Grade 9 Math
15 units matched to the Ontario Curriculum.
Overall expectations
- AA1 Social-Emotional Learning Skills: Develop and explore a variety of social-emotional learning skills in a context that supports and reflects this learning in connection with the expectations across all other strands
- A1 Mathematical Processes: Apply the mathematical processes to develop a conceptual understanding of, and procedural fluency with, the mathematics they are learning
- A2 Making Connections: Make connections between mathematics and various knowledge systems, their lived experiences, and various real-life applications of mathematics, including careers
- B1 Development of Numbers and Number Sets: Demonstrate an understanding of the development and use of numbers, and make connections between sets of numbers
- B2 Powers: Represent numbers in various ways, evaluate powers, and simplify expressions by using the relationships between powers and their exponents
- B3 Number Sense and Operations: Apply an understanding of rational numbers, ratios, rates, percentages, and proportions, in various mathematical contexts, and to solve problems
- C1 Algebraic Expressions and Equations: Demonstrate an understanding of the development and use of algebraic concepts and of their connection to numbers, using various tools and representations
- C2 Coding: Apply coding skills to represent mathematical concepts and relationships dynamically, and to solve problems, in algebra and across the other strands
- C3 Application of Relations: Represent and compare linear and non-linear relations that model real-life situations, and use these representations to make predictions
- C4 Characteristics of Relations: Demonstrate an understanding of the characteristics of various representations of linear and non-linear relations, using tools, including coding when appropriate
- D1 Collection, Representation, and Analysis of Data: Describe the collection and use of data, and represent and analyse data involving one and two variables
- D2 Mathematical Modelling: Apply the process of mathematical modelling, using data and mathematical concepts from other strands, to represent, analyse, make predictions, and provide insight into real-life situations
- E1 Geometric and Measurement Relationships: Demonstrate an understanding of the development and use of geometric and measurement relationships, and apply these relationships to solve problems, including problems involving real-life situations
- F1 Financial Decisions: Demonstrate the knowledge and skills needed to make informed financial decisions
Units
Unit 1
Number Sets
Natural numbers, whole numbers, integers, rational and irrational numbers, how they fit inside each other, and why there are always more numbers between any two rational numbers.
Expectation: B1.2, B1.3 · subsets of the number system, density, infinity and limits
Unit 2
Rational Numbers
Adding, subtracting, multiplying and dividing fractions and decimals that may be negative, converting between fractions and decimals, ordering rational numbers, and using BEDMAS.
Expectation: B3.1, B3.3, B3.4 · operations with positive and negative fractions, decimals and integers
Unit 3
Powers & Scientific Notation
Patterns that show why a power to the zero is 1 and a negative exponent makes a reciprocal, and writing very large and very small numbers in scientific notation.
Expectation: B2.1 · the sign and size of an exponent, and scientific notation
Unit 4
Exponents & Powers
Evaluating powers, using the product, quotient and power laws, working with powers of products and fractions, and order of operations with exponents.
Expectation: B2.2 · relationships between exponents and operations with powers
Unit 5
Rates & Percents
Unit rates and best buys, percent of an amount, percent increase and decrease, proportions in ratios, and negative rates such as a diver going down.
Expectation: B3.3, B3.5 · rates, percentages and proportions, and the effect of negative signs
Unit 6
Expressions
Writing an expression for a pattern or a sentence, deciding which expressions are equivalent, expanding brackets, and collecting like terms.
Expectation: C1.2, C1.3, C1.4 · creating algebraic expressions and finding equivalent ones
Unit 7
Polynomials
Naming polynomials by terms and degree, combining like terms, subtracting polynomials, multiplying and dividing by a constant, and substituting values for x.
Expectation: C1.3, C1.4 · comparing and simplifying algebraic expressions
Unit 8
Multi-Step Equations
Solving linear equations with brackets, fractions and variables on both sides, checking solutions, and turning word problems into equations.
Expectation: C1.5 · creating and solving equations and verifying solutions
Unit 9
Code Reader
Reading short programs with variables, loops, if statements and functions, predicting the output, and changing a parameter to get a new result. No typing is needed; the code is written in plain pseudocode.
Expectation: C2.1, C2.2, C2.3 · reading and altering code with variables, equations and inequalities
Unit 10
Linear Relations
Finding slope from points and graphs, reading y = mx + b, finding intercepts, deciding whether a point is on a line, spotting parallel lines, and using rates of change in stories.
Expectation: C3.2, C4.4 · linear relations, rates of change, slopes and intercepts
Unit 11
Lines & Intersections
Finding where two lines meet and what it means in a story, graphing x = k, y = k and ax + by = k, regions of an inequality, and translating, reflecting and rotating lines through the origin.
Expectation: C3.3, C4.2, C4.3 · comparing linear relations, graphing equations and inequalities, and transforming lines
Unit 12
Data & Scatter Plots
Finding the median and quartiles of a data set, reading a box plot, telling positive, negative and no correlation apart, and using a line of best fit to make predictions. Correlation does not prove one thing causes another.
Expectation: D1.1, D1.2, D1.3 · quartiles and box plots, scatter plots, correlation and lines of best fit
Unit 13
Right Triangles & Scaling
Using the Pythagorean relationship for ladders, ramps, roofs and diagonals, deciding whether a triangle is right-angled, and seeing how doubling or tripling dimensions changes perimeter, area and volume.
Expectation: E1.2, E1.4, E1.5 · triangle and circle properties, the right-triangle relationship, and how scaling affects measures
Unit 14
Volume & Units
A pyramid holds a third of the matching prism and a cone a third of the matching cylinder, plus converting between metric units and between metric and imperial units.
Expectation: E1.3, E1.6 · volume of pyramids and cones, and converting units within and between systems
Unit 15
Money Decisions
Items that gain or lose value over time, simple and compound interest, how rate, time and down payments change the cost of borrowing, adjusting a budget, and adding 13% HST.
Expectation: F1.1, F1.2, F1.3, F1.4 · appreciation and depreciation, borrowing costs, interest and changing a budget
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