General Education Mathematics MAT 125 HYBRID
Daily Schedule
DAY / ASSIGNMNT / MINI-LECTURE & Q/A / ACTIVITY or QUIZ1 / 1.1, 1.2, 1.3 / Model how to use MML using section 1.1; reading text, do check points, homework.
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 / § Syllabus Review and technology requirements (form groups of 4 – split/share report out)
§ Questionnaire for group formation and partner formation – complete in class.
§ Familiarize teams with student self evaluations.
2 / 2.1, 2.2 / 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 the n. / § Assign groups and partners; give time to meet each other and select a team name.
§ 1.1 Reasoning Activities; Write one list of numbers that has two patterns so that the next number in the list could be 2 different numbers. State the patterns. (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)
§ 1.3 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?
3 / 2.3, 2.4, 2.5
Chapter 1 Activity Due / 10 min lecture 2.3, 2.4, 2.5
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
2.4 (#1) De Morgan’s Laws
2.5 (#3) / § 2.1 (p. 54 #60, 64, 80, 86, 94)
§ 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?
§ 2.3 (p. 75 #98, 100, 102, 104, p. 76 #156 – 167)
4 / 3.1, 3.2 / 10 min lecture 3.1, 3.2
3.1 p/q notation, negation (careful to define; if statement is true the negation makes it false vise/versa, all/some (#1, 3)
3.2 Symbols and/or, inclusive OR, if-then, if and only if, dominance of connectives (#3, 4) / § 2.4 (p. 84, #14, 16, 18, 20, 22, 24, 54, 56, 58)
§ 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.
5 / 3.3, 3.4
Chapter 2 Activity Due / 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/bi-conditional / § 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
§ 3.2 (p. 121 – 122, #81 – 84, 97 – 100)
§ 3.2 Explain the difference between the inclusive and exclusive disjunctions.
6 / 3.5, 3.6 / 10 min lecture 3.5, 3.6
3.5 (#1c, 3a, 5b)
Equivalent statements, converse, inverse, contrapositives
3.6 (#1, 2)
Negations, DeMorgan’s Laws / § 3.3 (p. 136, #44, 58)
§ 3.4 (p. 146 – 147, #60, 72, 75, 92)
7 / 3.7, 3.8 / 10 min lecture 3.7, 3.8
3.7 Arguments and truth tables
(#1c, 2b)
3.8 / § 3.5 (p. 155, #12, 32, 35)
§ 3.6 (p. 162, #14, 40 48)
§ 3.6 Explain why the negation of p ʌ q is not ~p ʌ ~q.
8 / 10 min lecture 8.1, 8.2, 8.3
8.1 Percentages – out of one-hundred, insert % X 100, remove % divide by 100
Percent of decrease/increase
8.2 Income Tax
8.3 Simple interest, future value / § 3.7 (p. 173 – 177, #40, 78, 81, 86)
§ 3.8 (p. 186, #12, 19, 38)
9 / 8.1, 8.2, 8.3
Chapter 3 Activity Due / Review Chapters 1 - 3 / EXAM I Chapters 1, 2 & 3
10 / 8.4, 8.5, 8.6 / 10 min lecture 8.4, 8.5, 8.6
8.4 Compound Interest, present/future value, effective annual yield
8.5 Annuities
8.6 Car loans / § 8.1 When a store had a 60% off sale, and Julie had a coupon for an additional 40% off any item, she thought she should be able to obtain the dress that she wanted free. If you were the store manager, how would you explain the mathematics of the situation to her?
§ 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.
§ 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
§ 8.2 (p. 507 #43, 45)
§ 8.3 (p. 512 – 513 #10, 26, 36)
11 / 8.7, 8.8 / 10 min lecture 8.7, 8.8
8.7 The cost of home ownership
8.8 Credit card, average daily balance, installment loans / § 8.4 (p. 522 #54, 58)
§ 8.5 (p. 537 #28, p. 538 #56)
§ 8.6 (p. 547 #10, 17)
§ 8.6 (p. 547 #10, 17)
12 / 11.1, 11.2 / 10 min lecture 11.2, 11.2 / § 8.7 (p. 556 #5, 10, 16)
8.8 (p. 564 #3, 6)
13 / 11.3, 11.4, 11.5
Chapter 8 Activity Due / 10 min lecture 11.3, 11.4, 11.5
11.3 (#3 simplified, 6, 7)
Probability Fundamentals
11.4 (#2c, 3b)
Probability with the Fundamental Counting Principle, Permutations, and Combinations
11.5 (#2, 5) / § 11.1 (p. 607, #16, 22)
§ 11.1 Write and solve an original problem using both a tree diagram and the Fundamental Counting Principle. Describe one advantage of using the Fundamental Counting Principle rather than a tree diagram.
§ 11.2 (p. 614, #44, 54)
§ 11.2 Explain the best way to evaluate without using a calculator.
§ 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?
14 / 11.6, 11.7, 11.8 / 10 min lecture 11.6, 11.7, 11.8
Not (complement), Or, Odds
11.6 (#2abc, 5, 6)
And – Conditional Probability
11.7 (#1a, 3b, 4d)
11.8 Expected Value (#3) / § 11.3 (p. 620, #61, 63)
§ 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 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?
§ 11.5 (p. 634, #4, 8)
15 / Review Chapters 8 & 11 / § 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.
§ 11.7 (p. 656 – 657, #18, 38, 58)
§ 11.8 (p. 664 – 665, #6, 16)
16 / § Exam II Chapters 8 & 11
Partner 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?
Partner Set Activity Chapter 2
Select and complete one activity.
- Select three medications and find a resource on the internet that lists the possible major side effects of each.
Construct a Venn diagram.
If the three medications are labeled A, B, and C, find the following using roster notation;
a. (A B)’
b. (A B) C
c. A (B C)
d. A’ B’
- Select three possible careers (A, B, and C) you may pursue and list the job responsibilities you would have with each one.
What responsibilities do the jobs have in common? Describe this using set notation.
If you could combine these careers somehow, what would your new job responsibilities be? Describe this using set notation.
Find the following using roster notation;
a. (A B)’
b. A (B C)
c. A’ B’
Partner Logic Activity Chapter 3
Select and complete one activity.
- Write an argument, in words and symbols, matching the law of syllogism (transitive) that involves something about your school or real life. Then explain why the conclusion of your argument is valid. Use your knowledge of logic from Chapter 3.
- Write an example of the fallacy of the inverse, in words and symbols, which involves something about your school or real life.
Then explain why the conclusion of your arguments is invalid. Use your knowledge of logic from Chapter 3.
- Politicians argue in favor of positions all the time. Do a Google search for the text of a speech by each of the main candidates in a Presidential election.
Then find at least three logical arguments within the text, write the arguments in symbols, and use truth tables or commonly used argument forms to analyze the arguments, and see if they are valid.
Partner Consumer Mathematics Activity Chapter 8
Select and complete one activity.
- You have $1,000 to invest. Investigate the advantages and disadvantages of each type of investment; checking account, money market account, passbook savings account, and certificate of deposit. Write a short paper indicating which type of account you have chosen and why (in detail) you chose that account.
- There are many fees involved in buying or selling a home. Some of these include an appraisal fee, survey fee, etc. Consult a real estate agency to see what is necessary to purchase a home in your area and write a short paper on the necessary closing costs.
- Obtain applications or descriptive brochures for several different bank card programs, compare their features (including those in fine print), and explain which deal would be best for you, and why. Be specific.