Appendix A: Applications of Math 12 Prescribed Learning Outcomes

The organizers for Applications of Math 12 are as follows:

A: Problem Solving
B: Number (Number Operations)
C: Number (Number Operations II)
D: Patterns and Relations (Patterns)
E: Shape and Space (Measurement)
F: Shape and Space (3-D Objects and 2-D Shapes)
G: Statistics and Probability (Chance and Uncertainty)

It is expected that students will use a variety of methods to solve real-life, practical, technical, and theoretical problems

It is expected that students will:

A1. solve problems that involve a specific content area such as geometry, algebra, trigonometry, statistics, probability, etc.
A2. solve problems that involve more than one content area
A3. Solve problems that involve mathematics within other disciplines
A4. analyse problems and identify the significant elements
A5. develop specific skills in selecting and using an appropriate problem-solving strategy or combination of strategies chosen from, but not restricted to, the following:

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

A6. demonstrate the ability to work individually and co-operatively to solve problems
A7. determine that their solutions are correct and reasonable
A8. clearly communicate a solution to a problem and the process used to solve it
A9. use appropriate technology to assist in problem solving

B: Number (Number Operations)

It is expected that students will describe and apply operations on matrices to solve problems, using technology as required.

It is expected that students will:

B1. model and solve problems, including those solved previously, using technology to perform matrix operations of addition, subtraction, and scalar multiplication as required
B2. Model and solve consumer and network problems using technology to perform matrix multiplication as required

C: Number (Number Operations II)

It is expected that students will design or use a spreadsheet to make and justify financial decisions.

It is expected that students will:

C1. design a financial spreadsheet template to allow users to input their own variables
C2. analyse the costs and benefits of renting or buying an increasing asset, such as land or property, under various circumstances
C3. analyse the costs and benefits of leasing or buying a decreasing asset, such as a vehicle or computer, under various circumstances
C4. analyse an investment portfolio applying such concepts as interest rate, rate of return and total return

D: Patterns and Relations (Patterns)

It is expected that students will generate and analyze cyclic, recursive, and fractal patterns

It is expected that students will:

D1. describe periodic events, including those represented by sinusoidal curves, using the terms amplitude, period, maximum and minimum values, vertical and horizontal shift
D2. collect sinusoidal data; graph the graph using technology, and, represent the data with a best fit equation of the form: - y = a sin (bx + c) + d
D3. Use best fit sinusoidal equations, and their associated graphs, to make predictions (interpolation, extraction)
D4. Use technology to generate and graph sequences that model real-life phenomena
D5. Use technology to contruct a fractal pattern by repeatedly applying a procedure to a geometric figure
D6. use the concept of self-similarity to compare and/or predict the perimeters, areas

E: Shape and Space (Measurement)

It is expected that students will analyse objects, analyse objects, shapes and processes to solve cost and design problems

It is expected that students will:

E1. use dimensions and unit prices to solve problems involving perimeter, area and volume
E2. solve problems involving estimation and costing for objects, shapes or processes when a design is given
E3. design an object, shape, layout or process within a specified budget
E4. use simplified models to estimate the solutions to complex measurement problems

F: Shape and Space (3-D Objects and 2-D Shapes)

It is expected that students will solve problems involving polygons and vectors, including both 3-D and 2-D applications.

It is expected that students will:

F1. use appropriate terminology to describe:

• vectors (i.e., direction, magnitude)
• scalar quantities (i.e., magnitude)

F2. assign meaning to the multiplication of a vector by a scalar
F3. determine the magnitude and direction of a resultant vector, using triangle or parallelogram methods
F4. model and solve problems in 2-D and simple 3-D, using vector diagrams and technology

G: Statistics and Probability (Chance and Uncertainty)

It is expected that students will:

• use normal and binomial probability distributions to solve problems involving uncertainty.
• solve problems based on the counting of sets, using techniques such as the fundamental counting principle, permutations and combinations.
• model the probability of a compound event, and solve problems based on the combining of simpler probabilities

It is expected that students will:

G1. find the population standard deviation of a data set or a probability distribution, using technology
G2. use z-scores and the normal distribution to solve problems
G3. use the normal approximation to the binomial distribution to solve problems involving probability calculations for large samples (where npq>10)
G4. solve pathway problems, interpreting and applying any constraints
G5. use the fundamental counting principle to determine the number of different ways to perform multistep operations
G6. construct a sample space for two or three events
G7. classify events as independent or dependent
G8. solve problems, using the probabilities of mutually exclusive and complementary events

© 2000 Copyright. All Rights Reserved. Curriculum Branch.
Maintained by: Mathematics Coordinator
Revised: November 28, 2000

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