Mathematics 12 Pacing Guide - This pacing guide replaces the previous yearly plan. It has been updated to reflect removed outcomes and provide flexibility for responsive instruction.
Mathematics 12 Desmos Activity Collection - A collection of online student Desmos activities organized by unit.
LR03 - The goal of this outcome is to have students be proficient in organizing data based on characteristics and understanding relationships between elements, this is not meant to be a study in abstract algebra. The various notations should be the vehicle for communicating the connections in a mathematically valid way, but should be not the main focus of this outcome
Outcomes P01, P02, P03, and P04 should be considered collectively when planning.
P05 - This outcome should be taught in conjunction with P06.
P05 - It is intended that circular permutations not be included.
P05 - Students are not expected to solve equations involving factorial notation that result in a cubic function.
LR02 Students will be expected to solve problems that involve the application of set theory.
LR02.01 Provide examples of the empty set, disjoint sets, subsets, and universal sets in context, and explain the reasoning.
LR02.02 Organize information such as collected data and number properties using graphic organizers, and explain the reasoning.
LR02.03 Explain what a specified region in a Venn diagram represents, using connecting words (and, or, not) or set notation.
LR02.04 Determine the elements in the complement, the intersection, or the union of two sets.
LR02.05 Explain how set theory is used in applications such as Internet searches, database queries, data analysis, games, and puzzles.
LR02.06 Identify and correct errors in a given solution to a problem that involves sets.
LR02.07 Solve a contextual problem that involves sets, and record the solution, using set notation.
LR03 Students will be expected to solve problems that involve conditional statements.
LR03.01 Analyze an “if-then” statement, make a conclusion, and explain the reasoning.
LR03.02 Make and justify a decision, using “what if?” questions, in contexts such as probability, finance, sports, games, or puzzles, with or without technology.
LR03.03 Determine the converse, inverse, and contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a counterexample.
LR03.04 Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its converse or inverse.
LR03.05 Demonstrate, using examples, that the veracity of any statement does imply the veracity of its contrapositive.
LR03.06 Identify and describe contexts in which a biconditional statement can be justified.
LR03.07 Analyze and summarize, using a graphic organizer such as a truth table or Venn diagram, the possible results of given logical arguments that involve biconditional, converse, inverse or contrapositive statements.
P01 Students will be expected to interpret and assess the validity of odds and probability statements.
P01.01 Provide examples of statements of probability and odds found in fields such as media, biology, sports, medicine, sociology, and psychology.
P01.02 Explain, using examples, the relationship between odds (part-part) and probability (part-whole).
P01.03 Express odds as a probability and vice versa.
P01.04 Determine the probability of, or the odds for and against, an outcome in a situation.
P01.05 Explain, using examples, how decisions may be based on probability or odds and on subjective judgments.
P01.06 Solve a contextual problem that involves odds or probability.
P02 Students will be expected to solve problems that involve the probability of mutually exclusive and non-mutually exclusive events.
P02.01 Classify events as mutually exclusive or non-mutually exclusive, and explain the reasoning.
P02.02 Determine if two events are complementary, and explain the reasoning.
P02.03 Represent, using set notation or graphic organizers, mutually exclusive (including complementary) and non-mutually exclusive events.
P02.04 Solve a contextual problem that involves the probability of mutually exclusive or non-mutually exclusive events.
P02.05 Solve a contextual problem that involves the probability of complementary events.
P02.06 Create and solve a problem that involves mutually exclusive or non-mutually exclusive events.
P03 Students will be expected to solve problems that involve the probability of two events.
P03.01 Compare, using examples, dependent and independent events.
P03.02 Determine the probability of an event, given the occurrence of a previous event.
P03.03 Determine the probability of two dependent or two independent events.
P03.04 Create and solve a contextual problem that involves determining the probability of dependent or independent events.
P04 Students will be expected to solve problems that involve the fundamental counting principle.
P04.01 Represent and solve counting problems, using a graphic organizer.
P04.02 Generalize the fundamental counting principle, using inductive reasoning.
P04.03 Identify and explain assumptions made in solving a counting problem.
P04.04 Solve a contextual counting problem, using the fundamental counting principle, and explain the reasoning.
P05 Students will be expected to solve problems that involve permutations.
(It is intended that circular permutations not be included.)
P05.01 Represent the number of arrangements of n elements taken n at a time, using factorial notation.
P05.02 Determine, with or without technology, the value of a factorial.
P05.03 Simplify a numeric or algebraic fraction containing factorials in both the numerator and denominator.
P05.04 Solve an equation that involves factorials.
P05.05 Determine the number of permutations of n elements taken r at a time.
P05.06 Determine the number of permutations of n elements taken n at a time where some elements are not distinct.
P05.07 Explain, using examples, the effect on the total number of permutations of n elements when two or more elements are identical.
P05.08 Generalize strategies for determining the number of permutations of n elements taken r at a time.
P05.09 Solve a contextual problem that involves probability and permutations.
P06 Students will be expected to solve problems that involve combinations.
P06.01 Explain, using examples, why order is or is not important when solving problems that involve permutations or combinations.
P06.02 Determine the number of combinations of n elements taken r at a time.
P06.03 Generalize strategies for determining the number of combinations of n elements taken r at a time.
P06.04 Solve a contextual problem that involves combinations and probability
Additional Resources and Activities for LR02 (set theory):
Giant Venn Diagrams - “We could make giant Venn diagrams on the floor and bring in cupcakes and sort them into different categories!”
Venn Diagram Worksheets - There are some nice templates here to use. Set Theory Definitions, Venn Diagram - shade the regions given two sets, Venn Diagram Set Notation Problems Using Two Sets, Venn Diagram Word Problems Using Two Sets.
Online Venn Diagram Games - Five different online Venn Diagram pairs activities.
Venn Diagram Project - A project for students to answer several Venn diagram problems within a Google slides. This would be a good follow- up activity after completing an Introduction to Venn Diagrams Desmos activity.
Mutually Exclusive books - The sum of all knowledge in the world is captured in these two books.
Additional Resources and Activities for LR03 ( conditional, converse, inverse, contrapositive , biconditional statements):
Note: Outcome LR03 has been removed from Mathematics 12 Curriculum.
Additional Resources and Activities for P01, P02 and P03 (odds and probability):
Note: Outcome P02 has been removed from Mathematics 12 Curriculum.
The Better Bet - Which of the following is the better bet, if both games cost £1 to play? Game 1: Getting two heads and two tails on four coins wins you £3 or Game 2: You win £2 for every six that appears when three standard dice are rolled. You can make a guess and then use experimental probability to investigate this question.
Probability Carnival - Students play three different games with some aspect of probability and chance. After playing these games, students reflect how understanding probability may or may not help them play the games better.
The Great Races - Check out this simple probability game to get students thinking about the probabilities of rolling different sums on two dice.
100 Rolls Task - Show students an image of products from 100 rolls of two non-standard dice. Ask them to determine what numbers appears on the faces of each of these dice. They can look what 100 products from two standard dice would be and then record their thoughts about the mystery dice.
The last banana thought experiment a TEDEd video - This video explains a simple probability experiment with dice.
Virtual Adjustable Spinner - NCTM Illuminations
Additional Resources and Activities for P04, P05 and P06 (counting, combinations and permutations):
Oreo Flavor Combinations - You can create your own, custom-made Oreos by twisting apart different flavored cookies and combining them with other flavors. You can simply sandwich two Oreo halves together to create a simple, double decker cookie made up of two flavors. Or, you could get a little fancier by scraping off the filling and stacking creme upon creme to create multi-tiered cookies. You can use the Fundamental Counting Principle to research how many different ways of there of making a double decker cookie with the Oreos available at your local store.
Zero Factorial video - In this video, Dr. James Grimes explains why 0! = 1.
The Humble-Nishiyama Randomness Game - Mathematicians Steve Humble and Yutaka Nishiyama invented this game using playing cards to highlight a surprising result in probability, based on a principle discovered by Walter Penney.