A clear starting point for one class.

Junior secondary · pairs or groups of 2–4

Sampling: does more mean better?

Compare who is asked, how many are asked and what changes when you draw again.

45 min · bilingual guide · separate teacher reference

Introductory modeling · pairs

Mixing tank: can a smooth curve be trusted?

Derive a balance, complete two short functions and separate numerical checks from a physical assumption.

50 min · bilingual guide · separate teacher reference

Years 7–8 · projection and paper

Year 7, upper volume · Chapter 3 §3.2

Linear equations: collect like terms

Collect variable terms on the same side, handle negative coefficients and check each solution. A 40-minute projection and paper lesson.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7, upper volume · Chapter 3 §3.2

Linear equations: transpose and verify

Solve equations with variable terms on both sides, explain each sign change and verify in the original equation. A 40-minute paper-first lesson.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, upper volume · congruent triangles · angle bisectors

Angle bisectors: perpendicular distances and the forward proof

Distinguish distance from an oblique segment, practise equal lengths, and fade an AAS proof scaffold.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, upper volume · congruent triangles · angle bisectors

Angle bisectors: the converse and applications

Separate the two directions, construct an HL proof, and use equal distances in angle and perimeter problems.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, upper volume · reflection symmetry

Recognising reflection symmetry and counting axes

Use the fold test, distinguish a figure’s own symmetry from a pair of reflected figures, and count complete axes.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, upper volume · reflection symmetry

Perpendicular bisectors: properties and the SSS converse

Separate perpendicularity from midpoint information, prove equal endpoint distances, and use SSS for the converse.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, upper volume · reflection symmetry

Constructing symmetry axes with ruler and compass

Construct perpendicular bisectors, check one common axis against all supplied pairs, and draw complete axes of familiar figures.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7, upper volume · Chapter 1 · Rational numbers

Rational numbers: position, opposites and absolute value

Use signed quantities, number-line order, opposite numbers and distance from zero in a fixed core-practice lesson.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7, upper volume · Chapter 1 · Rational numbers

Rational numbers: operations, powers and large numbers

Select core signed arithmetic, fractions, powers, scientific notation and rounding after the relevant textbook periods.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7, upper volume · Chapter 2 · Adding and subtracting polynomials

Expressions: terms, coefficients and values

Read the structure of a monomial or polynomial, distinguish coefficient from degree, and substitute signed values.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7, upper volume · Chapter 2 · Adding and subtracting polynomials

Polynomials: collect terms and remove brackets

Keep signed coefficients, distinguish unlike powers, apply the distributive law and check by substitution.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7, upper volume · Chapter 3 · Linear equations

Equations: meaning, solutions and equal operations

Distinguish an expression from an equation in an unknown, test a solution and explain operations on both sides.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7, upper volume · Chapter 3 · Linear equations

Equations: brackets and constant denominators

Distribute to every term, clear constant denominators on the whole equality and verify in the original equation.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7, upper volume · Chapter 3 · Linear equations

Equations in context: quantities, rates and conditions

Choose representative cost, travel, work-rate, percentage, ratio and tiered-price models; verify the solution in context.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7, upper volume · Chapter 4 · Introduction to geometry

Geometric objects, segments and midpoints

Distinguish lines, rays and segments; count cube elements and use point order and midpoint conditions.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7, upper volume · Chapter 4 · Introduction to geometry

Angles: addition, bisectors, complements and supplements

Use ray order, degree-minute conversion, internal bisectors and the correct total for complementary or supplementary angles.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, upper · Chapter 11: triangles · lessons 1–2

Triangle sides, medians and altitudes

Consolidate strict triangle inequalities, perimeter and the definitions of supporting segments.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, upper · Chapter 11: triangles · lessons 3–6

Triangle and polygon angles

Choose the correct angle sum, distinguish adjacent and remote angles, and count polygon sides.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, upper · Chapter 12: congruent triangles · lessons 7–9

Congruence: correspondence, SSS and SAS

Read the vertex order, check included angles and build short justified proofs.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, upper · Chapter 12: congruent triangles · lessons 10–12

Congruence: ASA, AAS and right-triangle HL

Select a criterion from the actual givens and complete a short proof without circular assumptions.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, upper · Chapter 13: reflection symmetry · lessons 18–19

Reflecting whole figures and coordinates

Use a given axis to reflect every vertex, then connect the construction with x/y-coordinate rules.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, upper · Chapter 13: reflection symmetry · lessons 20–25

Isosceles, equilateral and special-triangle practice

Apply properties and converses with conditions; use 30° right triangles and an optional reflection shortest-path extension.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, upper · Chapter 14: polynomial operations and factorisation · lessons 26–31

Powers and polynomial multiplication

Consolidate the three power laws and distribute monomial or polynomial products accurately.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, upper · Chapter 14: polynomial operations and factorisation · lessons 32–36

Special products and polynomial division

Practise difference of squares, complete squares and every-term division while retaining nonzero divisors.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, upper · Chapter 14: polynomial operations and factorisation · lessons 37–39

Factorisation: common factors and square patterns

Choose a method, factor completely over integers and check by expanding.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, upper · Chapter 15: rational expressions · lessons 40–41

Rational expressions: meaning, domain and cancellation

Separate zero numerators from zero denominators and retain restrictions after cancellation.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, upper · Chapter 15: rational expressions · lessons 42–48

Rational operations, integer powers and scientific notation

Consolidate common denominators, multiplication/division and negative powers, with short scientific-notation checks.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, upper · Chapter 15: rational expressions · lessons 49–52

Rational equations: checking and applications

Clear denominators completely, check extraneous candidates, and model work-rate and travel problems.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7 lower · Chapter 5 Intersecting and parallel lines · text lessons 1–4

Intersections, perpendiculars and distance

Distinguish angle position from angle size, and perpendicular distance from an oblique segment.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7 lower · Chapter 5 Intersecting and parallel lines · text lessons 5–12

Parallel lines: conditions and reasoning

Use angle relations in the correct direction and distinguish a hypothesis from a conclusion.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7 lower · Chapter 5 Intersecting and parallel lines · text lessons 13–14

Translation: matching points and invariant lengths

Move a whole figure in one direction by one distance; distinguish translation from rotation or reflection.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7 lower · Chapter 6 Real numbers · text lessons 15–17

Square roots and cube roots: meanings and signs

Distinguish two square roots from one principal square root, and allow negative cube roots.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7 lower · Chapter 6 Real numbers · text lessons 18–19

Real numbers: classification, bounds and approximation

Use exact definitions and square comparisons; keep an approximation distinct from an equality.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7 lower · Chapter 7 Cartesian coordinates · text lessons 20–25

Coordinates: location and translation

Use ordered pairs, quadrants, map scales and one common coordinate change.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7 lower · Chapter 8 Simultaneous linear equations · text lessons 26–30

Two-variable systems: substitution and elimination

Reduce two unknowns to one, then recover the complete solution and check both equations.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7 lower · Chapter 8 Simultaneous linear equations · text lessons 31–33

Two-variable systems: quantities and models

Name unknowns, keep units consistent, build independent conditions and check contextual feasibility.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7 lower · Chapter 8 Simultaneous linear equations · text lessons 34–35

Three-variable systems: eliminate, solve and check

Eliminate the same unknown to obtain a two-variable system, then back-substitute all three values.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7 lower · Chapter 9 Inequalities and systems of inequalities · text lessons 36–39

Linear inequalities: direction and endpoints

Keep equivalent conditions, reverse for negative division and show the complete solution set.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7 lower · Chapter 9 Inequalities and systems of inequalities · text lessons 40–44

Inequality systems: overlap and feasible choices

Translate every restriction, take the overlap and then apply meaningful integer conditions.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7 lower · Chapter 10 Collecting, organising and displaying data · text lessons 45–47

Statistical surveys: samples, proportions and claims

Choose a defensible survey method, read proportions and state the limits of sample-based estimates.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 7 lower · Chapter 10 Collecting, organising and displaying data · text lessons 48–49

Grouped data and histograms: frequency and area

Count boundary values once, label the vertical measure, and use frequency per class width for unequal classes.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, lower volume · Chapter 16: Square-root expressions · lessons 1–2

Square roots: meaning, simplification and domain

Distinguish a square root from the solutions of a squared equation, and retain every real-domain condition.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, lower volume · Chapter 16: Square-root expressions · lessons 3–6

Square-root operations: factor, multiply and combine

Simplify square factors, apply real-domain product and quotient laws, then combine like radicals.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, lower volume · Chapter 17: Pythagorean theorem · lessons 7–9

Pythagoras: identify the sides and calculate lengths

Model right triangles, choose addition or subtraction of squares, and retain positive exact lengths.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, lower volume · Chapter 17: Pythagorean theorem · lessons 10–13

Pythagoras converse: conditions and combined problems

Test actual side data and combine the converse with length, midpoint and perpendicularity reasoning.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, lower volume · Chapter 18: Parallelograms · lessons 14–18

Parallelograms: properties, criteria and midsegments

Separate given facts from conclusions, use diagonals carefully, and prove the triangle midsegment theorem.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, lower volume · Chapter 18: Parallelograms · lessons 19–22

Rectangles and rhombi: diagonal conditions and converses

Keep the parallelogram premise, distinguish equal from perpendicular diagonals, and use the right-triangle median theorem.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, lower volume · Chapter 18: Parallelograms · lessons 23–24

Squares and inclusive quadrilateral classification

Combine rectangle and rhombus conditions, compare diagonals and reject unsupported converse statements.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, lower volume · Chapter 19: Linear functions · lessons 25–29

Functions: inputs, domains, tables and graphs

Decide whether a relation is a function, use three representations and check mathematical and contextual domains.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, lower volume · Chapter 19: Linear functions · lessons 30–33

Linear functions: coefficients, graphs and determination

Relate slope and intercept to the graph, distinguish constant functions, and determine a line from two distinct inputs.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, lower volume · Chapter 19: Linear functions · lessons 34–37

Linear models: equations, inequalities and intersections

Translate contextual conditions and connect graphical solutions with exact algebra.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, lower volume · Chapter 20: Analysing data · lessons 38–41

Data centres: weights, ordering and choosing a summary

Calculate weighted means, medians and all tied modes; distinguish grouped estimates from raw-data answers.

40 min · paper practice · projection and staged hints

Years 7–8 · projection and paper

Year 8, lower volume · Chapter 20: Analysing data · lessons 42–42

Variance: calculation, stability and transformations

Use the textbook’s n-denominator definition, compare data with the same centre and reason about shifts and scales.

40 min · paper practice · projection and staged hints