Ontario Grade 9 MTH1W Mathematics (Grade 9, De-streamed)
Chapters: 7
1. AA. Social-Emotional Learning (SEL) Skills in Mathematics
Social-Emotional Learning Skills
- Social-Emotional Skills and Mathematical Processes – Doing maths well is not only about numbers. Social-emotional skills help you notice your feelings, calm stress, keep going after mistakes, work well with others and believe you can grow. The mathematical processes are the habits good problem solvers use: understand the problem, make a plan, carry it out and look back; reason and prove; connect ideas; choose tools; represent ideas in words, tables, graphs and models; and communicate clearly.
2. A. Mathematical Thinking and Making Connections
A1 Mathematical Processes · A2 Making Connections
- Mathematical Processes: How Good Problem Solvers Think – Mathematical processes are the habits that turn facts into real maths skill. Problem solving is a loop: understand, plan, do, look back. Reasoning and proving means giving a reason that works every time, not just for one example. Reflecting means checking that an answer makes sense, often with an estimate. Connecting links ideas to each other and to life (½ = 50% = half price). Representing shows one idea in many forms: objects, pictures, numbers, symbols, tables and graphs. Selecting tools and strategies means choosing mental maths, paper, a calculator or a graph to suit the job. Communicating means writing clear steps, units and words so others can follow you.
- Career Planning: From Knowing Yourself to Your First Job – Career planning has five steps. 1) Know yourself: interests, skills and values. 2) Explore career families and find out the work, study needed, pay and demand. 3) Plan a pathway with SMART goals and a plan B. 4) Search for jobs with a CV, cover letter, digital portfolio and interview practice. 5) Make the move from school to work and keep learning, because careers change over a lifetime.
3. B. Number
B1 Development of Numbers and Number Sets · B2 Powers · B3 Number Sense and Operations
- Rational Numbers: Number Line, Density and Decimals – A rational number is any number that can be written as p/q, where p and q are integers and q is not 0. Examples: 3/4, −5/3, 7 (= 7/1), 0.25 (= 1/4). To place p/q on the number line, cut each unit into q equal parts and hop p parts from 0. Between any two rational numbers there is always another one (their average), so there are endlessly many between them. The decimal of a rational number either ends (terminating) or repeats a block for ever (non-terminating repeating).
- Laws of Exponents – An exponent tells how many times a base is multiplied by itself. Same base: multiply → add exponents, divide → subtract, power of a power → multiply. a⁰ = 1, a⁻ⁿ = 1/aⁿ and a^(1/n) is the nth root.
- Percentages – Per cent means "out of 100", so x% = x/100. To find x% of an amount, multiply by x/100. Percentage change = (change ÷ original) × 100. To increase by r%, multiply by (1 + r/100); to decrease by r%, multiply by (1 − r/100). Successive changes multiply their multipliers. For reverse percentage, divide the new value by the multiplier.
4. C. Algebra
C1 Algebraic Expressions and Equations · C2 Coding · C3 Application of Relations · C4 Characteristics of Relations
- Introduction to Polynomials – An algebraic expression is made of terms like 3x², −5x and 7. It is a polynomial when every power of the variable is a whole number (0, 1, 2, …). The degree is the biggest power. Degree 1 polynomials, y = ax + b, are called linear. They model things that grow or shrink by the same amount each step. a is the slope (change per step) and b is the y-intercept (starting value).
- Programming Basics: Sequence, Selection, Loops and Functions – A program is a set of exact instructions a computer follows. Every program is built from three structures: sequence (steps in order), selection (if/else choices) and iteration (loops). Variables store values. Functions group code into reusable, named blocks, which makes programs modular and easier to test, debug and maintain.
- Linear Functions – A linear function adds the same amount to y every time x goes up by 1. Its rule is y = mx + c (also written f(x) = mx + b). m is the slope: rise ÷ run, the change in y for each 1 step in x. c is the y-intercept: the value of y when x = 0. Its graph is always a straight line.
5. D. Data
D1 Collection, Representation, and Analysis of Data · D2 Mathematical Modelling
- Statistics: Asking Questions, Averages and Stacked Bar Graphs – Statistics starts with a question that has many possible answers. We collect data, organise it, show it in a graph, and find one number that sums it up. The mean is the fair share, the median is the middle value, and the mode is the most common value. A weighted average gives more importance to some values. Stacked and 100% stacked bar graphs show how a whole is split into parts.
- Mathematical Modelling: Using Maths to Describe the Real World – A mathematical model is an equation, graph or table that describes a real situation in a simple way. The modelling cycle: understand the real problem → choose variables and make assumptions → build a model (for example linear, quadratic or exponential) → solve and predict → check the answer against real data → improve the model or state its limits. No model is perfect; a good one is simple and close enough to be useful.
6. E. Geometry and Measurement
E1 Geometric and Measurement Relationships
- Geometry Basics: 2D Shapes, 3D Solids, Nets and Scale – Geometry is the maths of shape, size and position. A 2D (flat) shape has length and width only: triangles, squares, hexagons, circles. A 3D (solid) shape also has depth: cubes, prisms, pyramids, cylinders. A solid has faces (flat sides), edges (where two faces meet) and vertices (corners). A net is a flat pattern that folds into a solid. Two shapes are congruent if they have the same shape and size, and similar if they have the same shape but a different size. A tessellation covers a floor with shapes and leaves no gaps. A scale drawing shows a real object smaller or bigger by a fixed scale factor.
7. F. Financial Literacy
F1 Financial Decisions
- Smart Ways to Manage Your Finances – Inflation makes prices rise, so the same money buys less. Money kept in a bank earns interest: simple interest is paid only on the original amount, while compound interest also earns interest on earlier interest, so it grows faster over time. A budget plans income into needs, wants and savings. Savings are kept safe; investments can grow but carry risk, and higher possible returns mean higher risk. Insurance shares risk among many people. Income tax is paid on income above a limit, at rates that rise with income.