INSTRUCTORS MANUAL
for
Developmental Mathematics through
Applications: Basic College Mathematics
and Algebra, 1st edition
DR
Author (s): Geoffrey Akst, Sadie Bragg
E AM
SH
UB
_S
? ?
, Instructor’s Resource Manual Developmental Mathematics through Applications 1
Mini-Lecture 1.1
Introduction to Whole Numbers
Objectives:
A Read and write whole numbers.
B Write whole numbers in expanded form.
C Round whole numbers.
D Solve applied problems involving reading, writing, or rounding whole numbers.
DR
Examples:
1. Identify the place value of each digit in the numbers.
E
a) 3,654 b) 265,812 c) 56,203,411
AM
2. Write a word name for each number.
a) 325 b) 60,448 c) 9,542,006
3. Write a number for each word name.
a) two hundred fifty-three
SH
b) seven thousand, ninety-eight
c) three hundred forty million, one hundred thirty-two
4. What is wrong with the following:
“three hundred and sixty-four”
UB
5. When do we use a hyphen when writing whole numbers?
Teaching Notes:
_S
• Students who do not have English as their first language might need extra help learning the number period
vocabulary such as ones, thousands, millions, billions, etc. Refer them to the Place-value Chart in the
textbook.
•
?
Some students who do not have English as their first language are accustomed to using periods instead of
commas as above.
• Many examples of tables are available on the Internet. Request students to obtain copies and ask them to
?
explain how to read the tables and write the numbers in words.
Answers: 1a) 3-thousands,6-hundreds,5-tens,4-ones, b) 2-hundred thousands,6-ten thousands,5-thousands,8-
hundreds,1-ten,2-ones, c) 5-ten millions,6-millions,2-hundred thousands,3-thousands,4-hundreds,1-tens,1-ones; 2a)
three hundred twenty-five, b) sixty thousand, four hundred forty-eight, c) nine million, five hundred forty-two
thousand, six; 3a) 253, b) 7,098, c) 340,000,132; 4) The word “and” is never used when writing whole numbers.; 5)
A hyphen is used when writing the numbers 21–99, except for numbers ending in zero.
Copyright © 2014 Pearson Education, Inc.
,2 Instructor’s Resource Manual Developmental Mathematics through Applications
Mini-Lecture 1.2
Adding and Subtracting Whole Numbers
Objectives:
A Add and subtract whole numbers.
B Solve applied problems involving addition and subtraction of whole numbers.
DR
Examples:
1. Add when carrying is not required.
a) 53 b) 1123 c) 40,001
E
+ 12 + 345 32,442
+ 15,333
AM
2. Add with carrying required.
a) 96 b) 5678 c) 6505
+ 47 + 3574 173
7044
+ 168
SH
3. A plane is flying at an altitude of 5932 ft. It then increases its altitude by 7384 ft.
Find its new altitude.
4. Subtract when borrowing is not required.
a) 98 − 51 b) 54 – 22 c) 664
UB
− 51
5. Subtract with borrowing required.
a) 51 b) 1123 c) 40,001
− 12 − 345 − 15,333
_S
6. Earl has $729 in his checking account. After he writes a check to the
bookstore for $249, how much is remaining in his account?
?
Teaching Notes:
?
• Some students need to practice basic addition and subtraction facts at home in order to master them.
• Some students need to write the carry digit in order to get the correct answer for addition with carrying.
• Many need to write the borrowing step in order to get the correct answer for subtraction with borrowing.
• Point out that the commutative property deals with the order of the addends, whereas the associative
property deals with the grouping (order does not change) of the addends.
• Point out that the commutative and associative properties do not generally apply to subtraction problems.
Answers: 1a) 65, b) 1468, c) 87,776; 2a) 143, b) 9252, c) 13,890; 3) 13,316; 4a) 47, b) 32, c) 613; 5a) 39, b) 778,
c) 24,668; 6) $480
Copyright © 2014 Pearson Education, Inc.
, Instructor’s Resource Manual Developmental Mathematics through Applications 3
Mini-Lecture 1.3
Multiplying Whole Numbers
Objectives:
A Multiply whole numbers.
B Solve applied problems involving the multiplication of whole numbers.
DR
Examples:
1. Multiply.
a) 3 × 2 b) 3 ⋅ 2 ⋅ 1 c) 5 ⋅ 6 ⋅ 0 d) (2)(3)(7) e) 2 × 4 × 10
E
2. Multiply.
AM
a) 51 b) 1123 c) 40,001
× 2 × 5 × 3
3. Multiply by powers of 10.
a) 2 × 10 b) 2 × 100 c) 2 × 1000
SH
d) From the pattern you’ve observed, what would 754 ´ 10, 000 equal?
4. Multiply.
a) 18 b) 534 c) 4,302 d) 160
UB
× 22 × 54 × 107 × 200
5. a) Jenny pays $275 per month for her car payment. How much does she pay per year?
b) Frank bought 8 CDs at $15 each. How much did he pay total?
_S
Teaching Notes:
?
• Some students need to practice basic multiplication facts at home in order to master them.
• Some students do not know the different types of symbols that mean multiplication.
?
• 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.
Answers: 1a) 6, b) 6, c) 0, d) 42, e) 80; 2a) 102, b) 5615, c) 120,003; 3a) 20, b) 200, c) 2000, d) 7,540,000;
4a) 396, b) 28,836, c) 460,314, d) 32,000; 5a) $3300, b) $120
Copyright © 2014 Pearson Education, Inc.
for
Developmental Mathematics through
Applications: Basic College Mathematics
and Algebra, 1st edition
DR
Author (s): Geoffrey Akst, Sadie Bragg
E AM
SH
UB
_S
? ?
, Instructor’s Resource Manual Developmental Mathematics through Applications 1
Mini-Lecture 1.1
Introduction to Whole Numbers
Objectives:
A Read and write whole numbers.
B Write whole numbers in expanded form.
C Round whole numbers.
D Solve applied problems involving reading, writing, or rounding whole numbers.
DR
Examples:
1. Identify the place value of each digit in the numbers.
E
a) 3,654 b) 265,812 c) 56,203,411
AM
2. Write a word name for each number.
a) 325 b) 60,448 c) 9,542,006
3. Write a number for each word name.
a) two hundred fifty-three
SH
b) seven thousand, ninety-eight
c) three hundred forty million, one hundred thirty-two
4. What is wrong with the following:
“three hundred and sixty-four”
UB
5. When do we use a hyphen when writing whole numbers?
Teaching Notes:
_S
• Students who do not have English as their first language might need extra help learning the number period
vocabulary such as ones, thousands, millions, billions, etc. Refer them to the Place-value Chart in the
textbook.
•
?
Some students who do not have English as their first language are accustomed to using periods instead of
commas as above.
• Many examples of tables are available on the Internet. Request students to obtain copies and ask them to
?
explain how to read the tables and write the numbers in words.
Answers: 1a) 3-thousands,6-hundreds,5-tens,4-ones, b) 2-hundred thousands,6-ten thousands,5-thousands,8-
hundreds,1-ten,2-ones, c) 5-ten millions,6-millions,2-hundred thousands,3-thousands,4-hundreds,1-tens,1-ones; 2a)
three hundred twenty-five, b) sixty thousand, four hundred forty-eight, c) nine million, five hundred forty-two
thousand, six; 3a) 253, b) 7,098, c) 340,000,132; 4) The word “and” is never used when writing whole numbers.; 5)
A hyphen is used when writing the numbers 21–99, except for numbers ending in zero.
Copyright © 2014 Pearson Education, Inc.
,2 Instructor’s Resource Manual Developmental Mathematics through Applications
Mini-Lecture 1.2
Adding and Subtracting Whole Numbers
Objectives:
A Add and subtract whole numbers.
B Solve applied problems involving addition and subtraction of whole numbers.
DR
Examples:
1. Add when carrying is not required.
a) 53 b) 1123 c) 40,001
E
+ 12 + 345 32,442
+ 15,333
AM
2. Add with carrying required.
a) 96 b) 5678 c) 6505
+ 47 + 3574 173
7044
+ 168
SH
3. A plane is flying at an altitude of 5932 ft. It then increases its altitude by 7384 ft.
Find its new altitude.
4. Subtract when borrowing is not required.
a) 98 − 51 b) 54 – 22 c) 664
UB
− 51
5. Subtract with borrowing required.
a) 51 b) 1123 c) 40,001
− 12 − 345 − 15,333
_S
6. Earl has $729 in his checking account. After he writes a check to the
bookstore for $249, how much is remaining in his account?
?
Teaching Notes:
?
• Some students need to practice basic addition and subtraction facts at home in order to master them.
• Some students need to write the carry digit in order to get the correct answer for addition with carrying.
• Many need to write the borrowing step in order to get the correct answer for subtraction with borrowing.
• Point out that the commutative property deals with the order of the addends, whereas the associative
property deals with the grouping (order does not change) of the addends.
• Point out that the commutative and associative properties do not generally apply to subtraction problems.
Answers: 1a) 65, b) 1468, c) 87,776; 2a) 143, b) 9252, c) 13,890; 3) 13,316; 4a) 47, b) 32, c) 613; 5a) 39, b) 778,
c) 24,668; 6) $480
Copyright © 2014 Pearson Education, Inc.
, Instructor’s Resource Manual Developmental Mathematics through Applications 3
Mini-Lecture 1.3
Multiplying Whole Numbers
Objectives:
A Multiply whole numbers.
B Solve applied problems involving the multiplication of whole numbers.
DR
Examples:
1. Multiply.
a) 3 × 2 b) 3 ⋅ 2 ⋅ 1 c) 5 ⋅ 6 ⋅ 0 d) (2)(3)(7) e) 2 × 4 × 10
E
2. Multiply.
AM
a) 51 b) 1123 c) 40,001
× 2 × 5 × 3
3. Multiply by powers of 10.
a) 2 × 10 b) 2 × 100 c) 2 × 1000
SH
d) From the pattern you’ve observed, what would 754 ´ 10, 000 equal?
4. Multiply.
a) 18 b) 534 c) 4,302 d) 160
UB
× 22 × 54 × 107 × 200
5. a) Jenny pays $275 per month for her car payment. How much does she pay per year?
b) Frank bought 8 CDs at $15 each. How much did he pay total?
_S
Teaching Notes:
?
• Some students need to practice basic multiplication facts at home in order to master them.
• Some students do not know the different types of symbols that mean multiplication.
?
• 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.
Answers: 1a) 6, b) 6, c) 0, d) 42, e) 80; 2a) 102, b) 5615, c) 120,003; 3a) 20, b) 200, c) 2000, d) 7,540,000;
4a) 396, b) 28,836, c) 460,314, d) 32,000; 5a) $3300, b) $120
Copyright © 2014 Pearson Education, Inc.
