Multiplication Problems
Name
8.6
?
Number and Operations—3.4.K MATHEMATICAL PROCESSES 3.1.B, 3.1.F
PROBLEM SOLVING • Two-Step
Multiplication Problems
Essential Question
How can you use the strategy make a table to solve one-step and two-step multiplication problems?
Unlock Unlock the the Problem Problem Scott has a stamp album. Some pages have 1 stamp on them, and other pages have 2 stamps on them. If Scott has 18 stamps, show how many different ways he could put them in the album. Use the graphic organizer below to solve the problem.
Read What do I need to find?
Solve Make a table to show the number of pages with 1 stamp and with 2 stamps. Each row must equal
_ , the total number of stamps. Pages with 2 Stamps
Pages with 1 Stamp
Total Stamps
What information am I given?
8
2
18
Scott has _ stamps. Some album
7
4
18
pages have _ stamp on them, and
6
6
18
the other pages have _ stamps.
5 10
Plan
3
What is my plan or strategy?
© Houghton Mifflin Harcourt Publishing Company
I will make a _ showing all the different ways of arranging the stamps in the album.
1.
18 18
12
2
So, there are _ different ways.
What number patterns do you see in the table?
Module 8
267
Try Try Another Another Problem Problem What if Scott bought 3 more stamps and now has 21 stamps? Some album pages have 1 stamp and some pages have 2 stamps. Show how many different ways he could put the odd number of stamps in the album.
Read
Solve
What do I need to find?
What information am I given?
Plan What is my plan or strategy?
So, there are _ different ways. What patterns do you see in this table?
Math Talk Mathematical Processes
Explain how these patterns are different from the patterns in the table on page 267.
268
© Houghton Mifflin Harcourt Publishing Company
2.
Name
Share Share and and Show Show 1.
Aaron’s mother is making lemonade. For each pitcher, she uses 1 cup of lemon juice, 1 cup of sugar, and 6 cups of water. What is the total number of cups of ingredients she will use to make 5 pitchers of lemonade? First, make a table to show the number of cups of lemon juice, sugar, and water that are in 1 pitcher of lemonade. Next, multiply to find the number of cups of water needed for each pitcher of lemonade.
Think: For every pitcher, the number of cups of water increases by 6.
Last, use the table to solve the problem. Number of Pitchers
1
2
Cups of Lemon Juice
1
Cups of Sugar
1
2
Cups of Water
6
12
Total Number of Cups of Ingredients
8
3
5
3
24
So, in 5 pitchers of lemonade, there are _ cups of lemon juice, _ cups of sugar, and _ cups of water. This makes a total of _ cups of ingredients. 2.
What pattern do you see in the total number of cups of ingredients?
© Houghton Mifflin Harcourt Publishing Company
Problem Problem Solving Solving 3.
Multi-Step Cammi needs 36 postcards. She buys 4 packages of 10 postcards. How many postcards will Cammi have left over? Explain.
Module 8 • Lesson 6
269
Mathematical Processes M Model ¥ Reason ¥ Communicate M
Daily Daily Assessment Assessment Task Task Fill in the bubble for the correct answer choice. 4.
5.
6.
There are 5 boats in a race. Each boat has 6 rowers and 1 coach. How many people are in the race? Use the table to solve the problem. Number of Boats
1
2
Number of Rowers
6
12
Number of Coaches
1
2
Total Number of People
7
3
4
5
3
A
7
C
12
B
30
D
35
Apply For each pan of bread, you need 2 cups of white flour and 1 cup of wheat flour. What is the total number of cups of flour you will need to make 4 pans of bread? A
7 cups
C
8 cups
B
3 cups
D
12 cups
Multi-Step Sheri puts 16 pictures in an album. Some pages have 2 pictures. The other pages have 4 pictures. There are 3 pages with 4 pictures. How many pages have 2 pictures? A
3
C
4
B
2
D
1
7.
270
Each year for 8 years, the Williams family visited 6 different states on vacation. How many more states do they need to visit before they have seen all 50 states? A
36
C
48
B
14
D
2
© Houghton Mifflin Harcourt Publishing Company
TEXAS Test Prep
Number and Operations—3.4.K MATHEMATICAL PROCESSES 3.1.B, 3.1.F
H o mewo rk and Practice
8.6
Name
• Two-Step Multiplication Problems PROBLEM SOLVING
Make a table to solve the problem. 1.
Janey is making party mix. For each bowl of mix, she uses 2 cups of raisins, 1 cup of peanuts, and 4 cups of granola. What is the total number of cups of ingredients she will use to make 6 bowls of party mix? Number of Bowls
1
Cups of Raisins
2
Cups of Peanuts
1
Cups of Granola
4
Total Number of Cups
7
2
3
5
6
4 8
So, in 6 bowls of party mix, there are _ cups of raisins, _ cups of peanuts, and _ cups of granola. This makes a total of _ cups of ingredients.
Problem Problem Solving Solving
© Houghton Mifflin Harcourt Publishing Company
2.
To make an apple pie, Mimi needs 2 cups of flour and 3 cups of apples. How many cups of ingredients does Mimi need to make 5 pies?
3.
To make muffins, Seth needs 3 cups of mix and 1 cup of raisins. How many cups of ingredients does Seth need to make 3 batches of muffins?
Module 8 • Lesson 6 271
TEXAS Test Prep
Lesson Lesson Check Check
6.
8.
272
There are 6 relay teams at a race. Each team has 4 runners and 1 captain. How many people are in the race?
5.
Sara makes 7 fruit baskets for the senior center. She puts 3 apples and 4 pears in each basket. How many pieces of fruit are there?
A
11
A
14
B
30
B
21
C
24
C
49
D
25
D
28
Thomas wants to collect 40 toy cars for his collection. If he has 6 boxes of 4 toy cars each, how many more cars does Thomas need?
7.
Vernon needs to sell 60 granola bars for his scout troop. If he sells 4 boxes of 8 bars each, how many more bars does Vernon need to sell?
A
16
A
48
B
24
B
32
C
50
C
28
D
34
D
30
Multi-Step Jessie has 4 boxes of 8 crayons and 3 boxes of 5 markers and 2 single markers. How many more crayons than markers does Jessie have? A
17
B
22
C
15
D
20
9.
Multi-Step To make a salad, Alan needs 3 cups of lettuce and 1 cup of tomatoes. Alan makes 6 bowls of salad. How many more cups of lettuce than tomatoes does Alan need? A
10 cups
B
12 cups
C
2 cups
D
15 cups
© Houghton Mifflin Harcourt Publishing Company
4.
Name
Module 8 Assessment Vocabulary Vocabulary
Vocabulary
Choose the best term from the box to complete the sentence. 1.
Associative Property of Multiplication Distributive Property
The ___ Property of Multiplication states that when the grouping of factors is changed, the product is the same. (p. 243)
Concepts Concepts and and Skills Skills Use arrays to show each property. 2.
q TEKS 3.4.F, 3.5.B
Distributive Property
3.
Circle groups to show 3 × (2 × 3).
Break apart the array to show 8 × 6 = (4 × 6) + (4 × 6).
Find the product
© Houghton Mifflin Harcourt Publishing Company
4.
6 × 8 _
Associative Property of Multiplication
q TEKS 3.4.F, 3.5.B
7 × 4 _
5.
6.
5 × 9 _
7.
6 × 7 _
8.
7 × 8 _
9.
8 × 8 _
10.
9×0=_
11.
7×8=_
12.
4×8=_
13.
9×7=_
14.
9×9=_
15.
7×5=_
16.
5 × 10 = _
17.
7×3=_
Module 8
273
18.
Adele needs 5 pieces of ribbon, each 8 centimeters long. How many centimeters of ribbon does she need altogether? q TEKS 3.4.K Record your answer and fill in the bubbles on the grid. Be sure to use the correct place value.
TEXAS Test Prep 0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
Fill in the bubble for the correct answer choice.
20.
21.
22.
274
When Chloe finds the multiplication facts for 2, which digit will NOT be in the ones place of the products? q TEKS 3.4.E A
4
C
6
B
8
D
3
A honeybee is an insect. It has 6 legs. How many more legs do 9 honeybees have than 7 honeybees? q TEKS 3.4.K A
54
C
12
B
42
D
16
Jody has bags of shells. Each bag has 6 shells. She gives 3 bags each to 2 friends. How many shells did Jody give away? q TEKS 3.4.F, 3.4.K, 3.5.B A
36
C
18
B
6
D
12
Austin was on summer vacation for 7 weeks. He spent 3 weeks at band camp and the rest of the time at home. How many days did he spend at home? q TEKS 3.4.K, 3.5.B A
10 days
C
21 days
B
28 days
D
4 days
© Houghton Mifflin Harcourt Publishing Company
19.
8.6
?
Number and Operations—3.4.K MATHEMATICAL PROCESSES 3.1.B, 3.1.F
PROBLEM SOLVING • Two-Step
Multiplication Problems
Essential Question
How can you use the strategy make a table to solve one-step and two-step multiplication problems?
Unlock Unlock the the Problem Problem Scott has a stamp album. Some pages have 1 stamp on them, and other pages have 2 stamps on them. If Scott has 18 stamps, show how many different ways he could put them in the album. Use the graphic organizer below to solve the problem.
Read What do I need to find?
Solve Make a table to show the number of pages with 1 stamp and with 2 stamps. Each row must equal
_ , the total number of stamps. Pages with 2 Stamps
Pages with 1 Stamp
Total Stamps
What information am I given?
8
2
18
Scott has _ stamps. Some album
7
4
18
pages have _ stamp on them, and
6
6
18
the other pages have _ stamps.
5 10
Plan
3
What is my plan or strategy?
© Houghton Mifflin Harcourt Publishing Company
I will make a _ showing all the different ways of arranging the stamps in the album.
1.
18 18
12
2
So, there are _ different ways.
What number patterns do you see in the table?
Module 8
267
Try Try Another Another Problem Problem What if Scott bought 3 more stamps and now has 21 stamps? Some album pages have 1 stamp and some pages have 2 stamps. Show how many different ways he could put the odd number of stamps in the album.
Read
Solve
What do I need to find?
What information am I given?
Plan What is my plan or strategy?
So, there are _ different ways. What patterns do you see in this table?
Math Talk Mathematical Processes
Explain how these patterns are different from the patterns in the table on page 267.
268
© Houghton Mifflin Harcourt Publishing Company
2.
Name
Share Share and and Show Show 1.
Aaron’s mother is making lemonade. For each pitcher, she uses 1 cup of lemon juice, 1 cup of sugar, and 6 cups of water. What is the total number of cups of ingredients she will use to make 5 pitchers of lemonade? First, make a table to show the number of cups of lemon juice, sugar, and water that are in 1 pitcher of lemonade. Next, multiply to find the number of cups of water needed for each pitcher of lemonade.
Think: For every pitcher, the number of cups of water increases by 6.
Last, use the table to solve the problem. Number of Pitchers
1
2
Cups of Lemon Juice
1
Cups of Sugar
1
2
Cups of Water
6
12
Total Number of Cups of Ingredients
8
3
5
3
24
So, in 5 pitchers of lemonade, there are _ cups of lemon juice, _ cups of sugar, and _ cups of water. This makes a total of _ cups of ingredients. 2.
What pattern do you see in the total number of cups of ingredients?
© Houghton Mifflin Harcourt Publishing Company
Problem Problem Solving Solving 3.
Multi-Step Cammi needs 36 postcards. She buys 4 packages of 10 postcards. How many postcards will Cammi have left over? Explain.
Module 8 • Lesson 6
269
Mathematical Processes M Model ¥ Reason ¥ Communicate M
Daily Daily Assessment Assessment Task Task Fill in the bubble for the correct answer choice. 4.
5.
6.
There are 5 boats in a race. Each boat has 6 rowers and 1 coach. How many people are in the race? Use the table to solve the problem. Number of Boats
1
2
Number of Rowers
6
12
Number of Coaches
1
2
Total Number of People
7
3
4
5
3
A
7
C
12
B
30
D
35
Apply For each pan of bread, you need 2 cups of white flour and 1 cup of wheat flour. What is the total number of cups of flour you will need to make 4 pans of bread? A
7 cups
C
8 cups
B
3 cups
D
12 cups
Multi-Step Sheri puts 16 pictures in an album. Some pages have 2 pictures. The other pages have 4 pictures. There are 3 pages with 4 pictures. How many pages have 2 pictures? A
3
C
4
B
2
D
1
7.
270
Each year for 8 years, the Williams family visited 6 different states on vacation. How many more states do they need to visit before they have seen all 50 states? A
36
C
48
B
14
D
2
© Houghton Mifflin Harcourt Publishing Company
TEXAS Test Prep
Number and Operations—3.4.K MATHEMATICAL PROCESSES 3.1.B, 3.1.F
H o mewo rk and Practice
8.6
Name
• Two-Step Multiplication Problems PROBLEM SOLVING
Make a table to solve the problem. 1.
Janey is making party mix. For each bowl of mix, she uses 2 cups of raisins, 1 cup of peanuts, and 4 cups of granola. What is the total number of cups of ingredients she will use to make 6 bowls of party mix? Number of Bowls
1
Cups of Raisins
2
Cups of Peanuts
1
Cups of Granola
4
Total Number of Cups
7
2
3
5
6
4 8
So, in 6 bowls of party mix, there are _ cups of raisins, _ cups of peanuts, and _ cups of granola. This makes a total of _ cups of ingredients.
Problem Problem Solving Solving
© Houghton Mifflin Harcourt Publishing Company
2.
To make an apple pie, Mimi needs 2 cups of flour and 3 cups of apples. How many cups of ingredients does Mimi need to make 5 pies?
3.
To make muffins, Seth needs 3 cups of mix and 1 cup of raisins. How many cups of ingredients does Seth need to make 3 batches of muffins?
Module 8 • Lesson 6 271
TEXAS Test Prep
Lesson Lesson Check Check
6.
8.
272
There are 6 relay teams at a race. Each team has 4 runners and 1 captain. How many people are in the race?
5.
Sara makes 7 fruit baskets for the senior center. She puts 3 apples and 4 pears in each basket. How many pieces of fruit are there?
A
11
A
14
B
30
B
21
C
24
C
49
D
25
D
28
Thomas wants to collect 40 toy cars for his collection. If he has 6 boxes of 4 toy cars each, how many more cars does Thomas need?
7.
Vernon needs to sell 60 granola bars for his scout troop. If he sells 4 boxes of 8 bars each, how many more bars does Vernon need to sell?
A
16
A
48
B
24
B
32
C
50
C
28
D
34
D
30
Multi-Step Jessie has 4 boxes of 8 crayons and 3 boxes of 5 markers and 2 single markers. How many more crayons than markers does Jessie have? A
17
B
22
C
15
D
20
9.
Multi-Step To make a salad, Alan needs 3 cups of lettuce and 1 cup of tomatoes. Alan makes 6 bowls of salad. How many more cups of lettuce than tomatoes does Alan need? A
10 cups
B
12 cups
C
2 cups
D
15 cups
© Houghton Mifflin Harcourt Publishing Company
4.
Name
Module 8 Assessment Vocabulary Vocabulary
Vocabulary
Choose the best term from the box to complete the sentence. 1.
Associative Property of Multiplication Distributive Property
The ___ Property of Multiplication states that when the grouping of factors is changed, the product is the same. (p. 243)
Concepts Concepts and and Skills Skills Use arrays to show each property. 2.
q TEKS 3.4.F, 3.5.B
Distributive Property
3.
Circle groups to show 3 × (2 × 3).
Break apart the array to show 8 × 6 = (4 × 6) + (4 × 6).
Find the product
© Houghton Mifflin Harcourt Publishing Company
4.
6 × 8 _
Associative Property of Multiplication
q TEKS 3.4.F, 3.5.B
7 × 4 _
5.
6.
5 × 9 _
7.
6 × 7 _
8.
7 × 8 _
9.
8 × 8 _
10.
9×0=_
11.
7×8=_
12.
4×8=_
13.
9×7=_
14.
9×9=_
15.
7×5=_
16.
5 × 10 = _
17.
7×3=_
Module 8
273
18.
Adele needs 5 pieces of ribbon, each 8 centimeters long. How many centimeters of ribbon does she need altogether? q TEKS 3.4.K Record your answer and fill in the bubbles on the grid. Be sure to use the correct place value.
TEXAS Test Prep 0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
Fill in the bubble for the correct answer choice.
20.
21.
22.
274
When Chloe finds the multiplication facts for 2, which digit will NOT be in the ones place of the products? q TEKS 3.4.E A
4
C
6
B
8
D
3
A honeybee is an insect. It has 6 legs. How many more legs do 9 honeybees have than 7 honeybees? q TEKS 3.4.K A
54
C
12
B
42
D
16
Jody has bags of shells. Each bag has 6 shells. She gives 3 bags each to 2 friends. How many shells did Jody give away? q TEKS 3.4.F, 3.4.K, 3.5.B A
36
C
18
B
6
D
12
Austin was on summer vacation for 7 weeks. He spent 3 weeks at band camp and the rest of the time at home. How many days did he spend at home? q TEKS 3.4.K, 3.5.B A
10 days
C
21 days
B
28 days
D
4 days
© Houghton Mifflin Harcourt Publishing Company
19.
