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 Diagram Example: 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 What is Factorial Notation? Why are factorials important? Some more examples and important notes about factorials... (Note specifically the division!)
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, vice president 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 vice president. 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. Equation for Permutations and Clones: Example: Determine how many different ways the letters in "Mississippi". Example: Determine how many different ways the letters in "Mitchell". 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 n C r mean? What is the formula for n C r? What is the connection between n C r and Pascal's Triangle? Examples: How to evaluate n C r by hand.
Lesson4.notebook July 07, 2013 Examples: How to evaluate n C r with a calculator. (Find the n C r 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 What is the "NULL" set its notation. Explain how Real numbers can be broken into subsets. 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 real world 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 U U U U C) (A B)' C D) (A' B') C' 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