Appendix A: Applications of Math 11 Prescribed Learning Outcomes

The organizers for Applications of Math 11 are as follows:

Problem Solving
Number (Number Operations)
Patterns and Relations (Variables and Equations)
Patterns and Relations (Relations and Functions)
Shape and Space (Measurement)
Shape and Space (3-D Objects and 2-D Shapes)
Statistics and Probability (Data Analysis)

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:

• solve problems that involve a specific content area such as geometry, algebra, trigonometry, statistics, or probability
• solve problems that involve more than one content area
• solve problems that involve mathematics within other disciplines
• analyse problems and identify the significant elements
• 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
• demonstrate the ability to work individually and co-operatively to solve problems
• determine that their solutions are correct and reasonable
• clearly communicate a solution to a problem and the process used to solve it
• use appropriate technology to assist in problem solving

Number (Number Operations)

It is expected that students will solve consumer problems, using arithmetic operations.

It is expected that students will:

• solve consumer problems, including:
  • wages earned in various situations
  • property taxation
  • exchange rates
  • unit prices
• reconcile financial statements including:
  • cheque books with bank statements
  • cash register tallies with daily receipts
• solve budget problems, using graphs and tables to communicate solutions
• solve investment and credit problems involving simple and compound interest.

Patterns and Relations (Variables and Equations)

It is expected that students will:

• represent and analyse situations that involve expressions, equations and inequalities.
• use linear programming to solve optimization problems.

It is expected that students will:

• graph linear inequalities, in two variables
• solve systems of linear equations, in two variables:
  • algebraically (elimination and substitution)
  • graphically
• solve nonlinear equations, using a graphing tool.
• solve systems of linear inequalities in two variables using graphing technology
• design and solve linear and nonlinear systems, in two variables, to model problem situations
• apply linear programming to find optimal solutions to decision-making problems

Patterns and Relations (Relations and Functions)

It is expected that students will represent and analyse quadratic, polynomial and rational functions, using technology as appropriate.

It is expected that students will:

• determine the following characteristics of the graph of a quadratic function:
  • vertex
  • domain and range
  • axis of symmetry
  • intercepts

Shape and Space (Measurement)

It is expected that students will:

• demonstrate an understanding of scale factors, and their interrelationship with the dimensions of similar shapes and objects.
• Use measuring devices to make estimates and to perform calculations in solving problems.

It is expected that students will:

• enlarge or reduce a dimensioned object, according to a specified scale
• calculate maximum and minimum values, using tolerances, for lengths, areas and volumes
• solve problems involving percentage error when input variables are expressed with percentage errors
• design an appropriate measuring process or device to solve a problem
  

It is expected that students will develop and apply the geometric properties of circles and polygons to solve problems.

It is expected that students will:

• use technology with dynamic geometry software to confirm and apply the following properties:
  • the perpendicular from the centre of a circle to a chord bisects the chord
  • the measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc
  • the inscribed angles subtended by the same arc are congruent
  • the angle inscribed in a semicircle is a right angle
  • the opposite angles of a cyclic quadrilateral are supplementary
  • a tangent to a circle is perpendicular to the radius at the point of tangency
  • the tangent segments to a circle, from any external point, are congruent
  • the sum of the interior angles of an n-sided polygon is equal to (2n – 4) right angles
• use properties of circles and polygons to solve design and layout problems

Statistics and Probability (Data Analysis)

It is expected that students will analyse graphs or charts of given situations to derive specific information.

It is expected that students will:

• extract information from given graphs of discrete or continuous data, using:
  • time series
  • continuous data
  • contour lines
• draw and validate inferences, including interpolations and extrapolations, from graphical and tabular data
• design different ways of presenting data and analyzing results, by focusing on the truthful display of data and the clarity of presentation
• collect experimental data and use best-fit exponential and quadratic functions, to make predictions and solve problems

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

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