General Education Mathematics MAT 125
Daily Schedule F2014
DAY
1
2
ASSIGNMNT MINI-LECTURE & Q/A
1.1
Model how to use MML using
section 1.1; reading text, do check
points, homework.
1.2, 1.3
10 min lecture 1.2, 1.3
1.2 (#2a, 7), 1.3(#6)
Rounding with 9’s 129,876 to one
thousand
Use Polya’s steps very specifically
3
2.1, 2.2
4
10 min lecture 2.1, 2.2
2.1 (#3c, 6a, 7b)
Set-builder & roster notation.
Symbols is/is not an element of a
set, empty set, natural numbers,
cardinal number n(A),
equivalent/equal sets, finite/infinite
sets.
2.2 (#1a, 1d, 3b, 4c)
Symbols for subset, not a subset,
proper subset, number of subsets 2
to n.
ACTIVITY or QUIZ
 Syllabus Review and technology requirements (form groups of 4 – split/share report out)
 Questionnaire for group formation
 Familiarize teams with student/instructor evaluations.
 Assign groups; give time to meet each other and select a team name.
 Capture/Recapture Activity (*Problem Solving Unit; Estimation)
 1.1 Reasoning Activities; Write one list of numbers that has two patterns so that the next
number in the list can be 15 and the next number in that same list can be 20. (p.12 #72)
 1.1 Label each statement as inductive or deductive reasoning. (*Problem Solving Unit;
Inductive and Deductive Reasoning)
 1.2 Without writing down any numbers, but the final estimation, do all 4 problems. Put team
name and answers on one sheet of paper. Switch with another team, find the actual
answers, determine reasonableness of estimates, switch back. (p. 23 #14, 16, 24, 32)
 1.2 Give 3 examples of real-world situations where an estimate rather than an exact answer
is sufficient.
 1.3 Solve by showing and labeling each of Polya’s Problem Solving Steps. The perimeter of
a rectangle is 100. What is the shortest diagonal the rectangle could have?
Problem Solving Activity Chapter 1
 A fenced-in rectangular area has a perimeter of 40 ft. The fence has a post every 4 ft. how
many posts are there? Since there must be a post at the corners, what do you think the
length and width of the field are? Are there any other possible answers to the above? What?
 Alex and Katie started work on the same day. Alex will earn a salary of $28,000 the first year.
She will then receive a $4000 raise each year that follows. Katie’s salary for the first year is
$41000 Followed by a $1500 yearly raise. In what year will Alex’s salary be more than
Katie’s?

A 100-square foot box of plastic wrap costs $1.29 while a 200-square foot box costs
$2.19. If each box has an extra 100 square feet added free, which is the better buy?
 If a digital clock is the only light in an otherwise totally dark room, when will the
room be darkest? Brightest?
Chapter 1 Quiz
5
2.3
6
2.4
7
2.5
8
3.1
10 min lecture 2.3
Ask students; who prefers a dog as a
pet and who prefers a cat as a pet
and who prefers neither. Put their
names in a Venn diagram. Use the
terms to identify regions.
Venn diagrams, universal set,
complement, regions &
intersections, unions (stress
OR/AND) difference
10 min lecture 2.4
2.4 (#1) De Morgan’s Laws
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
Group consultation for Chapter 1 Quiz
2.1 (p. 54 #60, 64, 80, 86, 94)
2.1 Describe the three methods used to represent a set. Give an example of a set
represented by each method.
2.2 (p. 63 #14, 18, 32, 54, 65)
2.2 Explain what is meant by equivalent sets and what is meant by equal sets. What is the
difference?
2.2 Explain the difference between a subset and a proper subset.
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


2.3 (p. 75 #98, 100, 102, 104, p. 76 #156 – 167)
2.3 Explain the difference between the union and intersection of two sets.
Meet to discuss gathering data for a 3 circle diagram
2.4 (p. 84, #14, 16, 18, 20, 22, 24, 54, 56, 58)


10 min lecture 2.5
2.5 (#3)
10 min lecture 3.1

p/q notation, negation (careful to
define; if statement is true the
negation makes it false vise/versa,
all/some
(#1, 3)

9
2.5 Construct a Venn diagram of the following three sets (B, F & S).
Of seventy-five students surveyed;
45 like basketball (B), 45 like football (F), 58 like soccer (S)
28 like basketball and football,
37 like football and soccer,
40 like basketball and soccer,
25 like all three sports
Represent each set described in roster notation.
a. The set of students who like basketball or football,
b. The set of students who like at least one sport,
c. The set of students who like exactly one sport.
2.5 Venn Diagram Activity
Use the data your group gathered to construct a Venn Diagram; describe each of the
following regions using roster notation and, also, symbolic notation (p. 85 #75, 76, 77, 78)
Chapter 2 Quiz
10
3.2
10 min lecture 3.2

Symbols and/or, inclusive OR, if- 
then, if and only if, dominance of 
connectives
(#3, 4)
10 min group quiz consultation
3.1 (p. 109 – 110, #44, 45, 46, 48, 50)
3.1 Use the following pairs of words in quantified statements and draw a diagram of the
relationship of each pair. Use at least 4 different types of quantified statements.
a) Humans, mammals
b) Dogs, playful
c) Movies, comedies
d) Mothers, fathers
e) Cubs, World Series winners
11
3.3, 3.4
12
3.5, 3.6
13
14
3.7
15
16
3.8
11.1

f) Poets, writers
What is a statement? Explain why commands, questions, and opinions are not statements.
10 min lecture 3.3, 3.4
3.3 (#1d, 3c, 4a)
Truth tables; negation, conjunction,
disjunction, tautology
3.4 (#1c, 2b)
Truth tables; conditional/biconditional
10 min lecture 3.5
3.5 (#1c, 3a, 5b)
Equivalent statements, converse,
inverse, contrapositives



3.2 (p. 121 – 122, #81 – 84, 97 – 100)
3.2 Explain the difference between the inclusive and exclusive disjunctions.
3.2 Describe the hierarchy for the basic connectives.
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


3.3 (p. 136, #44, 58)
3.3 Explain the purpose of a truth table.
3.3 Describe how to construct a truth table for a compound statement
3.4 (p. 146 – 147, #60, 72, 75, 92)
10 min lecture 3.6
3.6 (#1, 2)
Negations, DeMorgan’s Laws
10 min lecture 3.7
Arguments and truth tables
(#1c, 2b)
10 min lecture 3.8
10 min lecture 11.1
Fundamental Counting Principle
(#1a, 2c)


3.5 (p. 155, #12, 32, 35)
3.5 Describe how to obtain the contrapositive of a conditional statement.


3.6 (p. 162, #14, 40 48)
3.6 Explain why the negation of p ʌ q is not ~p ʌ ~q.
17
18
11.2, 11.3
10 min lecture 11.2, 11.3
Permutations, Factorial Notation
(order matters-ssn#)



3.7 (p. 173 – 177, #40, 78, 81, 86)
3.8 (p. 186, #12, 19, 38)
3.8 Under what circumstances should Euler diagrams, rather than truth tables, be used to
determine whether or not an argument is valid?
Logic Activity
Draw a valid conclusion from the given premises using a truth table for one, the standard form of
valid arguments for one, and Euler Diagrams for one. Choose wisely.
a. All mammals are warm-blooded. All dogs are warm-blooded. Therefore, . . . (all dogs are
mammals).
b. If all electricity is off, then no lights work. Some lights work. Therefore. . . (Some electricity is
not off – contrapositive reasoning)
c. If you drive at 85 mph you are speeding. If you are speeding, you get to your destination
faster. Therefore, . . . (if you are speeding, you get to your destination faster – transitive
reasoning)
Chapter 3 Quiz
 10 minute group quiz consultation
 11.1 (p. 607, #16, 22)
 11.1 Write and solve an original problem using both a tree diagram and the Fundamental
11.2 (#1ab, 5)
Combinations (any order - lotto)
11.3 (#3 simplified, 6, 7)
19
11.4
10 min lecture 11.4
Probability Fundamentals
11.4 (#2c, 3b)
Counting Principle. Describe one advantage of using the Fundamental Counting Principle
rather than a tree diagram.
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
20
11.5
10 min lecture 11.5

Probability with the Fundamental
Counting Principle, Permutations,
and Combinations
11.5 (#2, 5)


11.2 (p. 614, #44, 54)
900 !
899 ! without using a calculator.
11.2 Explain the best way to evaluate
11.2 If 24 permutations can be formed using the letters in the word BAKE, why can’t 24
permutations also be formed using the letters in the word TATE? How is the number of
permutations in TATE determined?
11.3 (p. 620, #61, 63)
11.3 To open a combination lock, you must know the lock’s three-number sequence in its
proper order. Repetition of numbers is permitted. Why is this lock more like a permutation
lock than a combination lock? Why is it not a true permutation problem?
11.4 List the possible outcomes from a roll of two die (2 different colors)
Find the probability of getting: two even numbers, two numbers who sum is 5, then 7.
Now actually roll the die 50 times recording the outcomes. Find the empirical probabilities of
the above.
11.4 Color Chips
Each team has a bag of 25 chips.
Taking turns, without looking into the bag, remove a chip and record the color. Replace the
chip. Repeat 40 times, finding the empirical probability of getting each color.
Now look at all the chips and determine the theoretical probability of each color. Discuss the
difference.
11.4 A driver approaches a toll booth and randomly selects two coins from his pocket. If the
pocket contains two quarters, two dimes, and two nickels, what is the probability that the
two coins he selects will be at least enough to pay a thirty-cent toll?
21
11.6
10 min lecture 11.6
Not (complement), Or, Odds
11.6 (#2abc, 5, 6)

11.5 (p. 634, #4, 8)
22
11.7
10 min lecture 11.7
And – Conditional Probability
11.7 (#1a, 3b, 4d)


11.6 (p. 645 – 646, #28, 30, 68, 70, 72)
11.6 What are mutually exclusive events? Give an example of two events that are mutually
exclusive.
11.6 Explain how to find “or” probabilities with events that are not mutually exclusive. Give
an example.
11.7 (p. 656 – 657, #18, 38, 58)
11.7 Explain how to find “and” probabilities with dependent events. Give an example.
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23
11.8
10 min lecture 11.8
Expected Value


(#3)
24
8.1, 8.2
25
26
8.3, 8.4
27
8.5, 8.6

11.7 What is the difference between independent and dependent events? Give an example
of each.
10 min lecture
 11.8 (p. 664 – 665, #6, 16)
8.1 Percentages – out of one-  11.8 Describe a situation in which a business can use expected value.
hundred, insert % X 100, remove %
divide by 100
Percent of decrease/increase
8.2 Income Tax
Probability Activity; Deal or No Deal Game
Chapter 11 Quiz
10 min lecture
10 min group quiz consultation
8.3 Simple interest, future value
 8.1 When a store had a 60% off sale, and Julie had a coupon for an additional 40% off any
8.4
Compound
Interest,
item, she thought she should be able to obtain the dress that she wanted free. If you were
present/future value, effective
the store manager, how would you explain the mathematics of the situation to her?
annual yield
 8.1 The price of a $200 suit went on sale and was reduced by 25%. By what percent must the
price of the suit be increased to bring the price back to $200?
 8.1 Which of the following statements are true and which are false? Explain your answers.
a) Kevin got a 10% raise at the end of his first year on the job and a 10% raise after another
year. His total raise was 20% of his original salary.
b) Alex and Kate paid 45% of their first department store bill of $620 and 48% of the second
department store bill of $380. They paid 45% + 48% = 93% of the total bill of $1000.
c) Julie spent 25% of her salary on food and 40% on housing. Julie spent 25% + 40% = 65%
of her salary on food and housing.
d) In Mayberry, 65% of the adult population works in town, 25% works across the border,
and 15% is unemployed.
e) In Clean City, the fine for various polluting activities is a certain percentage of one’s
monthly income. The fine for smoking in public places is 40%, for driving a polluting car is
50%, and for littering is 30%. Mr. Schmutz committed all three polluting crimes in one
day and paid a fine of 120% of his monthly salary.
 8.1 Write and solve three original word problems; one with A missing, one with B missing
and one with C missing. A% of B is C
 8.2 (p. 507 #43, 45)
10 min lecture
 8.3 (p. 512 – 513 #10, 26, 36)
8.5 Annuities
 8.3 Explain how to calculate simple interest.
8.6 Car Loans
 8.3 Give three real-world examples when simple interest is used.
 8.4 (p. 522 #54, 58)
 8.4 Give two examples that illustrate the difference between a compound interest problem
involving future value and a compound interest problem involving present value.
28
8.7
29
8.8
30
31
10 min lecture 8.7
The cost of home ownership
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

8.4 What is effective annual yield?
8.5 (p. 537 #28, p. 538 #56)
8.5 Write and solve an original problem involving regular payments toward a goal. Include
the length of time required to reach that goal.
8.6 (p. 547 #10, 17)
8.7 (p. 556 #5, 10, 16)

10 min lecture 8.8

Credit card, average daily balance,
installment loans
 8.8 (p. 564 #3, 6)
 8.8 Describe two disadvantages of using credit cards.
Consumer Math Activity Chapter 8
Provide annual salary, % for deductions: find net pay
Provide mortgage info, car loan info & credit card info: find total payments
Students determine other required living expenses and devise a budget based upon the salary &
payments. Discussion.
52weeks *40hour/week*$25/hour = $52,000 annual salary352,000 * (.062 +.0145+ .1 + .05 +.03)
= $13,338 deductions
52000 – 13338 = $38662 net salary or $3221.83/month
149000 – (149000*.25) = $111,750 financed
PMT formula: $796.22/month
Other Expenses: Food, gas, car insurance, clothing, heat, electric, phone, entertainment, student
loan
($100 each * 9 = $900)
3221.83 – (796.22 + 900) = $1525.61
Chapter 8 Quiz
32
WRAP UP day/Snow day