Year 3
Maths
Y3 Maths 01: Number & Place Value
Reading, writing and representing numbers up to 10000.
Part of Years 3–4 Maths (Stage 2)
What each digit is worth; expanding and renaming numbers.
Part of Years 3–4 Maths (Stage 2)
Using place value to compare numbers and order them on a number line.
Part of Years 3–4 Maths (Stage 2)
Recognising odd and even numbers and what happens when you add them.
Part of Years 3–4 Maths (Stage 2)
Y3 Maths 02: Addition & Subtraction
Bridging to ten, split strategy and jump strategy for adding in your head.
Part of Years 3–4 Maths (Stage 2)
Column addition with carrying (trading) for 2- and 3-digit numbers.
Part of Years 3–4 Maths (Stage 2)
Counting up, jump-back and think-addition strategies.
Part of Years 3–4 Maths (Stage 2)
Column subtraction with borrowing (trading).
Part of Years 3–4 Maths (Stage 2)
Choosing the operation and writing the number sentence from a story.
Part of Years 3–4 Maths (Stage 2)
Y3 Maths 03: Multiplication & Division
Equal groups, arrays and repeated addition.
Part of Years 3–4 Maths (Stage 2)
Sharing equally and making groups; links to multiplication.
Part of Years 3–4 Maths (Stage 2)
Connecting multiplication and division facts (3 × 4 = 12, 12 ÷ 4 = 3).
Part of Years 3–4 Maths (Stage 2)
Y3 Maths 04: Fractions
Folding wholes into 2, 4 and 8 equal parts.
Part of Years 3–4 Maths (Stage 2)
Finding a half, third or quarter of a group of objects.
Part of Years 3–4 Maths (Stage 2)
Y3 Maths 05: Money
Australian notes and coins; making the same amount in different ways.
Part of Years 3–4 Maths (Stage 2)
Y3 Maths 06: Patterns & Algebra
Skip-counting patterns; finding and describing the rule.
Part of Years 3–4 Maths (Stage 2)
Balancing number sentences like 7 + ▢ = 15.
Part of Years 3–4 Maths (Stage 2)
Y3 Maths 07: Measurement
Choosing units, measuring and converting m/cm/mm.
Part of Years 3–4 Maths (Stage 2)
Distance around a shape and covering with squares.
Part of Years 3–4 Maths (Stage 2)
Y3 Maths 08: Time
Analog and digital clocks; minutes past and minutes to.
Part of Years 3–4 Maths (Stage 2)
Morning vs afternoon times and how long events take.
Part of Years 3–4 Maths (Stage 2)
Y3 Maths 09: Shape & Geometry
Sides, corners and describing triangles, quadrilaterals, pentagons, hexagons.
Part of Years 3–4 Maths (Stage 2)
Faces, edges and vertices of everyday 3D objects.
Part of Years 3–4 Maths (Stage 2)
Lines of symmetry and simple transformations.
Part of Years 3–4 Maths (Stage 2)
Quarter, half and full turns; comparing angles to a right angle.
Part of Years 3–4 Maths (Stage 2)
Y3 Maths 10: Position & Maps
Grid references, left/right/north/south and describing pathways.
Part of Years 3–4 Maths (Stage 2)
Y3 Maths 11: Data
Drawing and reading graphs with one-to-one scale.
Part of Years 3–4 Maths (Stage 2)
Y3 Maths 12: Chance
Everyday chance language and ordering events by likelihood.
Part of Years 3–4 Maths (Stage 2)
Y3 NAPLAN 01: Number Questions
NAPLAN-style questions on digit values, renaming and positioning numbers on a line.
Part of Year 3 NAPLAN
One- and two-step +/− problems in NAPLAN wording.
Part of Year 3 NAPLAN
Groups, arrays and sharing problems as asked in NAPLAN.
Part of Year 3 NAPLAN
Y3 NAPLAN 02: Patterns & Algebra Questions
Continuing patterns and identifying the rule under test conditions.
Part of Year 3 NAPLAN
Balance-style questions: find the number that makes it true.
Part of Year 3 NAPLAN
Y3 NAPLAN 03: Measurement & Time Questions
Choosing units, reading scales and comparing measurements.
Part of Year 3 NAPLAN
Reading clocks and calendars; elapsed-time questions.
Part of Year 3 NAPLAN
Y3 NAPLAN 04: Space Questions
Y3 NAPLAN 05: Data & Chance Questions
Extracting and comparing information from graphs and tables.
Part of Year 3 NAPLAN
Most likely / least likely spinner and marble questions.
Part of Year 3 NAPLAN
Y3 NAPLAN 06: Test Craft
Underlining what is actually asked; spotting traps in wording.
Part of Year 3 NAPLAN
Eliminating wrong answers, estimating first, checking units.
Part of Year 3 NAPLAN
Year 4
Maths
Ch 03: Multiplication & Division
Beyond the 10 × 10 tables: the area model first, then the written algorithm and carrying.
Part of Years 3–4 Maths (Stage 2)
Brackets, then multiply and divide, then add and subtract; left to right within a level. Not in Stage 2, but assumed by every OC paper.
Part of Years 3–4 Maths (Stage 2)
Ch 04: Fractions
Beyond the halving family: renaming both fractions into a shared denominator, and the compare-to-a-half shortcut.
Part of Years 3–4 Maths (Stage 2)
Counting past one whole, and converting between improper fractions and mixed numerals in both directions.
Part of Years 3–4 Maths (Stage 2)
Ch 05: Decimals & Money
Thousandths, comparing decimals of different lengths, and rounding to two places. Stage 2 stops at two.
Part of Years 3–4 Maths (Stage 2)
Extending the place-value chart past the ones column into tenths and hundredths, and the zero that holds a column empty.
Part of Years 3–4 Maths (Stage 2)
Why 0.7 beats 0.65: comparing column by column from the left, and evening up the places with zeros.
Part of Years 3–4 Maths (Stage 2)
A decimal is a fraction with 10 or 100 on the bottom. The hundred grid, and the six conversions worth memorising.
Part of Years 3–4 Maths (Stage 2)
Cents as hundredths of a dollar, reading a price, and adding, subtracting and giving change with the points lined up.
Part of Years 3–4 Maths (Stage 2)
Ch 06: Patterns & Reasoning
Inverse operations, and undoing a chain of machines in reverse order to find the starting number.
Part of Years 3–4 Maths (Stage 2)
Ch 07: Length, Perimeter & Area
The kilometre, converting to and from metres, and choosing a sensible unit for a distance.
Part of Years 3–4 Maths (Stage 2)
Stage 2 measures and compares area; calculating it from side lengths is Stage 3. Built from counting rows of squares.
Part of Years 3–4 Maths (Stage 2)
Ch 08: Volume, Capacity & Mass
Layers of cubes leading to length × width × height, and the link between cubic centimetres and millilitres.
Part of Years 3–4 Maths (Stage 2)
The gram-kilogram-tonne ladder, two-step conversions, and picking the unit that keeps the number sensible.
Part of Years 3–4 Maths (Stage 2)
Ch 09: Time
Counting through to 23:59, converting pm times by adding 12, the midnight and midday special cases, and reading timetables.
Part of Years 3–4 Maths (Stage 2)
Ch 10: Shape, Angles & Position
Measuring angles in degrees, the five angle names including reflex, and finding a reflex angle by subtracting from 360.
Part of Years 3–4 Maths (Stage 2)
Ch 11: Data & Chance
Cells that answer two questions at once, row and column totals, finding a missing value two ways, and NOT questions.
Part of Years 3–4 Maths (Stage 2)
When a line beats columns, reading values and shape, timelines as number lines of years, and misleading scales.
Part of Years 3–4 Maths (Stage 2)
Y4 OC 01: Number Reasoning
Large numbers, rounding and estimation for quick checking.
Part of Year 4 OC Mathematical Thinking
Fluent +, −, ×, ÷ with larger numbers under time pressure.
Part of Year 4 OC Mathematical Thinking
Evaluating and balancing multi-operation number sentences.
Part of Year 4 OC Mathematical Thinking
Y4 OC 02: Fractions & Decimals
Finding equivalent fractions and ordering fractions.
Part of Year 4 OC Mathematical Thinking
Decimal notation, money links and comparing decimals.
Part of Year 4 OC Mathematical Thinking
What one mark is worth, n jumps of a quarter turned into wholes and parts, placing a mixed number on a thirds or fifths line, which mixed number is closest to a whole, and how many jumps cover a distance.
Part of Year 4 OC Mathematical Thinking
Y4 OC 03: Patterns & Sequences
Finding rules, next terms and input-output machines.
Part of Year 4 OC Mathematical Thinking
Matchstick and tile patterns; predicting later terms.
Part of Year 4 OC Mathematical Thinking
Y4 OC 04: Word Problems & Logic
Breaking a problem into steps and keeping track of the goal.
Part of Year 4 OC Mathematical Thinking
Starting from the answer and reversing the operations.
Part of Year 4 OC Mathematical Thinking
Who-owns-what grids, truth-tellers and elimination reasoning.
Part of Year 4 OC Mathematical Thinking
Which methods balance the scales (find the gap first), "3 pears weigh the same as 5 plums" bag comparisons, made-up money chains converted one link at a time, and picture balances solved by swapping.
Part of Year 4 OC Mathematical Thinking
Which layer the last brick lands on (remainders), fewest bags under a mass limit (two roundings), two people sharing one job, everyone-plays-everyone tournaments, and steady money-box deposits with one unknown day.
Part of Year 4 OC Mathematical Thinking
Y4 OC 05: Measurement & Geometry Reasoning
Reasoning problems mixing lengths, perimeters and areas.
Part of Year 4 OC Mathematical Thinking
Elapsed time, schedules and timetable reading.
Part of Year 4 OC Mathematical Thinking
Nets, rotations, reflections and views of solids.
Part of Year 4 OC Mathematical Thinking
Quadrilateral families and "all squares are rectangles" statements, counting right angles in figures made of lines, and what one straight cut does to a shape.
Part of Year 4 OC Mathematical Thinking
Quarter and half turns chosen from picture options, reflecting on a grid with grid references, turned shapes versus mirror images, and tiles rotated in a wall.
Part of Year 4 OC Mathematical Thinking
Working out what one gap is worth, then reading thermometers with unlabelled ticks, jugs with unusual scales, map rulers in millimetres against a scale in centimetres, and graphs with a missing scale.
Part of Year 4 OC Mathematical Thinking
Counting cubes you cannot see, faces hidden by glued joins (2 per join), faces uncovered when a solid is broken apart, rebuilding from loose cubes, and the tallest stack three blocks can make.
Part of Year 4 OC Mathematical Thinking
Area on a grid with half squares, what doubling every side does to area (× 4) and volume (× 8), matching shaded areas across two squares cut into different pieces, water displaced by sinking blocks, and cut-and-rearrange invariance.
Part of Year 4 OC Mathematical Thinking
Y4 OC 06: Data Interpretation
Reading complex graphs and simple averages in test questions.
Part of Year 4 OC Mathematical Thinking
Chance words as counting words: boxes of discs, "blue or not blue", numbered counters with boundary numbers, spinners with unequal sectors, and changing a bag so two outcomes become equally likely.
Part of Year 4 OC Mathematical Thinking
Y4 OC 07: Test Technique
Time budgeting, elimination and educated guessing for OC format.
Part of Year 4 OC Mathematical Thinking
Thinking Skills
Y4 TS 01: Critical Thinking — Arguments
Pick the statement that, if true, best supports a claim. Telling relevant evidence apart from true-but-irrelevant facts.
Part of Year 4 OC Thinking Skills
A boxed rule + two speakers each draw a conclusion; decide who reasoned correctly. Only-if traps, reversing rules, denying the antecedent.
Part of Year 4 OC Thinking Skills
Identify the sentence that shows the flaw in someone’s reasoning: "must be" from "could be", minimum ≠ guarantee, more than one match.
Part of Year 4 OC Thinking Skills
Deductions that follow necessarily from if-then rules and conditions — versus what only might be true.
Part of Year 4 OC Thinking Skills
Y4 TS 02: Logical Deduction Puzzles
Left/right ordering from clues; multi-clue elimination puzzles (which chest holds the key). Draw the line, place the fixed facts first.
Part of Year 4 OC Thinking Skills
Round-table and facing arrangements; compass-direction town maps. Diagonally opposite, next to, north-east of.
Part of Year 4 OC Thinking Skills
Who-owns-what overlap questions and choose-one-from-each-list constraint puzzles.
Part of Year 4 OC Thinking Skills
Which single extra fact would settle the outcome? Testing each option against all remaining possibilities.
Part of Year 4 OC Thinking Skills
Y4 TS 03: Numerical Problem Solving
Twice/four-times-as-fast reasoning without formulas: same distance means the faster one takes the fraction of the time.
Part of Year 4 OC Thinking Skills
Counting performances, days and occurrences across a date range — inclusive counting and the fence-post trap.
Part of Year 4 OC Thinking Skills
Undo a chain of steps from the final state (folded string, halving-doubling puzzles). Reverse each step in reverse order.
Part of Year 4 OC Thinking Skills
Reading two tables together (biggest improvement) and recipe scaling where one ingredient runs out first.
Part of Year 4 OC Thinking Skills
Y4 TS 04: Spatial Reasoning
Which net folds into a normal dice? Opposite faces sum to 7; finding opposite pairs on a net without folding.
Part of Year 4 OC Thinking Skills
Which square is made of the same five pieces (turned or flipped)? Matching pieces by size and shape, not position.
Part of Year 4 OC Thinking Skills
Placing tiles under adjacency rules (no matching numbers touching); checking which combination cannot work.
Part of Year 4 OC Thinking Skills
Matching a floor plan to a 3-D view; top views, side views and what disappears from each.
Part of Year 4 OC Thinking Skills
Y4 TS 05: Test Technique
30 questions in 30 minutes, no penalty: answer everything, eliminate wrong options fast, flag and return, never stall.
Part of Year 4 OC Thinking Skills
A timed mixed set in the official format — every question type from Chapters 1–4 at test pace.
Part of Year 4 OC Thinking Skills
Year 5
Maths
Y5 Maths 01: Whole Numbers & Place Value
Six- and seven-digit numbers, the role of zero, and renaming in thousands and ten thousands.
Part of Stage 3 Core
Rounding to the nearest ten thousand, hundred thousand or million, and finding the difference between two roundings of the same number.
Part of Stage 3 Core
The 3 in 30 060 against the 6 — how many times one digit's value is another's.
Part of Stage 3 Core
Temperatures, depths and debts below zero; ordering and finding differences across zero.
Part of Stage 3 Core
Y5 Maths 02: Addition & Subtraction
Compensation, bridging and partitioning with four- and five-digit numbers.
Part of Stage 3 Core
Column addition and subtraction across zeros, with a rounded estimate before and a check after.
Part of Stage 3 Core
Money, millions and measurements — lining up the point and trading across it.
Part of Stage 3 Core
Undoing a chain of givings, halvings and spendings from the end to find where it started.
Part of Stage 3 Core
Y5 Maths 03: Multiplication & Division
The area model and the two-row algorithm, with an estimate to catch a slipped digit.
Part of Stage 3 Core
Listing factors in pairs, common multiples, and counting multiples of one number that are not multiples of another.
Part of Stage 3 Core
Testing for primes, and the square and triangular patterns as pictures.
Part of Stage 3 Core
Boxes, buses and biscuits — when the remainder means one more, and when it is left over.
Part of Stage 3 Core
Short division by 12, 15, 25 and friends, using known multiples.
Part of Stage 3 Core
The tests for 2, 3, 4, 5, 6, 8, 9 and 10, and why the digit-sum test works.
Part of Stage 3 Core
Y5 Maths 04: Number Sentences & Order of Operations
Writing a situation as 14 × 8 + 5 = 117, and recognising that 12 × 3 = 10 × 3 + 6.
Part of Stage 3 Core
Balancing 9 × □ = 108 and 67 − △ = 32 + 17 by doing the same to both sides.
Part of Stage 3 Core
Stars and hearts, medals and points — using one equation to unlock the other.
Part of Stage 3 Core
One complete row gives the total; each term the sum of the previous three.
Part of Stage 3 Core
Y5 Maths 05: Fractions
The same fraction on a strip, a 10 × 10 grid and a number line; closest position to a third.
Part of Stage 3 Core
Same denominators, then related ones — renaming one fraction so the pieces match.
Part of Stage 3 Core
Three people eat 4/5, 1 1/5 and 3/5 of four pizzas — how much is left for the fourth, and by how much more.
Part of Stage 3 Core
A half, quarter, fifth and tenth of measures and money, and building up to three-fifths of a wall.
Part of Stage 3 Core
Placing fifths and quarters on one line to judge "less than half" and "more than a quarter" claims.
Part of Stage 3 Core
Eight children and two pies — division as a fraction, and fractions as division.
Part of Stage 3 Core
Y5 Maths 06: Decimals & Percentages
0.1 against 0.08 against 0.0089 — lining up places before comparing digits.
Part of Stage 3 Core
Digits slide, the point stays: 34.2 × 10 and 342 ÷ 100 without a calculator.
Part of Stage 3 Core
One family of names: 1/4 = 0.25 = 25%, and the rest of the 10%, 20%, 50%, 75% table.
Part of Stage 3 Core
Finding 10% first and building the rest from it.
Part of Stage 3 Core
Four colours in a bag whose chances add to 1; one colour twice as likely as another.
Part of Stage 3 Core
15% of $40 from 10% and 5%; the price after a 30% discount.
Part of Stage 3 Core
Y5 Maths 07: Patterns & Algebra
Patterns that add then double, patterns in decimals and fractions, and finding the rule from three terms.
Part of Stage 3 Core
A rule like "double, then take 4" run forwards to the sixth term and backwards to the first.
Part of Stage 3 Core
Matchsticks and tiles into a table, the rule as words, and the 50th term without drawing it.
Part of Stage 3 Core
Y5 Maths 08: Length, Perimeter & Area
1500 cm is 15 m; 2.35 km is 2350 m — the ladder of thousands and tens.
Part of Stage 3 Core
L-shapes and steps where the unlabelled sides must add up to the labelled ones.
Part of Stage 3 Core
Split it, or take the hole away from the whole — two routes to the same area.
Part of Stage 3 Core
Cutting a parallelogram into a rectangle, and a triangle as half of one.
Part of Stage 3 Core
A 10 by 6 rectangle and a 4-wide one with the same area — find the other side; perimeter when a rectangle is attached.
Part of Stage 3 Core
Y5 Maths 09: Volume, Capacity & Mass
Jugs marked every 50 mL, kitchen scales marked every 2 kg, pointers halfway between marks.
Part of Stage 3 Core
Keeping track of a bottle and a glass through three moves.
Part of Stage 3 Core
Three boxes weighed two at a time — the total, and each one.
Part of Stage 3 Core
How much a box holds in millilitres from its sides in centimetres.
Part of Stage 3 Core
Y5 Maths 10: Time
From 9:50 pm to 6:30 am, and journeys that take more than a day, counted in hops.
Part of Stage 3 Core
Which film can be seen from start to finish between two pick-up times.
Part of Stage 3 Core
The third Sunday, and what day of the week it is six weeks after a Wednesday.
Part of Stage 3 Core
A 17-hour difference and a 20-hour flight: arriving on Monday morning when you left on Friday.
Part of Stage 3 Core
Y5 Maths 11: Angles
180° along a line and 360° around a point; the missing angle by subtraction.
Part of Stage 3 Core
Two crossing lines make two pairs of equal angles — and why.
Part of Stage 3 Core
A shape with one line of symmetry gives its angles in pairs; the one left over comes from 180°.
Part of Stage 3 Core
Y5 Maths 12: 2D Shapes & Transformations
Sides, angles and parallel pairs; which shape has no parallel sides.
Part of Stage 3 Core
Exactly two lines of symmetry; the largest two-digit number that is symmetrical; the fewest tiles to finish a symmetrical row.
Part of Stage 3 Core
Order of rotational symmetry, and how far a shape has turned after two steps.
Part of Stage 3 Core
Which tile covers a square four times; one grid unit stands for how many centimetres.
Part of Stage 3 Core
Y5 Maths 13: 3D Objects
Counting on a hexagonal pyramid, and on two solids glued together.
Part of Stage 3 Core
The eleven cube nets; which partial net can be finished with one more square.
Part of Stage 3 Core
Front, side and top views; which cubes you cannot see; how many have exactly two faces painted.
Part of Stage 3 Core
Y5 Maths 14: Position
Across then up; plotting and reading points, and the shape they make.
Part of Stage 3 Core
Reading a grid reference from one labelled cell; distance and direction between two places.
Part of Stage 3 Core
Negative coordinates, and where a point lands after a reflection or a quarter turn.
Part of Stage 3 Core
Y5 Maths 15: Data
One picture for five people; columns on an axis marked in twenties.
Part of Stage 3 Core
Two years on one graph; a quarter of a pie when the total is 600.
Part of Stage 3 Core
Three statements about a rainfall graph — which are correct, and what "more than twice" needs.
Part of Stage 3 Core
When the gridlines go up in twos or fifties and the point sits between them.
Part of Stage 3 Core
Y5 Maths 16: Chance
The same chance three ways; certain is 1 and impossible is 0.
Part of Stage 3 Core
Two coins, a spinner and a die — the full list, then the fraction that count.
Part of Stage 3 Core
Which statements about a spinner are correct, given the first spin.
Part of Stage 3 Core
Y5 Maths 17: Ratio (Extension)
$15 for 3 cars, so how many cars for $45; 2 red for every 3 blue.
Part of Stage 3 Core
Y5 NAPLAN 01: Test Craft
What "exactly", "not" and "smallest number of" do; typing a number the way the box wants it.
Part of Year 5 NAPLAN
The thirteen-of-forty typed items: whole numbers, money in cents, measurements without the unit.
Part of Year 5 NAPLAN
Perimeter in reverse, dividing to a decimal, and medal-and-points puzzles.
Part of Year 5 NAPLAN
Year 6
Maths
Y6 Selective 01: Number Reasoning
Smallest four-digit times largest two-digit; rounding twice and finding the difference.
Part of Year 6 Selective Maths
Money chains in reverse; two symbol equations that unlock each other.
Part of Year 6 Selective Maths
Mixed numbers, what is left, probabilities that sum to 1.
Part of Year 6 Selective Maths
Each term from the previous three; one complete row gives the total.
Part of Year 6 Selective Maths
Y6 Selective 02: Measurement Reasoning
Pointers between marks, axes in twos and fifties, and what to subtract first.
Part of Year 6 Selective Maths
Rectilinear shapes with missing sides; nested squares; a rectangle attached.
Part of Year 6 Selective Maths
24-hour conversions, across midnight, across days, across the world.
Part of Year 6 Selective Maths
Y6 Selective 03: Space Reasoning
Which nets complete; painted faces; line and rotational symmetry in degrees.
Part of Year 6 Selective Maths
Protractor constructions with a line of symmetry; faces, edges and vertices.
Part of Year 6 Selective Maths
Y6 Selective 04: Data & Chance Reasoning
The format itself: three claims against a graph, a table, a spinner or a number line.
Part of Year 6 Selective Maths
Given the first spin, which claims about the second are right.
Part of Year 6 Selective Maths
Y6 Selective 05: Test Technique
Five options, no calculator, no penalty: pacing, elimination, working from the options.
Part of Year 6 Selective Maths
Year 7
Mathematics
Maths
Ch 01: Fractions, Decimals and Percentages
What makes two fractions equal, how to build and simplify them, and using equivalence to compare.
Part of Year 7 Maths (Stage 4)
Common denominators, benchmarking against a half, and putting fractions in order confidently.
Part of Year 7 Maths (Stage 4)
The three ways of writing the same number, and moving between them in every direction.
Part of Year 7 Maths (Stage 4)
Putting mixed forms in order by converting to a common form first.
Part of Year 7 Maths (Stage 4)
Why some fractions stop and others repeat forever, dot notation, and predicting which is which.
Part of Year 7 Maths (Stage 4)
Ch 02: Probability
Describing likelihood in words and numbers, and placing events on a 0-to-1 scale.
Part of Year 7 Maths (Stage 4)
Listing every possible outcome, and when outcomes can be treated as equally likely.
Part of Year 7 Maths (Stage 4)
Favourable outcomes over total outcomes, as a fraction, decimal and percentage.
Part of Year 7 Maths (Stage 4)
Why probabilities sum to 1, and using "not happening" to solve problems faster.
Part of Year 7 Maths (Stage 4)
Ch 03: Data Classification and Displays
Numerical (discrete or continuous) versus categorical (nominal or ordinal), and why the type decides the graph.
Part of Year 7 Maths (Stage 4)
Organising raw data, grouping into intervals, and reading a frequency table.
Part of Year 7 Maths (Stage 4)
Column graphs, dot plots, line graphs and stem-and-leaf — matching the display to the data.
Part of Year 7 Maths (Stage 4)
Reading values, spotting trends, and recognising a misleading display.
Part of Year 7 Maths (Stage 4)
The three measures of centre plus range: how to find each and which one to trust.
Part of Year 7 Maths (Stage 4)
Ch 04: Integers and the Number Line
What negatives mean, where they sit, and reading them in real contexts.
Part of Year 7 Maths (Stage 4)
Which is bigger, why −8 is less than −3, and ordering with confidence.
Part of Year 7 Maths (Stage 4)
Axes, origin and four quadrants; plotting and naming points with coordinates.
Part of Year 7 Maths (Stage 4)
Expressing a part of a whole in all three forms, and what "of" really means.
Part of Year 7 Maths (Stage 4)
Ch 05: Equations
The difference between an expression and an equation, the balance-scale picture, and solving as peeling with inverses.
Part of Year 7 Maths (Stage 4)
Undoing addition, subtraction, multiplication and division, and reading which move to make before calculating.
Part of Year 7 Maths (Stage 4)
Undoing two operations in reverse order, and turning a word problem into an equation.
Part of Year 7 Maths (Stage 4)
Ch 05: Introducing Algebra
Why letters stand in for numbers, and reading algebraic notation correctly.
Part of Year 7 Maths (Stage 4)
Turning words into expressions, and the conventions for writing them.
Part of Year 7 Maths (Stage 4)
Replacing a pronumeral with a number and evaluating, including with negatives.
Part of Year 7 Maths (Stage 4)
Commutative, associative and distributive laws, and why they hold for letters too.
Part of Year 7 Maths (Stage 4)
Ch 06: Adding and Subtracting
Moving along the number line, and why subtracting a negative adds.
Part of Year 7 Maths (Stage 4)
Common denominators, mixed numbers, and keeping the whole intact.
Part of Year 7 Maths (Stage 4)
Lining up the decimal point, and checking answers by estimation.
Part of Year 7 Maths (Stage 4)
Which terms can be added, which cannot, and simplifying expressions.
Part of Year 7 Maths (Stage 4)
Ch 07: Multiplying and Dividing
The sign rules, why two negatives make a positive, and applying them reliably.
Part of Year 7 Maths (Stage 4)
Applying all four operations in the right order, brackets included.
Part of Year 7 Maths (Stage 4)
Why multiplying can make a number smaller, cancelling first, and mixed numbers.
Part of Year 7 Maths (Stage 4)
Reciprocals, why we flip and multiply, and what division by a fraction means.
Part of Year 7 Maths (Stage 4)
Placing the decimal point, dividing by a decimal, and estimating to check.
Part of Year 7 Maths (Stage 4)
Ch 08: Primes, Powers and Roots
What makes a number prime, why 1 is neither, and quick divisibility tests.
Part of Year 7 Maths (Stage 4)
Factor trees, writing a number as a product of prime powers, and why it is unique.
Part of Year 7 Maths (Stage 4)
Reading and writing powers, and what an index actually tells you to do.
Part of Year 7 Maths (Stage 4)
Undoing a power, perfect squares and cubes, and estimating roots that are not exact.
Part of Year 7 Maths (Stage 4)
Ch 09: Triangles and Quadrilaterals
Naming points, lines and angles; the marks that show equal sides, equal angles and parallels.
Part of Year 7 Maths (Stage 4)
Naming by sides and by angles, and why every triangle has a name from both lists.
Part of Year 7 Maths (Stage 4)
Why the three angles always total 180°, and using it to find a missing angle.
Part of Year 7 Maths (Stage 4)
The six special quadrilaterals, their properties, and how the families overlap.
Part of Year 7 Maths (Stage 4)
Finding unknown angles and sides by applying properties, with a reason for every step.
Part of Year 7 Maths (Stage 4)
Ch 10: Length, Perimeter and Area
Rounding to a given accuracy, and estimating to check a measurement answer.
Part of Year 7 Maths (Stage 4)
Distance around a shape, including composite figures and finding missing sides.
Part of Year 7 Maths (Stage 4)
Where the formulas come from, and why a triangle is half a rectangle.
Part of Year 7 Maths (Stage 4)
Cutting and rearranging into a rectangle, and finding the perpendicular height.
Part of Year 7 Maths (Stage 4)
Three more formulas, where each comes from, and choosing the right one.
Part of Year 7 Maths (Stage 4)
Why 1 m² is 10000 cm², and choosing a sensible unit for the job.
Part of Year 7 Maths (Stage 4)
Ch 11: Ratios
Comparing quantities by division, ratio notation, and the difference from a fraction.
Part of Year 7 Maths (Stage 4)
Dividing by the highest common factor, and handling ratios with units or fractions.
Part of Year 7 Maths (Stage 4)
Dividing a quantity in a given ratio, and working backwards from one part.
Part of Year 7 Maths (Stage 4)
Ch 12: Volume and Capacity
Naming prisms, and drawing the front, side and top views of a solid.
Part of Year 7 Maths (Stage 4)
Cross-section times length: one formula for every prism.
Part of Year 7 Maths (Stage 4)
Cubic units, the cm³/mL/L bridges, and converting sensibly.
Part of Year 7 Maths (Stage 4)
Splitting a solid into prisms, and adding or subtracting the parts.
Part of Year 7 Maths (Stage 4)
Year 8
Computing
Mathematics
Maths
Ch 01: Computation with Integers and Decimals
Operations with positive and negative integers (order of operations / BODMAS).
Part of Year 8 Maths (Stage 4)
Decimal operations, rounding, and significant figures.
Part of Year 8 Maths (Stage 4)
Terminating, recurring, and non-terminating decimals; converting between fractions and decimals.
Part of Year 8 Maths (Stage 4)
Rational numbers and operations on rational numbers.
Part of Year 8 Maths (Stage 4)
Ch 02: Fractions, Decimals and Percentages
Operations with positive and negative fractions.
Part of Year 8 Maths (Stage 4)
Percentage calculations, percentage of a quantity, and expressing one quantity as a percentage of another.
Part of Year 8 Maths (Stage 4)
Percentage increase and decrease, and the unitary method with percentages.
Part of Year 8 Maths (Stage 4)
Profit, loss, discount, and simple interest (I = Prt).
Part of Year 8 Maths (Stage 4)
Ch 03: Ratios, Rates and Time
Reading a journey off a graph: rising, flat and falling sections, speed as gradient, drawing from a description, and average speed including stops.
Part of Year 8 Maths (Stage 4)
Simplifying and equivalent ratios; dividing quantities in a given ratio.
Part of Year 8 Maths (Stage 4)
Scale drawings, maps, and scale factor applications.
Part of Year 8 Maths (Stage 4)
Rates and unit rates (e.g. speed = distance / time, cost per unit).
Part of Year 8 Maths (Stage 4)
Time calculations, 12-hour/24-hour time, and time zones.
Part of Year 8 Maths (Stage 4)
Ch 04: Algebraic Techniques
Index laws for numerical and algebraic bases (multiplication, division, power of a power, zero power).
Part of Year 8 Maths (Stage 4)
Variables, terms, coefficients, and constant terms.
Part of Year 8 Maths (Stage 4)
Multiplying and dividing algebraic terms.
Part of Year 8 Maths (Stage 4)
Expanding algebraic expressions using the distributive law: a(b + c).
Part of Year 8 Maths (Stage 4)
Factorising algebraic expressions using the highest common factor (HCF).
Part of Year 8 Maths (Stage 4)
Ch 05: Equations and Inequalities
Why squared equations have two answers, isolating x² before rooting, exact versus rounded answers, and rejecting the impossible one in real problems.
Part of Year 8 Maths (Stage 4)
Solving one-step, two-step, and multi-step linear equations.
Part of Year 8 Maths (Stage 4)
Solving equations containing grouping symbols (brackets).
Part of Year 8 Maths (Stage 4)
Solving linear equations with fractions and variables on both sides.
Part of Year 8 Maths (Stage 4)
Translating word problems into algebraic equations and solving.
Part of Year 8 Maths (Stage 4)
Graphing inequalities on the number line and solving basic linear inequalities.
Part of Year 8 Maths (Stage 4)
Ch 06: Indices and Scientific Notation
Prime versus composite, divisibility tests, factor trees, and using prime factorisation to find the HCF and LCM.
Part of Year 8 Maths (Stage 4)
Positive integer powers, square roots, and cube roots.
Part of Year 8 Maths (Stage 4)
Review and consolidation of index laws.
Part of Year 8 Maths (Stage 4)
Scientific notation (standard form) for large and small numbers.
Part of Year 8 Maths (Stage 4)
Rounding and significant figures in scientific notation.
Part of Year 8 Maths (Stage 4)
Ch 07: Linear Relationships
Common differences, finding the rule dn + b from the position, jumping to any term, decreasing and non-arithmetic patterns, and matchstick patterns.
Part of Year 8 Maths (Stage 4)
The Cartesian plane: reviewing quadrants and coordinates.
Part of Year 8 Maths (Stage 4)
Generating tables of values from linear rules.
Part of Year 8 Maths (Stage 4)
Graphing linear relationships by plotting coordinates.
Part of Year 8 Maths (Stage 4)
Finding and interpreting the gradient (slope) of a line: m = rise / run.
Part of Year 8 Maths (Stage 4)
The gradient-intercept form (y = mx + c) and horizontal/vertical lines (y = c, x = k).
Part of Year 8 Maths (Stage 4)
Ch 08: Length and Perimeter
Walking the boundary, deducing missing sides, semicircular edges, working backwards from a given perimeter, and getting the units right.
Part of Year 8 Maths (Stage 4)
Where π comes from, choosing C = πd or 2πr, arc length as a fraction of the circumference, the perimeter of a sector, and exact answers.
Part of Year 8 Maths (Stage 4)
Units of measurement and conversion of metric units.
Part of Year 8 Maths (Stage 4)
Perimeter and area of basic and composite 2D shapes.
Part of Year 8 Maths (Stage 4)
Ch 09: Area
Why the formula halves, finding the perpendicular height in any triangle, working backwards from the area, and squared-unit conversion.
Part of Year 8 Maths (Stage 4)
Where πr² comes from, halving the diameter first, sector area as a fraction, rings and holes, and working backwards.
Part of Year 8 Maths (Stage 4)
Split or subtract, tracking missing lengths, mixing rectangles, triangles and circles, shaded regions, and a six-step method.
Part of Year 8 Maths (Stage 4)
Special quadrilaterals: parallelograms, trapeziums, rhombuses, and kites.
Part of Year 8 Maths (Stage 4)
Ch 10: Volume and Capacity
V = cross-section × length for every prism, cuboids, triangular prisms and cylinders, cubic units and capacity, and composite solids.
Part of Year 8 Maths (Stage 4)
Why area and volume conversions are squared and cubed, the metric ladders, the cm³/mL/L bridges, and filling rates.
Part of Year 8 Maths (Stage 4)
Ch 11: Pythagoras' Theorem
Understanding right-angled triangles and the hypotenuse.
Part of Year 8 Maths (Stage 4)
Stating and applying Pythagoras' theorem (c² = a² + b²).
Part of Year 8 Maths (Stage 4)
Calculating the length of the hypotenuse: c = √(a² + b²).
Part of Year 8 Maths (Stage 4)
Calculating the length of a shorter side: a = √(c² − b²).
Part of Year 8 Maths (Stage 4)
Pythagorean triads and composite/practical 2D applications.
Part of Year 8 Maths (Stage 4)
Ch 12: Angle Relationships
The ten reasons, working in steps, reading diagram markings, angles inside shapes, and setting out a full-mark solution.
Part of Year 8 Maths (Stage 4)
Complementary, supplementary, vertically opposite angles, and angles around a point.
Part of Year 8 Maths (Stage 4)
Alternate, corresponding, and co-interior angles.
Part of Year 8 Maths (Stage 4)
Ch 13: Properties of Geometrical Figures
Naming by sides and by angles, the 180° angle sum, the isosceles rule, exterior angles, and giving a reason for every step.
Part of Year 8 Maths (Stage 4)
The 360° angle sum, the six special quadrilaterals and how they overlap, parallelogram angle rules, and what the diagonals prove.
Part of Year 8 Maths (Stage 4)
Angle sums of triangles (interior and exterior angle theorem) and quadrilaterals.
Part of Year 8 Maths (Stage 4)
Ch 14: Probability
Theoretical probability of simple events: P(E) = favourable outcomes / total outcomes.
Part of Year 8 Maths (Stage 4)
Why probabilities sum to 1, and using the complement to solve problems faster.
Part of Year 8 Maths (Stage 4)
Experimental probability and relative frequency.
Part of Year 8 Maths (Stage 4)
Two-step chance experiments using sample space lists, tree diagrams, and tables.
Part of Year 8 Maths (Stage 4)
Representing events using Venn diagrams and two-way tables.
Part of Year 8 Maths (Stage 4)
Ch 15: Data Analysis
Collecting and classifying data: categorical vs numerical; discrete vs continuous.
Part of Year 8 Maths (Stage 4)
Frequency distribution tables, grouped data, and cumulative frequency.
Part of Year 8 Maths (Stage 4)
Graphical representations: column graphs, histograms, dot plots, and stem-and-leaf plots.
Part of Year 8 Maths (Stage 4)
Measures of central tendency: mean, median, and mode.
Part of Year 8 Maths (Stage 4)
Analysing distributions (skewed vs symmetric data) and the effect of outliers.
Part of Year 8 Maths (Stage 4)
Ch 16: Stage 5 Extension
Surface area of rectangular and triangular prisms.
Part of Year 8 Maths (Stage 4)
Congruent figures and transformations: reflection, rotation, translation.
Part of Year 8 Maths (Stage 4)
The four congruence tests for triangles: SSS, SAS, AAS, and RHS.
Part of Year 8 Maths (Stage 4)
Formal geometric proofs using congruent triangles and quadrilateral properties.
Part of Year 8 Maths (Stage 4)
Maths · HAST Middle Secondary
Year 9
Mathematics
Maths
Y9 Maths 01: Numbers of Any Magnitude & Index Laws
Very large and very small measurements, and rounding to a given number of significant figures.
Part of Year 9 Maths (Stage 5)
Multiplying, dividing and raising powers — and the zero index.
Part of Year 9 Maths (Stage 5)
What a negative index means, and the index laws with negative-integer indices.
Part of Year 9 Maths (Stage 5)
Order-of-magnitude answers without a calculator, in scientific notation.
Part of Year 9 Maths (Stage 5)
Y9 Maths 02: Financial Maths A
Wages, commission and the simple interest formula, forwards and backwards.
Part of Year 9 Maths (Stage 5)
Increase, decrease, and finding the original amount.
Part of Year 9 Maths (Stage 5)
Unit prices, and why 20% off then 10% off is not 30% off.
Part of Year 9 Maths (Stage 5)
Y9 Maths 03: Algebraic Techniques
The distributive law with negatives and indices.
Part of Year 9 Maths (Stage 5)
Perfect squares and the difference of two squares — and using them for mental arithmetic.
Part of Year 9 Maths (Stage 5)
Taking out the highest common factor; factorising four terms in pairs.
Part of Year 9 Maths (Stage 5)
Adding, subtracting and simplifying.
Part of Year 9 Maths (Stage 5)
Y9 Maths 04: Equations & Inequalities
Solving, graphing on a number line, and flipping the sign.
Part of Year 9 Maths (Stage 5)
Changing the subject in one and several steps.
Part of Year 9 Maths (Stage 5)
Naming the unknown, writing the equation, checking the answer makes sense.
Part of Year 9 Maths (Stage 5)
Y9 Maths 05: Linear Relationships
Three measurements from two points.
Part of Year 9 Maths (Stage 5)
From a point and a gradient, or from two points.
Part of Year 9 Maths (Stage 5)
Equal gradients, and gradients that multiply to −1.
Part of Year 9 Maths (Stage 5)
Y9 Maths 06: Quadratics I
Two numbers that multiply to c and add to b.
Part of Year 9 Maths (Stage 5)
If a product is zero, a factor is zero.
Part of Year 9 Maths (Stage 5)
Areas and consecutive numbers — and rejecting the root that cannot be.
Part of Year 9 Maths (Stage 5)
Y9 Maths 07: Right-Angled Trigonometry
Opposite, adjacent, hypotenuse — and why the ratio depends only on the angle.
Part of Year 9 Maths (Stage 5)
Choosing the ratio that links what you know to what you want.
Part of Year 9 Maths (Stage 5)
Inverse ratios, and exact angles from 30°-60°-90° and 45° triangles.
Part of Year 9 Maths (Stage 5)
Drawing the diagram before anything else.
Part of Year 9 Maths (Stage 5)
Three-figure bearings, back bearings and two-leg journeys.
Part of Year 9 Maths (Stage 5)
Y9 Maths 08: Surface Area & Volume A
Curved surfaces, and the faces that disappear when solids join.
Part of Year 9 Maths (Stage 5)
Adding and subtracting prisms and cylinders.
Part of Year 9 Maths (Stage 5)
Y9 Maths 09: Similarity
Matching sides and finding the missing one.
Part of Year 9 Maths (Stage 5)
Scale factor k gives area k² and volume k³.
Part of Year 9 Maths (Stage 5)
Y9 Maths 10: Probability
Multiply along the branches, add across them.
Part of Year 9 Maths (Stage 5)
When the second draw depends on the first.
Part of Year 9 Maths (Stage 5)
And, or, not — and counting the overlap once.
Part of Year 9 Maths (Stage 5)
Probability given that something has happened: shrink the sample space.
Part of Year 9 Maths (Stage 5)
Y9 Maths 11: Data & Variation
Quartiles, interquartile range and outliers.
Part of Year 9 Maths (Stage 5)
y = k/x, and reading speed from a distance–time graph.
Part of Year 9 Maths (Stage 5)
Y9-10 Scholarship 01: Technique
Clean-number strategies, estimation, and working from the options.
Y9-10 Scholarship 02: Competition Reasoning
Multiply the choices; subtract the overcount.
Last digits, digit sums and remainders as cycles.
Label every angle you know, then follow the chain.
Cut, move and subtract instead of measuring.
What never changes tells you what can never happen.
Split into cases, and close every one.
All ages
Study Skills
FT 01: Foundations
Why three hours of highlighting leaves you with 10%: the fluency illusion, the forgetting curve, and why active beats passive.
Part of FAT Teacher — Study Skills
The four pillars — Fit to Learn, Ask to Learn, Test to Learn, Teach to Learn — how they reinforce each other, and how to start.
Part of FAT Teacher — Study Skills
Encoding, storage and recall; what your brain keeps (relevant + different); and pre-study, the routine that cuts total study time.
Part of FAT Teacher — Study Skills
FT 02: Fit to Learn
Your health is the foundation: the brain's energy budget, and why consistency beats intensity every time.
Part of FAT Teacher — Study Skills
Studying stores, sleep files: consolidation, deep vs REM sleep, the true cost of an all-nighter, and the two golden windows.
Part of FAT Teacher — Study Skills
Exercise as study equipment, the 2% dehydration problem, steady fuel versus sugar crashes, and the pre-session checklist.
Part of FAT Teacher — Study Skills
The habit loop, the 20-minute minimum viable routine, habit stacking, environment design, and studying at your own peak time.
Part of FAT Teacher — Study Skills
The 23-minute interruption cost, building focus stamina, energy waves, the 15-minute stuck rule, and the no-zero-days rule.
Part of FAT Teacher — Study Skills
FT 03: Ask to Learn
Why questions drive learning, plus ready-made question toolkits for fact subjects, maths and English.
Part of FAT Teacher — Study Skills
Six levels from no-questions to synthesis, Bloom's Taxonomy, the five elements of a powerful question, and six self-checks.
Part of FAT Teacher — Study Skills
5W1H on any sentence, the Question Formulation Technique, prioritising foundation→mechanism→application, and question stems.
Part of FAT Teacher — Study Skills
FT 04: Test to Learn
Testing as a learning tool: active recall, the forgetting curve, spaced repetition, and where to find practice tests.
Part of FAT Teacher — Study Skills
Recognition is not knowledge: free recall, cued recall, elaborative recall, application practice and concept mapping — and why difficulty is the point.
Part of FAT Teacher — Study Skills
The five question levels, the balanced 10-question recipe, three ten-minute question factories, and the five ways a self-made question goes wrong.
Part of FAT Teacher — Study Skills
Expanding intervals, the three-pile system, interleaving, and a week of reviews that takes 15-25 minutes a day.
Part of FAT Teacher — Study Skills
The four mistake types and their different fixes, the five-line error log, finding patterns, and the test-diagnose-fix-retest loop.
Part of FAT Teacher — Study Skills
FT 05: Teach to Learn
The Feynman Technique, the reality check, three ways to practise teaching, and drawing your own diagrams.
Part of FAT Teacher — Study Skills
Write it plainly, mark the cracks, repair only those, then simplify — plus self-explanation prompts and the four ways students fake it.
Part of FAT Teacher — Study Skills
Notes for a reader, diagrams drawn from memory, the one-page cheat sheet, the five-minute mini-lesson, and your own artifact library.
Part of FAT Teacher — Study Skills
The protege effect, four audiences, study-group rules that work, handling questions you cannot answer, and a weekly teaching rhythm.
Part of FAT Teacher — Study Skills
FT 06: Putting It Together
All four pillars in one session: the 60-minute cycle, the 25-minute version, daily/weekly/monthly rhythms, and what to do when it breaks down.
Part of FAT Teacher — Study Skills
The transcription trap, Cornell notes, labelled concept maps, the ten-minute same-day pass, and matching the system to the material.
Part of FAT Teacher — Study Skills
One pillar a week, a fifteen-second daily log, restarting after you fall off, and the five questions to answer on day 30.
Part of FAT Teacher — Study Skills
Study Skills · AI
AI 01: Using AI Honestly
What AI is genuinely good and bad at, the passive-AI trap, and the one rule that decides whether AI helps your learning or quietly erodes it.
Part of Using AI with FAT Teacher
AI 02: AI and the Four Pillars
Flipping AI from answering to questioning: the five master prompts, how to hold up your half of the dialogue, and the common pitfalls.
Part of Using AI with FAT Teacher
AI 03: Guardrails
Delegate vs engage and what the research actually found; the verification paradox and a spot-the-error drill; age and parental consent, school policy, what never to upload, and when to close the laptop.
Part of Using AI with FAT Teacher