Appendix A: Principles of Math 10 Prescribed Learning Outcomes

The organizers for Principles of Math 10 are as follows:

Problem Solving

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, 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 explain the solution to a problem and justify the processes used to solve it
use appropriate technology to assist in problem solving

Number (Number Concepts)

It is expected that students will:

analyse the numerical data in a table for trends, patterns and interrelationships.
explain and illustrate the structure and the interrelationship of the sets of numbers within the real number system.

It is expected that students will:

use words and algebraic expressions to describe the data and the interrelationships in a table with rows that are not related recursively (not calculated from previous data)
use words and algebraic expressions to describe the data and the interrelationships in a table with rows that are related recursively (calculated from previous data)
classify numbers as natural, whole, integer, rational or irrational, and show that these number sets are "nested" within the real number system

It is expected that students will:

use basic arithmetic operations on real numbers to solve problems.
describe and apply arithmetic operations on tables to solve problems, using technology as required.
use exact values, arithmetic operations and algebraic operation real numbers to solve problems.

It is expected that students will:

communicate a set of instructions used to solve an arithmetic problem
perform arithmetic operations on irrational numbers, using appropriate decimal approximations
create and modify tables from both recursive and nonrecursive situations
use and modify a spreadsheet template to model recursive situations
perform operations on irrational numbers of monomial and binomial form, using exact values
explain and apply the exponent laws for powers of numbers and for variables with rational exponents

Patterns and Relations (Patterns)

It is expected that students will generate and analyse number patterns.

It is expected that students will:

generate number patterns exhibiting arithmetic growth
use expressions to represent general terms and sums for arithmetic growth, and apply these expressions to solve problems
relate arithmetic sequences to linear functions defined over the natural numbers
generate number patterns exhibiting geometric growth

It is expected that students will generalize operations on polynomials to include rational expressions.

It is expected that students will:

factor polynomial expressions of the form
find the product of polynomials
divide a polynomial by a binomial and express the result in the forms:
determine equivalent forms of simple rational expressions with polynomial numerators, and denominators that are monomials, binomials or trinomials that can be factored
determine the nonpermissible values for the variable in rational expressions
perform the operations of addition, subtraction, multiplication, and division on rational expressions
find and verify the solutions of rational equations that reduce to linear form

It is expected that students will:

It is expected that students will:

plot linear and nonlinear data, using appropriate scales
represent data, using function models
use a graphing tool to draw the graph of a function from its equation
describe a function in terms of:
- ordered pairs
- a rule, in word or equation form
- a graph
use function notation to evaluate and represent functions
determine the domain and range of a relation from its graph
determine the following characteristics of the graph of a linear function, given its equation:
- intercepts
- slope
- domain
- range
use partial variation and arithmetic sequences as applications of linear functions

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.
solve problems involving triangles, including those found in 3-D and 2-D applications.

It is expected that students will:

calculate the volume and surface area of a sphere, using formulas that are provided
determine the relationships among linear scale factors, areas, the surface areas and the volumes of similar figures and objects
solve problems involving two right triangles
extend the concepts of sine and cosine for angles through to 180°
apply the sine and cosine laws, excluding the ambiguous case, to solve problems

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

It is expected that students will solve coordinate geometry problems involving lines and line segments.

It is expected that students will:

solve problems involving distances between points in the coordinate plane
solve problems involving midpoints of line segments
solve problems involving rise, run and slope of line segments
determine the equation of a line, given information that uniquely determines the line
solve problems using slopes of:
- parallel lines
- perpendicular lines

Statistics and Probability (Data Analysis)

It is expected that students will implement and analyse sampling procedures, and draw appropriate inferences from the data collected.

It is expected that students will:

choose, justify and apply sampling techniques that will result in an appropriate, unbiased sample from a given population
defend or oppose inferences and generalizations about populations, based on data from samples