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, TABLE OF CONTENTS
Solutions Manual: Mathematics for Elementary and Middle School
Teachers with Activities, 6th Edition
Author: Sybilla Beckmann (2021)
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Chapter 1. Numbers and the Base-Ten System
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Chapter 2. Fractions and Problem Solving
Chapter 3. Addition and Subtraction
Chapter 4. Multiplication
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Chapter 5. Multiplication of Fractions, Decimals, and Negative Numbers
Chapter 6. Division
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Chapter 7. Ratio and Proportional Relationships
Chapter 8. Number Theory
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Chapter 9. Algebra
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Chapter 10. Geometry
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Chapter 11. Measurement
Chapter 12. Area of Shapes
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Chapter 13. Solid Shapes and Their Volume and Surface Area
Chapter 14. Geometry of Motion and Change
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Chapter 15. Statistics
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Chapter 16. Probability
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, 1.1 The Counting Numbers 1-1
Chapter 1
Numbers and the Base-Ten System
1.1 The Counting Numbers
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1. Answers will vary. For example, when connecting the counting numbers as a list view of
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numbers with the number of objects in a set view of numbers, a child must learn to
associate each number in the list in a one to one correspondence with each object in the
set, starting with one. Also, the child must be able to learn that the last number from the
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list, used to connect with the last object in the set, is the number of objects in the set.
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2. Yes, there is a better way to respond. For instance, you could group the beads into sets of
10 beads in each group. Then you would have 3 groups of 10 beads in each group and
there would be 5 left over beads. This grouping would facilitate a discussion about place
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value and allow the conversation to focus on 3 tens.
3. a. You could group the beads into sets of 10 beads in each group. Then you would
have 4 groups of 10 beads in each group and there would be 7 left over beads.
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Using the place value system of representing numbers, 4 tens and 7 ones is 47.
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Figure 1.1 shows a simple math drawing that could be drawn.
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Figure 1.1: Representation of 47
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b. You could bag the toothpicks into sets of 10 toothpicks in each bag. Then when
you get 10 bags of 10 toothpicks in each, you could bundle, with a rubber band,
10 bags of 10 toothpicks to make sets of 100 toothpicks in each bundle. Then you
would have 3 bundles of 100 toothpicks in each bundle (or 3 hundreds) and you
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would have 2 bags of 10 toothpicks in each bag (or 2 tens) and there would be 8
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left over toothpicks. Using the place value system of representing numbers, 3
hundreds, 2 tens, and 8 ones is 328. Figure 1.2 shows a simple math drawing that
could be drawn.
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Copyright © 2022 Pearson Education, Inc.
, 1-2 Chapter 1: Numbers and the Base-Ten System
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Figure 1.2: Representation of 328
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c. You could bag the toothpicks into sets of 10 toothpicks in each bag. Then when
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you get 10 bags of 10 toothpicks in each, you could bundle, with a rubber band,
10 bags of 10 toothpicks to make sets of 100 toothpicks in each bundle. Then
when you have 10 bundles of 100 toothpicks, you could get a giant gallon sized
plastic bag and put them into it and group these 10 sets of 100 toothpicks into 1
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set of 1000 toothpicks. Using the place value system of representing numbers, 1
thousand is represented as 1000. Figure 1.3 shows a simple math drawing that
could be drawn.
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Figure 1.3: Representation of 1000
Copyright © 2022 Pearson Education, Inc.
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, TABLE OF CONTENTS
Solutions Manual: Mathematics for Elementary and Middle School
Teachers with Activities, 6th Edition
Author: Sybilla Beckmann (2021)
ST
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Chapter 1. Numbers and the Base-Ten System
UV
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Chapter 2. Fractions and Problem Solving
Chapter 3. Addition and Subtraction
Chapter 4. Multiplication
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Chapter 5. Multiplication of Fractions, Decimals, and Negative Numbers
Chapter 6. Division
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Chapter 7. Ratio and Proportional Relationships
Chapter 8. Number Theory
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Chapter 9. Algebra
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Chapter 10. Geometry
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Chapter 11. Measurement
Chapter 12. Area of Shapes
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Chapter 13. Solid Shapes and Their Volume and Surface Area
Chapter 14. Geometry of Motion and Change
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Chapter 15. Statistics
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Chapter 16. Probability
VI
ED
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ST
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, 1.1 The Counting Numbers 1-1
Chapter 1
Numbers and the Base-Ten System
1.1 The Counting Numbers
ST
1. Answers will vary. For example, when connecting the counting numbers as a list view of
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numbers with the number of objects in a set view of numbers, a child must learn to
associate each number in the list in a one to one correspondence with each object in the
set, starting with one. Also, the child must be able to learn that the last number from the
UV
list, used to connect with the last object in the set, is the number of objects in the set.
EK
2. Yes, there is a better way to respond. For instance, you could group the beads into sets of
10 beads in each group. Then you would have 3 groups of 10 beads in each group and
there would be 5 left over beads. This grouping would facilitate a discussion about place
GE
IA
value and allow the conversation to focus on 3 tens.
3. a. You could group the beads into sets of 10 beads in each group. Then you would
have 4 groups of 10 beads in each group and there would be 7 left over beads.
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Using the place value system of representing numbers, 4 tens and 7 ones is 47.
ED
Figure 1.1 shows a simple math drawing that could be drawn.
AP
M PR
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Figure 1.1: Representation of 47
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b. You could bag the toothpicks into sets of 10 toothpicks in each bag. Then when
you get 10 bags of 10 toothpicks in each, you could bundle, with a rubber band,
10 bags of 10 toothpicks to make sets of 100 toothpicks in each bundle. Then you
would have 3 bundles of 100 toothpicks in each bundle (or 3 hundreds) and you
UV
would have 2 bags of 10 toothpicks in each bag (or 2 tens) and there would be 8
ED
left over toothpicks. Using the place value system of representing numbers, 3
hundreds, 2 tens, and 8 ones is 328. Figure 1.2 shows a simple math drawing that
could be drawn.
ST
??
Copyright © 2022 Pearson Education, Inc.
, 1-2 Chapter 1: Numbers and the Base-Ten System
ST
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Figure 1.2: Representation of 328
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c. You could bag the toothpicks into sets of 10 toothpicks in each bag. Then when
EK
you get 10 bags of 10 toothpicks in each, you could bundle, with a rubber band,
10 bags of 10 toothpicks to make sets of 100 toothpicks in each bundle. Then
when you have 10 bundles of 100 toothpicks, you could get a giant gallon sized
plastic bag and put them into it and group these 10 sets of 100 toothpicks into 1
GE
IA
set of 1000 toothpicks. Using the place value system of representing numbers, 1
thousand is represented as 1000. Figure 1.3 shows a simple math drawing that
could be drawn.
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AP
M PR
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IA
OV
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ST
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Figure 1.3: Representation of 1000
Copyright © 2022 Pearson Education, Inc.
