General Notes

It is important that teachers view the nine specific outcomes in this topic as a package and not as individual outcomes. Teachers may choose to develop lessons and activities that include parts of several outcomes.

Prior knowledge from previous grade levels includes:

• an introduction to linear relations, including tables of values and graphs (Grade 7)
• graphing and analyzing two-variable linear relations (Grade 8)
• using linear relations to solve problems, including graphing, interpolation and extrapolation (Grade 9).

Technology [T] has been identified as one of the mathematical processes to be emphasized in completing this outcome. It is expected, however, that students will be able to graph both linear and nonlinear data with and without the use of technology.

Students are expected to draw graphs that include a title, properly label led axes and appropriate scales.

For a given context, students are expected to identify key points on a graph, such as intercepts or points where the graph changes direction.

While students may have previously discussed restrictions on the variables in a linear relation, this is the first time that the terms domain and range are addressed. Some ways students may describe the domain and range for a linear relation include:

• written or verbal descriptions
• lists
• set builder notation; e.g. ,{ x |–2  ≥  x < 3, x ∈  R }

• interval notation; e.g., (–2, 3).

It is essential that students understand and are able to use set builder notation and interval notation effectively since these will be the primary ways of describing sets of numbers in future courses including Mathematics 20-1 and 20-2.

Students are expected to distinguish between continuous and discrete data and understand their implications for a graph.

General Notes

This is the first time the concept of a function is introduced in the Kindergarten to Grade 12 Mathematics curriculum. Students are expected to develop a good understanding of the concept at this level as the study of functions is a recurring topic in grades 11 and 12.

Students are expected to discover, through investigation, the rules for distinguishing between relations and functions.

Students are expected to identify functions expressed in multiple formats; e.g., graphs, tables of values, lists of ordered pairs and mapping diagrams.

General Notes

Students are expected to investigate relations represented in a variety of ways and explain why a given relation is or is not a linear relation.

With the exception of Achievement Indicator 4.3, in determining whether a given relation is or is not a linear relation, the explanation should be more detailed than stating whether or not the graph is a straight line. For example, if the relation is given as a set of ordered pairs or a table of values (Achievement Indicator 4.4), the explanation should make reference to the constant rate of change (slope) between any two points.

Students may be familiar with some of the vocabulary used in representing relations and functions; the terms input and output values are sometimes used in previous grade levels. In science courses, students may encounter the terms manipulated and responding variables; however, students are expected to use the formal terminology generally used in mathematics courses; i.e., independent variable and dependent variable.

In Achievement Indicator 4.6, students are expected to investigate different equations and develop a rule for determining which equations represent linear relations.

In Achievement Indicator 4.7, students are expected to recognize different representations of the same linear relation; i.e., students are expected to select from a list those representations (words, ordered pairs, tables of values, graphs, equations) that represent the same linear relation.

General Notes

Slope, domain and range are introduced in other outcomes. In this outcome, students are expected to relate, through investigation, these characteristics to the graphs of linear relations.

Students are expected to indicate the significance of intercepts, slope, domain and range, within the context of a problem.

Students are expected to state any restrictions on the domain and range of a linear relation, within the context of a problem.

In Achievement Indicator 5.4, students are expected to determine, through investigation, how they would draw a line that has one, two or an infinite number of intercepts.

General Notes

It is important that students understand the meaning of the symbols used in function notation. Function notation will be used extensively to represent functions in grades 11 and 12.

In using function notation, students are expected to choose variables that are meaningful in the context being described; e.g., if a linear relation describes the height of an object as a function of time, then the variables selected should reflect these quantities, as in h(t) = 5t+ 20.

A function of an algebraic expression, such as f(2x–3), is not part of this outcome.

Students are expected to connect function notation to other representations of linear relations; i.e., words, ordered pairs, tables of values, graphs.