Mathematics (Grade 9)
35 of 35 topics written so far. Greyed-out topics are coming soon.
Unit 1: Number
- 1Number Systems
Natural numbers, whole numbers, integers, rational, irrational and real numbers — how the sets fit together, plus density, infinity and limits.
Draft - 2Integer Operations
Using positive and negative numbers for location, direction and change — adding, subtracting, multiplying and dividing integers, signs in fractions and rates, and order of operations.
Draft - 3Fraction Operations
Unit fractions and measuring tools, equivalent fractions, and adding, subtracting, multiplying and dividing positive and negative fractions and mixed numbers.
Draft - 4Ratios, Rates and Proportions
Ratios and equivalent ratios, unit rates and best buys, solving proportions, scale drawings and maps, and keeping track of units.
Draft - 5Percent Problems
Finding a percent of a number, finding the whole, percent increase and decrease, HST and discounts, and why successive percents don't simply add.
Draft - 6Scientific Notation
Patterns in powers of 10, how the sign and size of an exponent change a power, and writing, converting and calculating with very large and very small numbers.
Draft - 7Exponent Laws
The product, quotient and power laws, what zero and negative exponents mean, and how the graph of y = 2^x compares with y = x².
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Unit 2: Algebra
- 1Writing Algebraic Expressions
Variables, terms, coefficients and constants; turning words, patterns and tables into expressions; and checking whether two expressions are equivalent.
Draft - 2Simplifying Algebraic Expressions
Collecting like terms, using the distributive property (including with negatives), simplifying expressions with brackets, and multiplying and dividing monomials.
Draft - 3Solving Linear Equations
Solving one-step to multi-step linear equations, including brackets, fractions and variables on both sides; writing equations from word problems; and checking solutions.
Draft - 4Rearranging Formulas
Isolating a variable in a formula, substituting values (including fractions and negatives), and solving for one variable when you know the others.
Draft - 5Coding with Algebra
Using short Python programs to explore variables, parameters, equations and inequalities — evaluating expressions in a loop, making tables of values, solving by testing values, and reading and changing code.
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Unit 3: Linear and Non-linear Relations
- 1Linear and Non-linear Relations
Telling linear and non-linear relations apart from tables (first differences), graphs and equations, describing rates of change, and using patterns to make predictions.
Draft - 2Representing Linear Relations
Showing one linear relation as a situation, a table, a graph and an equation; rate of change and initial value; direct and partial variation.
Draft - 3Equations of Lines
The slope formula, zero and undefined slopes, finding a line's equation from a graph, a table, a point and slope, or two points, and switching between y = mx + b, Ax + By + C = 0 and Ax + By = D.
Draft - 4Graphing Lines and Regions
Graphing x = k, y = k, x + y = k, x − y = k, ax + by = k (intercept method) and xy = k, then graphing the matching inequalities and reading points and regions in context.
Draft - 5Transforming Lines
Starting from lines through the origin, y = ax, and translating them up or down, reflecting them in the axes, and rotating them about the origin, including a 90° rotation.
Draft - 6Comparing Linear Relations
Comparing two linear relations y = ax + b with tables, graphs and algebra, finding and interpreting the point of intersection, and recognizing parallel lines that never meet.
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Unit 4: Data
- 1Measures of Central Tendency
Mean, median, and mode; weighted means; estimating the mean from grouped data; the effect of outliers; and choosing the best measure.
Draft - 2Displaying One-Variable Data
Choosing the right graph for the data — bar and circle graphs, histograms, stem-and-leaf plots, and boxplots — and spotting graphs that mislead.
Draft - 3Quartiles and Percentiles
Quartiles, the interquartile range, the five-number summary, the 1.5 × IQR rule for outliers, boxplots, and percentiles.
Draft - 4Scatter Plots and Correlation
Independent and dependent variables, scatter plots, describing a relationship, the correlation coefficient r, and side-by-side boxplots.
Draft - 5Linear Regression
The line of best fit by least squares, interpreting slope and intercept, interpolation and extrapolation, residuals, and the effect of outliers.
Draft - 6The Mathematical Modelling Process
What a mathematical model is, the modelling cycle from a question to a revised model, building models from averages, rates, and lines of best fit, and how data in society can help or mislead.
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Unit 5: Geometry and Measurement
- 1Triangle and Circle Properties
Angle relationships, parallel lines, triangle and circle properties, and how to use them to analyse and create designs.
Draft - 2Measurement Conversions
Converting metric units of length, mass, capacity, area and volume, and converting between metric and imperial units with unit analysis.
Draft - 3The Pythagorean Theorem
The side-length relationship in right triangles — finding a hypotenuse or a leg, testing for right triangles, and solving real-life and composite-shape problems.
Draft - 4Changing Dimensions
How changing one or more dimensions affects perimeter, circumference, area, surface area and volume — scale factors, and the best rectangle for a fixed perimeter or area.
Draft - 5Surface Area of 3-D Objects
Using nets to find the surface area of prisms, cylinders, square-based pyramids and cones, including slant height and composite objects.
Draft - 6Volume of 3-D Objects
Volume of prisms, cylinders, pyramids and cones (and spheres), the one-third relationship, capacity in millilitres and litres, and composite objects.
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Unit 6: Financial Literacy
- 1Appreciation and Depreciation
How things gain or lose value over time — straight-line and percent depreciation, percent appreciation, year-by-year tables, reading value graphs, and buying new vs. used.
Draft - 2Simple Interest
Calculating interest with I = Prt, finding the total amount, and seeing why simple interest grows like an arithmetic sequence.
Draft - 3Compound Interest
Interest on interest — A = P(1 + i)^n, compounding periods, present value, and finding the rate or time.
Draft - 4The Cost of Borrowing
How interest rates, loan length, simple vs. compound interest, and down payments change the total cost of a purchase — phone plans, car loans, buy now pay later, and credit cards.
Draft - 5Budgets
Building and reading a monthly budget — income, fixed and variable expenses, and savings — shown as tables, bar graphs, and circle graphs, and changing a budget when life changes.
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