Canada · Ontario Curriculum Expectations
Grade 9 Mathematics
This course bridges the transition from arithmetic to abstract mathematical reasoning. Students explore the power of variables, the logic of spatial relationships, and the utility of data to solve complex real world problems.
01The Power of Number and Proportion
Exploration of rational numbers, powers, and proportional reasoning to model physical phenomena.
Students will define and classify numbers within the real number system, including rational and irrational numbers.
Students will practice adding, subtracting, multiplying, and dividing rational numbers, including fractions and decimals.
Students will define exponents, identify base and power, and evaluate expressions with positive integer exponents.
Students will discover and apply the product and quotient rules for exponents to simplify expressions.
Students will apply the power of a power rule and understand the concept of a zero exponent.
Students will interpret negative exponents and use scientific notation to represent very large or very small numbers.
Students will define and differentiate between ratios and rates, and simplify them to their lowest terms.
Students will set up and solve proportions using cross-multiplication and other algebraic methods.
Students will convert between fractions, decimals, and percentages, and solve problems involving percentage increase/decrease.
Students will distinguish between direct and inverse proportional relationships and model them with equations.
02Patterns and Algebraic Generalization
Moving from concrete patterns to abstract algebraic expressions and linear relationships.
Students will define variables, write algebraic expressions from verbal descriptions, and evaluate them.
Students will combine like terms and apply the distributive property to simplify algebraic expressions.
Students will identify linear patterns in tables of values, graphs, and verbal descriptions.
Students will plot points from tables of values and graph linear relations on a Cartesian plane.
Students will calculate the slope of a line from a graph, two points, and a table of values, interpreting it as a rate of change.
Students will identify the y-intercept and write the equation of a line in slope-intercept form.
Students will write linear equations given two points, a point and a slope, or a table of values.
Students will solve one-step linear equations involving addition, subtraction, multiplication, and division.
Students will solve multi-step linear equations requiring combining like terms and distributive property.
Students will solve linear equations where variables appear on both sides of the equality sign.
03Geometric Logic and Spatial Reasoning
Applying geometric theorems and properties to solve problems involving shapes and space.
Students will define and identify translations, reflections, and rotations as rigid transformations.
Students will perform and describe translations of figures using coordinate rules.
Students will perform and describe reflections of figures across the x-axis, y-axis, and other lines.
Students will perform and describe rotations of figures about the origin (90°, 180°, 270°).
Students will perform and describe dilations of figures, understanding the role of the scale factor and center of dilation.
Students will use sequences of transformations to determine if figures are congruent or similar.
Students will identify and apply the Angle-Angle (AA), Side-Side-Side (SSS), and Side-Angle-Side (SAS) similarity criteria for triangles.
Students will use properties of similar polygons to find unknown side lengths and angle measures.
Students will identify and define key parts of a circle, including radius, diameter, chord, tangent, and secant.
Students will explore the relationships between central angles, inscribed angles, and their intercepted arcs.
04Measurement and Dimensional Analysis
Calculating surface area and volume of complex 3D objects and understanding measurement limits.
Students will review and apply formulas for the area of basic 2D shapes (rectangles, triangles, circles, trapezoids).
Students will calculate the surface area of right prisms and cylinders using nets and formulas.
Students will calculate the surface area of right pyramids and cones, including the use of slant height.
Students will apply the formula to calculate the surface area of spheres and hemispheres.
Students will calculate the volume of right prisms and cylinders using the area of the base and height.
Students will calculate the volume of right pyramids and cones, understanding their relationship to prisms and cylinders.
Students will apply the formula to calculate the volume of spheres and hemispheres.
Students will calculate the volume and surface area of objects composed of two or more simple 3D shapes.
Students will convert between different units of length, area, and volume within and between measurement systems.
05Data, Probability, and Decision Making
Analyzing data sets and probability models to make informed predictions and critiques.
Students will explore different methods of data collection, including surveys, observations, and experiments.
Students will identify different sampling techniques and recognize potential sources of bias in data collection.
Students will calculate and interpret mean, median, and mode for various data sets.
Students will calculate and interpret range, interquartile range (IQR), and standard deviation (introduction) to describe data variability.
Students will construct and interpret frequency tables and histograms for numerical data.
Students will construct and interpret box plots, identifying quartiles and potential outliers.
Students will create and interpret scatter plots, identifying positive, negative, and no correlation.
Students will define probability, identify outcomes and events, and calculate theoretical probability.
Students will conduct experiments, collect data, and calculate experimental probability and relative frequency.
Students will calculate probabilities of compound events using tree diagrams and the multiplication rule.
06Financial Literacy and Economic Models
Applying mathematical principles to personal finance and economic decision making.
Students will calculate simple interest, principal, rate, and time using the simple interest formula.
Students will calculate compound interest and compare its growth to simple interest over time.
Students will explore different types of debt (e.g., loans, credit cards) and the mathematical implications of credit scores.
Students will develop personal budgets, categorizing income and expenses to manage finances effectively.
Students will explore different savings vehicles and basic investment concepts, including risk and return.
Students will understand different types of income, calculate gross and net pay, and explore basic tax concepts.
Students will calculate unit prices to compare product values and make informed purchasing decisions.
Students will calculate discounts, sales tax, and gratuities, applying percentages to real-world transactions.
Students will explore different types of loans (e.g., car, mortgage) and the concept of amortization schedules.