Year 8 Maths: Every Australian Curriculum Code, Explained

Year 8 Maths in the Australian Curriculum Version 9 is 27 content descriptions, AC9M8A01 through AC9M8ST04. That is three fewer than Year 7, and the count is the most misleading number on this page. Three of the 27 have no Year 7 ancestor at all: Pythagoras’ theorem, irrational numbers, and a Statistics strand that has changed job rather than grown.

This is a working guide to all 27 codes: what actually changes from Year 7, the four descriptors that decide whether Year 9 is workable, a term-by-term order, and seven checks that tell you whether a student is ready to move on.

What changes this year

Year 7 made the letter a number. Year 8 makes the expression the thing you operate on. AC9M8A01 asks students to “create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties”. Read the verbs: not one of them produces a number. Every algebra question in Year 7 ended with a value, because AC9M7A03 solved equations with natural number solutions and verified them by substitution. In Year 8 the answer to “expand 3(x + 2)” is another expression, and a student who has been trained that maths finishes with a number will keep trying to finish with one.

The second shift is that the number line stops being fillable. AC9M8N01 recognises irrational numbers in applied contexts including square roots and π, which is the first time in ten years of schooling that a student meets a quantity that cannot be written as a fraction. AC9M8N03, terminating and recurring decimals, is its partner and exists mainly to make the boundary visible: everything that terminates or recurs is rational, and what is left over is the new territory.

The third is Statistics, and it is the one most likely to be taught as though nothing happened. Year 7 had three descriptors about describing data you already hold: range, median, mean and mode, stem-and-leaf plots, shape and centre and spread. All four Year 8 descriptors are about sampling and inference, meaning claims about a population you cannot see, made from a sample you can. AC9M8ST03 in particular, comparing variation between random samples of the same size, has no counterpart anywhere in primary or Year 7.

The year at a glance

Measurement is the largest strand at seven of twenty-seven, and that is a first. Number has carried the biggest share of every year from Foundation through Year 7, and in Year 8 it drops to five and hands the lead over. If you are reusing a Year 7 scope and sequence with the topics swapped, this is the structural change most likely to catch you out: Measurement needs closer to a full term than the fortnight it usually gets, because Pythagoras and the circle both live in it.

Reading the codes

The pattern is unchanged: AC9M + year + strand + number, so AC9M8N04 is Year 8 Number, position 4. Strand letters are N Number, A Algebra, M Measurement, P Probability, SP Space, ST Statistics.

Two bundles are worth knowing about before you build a program, because both hide a major topic inside a descriptor named after something else. Multiplying and dividing negative numbers has no descriptor of its own: it is inside AC9M8N04, “use the 4 operations with integers”, and Year 7 only ever asked for two of those four. And solving linear equations algebraically is not its own descriptor either. It sits inside AC9M8A02 alongside graphing linear relations and solving one-variable inequalities, which means a single code carries three weeks of work that most textbooks split across three chapters.

Strand by strand

Number (AC9M8N01 to AC9M8N05)

AC9M8N04 is the load-bearing one and should be taught first, even though it is fourth in the list. It uses the four operations with integers and with rational numbers, choosing efficient strategies and digital tools where appropriate, and the genuinely new half of it is multiplication and division of negatives. Everything in Algebra depends on it: you cannot expand −2(x − 5) without knowing what a negative times a negative does, and that expansion turns up in the first week of AC9M8A01.

AC9M8N02 establishes and applies the exponent laws with positive integer exponents and the zero exponent, using exponent notation with numbers. Note the last three words. Year 8 does the laws on numbers only; extending them to variables is Year 9 (AC9M9A01). The word establish also matters, because the laws are meant to be derived by writing the factors out rather than handed over as three rules to memorise, and a class that derives them once almost never confuses them afterwards.

AC9M8N01 recognises irrational numbers in applied contexts, including square roots and π, and AC9M8N03 recognises terminating and recurring decimals using digital tools as appropriate. Teach them as one unit, in that order, because the point of the pair is the boundary between them: a decimal that terminates or recurs can be written as a fraction, and a number like the square root of 2 cannot. AC9M8N05 is the applied descriptor, mathematical modelling with rational numbers and percentages including financial contexts, with the formulate, interpret, communicate and review cycle written into it explicitly. It is the natural home for percentage increase and decrease, which AC9 never names as a topic of its own.

Algebra (AC9M8A01 to AC9M8A04)

Four descriptors, and they do not divide evenly. AC9M8A01 is the biggest single block of work in the year: creating, expanding, factorising, rearranging and simplifying linear expressions, applying the associative, commutative, identity, distributive and inverse properties. The property names are new here and they are not decoration. Naming the distributive property is what turns expanding and factorising into one idea read in two directions, rather than two unrelated procedures with confusingly similar names.

AC9M8A02 graphs linear relations on the Cartesian plane using digital tools where appropriate, solves linear equations and one-variable inequalities using graphical and algebraic techniques, and verifies solutions by substitution. Three things, one code. The inequalities are the part most often dropped, and they are the reason the descriptor says graphical and algebraic: an inequality has a solution set rather than a solution, which is much easier to see on a number line or a graph than in a line of working. AC9M8A03 is the modelling descriptor, applied problems involving linear relations including financial contexts, with the student choosing the representation. AC9M8A04 experiments with linear functions and relations using digital tools, making and testing conjectures and generalising emerging patterns, which is the one that builds gradient intuition before gradient is ever formally defined in Year 9.

Measurement (AC9M8M01 to AC9M8M07)

AC9M8M03 solves problems involving the circumference and area of a circle using formulas and appropriate units. Year 7 deliberately stopped at the relationship between π and the features of a circle (AC9M7M03), so both formulas are new. Teach this before AC9M8M01, area and perimeter of irregular and composite shapes, because composite shapes at this level routinely include semicircles and quadrants. AC9M8M02 solves problems involving the volume and capacity of right prisms, which needs area first for the same reason: a prism’s volume is a cross-sectional area multiplied by a length.

AC9M8M06 uses Pythagoras’ theorem to solve problems involving the side lengths of right-angled triangles. It is the single most recognisable topic in the year and it depends entirely on Year 7’s square and square root work being automatic. AC9M8M05 recognises and uses rates to compare two related quantities of different units of measure, which is the successor to Year 7 ratios, and AC9M8M07 applies both in modelling. AC9M8M04 solves problems involving duration including 12- and 24-hour time across multiple time zones, the one descriptor in the year with no dependency on anything else, which makes it useful filler when a week goes sideways.

Probability (AC9M8P01 to AC9M8P03)

AC9M8P01 recognises that complementary events have a combined probability of one and uses that to calculate probabilities in applied contexts. Small descriptor, large return: for a good number of questions the complement is far easier to count than the event, and students who never internalise it end up enumerating when they did not have to. AC9M8P02 determines all possible combinations for two events using two-way tables, tree diagrams and Venn diagrams, which is the step up from Year 7’s single-stage sample spaces. Teach all three representations, because they are not interchangeable: tree diagrams carry sequence, two-way tables carry cross-classification, and Venn diagrams carry overlap. AC9M8P03 conducts repeated experiments and simulations with digital tools to determine probabilities for compound events and describe results.

Space (AC9M8SP01 to AC9M8SP04)

AC9M8SP01 identifies the conditions for congruence and similarity of triangles and explains the conditions for other sets of common shapes to be congruent or similar, including those formed by transformations. This is the first time in the curriculum that a student is asked for a minimum sufficient set of facts, which is a different kind of thinking from anything before it. AC9M8SP02 then uses that machinery: establishing properties of quadrilaterals using congruent triangles and angle properties, and solving related problems explaining reasoning. The order is not optional, because congruent triangles are the tool AC9M8SP02 is built out of.

AC9M8SP03 describes the position and location of objects in 3 dimensions in different ways, including using a three-dimensional coordinate system with dynamic geometric software. AC9M8SP04 designs, creates and tests algorithms involving a sequence of steps and decisions that identify congruency or similarity of shapes, and describes how the algorithm works. That pairs directly with AC9M8SP01 and is a good way to assess it, because an algorithm that decides congruence has to state the conditions explicitly and in order.

Statistics (AC9M8ST01 to AC9M8ST04)

AC9M8ST01 investigates techniques for data collection including census, sampling, experiment and observation, and explains the practicalities and implications of each. AC9M8ST02 analyses and reports on distributions from primary and secondary sources using random and non-random sampling techniques to select and study samples. AC9M8ST03 compares variation in distributions and proportions obtained from random samples of the same size drawn from a population, and recognises the effect of sample size on that variation. AC9M8ST04 plans and conducts investigations involving samples, using ethical and fair methods to make inferences about the population and reporting findings while acknowledging uncertainty.

Read across those four and the through-line is uncertainty, not calculation. There is no new summary statistic in Year 8 Statistics and no new display type. What is new is that every number now comes with a question about how much it would move if you did it again, which is why AC9M8ST03 needs students to actually draw several samples of the same size and compare them rather than be told that variation exists.

The four codes that decide Year 9

AC9M8N04: the two-negatives rule does not apply to addition

The misconception: that “two negatives make a positive” is a fact about minus signs rather than a fact about multiplication and division. Once it is learned as a slogan it leaks straight into addition and subtraction, which Year 7 had already settled.

What you will see: a student who has just started multiplication of integers, and who was reliably answering −3 − 5 as −8 last term, starts answering it as 8. The tell is that the regression arrives after the new topic, so it looks like carelessness rather than the direct consequence of the slogan that it is. The matching error is −3 + −5 answered as 8.

The fix: never teach the rule as a rule about signs. Teach it as a rule about repeated subtraction, so −3 × 4 is four lots of −3, and then −3 × −4 is the opposite of that, which the student can see is 12 because the pattern −3 × 2, −3 × 1, −3 × 0, −3 × −1 climbs by 3 each step. Keep the words separate out loud: “negative times negative” and never “two negatives”. And re-test addition and subtraction deliberately a fortnight after teaching multiplication, because the regression does not show up on the topic test that follows the lesson.

AC9M8A01: the distributive property applies to every term, sign included

The misconception: that expanding means multiplying the front number by the first thing inside the bracket, with the rest copied down. Underneath it is the same problem as Year 7: the student is looking for an answer, and a bracket looks like something to get rid of rather than a structure to preserve.

What you will see: 3(x + 2) expanded as 3x + 2. Then, once the second term is being multiplied, −2(x − 5) expanded as −2x − 10, because the sign has been read as belonging to the bracket rather than to the multiplier. Factorising produces the mirror image: asked to factorise 6x + 9, a student writes 3(2x + 9) or 6(x + 9), dividing one term and not the other.

The fix: use an area model for as long as it takes. A rectangle 3 wide and (x + 2) long visibly splits into 3x and 6, and there is no version of the picture where the 6 does not appear. For the sign error, insist that the multiplier is written with its sign every single time, including in the working, so the student is multiplying by −2 rather than by 2 with a minus floating nearby. For factorising, make the check mandatory and cheap: expand what you wrote and see whether you get back what you started with. Because AC9M8A01 names the distributive property explicitly, ask for the property by name when the student justifies a step. A student who can say which property they used is not guessing.

AC9M8N02: the exponent laws are about counting factors

The misconception: that the laws are three arbitrary rules about what to do with the little numbers, so they get half-remembered and cross-applied. The zero exponent gets its own version: that anything to the power of zero is zero, because multiplying by nothing gives nothing.

What you will see: 2³ × 2⁴ answered as 4⁷, with both the bases and the exponents combined. Or as 2¹², with the multiplication applied to the exponents. And 5⁰ answered as 0. Students who get all three wrong are usually fast and confident, because they are pattern-matching on the shape of the question rather than reading it.

The fix: the descriptor says establish, so establish them. Write 2³ × 2⁴ out as 2×2×2 × 2×2×2×2 and count: seven twos, so 2⁷. The base cannot change, because there was never anything but a 2 on the page. Do the same for division by cancelling pairs. For the zero exponent, come at it downward: 2³ is 8, 2² is 4, 2¹ is 2, so each step down halves, and 2⁰ has to be 1. Do not let a student write an exponent law they have not written out in full at least once, and keep the perfect squares to 144 on the wall from Year 7, because AC9M8M06 assumes them.

AC9M8M06: decide which side is missing before you calculate

The misconception: that Pythagoras is one procedure, square both and add, applied to whatever two numbers are on the triangle. The theorem is being remembered as a formula rather than as a statement about the hypotenuse specifically.

What you will see: a right-angled triangle with a hypotenuse of 13 and a shorter side of 5, and the student answers 13.9, having added the squares when they should have subtracted. It is a good deal harder to spot than a wrong arithmetic answer, because the working looks correct. The second version is a triangle drawn with the right angle at the top or the hypotenuse vertical, which produces a confident wrong answer from a student who has only ever seen the standard orientation. A third, more basic version is answering 7 for legs of 3 and 4, treating the square root of a sum as the sum of the roots.

The fix: make identifying the hypotenuse a separate, marked step before any calculation, and define it as the side opposite the right angle, never as the longest side or the sloped one. Then require a one-line prediction: if the hypotenuse is missing the answer must be bigger than both given sides, and if a shorter side is missing it must be smaller than the hypotenuse. That single sentence catches the add-when-you-should-subtract error before it reaches the calculator. Rotate the triangles on every worksheet, and for the square-root-of-a-sum error, go back to squares as areas: 9 tiles and 16 tiles make 25 tiles, and the side of a 25-tile square is 5, not 7.

What students need to arrive with

Year 8 leans on five Year 7 codes hard enough that a gap in any of them surfaces within a fortnight. AC9M7N01 (square numbers and square roots) is the prerequisite for both AC9M8N02 and AC9M8M06, and it is the most expensive gap in the year, because Pythagoras with non-automatic square roots becomes a calculator exercise with no understanding attached. AC9M7N07 (comparing, ordering, adding and subtracting integers) is the prerequisite for AC9M8N04: multiplication of negatives cannot be built on shaky addition of them. AC9M7A01 and AC9M7A02 (substitution and formulating expressions) are the prerequisites for AC9M8A01, because Year 8 does not reteach what a variable is. AC9M7A05 (tables of values plotted on the Cartesian plane) is the prerequisite for AC9M8A02. And AC9M7N08 (ratios) is the prerequisite for AC9M8M05 rates, which is a ratio between quantities in different units and nothing more.

Where any of these is shaky, spend the first three weeks going back to Year 7’s squares, integers and expression work rather than opening on expanding brackets and rebuilding under pressure in Term 3. If you are supporting a student at home, helping with maths at home without a tutor covers how to run that kind of catch-up without turning every evening into a lesson.

What this year sets up

• AC9M8A01 (expanding and factorising linear expressions) becomes AC9M9A02, expanding binomial products and factorising monic quadratic expressions. The distributive property is applied twice instead of once, and nothing about it is retaught.
• AC9M8N02 (exponent laws on numbers) becomes AC9M9A01, applying the exponent laws to numerical expressions with integer exponents and extending them to variables. Note that it moves strand, from Number to Algebra.
• AC9M8N01 (irrational numbers) becomes AC9M9N01, recognising that the real number system includes both the rationals and the irrationals. That is the whole of Year 9 Number: one descriptor, because the rest of the number work has moved into Algebra.
• AC9M8M06 (Pythagoras) and AC9M8SP01 (similarity) become AC9M9SP01, the constancy of the sine, cosine and tangent ratios for a given angle, established using similarity. This is the pairing most people miss: trigonometry in Year 9 is built on similar triangles, not on Pythagoras.
• AC9M8A02 (graphing linear relations) becomes AC9M9A03 gradient, midpoint and distance, and AC9M9A04 quadratic functions graphed and solved.
• AC9M8M02 (volume of right prisms) becomes AC9M9M01, the volume and surface area of right prisms and cylinders.
• AC9M8P02 (combinations for two events) becomes AC9M9P01, listing outcomes for compound events both with and without replacement.
• AC9M8ST01 to AC9M8ST04 (sampling and inference) become AC9M9ST01 and AC9M9ST02, analysing published surveys for how the data was obtained and how sampling method and choice of representation can support a particular point of view.

Victorian families following VC2 should note that Level 8 covers this territory with 29 codes rather than 27, and that the code numbers stop matching after A03 and N04, so “VC2M8N05” is not the Victorian version of AC9M8N05, see Year 8 Maths under the Victorian Curriculum. NSW families should note that Year 8 is the second half of Stage 4, which covers Years 7 and 8 as one two-year stage with 15 outcomes, see Stage 4 Maths under the NSW syllabus. Our guide to which curriculum your state uses is worth a minute if you are unsure which applies. What Year 8 leads into nationally is set out in Year 9 Maths under the Australian Curriculum.

A term-by-term order

1. Term 1: close the number system. AC9M8N04 the four operations with integers and rational numbers, starting with multiplication and division of negatives, then AC9M8N02 the exponent laws established rather than stated, then AC9M8N01 irrational numbers and AC9M8N03 terminating and recurring decimals taught together as one unit about the rational boundary. AC9M8N04 goes first because every sign error in Term 2 traces back to it.
2. Term 2: algebra as transformation. AC9M8A01 creating, expanding, factorising, rearranging and simplifying linear expressions, which needs three to four weeks on its own, then AC9M8A02 graphing linear relations and solving equations and one-variable inequalities, then AC9M8A04 experimenting with linear functions using digital tools, then AC9M8A03 modelling with linear relations. Finish the term with AC9M8N05 financial modelling with percentages, which uses the same modelling cycle as AC9M8A03 and benefits from being taught next to it.
3. Term 3: measurement, in dependency order. AC9M8M03 the circumference and area of a circle, then AC9M8M01 area and perimeter of irregular and composite shapes, then AC9M8M02 volume and capacity of right prisms, then AC9M8M06 Pythagoras with a full three weeks, then AC9M8M05 rates and AC9M8M07 modelling with ratios and rates as one connected unit. AC9M8M04 duration and time zones fits anywhere and is the obvious short week.
4. Term 4: reasoning, then inference. AC9M8SP01 the conditions for congruence and similarity, then AC9M8SP02 quadrilateral properties established with congruent triangles, then AC9M8SP04 congruence and similarity algorithms, then AC9M8SP03 position and location in three dimensions. Follow with AC9M8P01 complementary events, AC9M8P02 combinations for two events, AC9M8P03 simulations, and AC9M8ST01 to AC9M8ST04 finishing with a full sampling investigation.

Five orderings matter more than the rest. AC9M8N04 comes before all of Algebra, because expanding a bracket with a negative multiplier is a Week 1 Term 2 task. AC9M8N02 comes before AC9M8N01, because irrational is defined against the roots that exponent work makes familiar. AC9M8M03 comes before AC9M8M01 and AC9M8M02, because composite shapes contain semicircles and a prism volume is an area times a length. AC9M8SP01 comes before AC9M8SP02, because congruent triangles are the tool the quadrilateral proofs are made of. And AC9M8P01 comes before AC9M8P02, because the complement is what makes two-event counting tractable.

Assessment checkpoints

• Number: ask for −3 × −5, then immediately for −3 − 5. Answers of 15 and −8 confirm AC9M8N04. 15 and 8 means the two-negatives slogan has leaked into subtraction, so return to repeated subtraction and re-test both operations together for a fortnight.
• Number: ask for 2³ × 2⁴, then for 5⁰. Answers of 2⁷ (or 128) and 1 confirm AC9M8N02. 4⁷means the bases were combined too, and 0 for 5⁰ means the law was memorised rather than established, so write the factors out in full and come at the zero exponent downward.
• Algebra: ask them to expand −2(x − 5), then to factorise 6x + 9. Answers of −2x + 10 and 3(2x + 3) confirm AC9M8A01. −2x − 10 means the sign is not travelling with the multiplier, and 3(2x + 9) means only one term is being divided, so go back to the area model and make the expand-to-check step mandatory.
• Measurement: give a right-angled triangle with a hypotenuse of 13 and one shorter side of 5, and ask for the third side. An answer of 12 confirms AC9M8M06; 13.9 means the theorem is being applied as one procedure regardless of which side is missing, so reinstate the identify-the-hypotenuse step and the size prediction before any calculation.
• Probability: a bag holds 3 red and 7 blue counters, and you ask for the probability of not drawing red. 7/10 straight away confirms AC9M8P01. An answer that arrives only after listing every counter is not wrong, but it means the complement is not being used, and AC9M8P02 counting will be slow and error-prone until it is.
• Space: show two triangles that share two pairs of equal sides and one pair of equal angles that is not between those sides, and ask whether they must be congruent. “No” with a reason about the angle needing to be included confirms AC9M8SP01. “Yes, three things match” means the conditions are being counted rather than checked, and AC9M8SP02 proofs will not hold up.
• Statistics: ask which gives a better estimate of a school’s average height, a random sample of 30 students or the first 300 students who walk past the canteen. The random 30, with a reason naming the bias in the larger sample, confirms AC9M8ST01 and AC9M8ST03. “The 300, because it is bigger” means size is being treated as the only thing that matters, which is exactly the belief AC9M8ST02 exists to dismantle.

Recording the alignment

Whether you are programming for a class or building evidence for a homeschool registration review, record the code on the activity as you go. “Algebra worksheet” tells a reviewer nothing; “AC9M8A01, expanding and factorising with the area model, 14 May” answers the question before it is asked. Year 8 is the year this matters most so far, because AC9M8A02 and AC9M8N04 each bundle three separate topics under one code, and six months later it is genuinely hard to reconstruct which parts of each were actually taught. Our guide to state-by-state registration requirements covers what reviewers ask for, and teaching maths through interests covers how to wrap these codes around whatever your student is currently into, which is harder and more necessary at Year 8 than at any earlier level.

Sprout Lessons builds a full interactive lesson from any of these 27 codes, pitched at Year 8 and wrapped in whatever your student is into, with self-checking practice that hints rather than just marking wrong, and the exact AC9 code recorded in the lesson footer. It is most useful on AC9M8A01 and AC9M8M06, where students need many more worked variations than a single worksheet carries, and where the hint at the moment of the error is worth more than the mark at the end. Try it free and generate a Year 8 Maths lesson in about a minute.

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