Ontario Grade 8 Mathematics (Grade 8)
Chapters: 6
1. A. Social-Emotional Learning (SEL) Skills in Mathematics and the Mathematical Processes
A1 Social-Emotional Learning (SEL) Skills and the Mathematical Processes
- 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. B. Number
B1 Number Sense · B2 Operations
- Number Sense: Big Numbers, Tiny Numbers and Square Roots – Number sense means you can feel how big a number is, compare numbers and estimate quickly. Each place is 10 times the one on its right, so very large and very small numbers are written with powers of 10 (scientific notation: a × 10ⁿ with 1 ≤ a < 10). All real numbers — whole numbers, negatives, fractions, decimals and irrationals like √2 — sit in order on one number line. A square root can be estimated by finding the two perfect squares around the number. Fractions, decimals and percents are three ways to write the same amount.
- Operations with Integers and Fractions – Work out expressions in a fixed order: brackets, powers (exponents), × and ÷ from left to right, then + and − from left to right. To add integers, cancel zero pairs (+1 and −1); to subtract, add the opposite. For × and ÷, same signs give a positive answer, different signs give a negative answer. Fractions need a common denominator to add or subtract; to multiply, multiply tops and bottoms; to divide, keep, change, flip. In a proportion two ratios are equal, so an unknown is found with the unit rate or by scaling.
3. C. Algebra
C1 Patterns and Relationships · C2 Equations and Inequalities · C3 Coding · C4 Mathematical Modelling
- Sequences and Progressions – A sequence is a list of numbers in a fixed order. We can describe it with a recursive rule (how to get the next term from the last one) or an explicit rule (a formula for term n). In an arithmetic progression (AP) we add the same number every time. In a geometric progression (GP) we multiply by the same number every time. Fractals and the Tower of Hanoi are fun patterns that hide these rules.
- Linear Equations in One Variable – A linear equation in one variable has one unknown (like x) with power 1, for example 2x + 3 = 11. An equation is like a balance: both sides are equal. To solve it, do the same thing to both sides (add, subtract, multiply or divide by the same non-zero number) until x is alone. Always check by putting the answer back in.
- 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.
- 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.
4. D. Data
D1 Data Literacy · D2 Probability
- Data Analysis – Data analysis means turning raw data into answers. It follows a cycle: ask a question, collect data, clean it (remove errors, repeats and blanks), organise and transform it, analyse it with summaries such as mean, median, range and patterns, show it with a good chart, and draw a careful conclusion. Watch for outliers, small samples and bias, and remember that a correlation between two things does not prove that one causes the other. Data must also be stored safely and used with permission.
- Introduction to Probability: Scale, Experiments, Sample Spaces and Trees – Probability is a number from 0 to 1 that tells how likely something is. 0 means it can never happen, 1 means it will surely happen. We can find it by doing an experiment many times (empirical probability), or by listing every possible result (the sample space) and counting the ones we want. Tree diagrams and tables help us list results when two things happen together.
5. E. Spatial Sense
E1 Geometric and Spatial Reasoning · E2 Measurement
- 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.
- Surface Area and Volume of Cuboid, Cylinder, Cone, Pyramid and Sphere – Surface area is the total area of the outside skin of a solid, like the paper needed to wrap it. Volume is the space inside, like the water it can hold. A cuboid's volume is the number of 1 cm cubes that fit in it. A cone holds one third of a cylinder with the same base and height, and a pyramid holds one third of the matching prism.
6. F. Financial Literacy
F1 Money and Finances
- 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.