Mathematics, Secondary 3

Rational versus irrational numbers

I can distinguish rational numbers from irrational numbers in the set of real numbers.

Representing subsets of the real numbers

I can represent subsets of the real numbers (discrete or continuous) using intervals, lists/rosters, or a number line.

The concept of absolute value

I can define and use absolute value as a distance, for example the difference between two numbers or the distance between two points.

Relating first-degree/rational functions to proportional situations

I can establish the relationship between first-degree or rational functions and proportional situations (direct or inverse variation).

Numbers in scientific notation

I can compute with numbers written in scientific notation.

Cubes and cube roots

I can compute cubes and cube roots within a sequence of operations.

Powers with fractional exponents

I can compute numbers in exponential notation with fractional exponents.

Estimating the value of a power

I can estimate the value of a power from its base and exponent (base between 0 and 1 or greater than 1; positive/negative, integral/fractional exponent).

Order of magnitude with scientific notation

I can estimate the order of magnitude of a real number using scientific notation.

Operating with numbers in exponential and radical form

I can compute with numbers written in exponential and radical notation using the laws of exponents.

Integral and fractional exponents on a rational base

I can operate with integral exponents (rational base) and fractional exponents.

Operating on numbers in fractional notation

I can carry out operations on numbers written in fractional notation, including negatives.

The idea of a parameter

I can identify a parameter — a constant in a rule that sets its shape but can be changed between situations.

Algebraic expressions of degree less than 3

I can work with algebraic expressions of degree less than 3 (constant, first- and second-degree).

Distinguishing an unknown from a variable

I can distinguish an unknown (a value to find) from a variable (a quantity that varies).

Choosing the dependent and independent variables

I can choose the dependent variable and the independent variable in a relationship.

The rule for inequalities with negatives

I can transform inequalities involving multiplication or division by a negative, reversing the inequality sign.

Transforming inequalities

I can transform inequalities to maintain equivalence and justify the steps.

Multiplying an algebraic expression by a monomial

I can multiply algebraic expressions by a monomial using the distributive property.

Representing an inequality another way

I can represent an inequality using another type of representation when it helps.

Validating a solution

I can validate a solution, with or without technological tools, by substitution.

Relations, functions and inverses

I can recognize relations, functions and their inverses.

Reading a common factor in context

I can interpret the common factor in an algebraic expression in light of the context.

Interpreting a solution or making a decision

I can interpret the solution or make a decision, if necessary, depending on the context.

Describing a situation with an inequality

I can describe a situation using an inequality.

Describing a pattern with an equation (deeper)

I can describe a numerical pattern with an equation and connect it to a function.

Describing relations or formulas

I can describe, in words and mathematical language, a series of numbers using relations or formulas.

Describing patterns with equations

I can describe numerical patterns using equations.

Solving first-degree inequalities in one variable

I can solve a first-degree inequality in one variable and describe its solution set.

Solving systems of two first-degree equations

I can solve a system of first-degree equations in two variables (y = ax + b form) using tables, graphs or algebra (comparison).

Polynomial functions of degree 0 or 1

I can work with polynomial functions of degree 0 (constant) or 1 (first-degree/linear).

The first-degree function y = ax + b

I can analyze the first-degree function of the form ax + b.

Piecewise functions

I can read and use a piecewise function, applying the right rule on each interval.

Legs and hypotenuse of a right triangle

I can identify the legs and the hypotenuse of a right triangle.

Right cones and spheres

I can identify right cones and spheres and their measurements.

Representing 3-D figures in the plane

I can represent three-dimensional figures in the plane using nets, projections and perspective.

Justifying statements about volume or capacity

I can justify statements concerning measures of volume or capacity.

Segments in a solid from isometry or similarity

I can find segments in a solid resulting from an isometry or a similarity transformation.

Area of a right cone and a sphere

I can use relations to calculate the area of a right cone and a sphere.

Volume relations for cylinders, pyramids, cones, spheres

I can construct and use relations to calculate volumes of right cylinders, right pyramids, right cones and spheres.

The Pythagorean relation

I can use the Pythagorean relation in a right triangle: leg² + leg² = hypotenuse².

Area under a similarity transformation

I can find the area of a figure resulting from a similarity transformation.

Area of spheres, cones and decomposable solids

I can compute the area of a sphere, the lateral or total area of right cones, and of decomposable solids.

Volume of prisms, cylinders, pyramids, cones and spheres

I can compute the volume of right prisms, right cylinders, right pyramids, right cones and spheres.

Volume of decomposable solids

I can compute the volume of solids that split into prisms, cylinders, pyramids, cones and spheres.

Volume of solids under isometry or similarity

I can find the volume of solids resulting from an isometry or a similarity transformation.

Relationships between SI units of volume

I can establish relationships between SI units of volume.

Measures of capacity

I can work with measures of capacity and relate them to volume.

Measures of volume and capacity

I can work with measures of volume and of capacity and convert between them.

Metric relations in plane figures

I can determine, through exploration or deduction, different metric relations in plane figures.

Metric relations in a right triangle

I can use the metric relations in a right triangle involving the altitude to the hypotenuse and geometric means.

Distance between two points

I can calculate the distance between two points in the Cartesian plane.

Slope of a line

I can calculate and interpret the slope of a line.

Relative position of two lines by slope

I can determine the relative position of two straight lines using their slopes.

Equations of straight lines

I can work with straight lines graphically and algebraically.

Grouped data, histograms and box plots

I can represent data with a table of grouped data (classes), a histogram, or a box-and-whisker plot.

Measures of central tendency

I can find and interpret the mode, median and weighted mean.

Comparing experimental and theoretical data

I can compare experimental data with theoretical expectations.

Discrete versus continuous random variables

I can identify the type of a random variable: discrete or continuous.

Geometric probability

I can apply odds/chance using geometric figures (areas or lengths).

Arrangements, permutations and combinations

I can count outcomes involving arrangements, permutations or combinations.

Conditional probability

I can calculate conditional probabilities.