Canada · Ontario Curriculum Expectations
Grade 8 Mathematics
This course bridges concrete arithmetic and abstract algebraic reasoning through the study of proportional relationships, geometric transformations, and data modeling. Students develop critical thinking skills by justifying mathematical conjectures and applying multiple representations to solve complex real world problems.
01Number Systems and Radical Thinking
Students explore the expansion of the number system to include irrational numbers and develop fluency with powers and roots.
Distinguishing between rational and irrational numbers using decimal expansions and geometric models.
Locating and comparing irrational numbers on a number line by approximating their values.
Applying laws of integer exponents to simplify numerical expressions.
Using scientific notation to express and compute with very large and very small quantities.
Performing multiplication, division, addition, and subtraction with numbers in scientific notation.
Evaluating square and cube roots to solve equations and understand geometric area and volume.
Solving simple equations involving squares and cubes by using square roots and cube roots.
Classifying numbers within the real number system, including natural, whole, integers, rational, and irrational numbers.
Exploring the commutative, associative, and distributive properties within the real number system.
02Exploring Linear Relationships
An investigation into how quantities change together and how to represent these relationships through tables, graphs, and equations.
Defining functions as a rule that assigns to each input exactly one output, using various representations.
Comparing properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
Sketching and interpreting graphs that model the functional relationship between two quantities.
Defining slope through similar triangles and interpreting it as a constant rate of change in various contexts.
Graphing proportional relationships, interpreting the unit rate as the slope of the graph.
Connecting unit rates to the equation y = mx + b and comparing different representations of functions.
Graphing linear equations in the form y = mx + b and understanding the role of slope and y-intercept.
Writing the equation of a line in y=mx+b form given its graph.
Writing the equation of a line in y=mx+b form given a table of values.
03Solving Linear Equations
Mastering the manipulation of algebraic expressions to solve multi-step equations and systems of linear equations.
Using the distributive property and combining like terms to solve equations with variables on both sides.
Solving linear equations with rational number coefficients, including those whose solutions require expanding expressions.
Understanding what a system of two linear equations in two variables is and what its solution represents.
Finding the intersection of two lines to determine the simultaneous solution for two linear equations.
Solving systems of equations using the substitution method to find exact values.
Solving systems of equations using the elimination method to find exact values.
Applying systems of linear equations to solve real-world problems.
Analyzing linear equations to determine if they have one solution, no solution, or infinitely many solutions.
Mastering techniques to solve linear equations where variables appear on both sides of the equals sign.
04Geometry in Motion
Exploring congruence and similarity through physical and coordinate transformations of geometric figures.
Investigating translations to understand how figures move without changing size or shape.
Investigating reflections across axes and other lines to understand congruence.
Investigating rotations about the origin and other points to understand congruence.
Describing a sequence of transformations that maps one figure onto another to prove congruence.
Using scale factors and centers of dilation to create similar figures and understand proportional growth.
Understanding similarity in terms of transformations and using similar figures to solve problems.
Using the properties of parallel lines and transversals to determine unknown angle measures.
Proving that the sum of the angles in a triangle is 180 degrees and applying this to solve problems.
Understanding and applying the Exterior Angle Theorem to find unknown angle measures in triangles.
05The Power of Pythagoras
Applying the Pythagorean Theorem to solve real-world problems and finding volumes of curved three-dimensional shapes.
Exploring various geometric proofs of the theorem and its converse to understand right triangle relationships.
Using the Pythagorean theorem to find unknown side lengths in right triangles.
Using the converse of the Pythagorean theorem to determine if a triangle is a right triangle.
Using the Pythagorean theorem to find distances between two points on the coordinate plane.
Using the Pythagorean theorem to find lengths within three-dimensional objects.
Developing and using formulas for the volume of cylinders to solve problems.
Developing and using formulas for the volume of cones to solve problems.
Developing and using formulas for the volume of spheres to solve problems.
Calculating the surface area of cylinders using nets and formulas.
06Patterns in Data
Analyzing bivariate data through scatter plots and two-way tables to identify trends and associations.
Constructing scatter plots for bivariate measurement data to observe patterns.
Interpreting scatter plots to look for patterns, clusters, and outliers in data sets.
Informally fitting a straight line to data and using the equation of that line to make predictions.
Using the equation of a linear model to solve problems in the context of bivariate measurement data.
Understanding that correlation does not imply causation.
Using two-way tables to summarize bivariate categorical data.
Calculating relative frequencies for two-way tables and identifying possible associations between the two categories.
Identifying and critiquing misleading representations of data in graphs and statistics.
Exploring different methods of collecting data, including surveys, experiments, and observational studies.
07Financial Literacy and Consumer Math
Applying mathematical concepts to personal finance, including budgeting, interest, and financial planning.
Creating and analyzing personal budgets, understanding income, expenses, and savings.
Calculating simple and compound interest and understanding their impact on savings and loans.
Exploring the concepts of credit scores, loans, and responsible debt management.
Understanding different types of taxes (income, sales, property) and their impact on personal income.
Introduction to basic investment concepts, including stocks, bonds, and mutual funds.
Calculating discounts, sales tax, and total costs for consumer purchases.