Developmental Mathematics with Applications and Visualization: Prealgebra, Beginning Algebra, and Intermediate Algebra – 2nd Edition – Gary K. Rockswold – Instructor’s Solutions Manual

INSTRUCTORS MANUAL
for
Developmental Mathematics with
Applications and Visualization
Author (s): Gary K. Rockswold, Terry A. Krieger
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EAM
SH
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,Mini-Lecture 1.1 DEVELOPMENTAL MATHEMATICS


Introduction to Whole Numbers
Objectives:

• Reviewing Natural Numbers and Whole Numbers
• Understanding Place Value
• Writing Whole Numbers in Word Form
• Writing Whole Numbers in Expanded Form
• Graphing Whole Numbers on the Number Line
o Graphing Whole Numbers
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o Comparing Whole Numbers
• Reading Graphs and Tables
o Bar Graphs
o Line Graphs
o Spider Charts
o Tables
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Examples:
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1. Identify the whole number(s).
2
a) 9 b) 7 c) 0 d) 5.631
3
9
e) –3 f) 2.1 g) 4 h)
5
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2. Identify the place value of the digit 2 in each number.
a) 72,365 b) 126,301,840 c) 296,431,860,806

3. Write each number in word form.
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a) 5302 b) 3,643,112 c) 502,000,076,000

4. Write each number in standard form.
a) two million, three hundred thousand, three
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b) thirty-eight billion, five hundred forty-one million, seventy four thousand, eight hundred two

c) one hundred six trillion, four hundred two million
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Teaching Notes:
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• Some ESL students may need extra help learning the number period vocabulary such as ones, thousands,
millions, billions, trillions, etc. They may be accustomed to using periods instead of commas in place value.
• Many examples of tables are available on the Internet. Assign students to find examples and ask them to
explain how to read the tables and write the numbers in words.


Answers: 1) choices a, c, and g are whole numbers; 2a) thousands, b) ten-millions, c) hundred-billions; 3a) five
thousand, three hundred two, b) three million, six hundred forty-three thousand, one hundred twelve, c) five hundred
two billion, seventy-six thousand; 4a) 2,300,003, b) 38,541,074,802, c) 106,000,402,000,000
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,DEVELOPMENTAL MATHEMATICS Mini-Lecture 1.2


Adding and Subtracting Whole Numbers; Perimeter
Objectives:

• Adding Whole Numbers
o Adding Whole Numbers without Regrouping
o Adding Whole Numbers with Regrouping
• Using Properties of Addition
o Commutative Property
o Associative Property
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o Identity Property
• Recognizing Words Associated with Addition
• Subtracting Whole Numbers
o Subtracting Whole Numbers without Regrouping
o Subtracting Whole Numbers with Regrouping
• Using Properties of Subtraction
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• Recognizing Words Associated with Subtraction
• Solving Equations Involving Addition and Subtraction
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• Solving Perimeter and Other Applications Involving Addition and Subtraction

Examples:
1. Add.
a) 5+ 3 b) 4+7 c) 8+9 d) 6+2
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e) 3+ 3 f) 6 + 4 + 3+ 7 g) 8+8+0+5

2. Add.
40,001 6505
53 1123 96 5678
32, 442 173
+ 12 + 345
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a) b) c) d) + 47 e) + 3574 f)
+ 15,333 7044
+ 168
3. Solve each equation by finding the unknown value.
a) 13 − =8 b) − 14 = 3 c) 26 + = 54
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4. Subtract.
664 51 1123 40,001
a) 98 − 51 b) 54 − 22 c) d) e) f)
− 51 − 12 − 345 − 15, 333
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5. Find the perimeter of a triangle with sides of length 12 ft, 22 ft, and 25 ft.
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Teaching Notes:

• Point out that the commutative property deals with the order of addends, whereas the associative property
deals with the grouping (order does not change) of addends.
• Have students practice basic subtraction facts. Some have trouble borrowing when zeros are involved.

Answers: 1a) 8, b) 11, c) 17, d) 8, e) 6, f) 20, g) 21; 2a) 65, b) 1468, c) 87,776, d) 143, e) 9252, f) 13,890; 3a) 4, b)
17, c) 28; 4a) 47, b) 32, c) 613, d) 39, e) 778, f) 24,668; 5) 59 ft
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, Mini-Lecture 1.3 DEVELOPMENTAL MATHEMATICS


Multiplying and Dividing Whole Numbers; Area
Objectives:

• Multiplying Whole Numbers
• Using Properties of Multiplication
o Commutative Property
o Associative Property
o Identity and Zero
o Properties
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o Distributive Properties
• Multiplying Larger Whole Numbers
o Multiplying Whole Numbers Ending in Zeros
• Recognizing Words Associated with Multiplication
• Dividing Whole Numbers
o Remainders
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• Using Properties of Division
• Performing Long Division
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• Recognizing Words Associated with Division
• Solving Equations Involving Multiplication and Division
• Solving Area and Other Applications Involving Multiplication and Division

Examples:
1. Multiply.
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a) 3× 2 b) 5 ×1 c) 11 ⋅ 0 d) ( 3)( 7 ) e) 42 (153)

2. Multiply.
a) 51 b) 1123 c) 18 d) 534 e) 160
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×2 × 5 × 22 × 54 × 200

3. Divide.
a) 189 ÷ 9 b) 324 ÷ 6 c) 488 ÷ 61
d) 1290 ÷ 4 e) 2272 ÷ 23 f) 9360 ÷ 13
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4. Solve each equation by finding the unknown value.

a) 56 ÷ =8 b) 15 × = 90 c) 24 ÷ =6
5. Find the area of a rectangular garden with length 16 meters and width 9 meters.
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Teaching Notes:
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• Some students need to practice basic multiplication and division facts at home in order to master them.
• Some students are not sure how to multiply by factors which have zeros.
• Some students are not sure how to align the products when the multiplier contains zero.
• Remind students that division by zero is “undefined” and dividing zero by any non-zero number is zero.
• Some students do not know how to check a division problem if there is a remainder.

Answers: 1a) 6, b) 5, c) 0, d) 21, e) 6426; 2a) 102, b) 5615, c) 396, d) 28,836, e) 32,000; 3a) 21, b) 54, c) 8,
d) 322 R2, e) 98 R18, f) 720; 4a) 7, b) 6, c) 4; 5) 144 square meters
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