How to learn High school: Mathematics

Manitoba curriculum: Mathematics, High school

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1. Statistics and Probability

Tree diagrams: Generate theoretical sample spaces for single and combined events using listing, tables, and tree diagrams, and calculate theoretical probabilities as the number of favourable outcomes divided by the total number of equally likely outcomes

Coordinate Transformations: Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original
Properties of triangles and quadrilaterals: Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths

Ratio Notation and Relationships: Understand that a multiplicative relationship between two quantities can be expressed as a ratio; use ratio notation; simplify ratios
Solving Linear Equations: Use algebraic methods to solve linear equations in one variable, including equations that require rearrangement, expanding brackets, and collecting terms on both sides; solve equations with rational number coefficients
Scatter Graphs & Correlation: Describe simple mathematical relationships between two variables using scatter graphs, identify positive, negative, or no correlation, and use a line of best fit to make predictions

Square and cube numbers: Use integer powers and associated real roots (square, cube, and higher); recognise powers of 2, 3, 4, and 5; distinguish between exact representations of roots and their decimal approximations
Number Sets & Infinity: Appreciate the infinite nature of the sets of integers, real numbers, and rational numbers; position integers on a number line and distinguish between rational and irrational numbers

Angles with parallel lines: Understand and use the relationship between parallel lines cut by a transversal: corresponding angles, alternate interior angles, and co-interior (same-side interior) angles; use these to find unknown angles
Understanding angles (age 12+): Use ruler and compasses to perform standard constructions: perpendicular bisector of a line segment, perpendicular to a line from or at a given point, and bisecting an angle

Compound Units: Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units

Angle sums in triangles and polygons: Derive and use the angle sum in a triangle (180°), use it to deduce the angle sum in any polygon ((n−2) × 180°), and calculate interior and exterior angles of regular polygons
Types of angles (age 13+): Apply Pythagoras’ Theorem (a² + b² = c²) to calculate unknown side lengths in right-angled triangles, including in real-world and coordinate-geometry contexts
Trigonometry basics: Use the trigonometric ratios sin, cos, and tan in right-angled triangles to find unknown sides and angles, including setting up the correct ratio for a given problem
Plotting Linear Graphs: Plot linear graphs by generating a table of values, reduce a two-variable linear equation to the form y = mx + c, and calculate gradients from two points on a line

Circles: Circumference & Area: Calculate the circumference and area of circles using the formulae C = πd (or 2πr) and A = πr², and solve problems involving perimeters and areas of composite shapes that include circular parts

Simultaneous Equations: Understand that two linear equations can be solved simultaneously by finding the point where their graphs intersect, and interpret this graphically and algebraically as the pair of values satisfying both equations
Linear Function Graphs: Recognise that a linear function produces a straight-line graph, understand the relationship between an equation of the form y = mx + c and its graphical representation, and interpret gradient and y-intercept in context
Proportion Graphs: Represent proportional relationships using double number lines (two parallel number lines aligned at 0) and ratio tables; recognise that equivalent ratios generate straight lines through the origin when graphed
Quadratic Graphs: Recognise that quadratic functions produce curved (parabolic) graphs, distinguish them from linear graphs, and use plotted quadratic graphs to estimate values and find approximate solutions

Factorising Expressions: Factorise algebraic expressions by taking out common factors — identify the highest common factor of all terms and write the expression as a product, e.g., 6x + 9 = 3(2x + 3)
Simple formulae: Understand and use standard mathematical formulae; rearrange formulae to change the subject, performing inverse operations to isolate a different variable
Numbers on a number line: Understand the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as magnitude in real-world contexts; distinguish absolute value comparisons from ordering statements

Proportional Reasoning Vocabulary: Know and use advanced vocabulary of multiplicative reasoning — direct proportion, inverse proportion, ratio, rate, unit rate, compound unit, scale factor — accurately in problem-solving contexts
Coordinates (age 12+): Understand similarity as a relationship where one shape is an enlargement of another; construct similar shapes by enlargement with a given scale factor and centre, with and without coordinate grids
Proportion: Recognise and solve problems involving direct proportion (as one quantity increases, the other increases at a constant rate) and inverse proportion (as one increases, the other decreases), including graphical and algebraic representations

Pictograms and tally charts (age 11+): Construct and interpret frequency tables, bar charts, pie charts, pictograms, and vertical line charts for both categorical and grouped numerical data, choosing appropriate representations for the data type
Comparing measurements: Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers

The Probability Scale: Understand probability as a measure on a scale from 0 (impossible) to 1 (certain); use the language of probability including likely, unlikely, certain, and impossible
Complementary events: Understand and apply the rule that probabilities of all mutually exclusive outcomes sum to one; use this to find the probability of a complementary event (P(not A) = 1 − P(A))

Expanding Single Brackets: Expand (multiply out) a single term over a bracket using the distributive property, e.g., 3(2x + 5) = 6x + 15; expand expressions involving negative multipliers