Program of Studies: [Math 10C] [Math 10-3] [Math 10-4] [Math 20-1] [Math 20-2] [Math 20-3] [Math 20-4] [Math 30-1] [Math 30-2] [Math 30-3]

## MATHEMATICS 20-2

[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation

[PS] Problem Solving
[R] Reasoning
[T] Technology
[V] Visualization

### MeasurementGeometryNumber and LogicStatisticsRelations and FunctionsMathematics Research Project

General Outcome: Develop number sense and logical reasoning.

Specific Outcomes: It is expected that students will:

1. Analyze and prove conjectures, using inductive and deductive reasoning, to solve problems. [C, CN, PS, R]

1.1 Make conjectures by observing patterns and identifying properties, and justify the reasoning.
1.2 Explain why inductive reasoning may lead to a false conjecture.
1.3 Compare, using examples, inductive and deductive reasoning.
1.4 Provide and explain a counterexample to disprove a given conjecture.
1.5Prove algebraic and number relationships such as divisibility rules, number properties, mental mathematics strategies or algebraic number tricks.
1.6 Prove a conjecture, using deductive reasoning (not limited to two column proofs). 1.7 Determine if a given argument is valid, and justify the reasoning.
1.8 dentify errors in a given proof; e.g., a proof that ends with 2 = 1.
1.9 Solve a contextual problem that involves inductive or deductive reasoning.

1. Analyze puzzles and games that involve spatial reasoning, using problem-solving strategies.
[CN, PS, R, V]
2. (It is intended that this outcome be integrated throughout the course by using sliding, rotation, construction, deconstruction and similar puzzles and games.)

2.1 Determine, explain and verify a strategy to solve a puzzle or to win a game; e.g.,

• guess and check
• look for a pattern
• make a systematic list
• draw or model
• eliminate possibilities
• simplify the original problem
• work backward
• develop alternative approaches.

2.2 Identify and correct errors in a solution to a puzzle or in a strategy for winning a game.
2.3 Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.

1. Solve problems that involve operations on radicals and radical expressions with numerical and variable radicands (limited to square roots).
[CN, ME, PS, R]

3.4 Perform one or more operations to simplify radical expressions with numerical or variable radicands.
3.5 Rationalize the monomial denominator of a radical expression.
3.6 Identify values of the variable for which the radical expression is defined.

1. Solve problems that involve radical equations (limited to square roots or cube roots).
[C, PS, R]

(It is intended that the equations have only one radical.)

4.1 Determine any restrictions on values for the variable in a radical equation.
4.2 Determine, algebraically, the roots of a radical equation, and explain the process used to solve the equation.
4.3 Verify, by substitution, that the values determined in solving a radical equation are roots of the equation.
4.4 Explain why some roots determined in solving a radical equation are extraneous. 4.5 Solve problems by modelling a situation with a radical equation and solving the equation.

2008 Program of Studies with Achievement Indicators: http://education.alberta.ca/media/823110/math10to12_ind.pdf

Authorized Resources: http://www.education.alberta.ca/teachers/program/math/educator/resources.aspx