2 dog biscuits a day for the next 5 days. How many biscuits did Zach give to his dog? q TEKS 3.4.E, 3.4.K
16.
A
5
C 15
B
30
D 7
Annette bought 4 boxes of pencils. If there are 8 pencils in each box, how many pencils did she buy? q TEKS 3.4.E, 3.4.K A
32
B
12
C 16 D 24
Shelly can paint 4 pictures in a day. How many pictures can she paint in 7 days? q TEKS 3.4.E, 3.4.K
Record your answer and fill in the bubbles on the grid. Be sure to use the correct place value.
236
.
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
© Houghton Mifflin Harcourt Publishing Company
17.
7.4 ?
Number and Operations—3.4.E, 3.4.K Algebraic Reasoning— 3.5.B Also 3.4.D, 3.5.D MATHEMATICAL PROCESSES 3.1.C, 3.1.D, 3.1.E
Distributive Property
ALGEBRA
Essential Question
How can you use the Distributive Property to find products?
Unlock Unlock the the Problem Problem Mark bought 6 new fish for his aquarium. He paid $7 for each fish. How much did he spend in all?
• Describe the groups in this problem. • Circle the numbers you will use to
Find 6 × $7.
solve the problem.
You can use the Distributive Property to solve the problem. The Distributive Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
Activity
Materials ■ square tiles
Make an array with tiles to show 6 rows of 7.
© Houghton Mifflin Harcourt Publishing Company
6×7=
Remember sum—the answer to an addition problem addends—the numbers being added Hands On
Break apart the array to make two smaller arrays for facts you know.
■
6×5
6×7=■ 6 × 7 = 6 × (5 + 2) Think: 7 = 5 + 2 6 × 7 = (6 × 5) + (6 × 2) Multiply each addend by 6. 6×7=_+_
Add the products.
6×7=_
6×2
Math Talk Mathematical Processes
What other ways could you break apart the 6 × 7 array?
So, Mark spent $ _ for his new fish. Module 7
229
Share Share and and Show Show Draw a line to show how you could break apart this 6 × 8 array into two smaller arrays for facts you know.
1.
• What numbers do you multiply? _ and _
_ and _ • What numbers do you add? _ + _ 6 × 8 = 6 × (_ + _)
Math Talk Mathematical Processes
6 × 8 = (_ × _) + (_ × _) 6×8=_+_ 6×8=_
Why do you have to add to find the total product when you use the Distributive Property?
Write one way to break apart the array. Then find the product. 2.
3.
Problem Problem Solving Solving
230
Shade tiles to make an array that shows a fact with 7, 8, or 9 as a factor. Write the fact. Explain how you found the product. © Houghton Mifflin Harcourt Publishing Company
4.
Name
Problem Problem Solving Solving 5.
Sense or Nonsense? Robin says, “I can find 8 × 7 by multiplying 3 × 7 and doubling it.“ Does her statement make sense? Justify your answer.
6.
Multi-Step Brandon needs 8 boxes of spinners for his fishing club. The cost of each box is $9. How much will Brandon pay? 8 × $9 = ■
Look at how Brandon solved the problem. Find and describe his error.
8 × 9 = (4 × 9) + (5 × 9) 8 × 9 = 36 + 45 8 × 9 = 81
Use the array to help solve the problem and correct Brandon’s error.
8 × 9 = (4 + 4) × 9
© Houghton Mifflin Harcourt Publishing Company
8 × 9 = (_ × _) + (_ × _) 8×9=_+_ 8×9=_
So, Brandon will pay $ _ for the spinners.
Module 7 • Lesson 4 231
Mathematical Processes M Model ¥ Reason ¥ Communicate M
Daily Daily Assessment Assessment Task Task Fill in the bubble for the correct answer choice. You may use models or strategies to solve. 7.
8.
9.
Use Diagrams Maurice planted 8 rows of popcorn plants. There are 6 plants in each row. The array shows Maurice’s garden. How many popcorn plants does Maurice have? A
36
C
48
B
42
D
64
At a grocery store, the cans of nuts are arranged in 9 rows. There are 6 cans in each row. Which shows one way to find the total number of cans of nuts? A
(5 + 4) × 6
B
(3 + 3) × 6
C
(5 + 5) × 6
D
(5 + 3) × 6
Multi-Step Jillian bought 6 books for $7 each. She paid with $50. How much change should Jillian receive? A
$37
C
$43
B
$18
D
$8
TEXAS Test Prep
232
Representation Which number sentence below is an example of the Distributive Property? A
6 × 8 = 40 + 8
B
(8 × 2) × 3 = 8 × (2 × 3)
C
6×8=8×6
D
6 × 8 = (6 × 2) + (6 × 6)
© Houghton Mifflin Harcourt Publishing Company
10.
H o mewo rk and Practice
7.4
Number and Operations—3.4.E, 3.4.K Algebraic Reasoning—3.5.B Also 3.4.D, 3.5.D MATHEMATICAL PROCESSES 3.1.C, 3.1.D, 3.1.E
Name
Distributive Property
ALGEBRA
Write one way to break apart the array. Then find the product. 1.
3.
2.
Shade tiles to make an array that shows a fact with 5, 6, or 7 as a factor. Explain how you found the product.
Problem Problem Solving Solving
© Houghton Mifflin Harcourt Publishing Company
4.
Shawn makes a tile design by using 7 rows of 8 tiles. Explain how Shawn can break apart his design to find how many tiles he used.
Module 7 • Lesson 4 233
TEXAS Test Prep
Lesson Lesson Check Check Fill in the bubble completely to show your answer.
7.
9.
234
There are 8 tables in the art class. Five students sit at each table. How many students are in the art class?
6.
Seven large trucks are in a parking lot. Each truck has 6 wheels. How many wheels are there in all?
A
13
A
67
B
40
B
40
C
45
C
42
D
85
D
13
Jonas buys 6 packages of corn. Each package has 8 ears of corn. Which way can Jonas use to show how many ears of corn he buys?
8.
A store sells bags of 9 apples. Mr. Hyon buys 5 bags of apples to make pies. Which way can Mr. Hyon use to show how many apples he buys?
A
(4 + 2) × 8
B
(3 + 2) × 8
A
(4 × 9) + (5 × 9)
C
(6 + 6) × 8
B
(3 × 5) + (6 × 5)
D
(4 + 4) × 6
C
(4 × 5) + (5 × 9)
D
(3 × 5) + (9 × 5)
Multi-Step Minka buys 8 CDs for $6 each. She pays with three $20 bills. How much change should Minka receive?
10.
Multi-Step Kent buys 5 bags of potatoes that cost $7 each. He gives the clerk $40. How much change should Kent receive?
A
$48
A
$35
B
$12
B
$12
C
$34
C
$5
D
$68
D
$52
© Houghton Mifflin Harcourt Publishing Company
5.
Name
Module 7 Assessment Vocabulary Vocabulary
Vocabulary Commutative Property
Choose the best term from the box to complete the sentence.
of Multiplication
1.
A ___ of 4 is any product that has 4 as one of its factors. (p. 217)
2.
This is an example of the ___ Property.
Distributive Property multiple
3 × 8 = (3 × 6) + (3 × 2) This property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. (p. 229)
Concepts Concepts and and Skills Skills Write one way to break apart the array. Then find the product. q TEKS 3.4.E, 3.4.K 3.
4.
© Houghton Mifflin Harcourt Publishing Company
Find the product. 5.
3×1=_
9.
2 ×1 _
q TEKS 3.4.E, 3.4.K
6.
10.
5×6=_
6 ×6 _
11.
7.
6 ×7 _
4×7=_ 12.
6 ×3 _
8.
2 × 10 = _ 13.
3 ×8 _
Module 7
235
TEXAS Test Prep
Fill in the bubble for the correct answer choice. You may use models to solve. 14. Lori saw 6 lightning bugs. They each had 6 legs. How many legs did the lightning bugs have in all? q TEKS 3.4.E, 3.4.K
A
36
B
6
C 12 D 24 15.
Zach gave his dog 1 dog biscuit each day, for 5 days. Then he gave his dog 2 dog biscuits a day for the next 5 days. How many biscuits did Zach give to his dog? q TEKS 3.4.E, 3.4.K
16.
A
5
C 15
B
30
D 7
Annette bought 4 boxes of pencils. If there are 8 pencils in each box, how many pencils did she buy? q TEKS 3.4.E, 3.4.K A
32
B
12
C 16 D 24
Shelly can paint 4 pictures in a day. How many pictures can she paint in 7 days? q TEKS 3.4.E, 3.4.K
Record your answer and fill in the bubbles on the grid. Be sure to use the correct place value.
236
.
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
© Houghton Mifflin Harcourt Publishing Company
17.
