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Mitchell District High School Mathematics of Data Management
Grade 12, University MDM 4U
Course Outline
Contents
Topic Number of Lessons
Course Project – Presentations, research methods, probability analysis… 10 Counting – Permutations, combinations, tree diagrams, etc… 8 Probability – Independent and dependent events, VENN diagrams, etc… 6 Statistical Analysis – Measures of spread, variance, etc… 6 Probability Distributions – Uniform, Binomial, etc… 8
Evaluation 1. Course Material 60%
Each of the 4 units counts as 15% of your mark (Test 12%, Thinking Task 8%)
2. Project 40% Broken into 4 components:
Annotated Bibliography (8%) Variable Analysis, Mind Map and Hypothesis (8%) Google Survey (8%) Data Analysis from Survey (16%)
3. Study Skills and Work Habits
You will be assessed on responsibility, organization, independent work, collaboration, initiative and self-regulation throughout the semester.
The Flipped Classroom
• Keep your notes neat and orderly. • You may print the template for each note from the website and fill it in as you
watch the video. • You are expected to watch the videos at home, and complete the assigned
practice questions during class time. • If you are away from class for ANY reason, you will need to complete some
practice questions outside of class to catch up. • Complete all assigned practice problems, CHECK YOUR ANSWERS and
discuss any questions you did not get correct with the teacher or with your collaborative group.
• Complete the journal question for each lesson and have the teacher “mark” it during class. You should complete each journal BEFORE moving on to the next lesson
• Journal duo tangs DO NOT leave the classroom with you.
Mrs K Caldwell W114 Lesson site: mdhsmath.pbworks.com
MDM
4U L
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2019
-202
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MDM 4U Data Management
Grade 12 University
Mitchell District High School
Unit 1 Counting
8 Video Lessons
Lesson # Lesson Title Questions to Ask About
1 Counting Principles
2 Factorial Notation and
Permutations
3 Permutations and Clones
4 Pascal’s Triangle and Applying
Pascal’s Method
5 Set Theory
6 VENN Diagrams
7 Combinations
8 Combinations and Permutations
Review
(Look on the website for review
pages)
Test Written on : _______________________________________
Lesson1.notebook July 07, 2013
Topic: Counting Principles
Today's Learning goal: I can use tree diagrams, Fundamental counting principle and indirect methods to determine the number of outcomes.
Tree DiagramExample: Jenny is heading out for a night on the town. She has 3 pairs of shoes, 2 dresses and 5 shades of lipstick to choose from. Determine how many option does Jenny have for her night out.
Explain when / how tree diagrams can be used. Provide some of your own examples.
Fundamental Counting Principle
What is the Fundamental Counting Principle?
Example: Barnie is choosing an apartment. If he can has a choice of 2 types of flooring, 3 different layouts and his choice of any 10 floors for each model, determine how many apartment options are available.
Example: A car comes in 5 different colours, 3 different interior colours, 3 different engines, 2 different types of rims and 4 different radios. Determine how many ways can the new car be ordered.
Lesson1.notebook July 07, 2013
Example: How many different 4 letter call names for radio stations can there if the FIRST letter must be a 'w' or 'k'?
Example: How many different SIN's can be created using the number 0 9 when each SIN has 9 digits?
Indirect method and Fundamental Counting Principle
Example: An athlete has four pairs of running shoes in her gym bag. Determine how many ways she can pull out two unmatched shoes one after another.
Homework:
pg. 229, 1 24
Lesson2.notebook July 07, 2013
Topic: Factorial Notation and Permutations
Today's Learning goal: I can explain Factorial Notation and apply factorials to simple problems and to applications like permutations.
Definitions with counting principles:
Rule of Sum: How many ways one or another event can occur. Usually the work "or" appears in the question.
Example: How many ways can you draw a 4 OR a queen from a deck of cards? Answer: 4 + 4 = 8
Rule of Product: How many ways can two or more events occur ONE AFTER ANOTHER. Usually the word "and" appears in the question.
Example: How many ways can you draw a 4 and then a queen from a deck of cards? Answer: 4 x 4 = 16
Why are factorials important?
Some more examples and important notes about factorials... (Note specifically the division!)
What is Factorial Notation?
Lesson2.notebook July 07, 2013
Permutations
What is a Permutation? What is the notation? What is the formula?
Example: Give the colours blue, yellow, white, red, orange and green. Determine how many different 4 colour combinations are possible if no colour can be repeated.
Example: A club of 9 people wants to pick a president, vicepresident and secretary. Determine how many different ways it is possible to choose the positions.
Example: 10 horses run a race. Determine how many different ways you can have a first, second and third place winner in the race.
Example: A class of 20 want to elect a principle and vicepresident. Determine how many different ways these positions can be filled.
Example: A softball team has 10 players. Determine how many different batting orders there can be if everybody get to have a chance to bat.
Homework:
pg. 239, 1 16
Lesson3.notebook July 07, 2013
Topic: Permutations and Clones
Today's Learning goal: I can solve problems that involve arrangements using identical objects.
Example: Determine how many unique arrangements there are using the letters ABEE.
Example: Determine how many unique arrangements there are using the letters ABBB.
Example: Determine how many different ways the letters in "Mississippi".
Example: Determine how many different ways the letters in "Mitchell".
Equation for Permutations and Clones:
Homework: pg. 245, 1 13
Lesson4.notebook July 07, 2013
Topic: Pascal's Triangle
Today's Learning goal: I can explain and apply Pascal's Triangle to a variety of real world applications.
Pascal's Triangle and properties:
Example: (to row # 8) Properties:
What does nCr mean?
What is the formula for nCr?
What is the connection between nCr and Pascal's Triangle?
Examples: How to evaluate nCr by hand.
Lesson4.notebook July 07, 2013
Examples: How to evaluate nCr with a calculator. (Find the nCr on your calculator!)
Example: How many different ways are there to get from A to B.
A
B
Example: What happens if the shape is not symmetrical? How many ways are there from point A to B?
Homework:
pg 256, #1 10
Lesson5.notebook July 07, 2013
Topic: Set Theory
Today's Learning goal: I can explain and apply set theory when given a set of data.
Set and Element
A SET is
Example:
An ELEMENT is
Example:
Subsets
What is a subset?
Example:
Subset notation:
Unions
A UNION is a set
Example: If A = {1, 2, 3}, B = {1, 3, 5} then, A U B =
Intersections
An INTERSECTION is a set
Example: If A = {1, 2, 3}, B = {1, 3, 5} then, A B =
A Disjoint set occurs when
Example:
A UNIVERSAL set is
Example: S =
A COMPLEMENT set is
Notation of the complement:
Example: If A = {Monday, Wednesday, Thursday}then A' =
Lesson5.notebook July 07, 2013
Explain how Real numbers can be broken into subsets.
What is the "NULL" set its notation.
Explain what the cardinality of a set is. Provide an example.
How are 2 sets equivalent?
What notation is used to indicate 2 sets are equivalent:
Example: If the Universal set (S) is defined as the letters in the alphabet and one subset (V) is the vowels, another subset is the consonants (C) and a final subset (M) if the letters found in "Mitchell" answer the following:A) V C = B) M C =
C) n(V) = D) n(M C) =
E) V' = F) n(V M)' =
Homework: Handout
Lesson6.notebook July 07, 2013
Topic: VENN Diagrams
Today's Learning goal: I can interpret, sketch and use VENN diagrams in realworld situations.
What do VENN diagrams look like when:
There is intersection? There is union? There is a complement?
Examples: Shade the indicated regions.
A) A ∩ B B) (A ∩ B)' C) A ∪ B
Examples: Shade in the indicated regions.
A) (A B) C B) (A U B) C
UU U
C) (A B)' C D) (A' B') C' U
U U U
Lesson6.notebook July 07, 2013
Example: 350 visitors were polled. The following information was collected.
2 people enjoyed all 3 activities.2 people enjoy snowboarding and ice skating.15 people enjoy skiing and ice skating.49 people enjoy skiing and snowboarding.57 people enjoy ice skating.154 people enjoy snowboarding.178 people enjoy skiing.
A) Determine how many people DO NOT enjoy any of the three activities.B) Determine how many people only enjoy ONE activity.C) Determine how many people enjoy snowboarding and ice skating but NOT skiing.D) Determine how many people only enjoy skiing.
Homework: Handout pg 270, 1 7, 9
Lesson7.notebook July 07, 2013
Topic: Combinations
Today's Learning goal: I can explain and apply combinations to real world applications.
Review of Permutations (Remember, ORDER matters!)
Combinations
What makes combinations different from permutations?
What is the notation for combinations?
Example: How many ways can 3 seats be filled from a selection of 5 people where order does not matter?
Example: A job requires a plumbing company to send a team to fix a problem. The company has 4 experienced plumbers and 4 trainees. If a team consists of 3 plumbers, determine how many teams exist if each team need 1 experienced plumbers and 2 trainees.
Example: There are 5 boys and 7 girls in a room. Determine how many 2 boys and 3 girls be selected to move to another room.
Lesson7.notebook July 07, 2013
Example: There are 5 married couples at a party.A) Determine how many ways a man and woman can be selected to play chess if the CANNOT be married.
B) Determine how many ways can 2 men and 2 women be selected if none of them can be married.
Homework: pg. 279, 3 9, 11 16
Lesson8.notebook July 07, 2013
Topic: Combinations and Permutations
Today's Learning goal: I can identify whether the question is a combination or permutation and apply the appropriate strategy.
Explain the difference between Combinations and Permutations. Provide an example of each.
Example: Determine how many ways you can choose 3 bikes from a group of 7. Explain why it is a permutation or a combination.
Example: Joe and his friends are practicing for a relay race. If there are 6 people on the team determine how many ways lineup can be determine for a 4 person team. Explain why it is a permutation or a combination.
Example: How many ways can you sit 3 people at a table when you have 5 people to choose from when:
A) Order matters.
B) Order does not matter.
Example: Given the letters {a, b, c, d, e, f, g}, determine how many:
A) Permutations of 3 letters exist.
B) Combinations of 3 letters exist.
Homework: Handout
PERMUTATIONS AND COMBINATIONS WORKSHEETCTQR 150
1. If the NCAA has applications from 6 universities for hosting its intercollegiate tennis cham-pionships in 2008 and 2009, how many ways may they select the hosts for these champi-onships
a) if they are not both to be held at the same university?b) if they may both be held at the same university?
2. There are five finalists in the Mr. Rock Hill pageant. In how many ways may the judgeschoose a winner and a first runner-up?
3. In a primary election, there are four candidates for mayor, five candidates for city treasurer,and two candidates for county attorney. In how many ways may voters mark their ballots
a) if they vote in all three of the races?b) if they exercise their right not to vote in any or all of the races?
4. A multiple-choice test consists of 15 questions, each permitting a choice of 5 alternatives. Inhow many ways may a student fill in the answers if they answer each question?
5. A television director is scheduling a certain sponsor’s commercials for an upcoming broad-cast. There are six slots available for commercials. In how many ways may the directorschedule the commercials
a) If the sponsor has six different commercials, each to be shown once?b) If the sponsor has three different commercials, each to be shown twice?c) If the sponsor has two different commercials, each to be shown three times?d) If the sponsor has three different commercials, the first of which is to be shown threetimes, the second two times, and the third once?
6. In how many ways may can five persons line up to get on a bus?
7. In how many ways may these same people line up if two of the people refuse to stand nextto each other?
8. In how many ways may 8 people form a circle for a folk dance?
9. How many permutations are there of the letters in the word “great”?
10. How many permutations are there of the letters in the word “greet”?
11. How many distinct permutations are there of the word “statistics”?
12. How many distinct permutations of the word “statistics” begin and end with the letter “s”?
1
2
13. A college football team plays 10 games during the season. In how many ways can it end theseason with 5 wins, 4 losses, and 1 tie?
14. If eight people eat dinner together, in how many different ways may 3 order chicken, 4 ordersteak, and 1 order lobster?
15. Suppose a True-False test has 20 questions.
a) In how many ways may a student mark the test, if each question is answered?b) In how many ways may a student mark the test, if 7 questions are marked correctly and13 incorrectly?
c) In how many ways may a student mark the test, if 10 questions are marked correctlyand 10 incorrectly?
16. Among the seven nominees for two vacancies on the city council are three men and fourwomen. In how many ways may these vacancies be filled
a) with any two of the nominees?b) with any two of the women?c) with one of the men and one of the women?
17. Mr. Jones owns 4 pairs of pants, 7 shirts, and 3 sweaters. In how many ways may he choose2 of the pairs of pants, 3 of the shirts, and 1 of the sweaters to pack for a trip?
18. In how many ways may one A, three B’s, two C’s, and one F be distributed among sevenstudents in a CTQR 150 class?
19. An art collector, who owns 10 original paintings, is preparing a will. In how many ways maythe collector leave these paintings to three heirs?
20. A baseball fan has a pair of tickets to 6 different home games of the Chicago Cubs. If the fanhas five friends who like baseball, how many ways may he take one of them along to each ofthe six games?
3
ANSWERSPERMUTATIONS AND COMBINATIONS WORKSHEET
1. a) 6 · 5 = 30 b) 6 · 6 = 36
2. 5 · 4 = 20
3. a) 4 · 5 · 2 = 40 b) 5 · 6 · 3 = 90
4. 515 = 30, 517, 578, 125
5. a) 6! = 720 b) C(6, 2) ·C(4, 2) = 90 c) C(6, 3) = 20 d) C(6, 3) ·C(3, 2) = 60
6. P (5, 5) = 5! = 120
7. 5! − 4 · 2 · 3! = 72
8.8!
8= 7! = 5040
9. 5! = 120
10.5!
2!= 60
11.10!
3!3!2!= 50, 400
12.8!
3!2!= 3360
13. C(10, 5) · C(5, 4) = 1260
14. C(8, 3) · C(5, 4) = 280
15. a) 220 = 1, 048, 576 b) C(20, 7) = 77, 520 c) C(20, 10) = 184, 756
16. a) C(7, 2) = 21 b) C(4, 2) = 6 c) C(4, 1) · C(3, 1) = 12
17. C(4, 2) · C(7, 3) · C(3, 1) = 630
18. C(7, 1) · C(6, 3) · C(3, 2) = 420
19. 310 = 59, 049
20. 56 = 15, 625
