Multiply with 1 and 0
Name
6.6
Number and Operations—3.4.K Also 3.4.E MATHEMATICAL PROCESSES 3.1.E, 3.1.G
Multiply with 1 and 0
ALGEBRA
?
Essential Question
What happens when you multiply a number by 0 or 1?
Unlock Unlock the the Problem Problem Luke sees 4 birdbaths. Each birdbath has 2 birds in it. What multiplication sentence tells how many birds there are? Draw a quick picture to show the birds in the birdbaths.
• How many birdbaths are there? • How many birds are in each birdbath to start? __
_×_=_ One bird flies away from each birdbath. Cross out 1 bird in each birdbath above. What multiplication sentence shows the total number of birds left?
_ →
=
→
_
→
×
birdbaths
bird left in each birdbath
total number of birds
Now cross out another bird in each birdbath. What multiplication sentence shows the total number of birds left in the birdbaths?
_
=
_ →
×
→
_ →
© Houghton Mifflin Harcourt Publishing Company • Image Credits:
_
birdbaths
birds left in each birdbath
total number of birds
Math Talk Mathematical Processes
What if there were 5 birdbaths with 0 birds in each of them? What would be the product? Explain.
• How do the birdbaths look now? _______
Module 6
203
Connect You have multiplied with 1 and 0. Now you will learn two properties that will help you find products when multiplying a number by 1 or by 0. The Identity Property of Multiplication states that the product of any number and 1 is that number. 7×1=7
6×1=6
1×7=7
1×6=6
The Zero Property of Multiplication states that the product of zero and any number is zero. 0×5=0
0×8=0
5×0=0
8×0=0
Share Share and and Show Show Find the product. Write the multiplication property you used.
1.
1×3=_
__ Property of Multiplication
Find the product. 2.
5×1=_
3.
0×2=_
4.
4×0=_
5.
1×6=_
6.
3×0=_
7.
1×7=_
8.
0×0=_
9.
8×1=_
Math Talk Mathematical Processes
Explain how 3 × 1 and 3 + 1 are different.
Problem Problem Solving Solving What pattern do you see when you multiply numbers with 0 as a factor?
Algebra Complete the multiplication sentence. 11.
_ × 1 = 15
12.
1 × 28 = _
13.
0 × 46 = _
14.
36 × 0 = _
15.
_×5=5
16.
19 × _ = 0
17.
_×0=0
18.
7×_=7
204
© Houghton Mifflin Harcourt Publishing Company
10.
Name
Problem Problem Solving Solving Use the table for 19–21. 19.
Communicate At the circus Jon saw 5 unicycles. How many wheels were on the unicycles in all? Write a multiplication sentence.
_ × _ = __ 20.
21.
What’s the Question? Julia used multiplication with 1 and the information in the table. The answer is 3.
22.
Multi-Step Mason and Alexis each have 1 bag of marbles. There are 9 marbles in each bag. How many marbles do they have altogether?
23.
© Houghton Mifflin Harcourt Publishing Company
Multi-Step Brian saw some circus vehicles. He saw 17 wheels in all. If 2 of the vehicles are cars, how many vehicles are bicycles and tricycles?
Circus Vehicles Type of Vehicle
Number of Wheels
Car
4
Tricycle
3
Bicycle
2
Unicycle
1
Write Math
Show Your Work
Write Math
Write a word problem that uses multiplying with 1 or 0. Show how to solve your problem.
Module 6 • Lesson 6 205
Mathematical Processes M Model ¥ Reason ¥ Communicate M
Daily Daily Assessment Assessment Task Task Fill in the bubble for the correct answer choice. 24.
25.
26.
Use Symbols Maria sees 6 snakes at the zoo. Each snake has 1 tongue. Which multiplication sentence shows how many tongues the snakes have in all? A
6×0=0
C
6×1=6
B
1×1=1
D
6 × 6 = 36
Each box of crayons holds 8 crayons. Robbie has 1 box of crayons. How many crayons does Robbie have in all? A
9
C
1
B
8
D
0
Multi-Step Each package of wildflower seeds holds 4 daisy seeds and 5 violet seeds. Haley has 0 packages of seeds. Which number sentence shows how many seeds Haley has? A
0×9=0
B
9−1=0
C
9 + 1 = 10
D
1×9=9
TEXAS Test Prep
206
Use Symbols Eric has 1 pencil box at school. There are 6 pencils in the box. Which number sentence shows how many pencils there are in Eric’s pencil box? A
6+1=7
B
0×6=0
C
6−1=5
D
1×6=6
© Houghton Mifflin Harcourt Publishing Company
27.
Number and Operations—3.4.K Also 3.4.E MATHEMATICAL PROCESSES 3.1.E, 3.1.G
H o mewo rk and Practice
6.6
Name
Multiply with 1 and 0
ALGEBRA
Find the product. 1. 6 × 1 = _
2.
0×3=_
3. 1 × 8 = _
4. 4 × 0 = _
5.
9×1=_
6.
Use the table for 7–9. 7.
Patterns of Beads on a Necklace
Walt strings 1 pattern of yellow beads on his necklace. Write a multiplication sentence to show how many yellow beads he uses in all.
Color
_×_=_
8.
Shoshona uses 1 pattern of red beads. Write a multiplication sentence to show how many red beads she uses in all.
0×1=_
Number of Beads
Red
6
Blue
2
Yellow
3
Green
4
9.
Ella strings 1 pattern of green beads and 1 pattern of blue beads. How many beads does she use in all?
11.
There are 3 frogs on each of 5 lily pads. Two frogs jump off of each lily pad. Write a multiplication sentence to show how many frogs are still on the lily pads.
_×_=_ Problem Problem Solving Solving
© Houghton Mifflin Harcourt Publishing Company
10.
There are 2 pancakes on each of 4 plates. The 4 people in the Matsui family eat all of their pancakes. Write a number sentence to show how many pancakes are left on the plates.
_×_=_
_×_=_
Module 6 • Lesson 6
207
TEXAS Test Prep
Lesson Lesson Check Check
14.
16.
208
Frank puts 8 placemats on the table. Each placemat gets 1 plate. Which multiplication sentence shows how many plates there are?
13.
Julia has 9 boxes. There is 1 model car in each box. Which multiplication sentence shows how many model cars Julia has?
A
8×1=8
A
0×9=9
B
8 × 8 = 64
B
1×9=1
C
8×0=0
C
9 × 9 = 18
D
8×1=1
D
9×1=9
Each basket hold 5 melons. Mr. Chavez buys 1 basket. How many melons does Mr. Chavez have? A
1
B
5
C
10
D
6
Multi-Step Jayne has 1 box with 4 red crayons and 3 blue crayons. Which number sentence shows how many crayons Jayne has?
15.
17.
Noah sets out 7 baskets at the Farmers’ Market. Each basket holds 1 watermelon. How many watermelons does Noah set out? A
14
B
7
C
8
D
1
Multi-Step Each box holds 6 black markers and 4 red markers. Derek has 0 boxes of markers. Which number sentence shows how many markers Derek has?
A
1×4=4
B
1×3=3
A
10 × 0 = 10
C
1×7=7
B
0 × 10 = 0
D
3 × 4 = 12
C
10 × 1 = 10
D
10 × 1 = 1
© Houghton Mifflin Harcourt Publishing Company
12.
Name
Module 6 Assessment Vocabulary Vocabulary
Vocabulary
Choose the best term from the box. 1.
factors
The answer in a multiplication problem is called the __.
2.
equal groups product
(p. 174)
The numbers you multiply are called the __.
(p. 174)
Concepts Concepts and and Skills Skills Write related addition and multiplication sentences. 3.
3 groups of 9
4.
q TEKS 3.4.D, 3.4.E
5 groups of 7
_+_+_=_
_+_+_+_+_=_
_×_=_
_×_=_
Draw jumps on the number line to show equal groups. Find the product. q TEKS 3.4.E, 3.4.K 5.
6 groups of 3
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
_×_=_ Write a multiplication sentence for the model. Then use the Commutative Property of Multiplication to write a related multiplication sentence. q TEKS 3.4.D, 3.4.E, 3.4.K, 3.5.B © Houghton Mifflin Harcourt Publishing Company
6.
7.
8.
_×_=_
_×_=_
_×_=_
_×_=_
_×_=_
_×_=_ Module 6
209
TEXAS Test Prep
Fill in the bubble for the correct answer choice. You can use objects or models to solve. 9. Beth’s mother made some cookies. She put 4 cookies on each of 8 plates. Which equation can be used to find the number of cookies Beth’s mother put on the plates? q TEKS 3.4.D, 3.4.E, 3.5.B
A
8 + 4 = ■
B
4 × 4 = ■
C 8 × 4 = ■ D 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = ■
10. Josh has 4 dogs. Each dog gets 2 dog biscuits every day. How many biscuits will Josh need for all of his dogs for Saturday and Sunday? q TEKS 3.4.E, 3.4.K, 3.5.B A
4
B
12
C 8 D 16
11. A unicycle has only 1 wheel. How many wheels are there on 9 unicycles? q TEKS 3.4.K 11
C 1
B
9
D 10
Lindsey needs 3 lengths of ribbon, each 5 inches long. Caleb needs 2 lengths of ribbon, each 6 inches long. How many inches of ribbon do they need altogether? q TEKS 3.4.E, 3.4.K, 3.5.B
Record your answer and fill in the bubbles on the grid. Be sure to use the correct place value.
210
.
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
2. 1
A
6.6
Number and Operations—3.4.K Also 3.4.E MATHEMATICAL PROCESSES 3.1.E, 3.1.G
Multiply with 1 and 0
ALGEBRA
?
Essential Question
What happens when you multiply a number by 0 or 1?
Unlock Unlock the the Problem Problem Luke sees 4 birdbaths. Each birdbath has 2 birds in it. What multiplication sentence tells how many birds there are? Draw a quick picture to show the birds in the birdbaths.
• How many birdbaths are there? • How many birds are in each birdbath to start? __
_×_=_ One bird flies away from each birdbath. Cross out 1 bird in each birdbath above. What multiplication sentence shows the total number of birds left?
_ →
=
→
_
→
×
birdbaths
bird left in each birdbath
total number of birds
Now cross out another bird in each birdbath. What multiplication sentence shows the total number of birds left in the birdbaths?
_
=
_ →
×
→
_ →
© Houghton Mifflin Harcourt Publishing Company • Image Credits:
_
birdbaths
birds left in each birdbath
total number of birds
Math Talk Mathematical Processes
What if there were 5 birdbaths with 0 birds in each of them? What would be the product? Explain.
• How do the birdbaths look now? _______
Module 6
203
Connect You have multiplied with 1 and 0. Now you will learn two properties that will help you find products when multiplying a number by 1 or by 0. The Identity Property of Multiplication states that the product of any number and 1 is that number. 7×1=7
6×1=6
1×7=7
1×6=6
The Zero Property of Multiplication states that the product of zero and any number is zero. 0×5=0
0×8=0
5×0=0
8×0=0
Share Share and and Show Show Find the product. Write the multiplication property you used.
1.
1×3=_
__ Property of Multiplication
Find the product. 2.
5×1=_
3.
0×2=_
4.
4×0=_
5.
1×6=_
6.
3×0=_
7.
1×7=_
8.
0×0=_
9.
8×1=_
Math Talk Mathematical Processes
Explain how 3 × 1 and 3 + 1 are different.
Problem Problem Solving Solving What pattern do you see when you multiply numbers with 0 as a factor?
Algebra Complete the multiplication sentence. 11.
_ × 1 = 15
12.
1 × 28 = _
13.
0 × 46 = _
14.
36 × 0 = _
15.
_×5=5
16.
19 × _ = 0
17.
_×0=0
18.
7×_=7
204
© Houghton Mifflin Harcourt Publishing Company
10.
Name
Problem Problem Solving Solving Use the table for 19–21. 19.
Communicate At the circus Jon saw 5 unicycles. How many wheels were on the unicycles in all? Write a multiplication sentence.
_ × _ = __ 20.
21.
What’s the Question? Julia used multiplication with 1 and the information in the table. The answer is 3.
22.
Multi-Step Mason and Alexis each have 1 bag of marbles. There are 9 marbles in each bag. How many marbles do they have altogether?
23.
© Houghton Mifflin Harcourt Publishing Company
Multi-Step Brian saw some circus vehicles. He saw 17 wheels in all. If 2 of the vehicles are cars, how many vehicles are bicycles and tricycles?
Circus Vehicles Type of Vehicle
Number of Wheels
Car
4
Tricycle
3
Bicycle
2
Unicycle
1
Write Math
Show Your Work
Write Math
Write a word problem that uses multiplying with 1 or 0. Show how to solve your problem.
Module 6 • Lesson 6 205
Mathematical Processes M Model ¥ Reason ¥ Communicate M
Daily Daily Assessment Assessment Task Task Fill in the bubble for the correct answer choice. 24.
25.
26.
Use Symbols Maria sees 6 snakes at the zoo. Each snake has 1 tongue. Which multiplication sentence shows how many tongues the snakes have in all? A
6×0=0
C
6×1=6
B
1×1=1
D
6 × 6 = 36
Each box of crayons holds 8 crayons. Robbie has 1 box of crayons. How many crayons does Robbie have in all? A
9
C
1
B
8
D
0
Multi-Step Each package of wildflower seeds holds 4 daisy seeds and 5 violet seeds. Haley has 0 packages of seeds. Which number sentence shows how many seeds Haley has? A
0×9=0
B
9−1=0
C
9 + 1 = 10
D
1×9=9
TEXAS Test Prep
206
Use Symbols Eric has 1 pencil box at school. There are 6 pencils in the box. Which number sentence shows how many pencils there are in Eric’s pencil box? A
6+1=7
B
0×6=0
C
6−1=5
D
1×6=6
© Houghton Mifflin Harcourt Publishing Company
27.
Number and Operations—3.4.K Also 3.4.E MATHEMATICAL PROCESSES 3.1.E, 3.1.G
H o mewo rk and Practice
6.6
Name
Multiply with 1 and 0
ALGEBRA
Find the product. 1. 6 × 1 = _
2.
0×3=_
3. 1 × 8 = _
4. 4 × 0 = _
5.
9×1=_
6.
Use the table for 7–9. 7.
Patterns of Beads on a Necklace
Walt strings 1 pattern of yellow beads on his necklace. Write a multiplication sentence to show how many yellow beads he uses in all.
Color
_×_=_
8.
Shoshona uses 1 pattern of red beads. Write a multiplication sentence to show how many red beads she uses in all.
0×1=_
Number of Beads
Red
6
Blue
2
Yellow
3
Green
4
9.
Ella strings 1 pattern of green beads and 1 pattern of blue beads. How many beads does she use in all?
11.
There are 3 frogs on each of 5 lily pads. Two frogs jump off of each lily pad. Write a multiplication sentence to show how many frogs are still on the lily pads.
_×_=_ Problem Problem Solving Solving
© Houghton Mifflin Harcourt Publishing Company
10.
There are 2 pancakes on each of 4 plates. The 4 people in the Matsui family eat all of their pancakes. Write a number sentence to show how many pancakes are left on the plates.
_×_=_
_×_=_
Module 6 • Lesson 6
207
TEXAS Test Prep
Lesson Lesson Check Check
14.
16.
208
Frank puts 8 placemats on the table. Each placemat gets 1 plate. Which multiplication sentence shows how many plates there are?
13.
Julia has 9 boxes. There is 1 model car in each box. Which multiplication sentence shows how many model cars Julia has?
A
8×1=8
A
0×9=9
B
8 × 8 = 64
B
1×9=1
C
8×0=0
C
9 × 9 = 18
D
8×1=1
D
9×1=9
Each basket hold 5 melons. Mr. Chavez buys 1 basket. How many melons does Mr. Chavez have? A
1
B
5
C
10
D
6
Multi-Step Jayne has 1 box with 4 red crayons and 3 blue crayons. Which number sentence shows how many crayons Jayne has?
15.
17.
Noah sets out 7 baskets at the Farmers’ Market. Each basket holds 1 watermelon. How many watermelons does Noah set out? A
14
B
7
C
8
D
1
Multi-Step Each box holds 6 black markers and 4 red markers. Derek has 0 boxes of markers. Which number sentence shows how many markers Derek has?
A
1×4=4
B
1×3=3
A
10 × 0 = 10
C
1×7=7
B
0 × 10 = 0
D
3 × 4 = 12
C
10 × 1 = 10
D
10 × 1 = 1
© Houghton Mifflin Harcourt Publishing Company
12.
Name
Module 6 Assessment Vocabulary Vocabulary
Vocabulary
Choose the best term from the box. 1.
factors
The answer in a multiplication problem is called the __.
2.
equal groups product
(p. 174)
The numbers you multiply are called the __.
(p. 174)
Concepts Concepts and and Skills Skills Write related addition and multiplication sentences. 3.
3 groups of 9
4.
q TEKS 3.4.D, 3.4.E
5 groups of 7
_+_+_=_
_+_+_+_+_=_
_×_=_
_×_=_
Draw jumps on the number line to show equal groups. Find the product. q TEKS 3.4.E, 3.4.K 5.
6 groups of 3
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
_×_=_ Write a multiplication sentence for the model. Then use the Commutative Property of Multiplication to write a related multiplication sentence. q TEKS 3.4.D, 3.4.E, 3.4.K, 3.5.B © Houghton Mifflin Harcourt Publishing Company
6.
7.
8.
_×_=_
_×_=_
_×_=_
_×_=_
_×_=_
_×_=_ Module 6
209
TEXAS Test Prep
Fill in the bubble for the correct answer choice. You can use objects or models to solve. 9. Beth’s mother made some cookies. She put 4 cookies on each of 8 plates. Which equation can be used to find the number of cookies Beth’s mother put on the plates? q TEKS 3.4.D, 3.4.E, 3.5.B
A
8 + 4 = ■
B
4 × 4 = ■
C 8 × 4 = ■ D 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = ■
10. Josh has 4 dogs. Each dog gets 2 dog biscuits every day. How many biscuits will Josh need for all of his dogs for Saturday and Sunday? q TEKS 3.4.E, 3.4.K, 3.5.B A
4
B
12
C 8 D 16
11. A unicycle has only 1 wheel. How many wheels are there on 9 unicycles? q TEKS 3.4.K 11
C 1
B
9
D 10
Lindsey needs 3 lengths of ribbon, each 5 inches long. Caleb needs 2 lengths of ribbon, each 6 inches long. How many inches of ribbon do they need altogether? q TEKS 3.4.E, 3.4.K, 3.5.B
Record your answer and fill in the bubbles on the grid. Be sure to use the correct place value.
210
.
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
2. 1
A
