Relate Addition and Multiplication
Name
6.1 ALGEBRA
?
Number and Operations—3.4.D, 3.4.E MATHEMATICAL PROCESSES 3.1.E, 3.1.F
Relate Addition and Multiplication
Essential Question How is multiplication like addition? How is it different?
Unlock Unlock the the Problem Problem Tomeka needs 3 apples to make one apple cake. Each cake has the same number of apples. How many apples does Tomeka need to make 4 cakes? Equal groups have the same number of objects in each group.
• How many cakes is Tomeka making? • How many apples are in each cake? • How can you solve the problem?
One Way Add equal groups. Use the 4 circles to show the 4 cakes. Draw 3 counters in each circle to show the apples Tomeka needs for each cake.
© Houghton Mifflin Harcourt Publishing Company
Find the number of counters in all. Complete the addition sentence. 3+_+_+_=_ So, Tomeka needs _ apples to
Math Talk Mathematical Processes
Explain how the picture you drew shows groups of equal size.
make _ cakes.
Module 6
173
Another Way
Multiply.
When you combine equal groups, you can multiply to find how many in all. Think: 4 groups of 3
Draw 3 counters in each circle. Since there are the same number of counters in each circle, you can multiply to find how many in all.
←
←
←
Multiplication is another way to find how many there are altogether in equal groups. 3 ← factor Write: 4 × 3 = 12 or _ × 4 ← factor 12 ← product factor
factor
product
Read: Four times three equals twelve. The factors are the numbers multiplied. The product is the answer to a multiplication problem.
Share Share and and Show Show 1.
Write related addition and multiplication sentences for the model.
Math Talk
_+_+_+ _ = _ _×_=_
174
How would you change this model so you could write a multiplication sentence to match it?
© Houghton Mifflin Harcourt Publishing Company
Mathematical Processes
Name
Draw a quick picture to show the equal groups. Then write related addition and multiplication sentences. 2.
3 groups of 6
3.
2 groups of 3
_+_+_ = _
_+_=_
_×_=_
_×_=_
Problem Problem Solving Solving Use the table for 4–5. 4.
5.
© Houghton Mifflin Harcourt Publishing Company
6.
Average Weight of Fruits
Record Morris bought 4 peaches. How much do the peaches weigh in all? Write a multiplication sentence to find the weight of the peaches.
Apple
6
Orange
5
Peach
3
_ × _ = _ ounces
Banana
4
Multi-Step Thomas bought 2 apples. Sydney bought 4 bananas. Which weighed more—the 2 apples or the 4 bananas? How much more? Explain how you know.
Fruit
Write Math
Weight in Ounces
Show Your Work
Write Math
Write a word problem that can be solved using 3 × 4. Solve the problem.
Module 6 • Lesson 1 175
Mathematical Processes M Model ¥ Reason ¥ Communicate M
Daily Daily Assessment Assessment Task Task Fill in the bubble for the correct answer choice.
8.
9.
Apply Laura and her mother make jam from berries and apples. When they are finished, they have 9 jars of apple jam and 9 jars of berry jam. Which multiplication sentence shows how many jars they made? A
1×9=9
B
2×2=4
C
9 × 9 = 81
D
2 × 9 = 18
Billy has 3 stacks of books. Each stack has 6 books. Billy says that the number of books is equal to 6 + 6 + 6. Which is another way to find the number of books? A
6 × 6 = 36
B
3 × 6 = 18
C
6×1=6
D
3×3=9
Multi-Step Carlos buys 4 packs of regular pencils. He buys 2 packs of color pencils. There are 4 pencils in each kind of pack. How many pencils did Carlos buy? A
24
C
32
B
16
D
12
TEXAS Test Prep 10.
176
Which is another way to show 2 + 2 + 2 + 2? A
2×2
C
4×2
B
5×2
D
2×8
© Houghton Mifflin Harcourt Publishing Company
7.
H o mewo rk and Practice
6.1
Number and Operations—3.4.D, 3.4.E MATHEMATICAL PROCESSES 3.1.E, 3.1.F
Name
Relate Addition and Multiplication
ALGEBRA
Draw a quick picture to show equal groups. Then write related addition and multiplication sentences. 1.
3 groups of 4
2.
4 groups of 2
_+_+_=_
_+_+_+_=_
_×_=_
_×_=_
Use the table for 3–4. 3.
Kaymer buys 2 boxes of crayons. Write a multiplication sentence to find how many crayons Kaymer buys.
Boxes of School Supplies Box
_ × _= _ 4.
Mya buys 4 boxes of pencils. Write a multiplication sentence to find how many pencils Mya buys.
Number in Each
Crayons
6
Markers
4
Pencils
3
_×_=_ Problem Problem Solving Solving
© Houghton Mifflin Harcourt Publishing Company
5.
Zach buys 4 boxes of pens. Each pack has 4 pens. Write a multiplication sentence to show how many pens Zach buys.
_×_=_
6.
Ada has 3 vases. She puts 5 flowers in each vase. Write a multiplication sentence to show how many flowers Ada puts in the vases.
_×_=_
Module 6 • Lesson 1 177
TEXAS Test Prep
Lesson Lesson Check Check
9.
11.
178
Jada makes 3 trays of muffins. Each tray holds 6 muffins. Which equation shows how many muffins Jada makes?
8.
Robinson puts 5 books on 2 shelves. Which equation shows how many books Robinson puts on the shelves?
A
3 × 6 = 18
A
2 + 5 = 10
B
3+6=9
B
5+2=7
C
6×3=9
C
5 × 2 = 10
D
6 × 3 = 12
D
2×5=7
Midori puts 5 flowers in each of 3 vases. She says the number of flowers is equal to 5 + 5 + 5. Which is another way to find the number of flowers?
10.
Pete has 5 boxes. Each box has 4 toy cars in it. Pete says the number of cars is equal to 4 + 4 + 4 + 4 + 4. Which is another way to find the number of cars?
A
3×3
A
5+4
B
3×5
B
4×4
C
5+5
C
5×5
D
3+5
D
5×4
Multi-Step Mrs. Tomar buys 2 packs of vanilla yogurt and 3 packs of strawberry yogurt. Each pack has 4 yogurts. How many yogurts does Mrs. Tomar buy?
12.
Multi-Step Murray buys 3 packs of red peppers and 4 packs of green peppers. Each pack has 4 peppers. How many peppers does Murray buy?
A
20
A
16
B
9
B
12
C
12
C
28
D
24
D
48
© Houghton Mifflin Harcourt Publishing Company
7.
6.1 ALGEBRA
?
Number and Operations—3.4.D, 3.4.E MATHEMATICAL PROCESSES 3.1.E, 3.1.F
Relate Addition and Multiplication
Essential Question How is multiplication like addition? How is it different?
Unlock Unlock the the Problem Problem Tomeka needs 3 apples to make one apple cake. Each cake has the same number of apples. How many apples does Tomeka need to make 4 cakes? Equal groups have the same number of objects in each group.
• How many cakes is Tomeka making? • How many apples are in each cake? • How can you solve the problem?
One Way Add equal groups. Use the 4 circles to show the 4 cakes. Draw 3 counters in each circle to show the apples Tomeka needs for each cake.
© Houghton Mifflin Harcourt Publishing Company
Find the number of counters in all. Complete the addition sentence. 3+_+_+_=_ So, Tomeka needs _ apples to
Math Talk Mathematical Processes
Explain how the picture you drew shows groups of equal size.
make _ cakes.
Module 6
173
Another Way
Multiply.
When you combine equal groups, you can multiply to find how many in all. Think: 4 groups of 3
Draw 3 counters in each circle. Since there are the same number of counters in each circle, you can multiply to find how many in all.
←
←
←
Multiplication is another way to find how many there are altogether in equal groups. 3 ← factor Write: 4 × 3 = 12 or _ × 4 ← factor 12 ← product factor
factor
product
Read: Four times three equals twelve. The factors are the numbers multiplied. The product is the answer to a multiplication problem.
Share Share and and Show Show 1.
Write related addition and multiplication sentences for the model.
Math Talk
_+_+_+ _ = _ _×_=_
174
How would you change this model so you could write a multiplication sentence to match it?
© Houghton Mifflin Harcourt Publishing Company
Mathematical Processes
Name
Draw a quick picture to show the equal groups. Then write related addition and multiplication sentences. 2.
3 groups of 6
3.
2 groups of 3
_+_+_ = _
_+_=_
_×_=_
_×_=_
Problem Problem Solving Solving Use the table for 4–5. 4.
5.
© Houghton Mifflin Harcourt Publishing Company
6.
Average Weight of Fruits
Record Morris bought 4 peaches. How much do the peaches weigh in all? Write a multiplication sentence to find the weight of the peaches.
Apple
6
Orange
5
Peach
3
_ × _ = _ ounces
Banana
4
Multi-Step Thomas bought 2 apples. Sydney bought 4 bananas. Which weighed more—the 2 apples or the 4 bananas? How much more? Explain how you know.
Fruit
Write Math
Weight in Ounces
Show Your Work
Write Math
Write a word problem that can be solved using 3 × 4. Solve the problem.
Module 6 • Lesson 1 175
Mathematical Processes M Model ¥ Reason ¥ Communicate M
Daily Daily Assessment Assessment Task Task Fill in the bubble for the correct answer choice.
8.
9.
Apply Laura and her mother make jam from berries and apples. When they are finished, they have 9 jars of apple jam and 9 jars of berry jam. Which multiplication sentence shows how many jars they made? A
1×9=9
B
2×2=4
C
9 × 9 = 81
D
2 × 9 = 18
Billy has 3 stacks of books. Each stack has 6 books. Billy says that the number of books is equal to 6 + 6 + 6. Which is another way to find the number of books? A
6 × 6 = 36
B
3 × 6 = 18
C
6×1=6
D
3×3=9
Multi-Step Carlos buys 4 packs of regular pencils. He buys 2 packs of color pencils. There are 4 pencils in each kind of pack. How many pencils did Carlos buy? A
24
C
32
B
16
D
12
TEXAS Test Prep 10.
176
Which is another way to show 2 + 2 + 2 + 2? A
2×2
C
4×2
B
5×2
D
2×8
© Houghton Mifflin Harcourt Publishing Company
7.
H o mewo rk and Practice
6.1
Number and Operations—3.4.D, 3.4.E MATHEMATICAL PROCESSES 3.1.E, 3.1.F
Name
Relate Addition and Multiplication
ALGEBRA
Draw a quick picture to show equal groups. Then write related addition and multiplication sentences. 1.
3 groups of 4
2.
4 groups of 2
_+_+_=_
_+_+_+_=_
_×_=_
_×_=_
Use the table for 3–4. 3.
Kaymer buys 2 boxes of crayons. Write a multiplication sentence to find how many crayons Kaymer buys.
Boxes of School Supplies Box
_ × _= _ 4.
Mya buys 4 boxes of pencils. Write a multiplication sentence to find how many pencils Mya buys.
Number in Each
Crayons
6
Markers
4
Pencils
3
_×_=_ Problem Problem Solving Solving
© Houghton Mifflin Harcourt Publishing Company
5.
Zach buys 4 boxes of pens. Each pack has 4 pens. Write a multiplication sentence to show how many pens Zach buys.
_×_=_
6.
Ada has 3 vases. She puts 5 flowers in each vase. Write a multiplication sentence to show how many flowers Ada puts in the vases.
_×_=_
Module 6 • Lesson 1 177
TEXAS Test Prep
Lesson Lesson Check Check
9.
11.
178
Jada makes 3 trays of muffins. Each tray holds 6 muffins. Which equation shows how many muffins Jada makes?
8.
Robinson puts 5 books on 2 shelves. Which equation shows how many books Robinson puts on the shelves?
A
3 × 6 = 18
A
2 + 5 = 10
B
3+6=9
B
5+2=7
C
6×3=9
C
5 × 2 = 10
D
6 × 3 = 12
D
2×5=7
Midori puts 5 flowers in each of 3 vases. She says the number of flowers is equal to 5 + 5 + 5. Which is another way to find the number of flowers?
10.
Pete has 5 boxes. Each box has 4 toy cars in it. Pete says the number of cars is equal to 4 + 4 + 4 + 4 + 4. Which is another way to find the number of cars?
A
3×3
A
5+4
B
3×5
B
4×4
C
5+5
C
5×5
D
3+5
D
5×4
Multi-Step Mrs. Tomar buys 2 packs of vanilla yogurt and 3 packs of strawberry yogurt. Each pack has 4 yogurts. How many yogurts does Mrs. Tomar buy?
12.
Multi-Step Murray buys 3 packs of red peppers and 4 packs of green peppers. Each pack has 4 peppers. How many peppers does Murray buy?
A
20
A
16
B
9
B
12
C
12
C
28
D
24
D
48
© Houghton Mifflin Harcourt Publishing Company
7.
