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Table of COntents
Introduction – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 3
Format of Books – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 4
Suggestions for Use – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 7
Annotated Answer Key and Extension Activities – – – – – – – – – – – 9
Reproducible Tool Set – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 176
ISBN 978-0-8454-8718-1
Copyright © 2015 The Continental Press, Inc.
Excepting the designated reproducible blackline masters, no part of this publication may be reproduced
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17 One-Step Word Problems with
Multiplication and Division
Pages
139 and 140
Objective
To solve multiplication and division word problems
PAR
T
1 Introduction
Introduction
Review words that are clues for the operations of
multiplication and division. Students should recognize
that into equal groups is a signal to divide. Then
guide the students in writing a representative number
sentence for a word problem, using a variable to
represent the unknown. Relate this to the array on
the page. Repeat with the example of a multiplication
situation. Emphasize that in a number sentence, one
expression, such as 2 3 b, is equal to another, i.e., the
expressions name the same number in different ways.
Think About It
Students should recognize the length of the classroom
in feet as the dividend and the number of steps as the
divisor, and write a sentence such as 24 4 12 5 s.
Common Core State Standard
3.OA.3 Use multiplication and division within 100
to solve word problems in situations involving equal
groups, arrays, and measurement quantities, e.g., by
using drawings and equations with a symbol for the
unknown number to represent the problem.
36
4 and the number of rows
4 3 r 5 36
the dividend
Vocabulary
equation: a number sentence that says two
expressions are equal
expression: a grouping of numbers and operations
that shows the value of something
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36 4 4 5 r
9
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PAGES
LESSON
141 AND 142
17 O
ne-Step Word Problems with
Multiplication and Division
PAR
T
the hours it takes to get to the beach
Answers will vary.
2
3 times as long
multiplication
3325h
6
45 4 9 5 n or equivalent
2 Focused
Instruction
Focused
Instruction
Students change a word problem into a representative
division sentence and then solve it. The questions help
students to identify what the numbers represent and
to write the sentence. They should recognize that to
solve the division problem, they can use the inverse
operation of multiplication.
In a second example, students decipher the clue words
in a problem to determine a multiplication situation,
write appropriate expressions, and finally write and
solve a multiplication sentence with a variable for the
unknown.
Conclude the Focused Instruction section by having
students answer the two word problems.
8 3 3 5 t or equivalent
PAR
T
2 3 w 5 14
Practice
Guided
Practice
3 Guided
Students should complete the Guided Practice section
on their own. Offer assistance as needed, pointing out
the reminder and hint boxes along the right side of
the page.
14 4 2 5 w
7
5 3 a 5 30
6
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••••••
••••••
••••••
4
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Connections to Standards for
Mathematical Practice
• Make sense of problems and persevere in solving
them.
• Reason abstractly and quantitatively.
• Model with mathematics.
• Use appropriate tools strategically.
• Attend to precision.
• Look for and make use of structure.
UNIT 4
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LESSON
17 O
ne-Step Word Problems with
Multiplication and Division
PAGES
143 AND 144
PAR
T
Practice
I ndependent
Practice
4 Independent
Answer Rationales
1
In choice A, the student likely misinterpreted the
word twice as the answer 2. In choice C, the student
added 2 instead of dividing by 2. In choice D, the
student multiplied the ears of corn by 2 instead of
dividing. Choice B is correct. There are twice as many
ears of corn as pumpkins, so there are half as many
pumpkins as ears of corn. Divide: 48 4 2 5 24.
2
Think of the question, “How many times can groups
of 8 be taken out of 56?” So the equation should
show the number of pieces of gum divided by
the number of pieces per pack, which equals the
number of packs: 56 4 8 5 g, so g 5 7.
DOK 2
3.OA.3
DOK 2
3.OA.3
56 4 8 5 g or equivalent; g 5 7
DOK 2
3.OA.3
She is not correct. She should have written 3 3 n 5 15.
3
Andrea’s number of tickets is 3 times as many as
Bill’s, which means you must multiply by 3. Her
number of tickets is equal to 15, so 3 times some
number equals 15. That means Bill has taken
5 tickets because 3 3 5 5 15.
4
Part A There are a total of 54 swimmers. Each
team is made up of 9 swimmers. Use division to find
the number of teams by dividing the total number of
swimmers by the number on each team: 54 4 9 5 s.
Use multiplication by multiplying the number of teams
and the number of swimmers on each team to get
the total number of swimmers: 9 3 s 5 54. In both
equations, s 5 6, so there are 6 teams.
Part B The words twice as many mean “multiply
by 2.” The number of girls is unknown, g. So g
multiplied by 2 equals the number of boys, 36:
2 3 g 5 36. So there were 18 girls because
2 3 18 5 36.
5
Parts A and B If the worker makes 3 rows of
cans, there will be 8 cans in each row because
3 3 8 5 24. The array will show 3 rows of 8. The
worker could also make 8 rows with 3 cans in each
row. If the worker makes 4 rows of cans, there
will be 6 cans in each row because 4 3 6 5 24.
He could also make 6 rows with 4 cans in each
row. Arrays can show the number of rows and the
number of cans in each row.
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DOK 3
3.OA.3
9 3 s 5 54 or 54 4 9 5 s; s 5 6
18
DOK 3
3.OA.3
Answers may vary:
••••••
••••••
••••••
••••••
••••••••
••••••••
••••••••
4 3 6 5 24 and 3 3 8 5 24
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PAGE
LESSON
145
DOK 3
3.OA.3
32 4 4 5 8
17 O
ne-Step Word Problems with
Multiplication and Division
6
Part A Each frame needs 4 10-inch pieces of
wood. To find the number of frames Jared can make
with 32 pieces of wood, divide the total number of
pieces by the number needed for each frame. The
quotient is the number of frames he can make:
32 4 4 5 8.
Part B Since each frame is $9, divide the total
amount Jared wants to make by the cost of each
frame. The quotient is the number of frames he
needs to sell: $72 4 $9 5 8 frames.
He needs to sell 8 frames because 72 4 9 5 8.
Extension Activity
Select a topic that students are likely to have had
firsthand experience with—a fair or festival, a class
trip to a museum or other venue, a yard sale. Tell
the class that they are going to write one-step word
problems about this topic, and brainstorm some
ideas for problems, noting them on the board. Give
each student four 4-3-6-inch index cards. Direct the
students to write one problem for each operation:
addition, subtraction, multiplication, and division.
Encourage creativity and the use of as many basic
facts as they can. On the back of each card, the
student should note the operation and the correct
number sentence with answer. Collect the problems
to share with the class and store them in a labeled
folder.
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