Mathematics lesson library
36 of 36 lessons
Probability Rules, Counting and the Normal Distribution
Grade 10: Probability Rules and Distributions → Probability, Counting and Distributions
Combine probabilities with the addition and multiplication rules, count outcomes, and model data with the normal curve.
Scale Drawings and Triangle Constructions
Grade 7: Scale, Circles and Angles → Scale, Circles and Angles
Work with scale factors for length and area, and find out when three measurements fix a unique triangle.
Random Sampling and Comparing Populations
Grade 7: Sampling and Probability → Sampling and Probability
Use random samples to make inferences and compare two distributions using centre and spread.
Rational, Irrational Numbers and Exponent Laws
Grade 8: Real Numbers, Exponents and Scientific Notation → Real Numbers, Exponents and Scale
Sort numbers into rational and irrational, approximate surds on a number line and apply the laws of integer exponents.
Linear Equations, Slope and y = mx + c
Grade 8: Linear Equations, Systems and Functions → Linear Relationships and Functions
Solve linear equations with one, no or infinitely many solutions, and connect slope to similar triangles and graphs.
Transformations, Congruence and Similarity
Grade 8: Transformations, Pythagoras and Volume → Transformations, Pythagoras and Volume
Translate, reflect, rotate and dilate figures, and use transformations to define congruence and similarity.
Scatter Plots, Trend Lines and Two-Way Tables
Grade 8: Bivariate Data → Bivariate Data
Describe association in bivariate data, fit a line of best fit and read relative frequencies from two-way tables.
Radicals, Rational Exponents and Precision
Grade 9: Radicals, Rational Exponents and Quantities → Radicals, Indices and Precision
Simplify surds, move between radical and index form, and report answers to a sensible accuracy.
Expression Structure, Equations and Systems
Grade 9: Algebra, Quadratics and Functions → Algebraic Structure, Quadratics and Growth
Rewrite and factorise expressions, create equations from constraints and solve systems including inequalities.
Congruence Proof and Similar Figures
Grade 9: Proof, Similarity and Trigonometry → Proof, Similarity and Right-Triangle Trigonometry
Prove theorems about lines, angles and triangles, then scale lengths, areas and volumes.
Data Analysis, Regression and Conditional Probability
Grade 9: Statistical Analysis and Probability → Statistical Analysis and Probability
Compare distributions, fit and judge a regression line, and compute conditional probabilities.
Exact Values and Financial Mathematics
Grade 10: Exact Values and Financial Mathematics → Exact Values and Financial Mathematics
Choose exact or approximate form wisely, then model interest, appreciation, depreciation and inflation.
Polynomials and Rational Expressions
Grade 10: Polynomials, Models and Function Behaviour → Polynomials, Models and Function Behaviour
Operate with polynomials, use zeros to sketch graphs, and simplify rational expressions safely.
Circle Theorems, Arcs and Sectors
Grade 10: Circle Geometry and Trigonometry → Circle Geometry, Trigonometry and Solids
Prove circle relationships and measure arc length, sector area and circle equations.
Ratios, Rates and Unit Rates
Grade 6: Number, Ratio and Percent → Ratio, Rate and Percent
Compare quantities with ratio language, build equivalent-ratio tables and find the unit rate that makes shopping decisions easy.
Fractions, Decimals and Integers
Grade 6: Number, Ratio and Percent → Fractions, Decimals and Integers
Divide fractions by fractions, compute fluently with decimals, and place positive and negative numbers on the number line and coordinate plane.
Expressions, Equations and Inequalities
Grade 6: Expressions and Equations → Expressions, Equations and Relationships
Translate words into algebra, generate equivalent expressions, solve one-step equations and graph inequalities.
Area, Volume and Surface Area
Grade 6: Area, Volume and Surface Area → Measurement of Shapes and Solids
Decompose polygons to find area, build nets for surface area and measure volume with fractional edge lengths.
Statistical Questions and Distributions
Grade 6: Data and Distributions → Describing Data
Ask questions that expect variability, display data three ways and describe centre, spread and shape.
Proportional Relationships and the Constant of Proportionality
Grade 7: Proportional Reasoning and Rational Numbers → Proportional Relationships and Percent
Test whether two quantities are proportional, find k, and write y = kx from tables, graphs and words.
Operations with Rational Numbers
Grade 7: Proportional Reasoning and Rational Numbers → Operations with Rational Numbers
Add, subtract, multiply and divide signed rationals with confidence, and convert them to decimal form.
Linear Expressions, Equations and Inequalities
Grade 7: Linear Expressions, Equations and Inequalities → Linear Expressions, Equations and Inequalities
Expand, factorise and rewrite linear expressions, then solve px + q = r, p(x + q) = r and matching inequalities.
Scientific Notation and Orders of Magnitude
Grade 8: Real Numbers, Exponents and Scientific Notation → Real Numbers, Exponents and Scale
Compress very large and very small numbers into powers of ten and compute with them.
Quadratic Equations and Their Graphs
Grade 9: Algebra, Quadratics and Functions → Algebraic Structure, Quadratics and Growth
Solve quadratics four ways and read the vertex, intercepts and symmetry straight from the graph.
Circles, Angles and Composite Measurement
Grade 7: Scale, Circles and Angles → Scale, Circles and Angles
Derive circumference and area of circles, and use angle relationships to find unknown measures.
Probability Models and Compound Events
Grade 7: Sampling and Probability → Sampling and Probability
Move between theoretical and experimental probability, then count compound outcomes with lists, tables and tree diagrams.
Percent and Unit Conversion
Grade 6: Number, Ratio and Percent → Ratio, Rate and Percent
Treat percent as a rate per hundred, find parts and wholes, and convert measurement units using ratio reasoning.
Systems of Linear Equations
Grade 8: Linear Equations, Systems and Functions → Linear Relationships and Functions
Find where two lines meet, graphically and algebraically, and use systems to make real decisions.
Sine Rule, Cosine Rule and Solids
Grade 10: Circle Geometry and Trigonometry → Circle Geometry, Trigonometry and Solids
Solve any triangle, then apply the same reasoning to surface area and volume of composite solids.
The Pythagorean Theorem and Curved Solids
Grade 8: Transformations, Pythagoras and Volume → Transformations, Pythagoras and Volume
Prove and apply a² + b² = c² in two and three dimensions, then measure cones, cylinders and spheres.
Percent Change: Tax, Discount, Interest and Error
Grade 7: Proportional Reasoning and Rational Numbers → Proportional Relationships and Percent
Solve multi-step percent problems using multipliers, and interpret percent increase, decrease and error.
Right-Triangle Trigonometry and Coordinate Geometry
Grade 9: Proof, Similarity and Trigonometry → Proof, Similarity and Right-Triangle Trigonometry
Define sine, cosine and tangent from similar triangles, then prove geometric facts with coordinates.
Quadratic and Exponential Models
Grade 10: Polynomials, Models and Function Behaviour → Polynomials, Models and Function Behaviour
Build models from data, convert between quadratic forms and solve exponential equations with logarithms.
Functions: Rules, Graphs and Models
Grade 8: Linear Equations, Systems and Functions → Linear Relationships and Functions
Define a function, compare functions across representations and build a linear model from data.
Functions, Sequences and Exponential Growth
Grade 9: Algebra, Quadratics and Functions → Algebraic Structure, Quadratics and Growth
Use function notation, describe key graph features, and tell arithmetic, geometric and exponential growth apart.
Transformations, Inverses and Composition
Grade 10: Polynomials, Models and Function Behaviour → Polynomials, Models and Function Behaviour
Shift, stretch and reflect graphs deliberately, then undo and chain functions.