Year 7 Maths: Every Australian Curriculum Code, Explained

Year 7 Maths in the Australian Curriculum Version 9 is 30 content descriptions, AC9M7A01 through AC9M7ST03. That is six more than Year 6, and every one of the six extra sits in Algebra or Measurement. The headline change is not the count, though. It is that the letter arrives: Algebra doubles from three descriptors to six, and all six use variables rather than the numerical patterns and missing-number sentences that carried Year 6.

This is a working guide to all 30 codes: what actually changes from Year 6, the four descriptors that decide whether Year 8 goes well, a term-by-term order, and six checks that tell you whether a student is ready to move on.

What changes this year

Year 6 finished primary maths with integers as positions on a number line and equations with brackets and mixed operations. Year 7 takes both and makes them abstract. AC9M7A01 asks students to “recognise and use variables to represent everyday formulas algebraically and substitute values into formulas to determine an unknown”, and AC9M7A02 asks them to “formulate algebraic expressions using constants, variables, operations and brackets”. Between those two descriptors, a letter stops being a placeholder in a puzzle and becomes a number whose value has not been fixed yet. That is the single hardest idea in the year and it is the one that decides whether the next three years are workable.

Two other genuinely new things arrive, both of them without a Year 6 ancestor. Ratios appear twice, in AC9M7N08 and again in AC9M7M06, and nothing in the primary curriculum builds them: Year 6 stopped at fractions, decimals and percentages of a quantity. And integers become something you operate on rather than something you locate, in AC9M7N07, which is where the two jobs of the minus sign finally collide in the same expression.

The third shift is structural. Measurement grows from four descriptors to six and picks up the geometry that primary handled as isolated angle facts: parallel lines cut by a transversal (AC9M7M04) and the interior angle sum of a triangle (AC9M7M05) are both written as reasoning descriptors, with “explain reasons” and “demonstrate” in the verb. Year 7 is where a maths answer starts needing a justification attached to it.

The year at a glance

Number still carries the largest single share at nine of thirty, but Year 7 is the first year where it is not a majority of the workload in practice. Algebra and Measurement together carry twelve descriptors, and both of those strands assume Number fluency rather than building it, which is why the term order below front-loads Number and does not spread it across the year.

Reading the codes

The pattern is unchanged from primary: AC9M + year + strand + number, so AC9M7N01 is Year 7 Number, position 1. Strand letters are still N Number, A Algebra, M Measurement, P Probability, SP Space, ST Statistics. One thing worth flagging for anyone mapping a scope and sequence across the primary boundary: the strand a topic lives in can move. The angle work that sat in Year 6 Measurement stays in Measurement here (AC9M7M04, AC9M7M05), but the Cartesian plane work that was Year 6 Space (AC9M6SP02) now appears in both Algebra (AC9M7A05) and Space (AC9M7SP03), because the plane is being used for two different jobs.

Strand by strand

Number (AC9M7N01 to AC9M7N09)

AC9M7N01 describes the relationship between perfect square numbers and square roots and uses both to solve problems, the descriptor commonly called the Year 7 wall because it introduces two inverse operations at once when students have only ever met addition and multiplication as an inverse pair. AC9M7N02 represents natural numbers as products of powers of prime numbers using exponent notation, which is why it must follow AC9M7N01: the notation is introduced by squares and then generalised here. AC9M7N03 represents natural numbers in expanded notation using place value and powers of 10, the same idea pointed the other way.

AC9M7N04 finds equivalent representations of rational numbers and represents them on a number line, the descriptor that finally puts fractions, decimals, percentages and negatives on one object. AC9M7N05 rounds decimals to an accuracy appropriate to the context and uses rounding and estimation to check reasonableness, which is a habit descriptor rather than a topic and should be taught as an ongoing requirement rather than a fortnight. AC9M7N06 uses the four operations with positive rational numbers including fractions, decimals and percentages, which is the largest single block of computational work in the year and quietly contains multiplying and dividing fractions, a topic AC9 never gives its own descriptor.

AC9M7N07 compares, orders and solves problems involving addition and subtraction of integers, covered in detail below. AC9M7N08 recognises, represents and solves problems involving ratios, the year’s genuinely new topic. AC9M7N09 is the applied descriptor, mathematical modelling of practical problems involving rational numbers and percentages including financial contexts, with the formulate-interpret-communicate cycle written into it explicitly.

Algebra (AC9M7A01 to AC9M7A06)

This is where the year is won or lost, and the order the six descriptors are published in is very close to the order they should be taught in. AC9M7A01 starts from everyday formulas (perimeter, area, cost per item, distance) and asks for substitution, which is deliberately the gentlest possible entry: the letter arrives already attached to a meaning the student already has. AC9M7A02 then reverses it, asking students to build expressions from a situation using constants, variables, operations and brackets. AC9M7A03 solves one-variable linear equations with natural number solutions and, critically, verifies the solution by substitution, which closes the loop back to AC9M7A01.

The remaining three are the graphical half. AC9M7A04 describes relationships between variables represented in graphs of functions from authentic data, reading rather than constructing. AC9M7A05 generates tables of values from visually growing patterns or from the rule of a function and plots those relationships on the Cartesian plane, which is the bridge from Year 6’s pattern work into the linear relations of Year 8. AC9M7A06 manipulates formulas involving several variables using digital tools and describes the effect of systematically varying the values, which is the descriptor most often skipped and the one that builds the strongest intuition, because a student who has watched an answer move as a variable changes has stopped thinking of a formula as a fixed recipe.

Measurement (AC9M7M01 to AC9M7M06)

AC9M7M01 solves problems involving the area of triangles and parallelograms using established formulas. Read that carefully if you are coming from primary: Year 6 asked students to establish the rectangle formula, and Year 7 explicitly permits established formulas for triangles and parallelograms. The derivation work belongs to the Year 5 and 6 syllabuses, so if it never happened, this descriptor will land as a formula to memorise. AC9M7M02 does the same for the volume of right prisms including rectangular and triangular prisms.

AC9M7M03 describes the relationship between π and the features of circles including circumference, radius and diameter. Note what it does not say: it does not ask for the area of a circle, which is Year 8 (AC9M8M03). AC9M7M04 identifies corresponding, alternate and co-interior relationships between angles formed when parallel lines are crossed by a transversal, and uses them to solve problems and explain reasons. AC9M7M05 demonstrates that the interior angle sum of a triangle is 180 degrees and applies it to other shapes and unknown angles. Those two are the deductive core of the year and they belong together in the same unit. AC9M7M06 uses mathematical modelling to solve practical problems involving ratios, which is why ratio should be taught in Number first and applied here second.

Probability (AC9M7P01, AC9M7P02)

AC9M7P01 identifies the sample space for single-stage events, assigns probabilities to the outcomes and predicts relative frequencies for related events. The phrase doing the work is sample space: Year 6 estimated probabilities on a scale, Year 7 lists what can happen and counts it. AC9M7P02 conducts repeated chance experiments and runs simulations with a large number of trials using digital tools, then compares predictions with observed results and explains the differences. The digital-tool clause matters, because the whole point is that a thousand trials behave differently from thirty, and thirty is all you get by hand in a lesson.

Space (AC9M7SP01 to AC9M7SP04)

AC9M7SP01 represents objects in two dimensions and reasons about the advantages and disadvantages of different representations, which covers nets, plans and elevations, and isometric drawing, and asks students to argue about which one suits a purpose. AC9M7SP02 classifies triangles, quadrilaterals and other polygons according to side and angle properties and reasons about the relationships, the descriptor that makes “a square is a rectangle” something a student can justify rather than a fact they resent. AC9M7SP03 describes transformations of a set of points using coordinates, including translations, reflections in an axis and rotations about a given point. AC9M7SP04 designs and creates algorithms that sort and classify sets of shapes by attribute and describes how they work, which pairs naturally with AC9M7SP02 rather than standing alone.

Statistics (AC9M7ST01 to AC9M7ST03)

AC9M7ST01 acquires data sets for discrete and continuous numerical variables and calculates the range, median, mean and mode, then makes and justifies decisions about which measure of central tendency gives useful insight. The justification clause is the assessable part, and it is routinely reduced to a calculation exercise. AC9M7ST02 creates different types of numerical displays including stem-and-leaf plots and describes and compares distributions by shape, centre and spread including outliers. AC9M7ST03 plans and conducts full statistical investigations and reports findings in terms of shape and summary statistics.

The four codes that decide Year 8

AC9M7A02: the letter is a number, not a label

The misconception: that a variable abbreviates an object rather than standing for a quantity, so a means apples and 3a means three apples. Its constant companion is reading juxtaposition as concatenation, so 3a with a = 4 becomes 34.

What you will see: asked to write an expression for “5 more than a number n”, a student writes 5n. Asked to write “there are 6 times as many students as teachers”, they write 6s = t, putting the 6 next to the thing there is more of. Both errors come from the same place: the letter is being read as a name for a thing rather than as a count of it.

The fix: start with AC9M7A01 and never with AC9M7A02. Substitution comes first because it forces the letter to hold a number before the student is asked to invent one. Use formulas the student can already state in words, such as cost equals price times quantity, and substitute three or four different values into the same formula in the same minute, so the letter is visibly a slot rather than a fixed thing. When you move to writing expressions, always ask “what does n count?” and require a written sentence such as “n is the number of students” before any expression is accepted. That one sentence kills the label reading, because “the number of students” cannot be multiplied by 6 to give a teacher.

AC9M7N01: squaring is not doubling, and rooting is not halving

The misconception: that the small 2 is an instruction to multiply by 2, and that the root sign undoes it by dividing by 2. Behind it sits a deeper one: that a square root is a new operation to memorise, rather than the inverse of an operation the student already knows.

What you will see: 7² answered as 14, and the square root of 36 answered as 18. The tell is that these students are usually confident, because both answers come from a rule that has worked before. A second, subtler version shows up in AC9M7N02: asked for the prime factorisation of 12, a student writes 2 × 2 × 3 correctly and then renders it as 2² × 3 by copying the shape rather than counting the factors, and gets 2³ × 3 for 24 wrong because they counted the numbers rather than the twos.

The fix: teach squares as areas before they are ever written as notation. Build 1 by 1, 2 by 2, 3 by 3 arrays on grid paper, list the counts, and let the student name the pattern. Then the square root is the visible question “this square has 36 tiles, how long is its side?”, which is not a new operation at all. Keep the perfect squares to 144 on the wall for the rest of the year, because AC9M7N02, the Year 8 exponent laws and Pythagoras in Year 8 all assume instant recall of them. Do not accept a calculator answer for a perfect square this year.

AC9M7N07: the minus sign is doing two jobs in the same expression

The misconception: that the sign in −3 and the operation in 8 − 3 are the same symbol doing the same job. Year 6 built negatives as positions (AC9M6N01) but never asked for an operation on them, so the collision happens for the first time here.

What you will see: −3 − 5 answered as −2, by subtracting the magnitudes, or as 2, by treating both minus signs as a cancellation. The same student will usually get “the temperature was −3 and dropped 5 degrees” right, which is the diagnostic: the context supplies the reasoning that the bare symbols do not.

The fix: keep every integer calculation attached to a number line for longer than feels necessary, and read the operation as movement rather than as arithmetic: subtracting is going left, adding is going right, and the sign in front of the number tells you where you started. Say “negative three” and “take away five” out loud so the two roles sound different even when they look identical. Money and temperature are the two contexts where students self-correct, so use them to build the rules and then strip the context deliberately, one step at a time, rather than starting bare and hoping.

AC9M7N08: a ratio names the parts, not the whole

The misconception: that the numbers in a ratio behave like the numerator and denominator of a fraction, so 2:3 means two-thirds. It is an easy mistake to make and almost nothing in the primary curriculum prepares against it, because ratio has no Year 6 ancestor at all.

What you will see: a mix of cordial and water in the ratio 2:3, and a student says the drink is two-thirds cordial rather than two-fifths. Or, in a scaling problem, they keep the ratio 2:3 and scale it to 3:4 by adding one to each part, which is the additive version of the same error and is much harder to spot because the numbers still look ordered.

The fix: build every ratio out of physical parts before it is written down. Two cups and three cups, on the bench, and then the question that fixes it: how many cups altogether? The whole has to be constructed by the student rather than supplied, because the whole is exactly the thing the notation does not show. For scaling, insist on the phrase “how many times bigger” rather than “how much bigger”, which forces multiplication and rules out the additive error. AC9M7M06 exists to apply this in context, so do not teach ratio purely as notation and then hope the modelling descriptor rescues it.

What students need to arrive with

Year 7 leans on four Year 6 codes hard enough that a gap in any of them will surface within a fortnight. AC9M6N02 (prime, composite and square numbers) is the prerequisite for both AC9M7N01 and AC9M7N02: a student who cannot say why 51 is composite cannot factorise it. AC9M6N01 (integers as positions) is the prerequisite for AC9M7N07, and it is the single most common gap, because it is the last topic of a primary year and often gets a week it needed a month of. AC9M6N05 and AC9M6N07 (adding and subtracting fractions, and percentages of quantities) are the prerequisites for AC9M7N06, which assumes both are fluent and adds multiplication and division on top. AC9M6A02 (equations with brackets and mixed operations) is the prerequisite for AC9M7A02 and AC9M7A03, because the order of operations does not get retaught once letters arrive.

Where any of these is shaky, the honest fix is a short, deliberate return to Year 6’s integers, fractions and percentage work in the first three weeks, rather than starting algebra on an unstable base 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 do that without turning every evening into a lesson.

What this year sets up

• AC9M7A02 and AC9M7A03 (building expressions and solving one-variable equations) become AC9M8A01, creating, expanding, factorising, rearranging and simplifying linear expressions. Year 8 does not reteach what a variable is.
• AC9M7N01 and AC9M7N02 (squares, roots and exponent notation) become AC9M8N02, establishing and applying the exponent laws with positive integer exponents and the zero exponent, and AC9M8N01, recognising irrational numbers including square roots and π.
• AC9M7N07 (adding and subtracting integers) becomes AC9M8N04, using all four operations with integers and rational numbers, where multiplication and division of negatives arrive.
• AC9M7N08 and AC9M7M06 (ratios) become AC9M8M05 rates, comparing two related quantities of different units, and then AC9M9M05 direct proportion, rates, ratio and scale.
• AC9M7A05 (tables of values plotted on the Cartesian plane) becomes AC9M8A02, graphing linear relations and solving linear equations graphically and algebraically.
• AC9M7M03 (π and the features of circles) becomes AC9M8M03, the circumference and area of a circle. The area formula is deliberately not Year 7 work.
• AC9M7M05 (interior angle sum) and AC9M7SP02 (classifying polygons) become AC9M8SP01 and AC9M8SP02, congruence and similarity, and establishing quadrilateral properties using congruent triangles.

Victorian families following VC2 should note that Level 7 covers this territory under near-identical code numbering, but splits the Number strand differently and asks students to establish the area formulas rather than use established ones, see Year 7 Maths under the Victorian Curriculum. NSW families should note that Stage 4 bundles Year 7 and Year 8 into 15 outcomes, so the content below is roughly the first half of a two-year stage, 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.

A term-by-term order

1. Term 1: rebuild number for secondary. AC9M7N03 expanded notation with powers of 10, AC9M7N01 square numbers and square roots, AC9M7N02 prime factorisation in exponent notation, AC9M7N07 comparing, ordering, adding and subtracting integers, and AC9M7N05 rounding and estimation started here and required for the rest of the year. This term is deliberately unglamorous. Every fluency Algebra assumes is built in it.
2. Term 2: rational number fluency, then variables. AC9M7N04 equivalent representations of rational numbers on a number line and AC9M7N06 the four operations with positive rational numbers, then the algebra sequence in publication order: AC9M7A01 substitution into everyday formulas, AC9M7A02 formulating expressions, AC9M7A03 one-variable linear equations verified by substitution, and AC9M7A06 manipulating formulas with digital tools.
3. Term 3: the Cartesian plane and deductive geometry. AC9M7A05 tables of values plotted on the plane and AC9M7A04 reading relationships from graphs of authentic data, then AC9M7SP03 transformations described with coordinates while the plane is still fresh. Follow with AC9M7M04 parallel lines and transversals, AC9M7M05 the interior angle sum, AC9M7SP02 classifying polygons and AC9M7SP04 sorting algorithms, which is the natural partner to the classification work.
4. Term 4: proportion, formulas and data. AC9M7N08 ratios, then AC9M7M06 modelling with ratios, AC9M7M01 area of triangles and parallelograms, AC9M7M02 volume of right prisms, AC9M7M03 π and the circle, AC9M7SP01 two-dimensional representations, AC9M7N09 financial modelling, AC9M7P01 sample spaces, AC9M7P02 simulations, and AC9M7ST01 to AC9M7ST03 measures of centre with justification, stem-and-leaf plots, and a full statistical investigation to finish.

Four orderings matter more than the rest. AC9M7N01 comes before AC9M7N02, because exponent notation is introduced by squares and generalised by prime factorisation, not the other way round. AC9M7N07 comes before all of Algebra, because substituting a negative value into a formula turns up in the first week of AC9M7A01 and a student who is still shaky on −3 − 5 will read that as an algebra failure rather than a number one. AC9M7A01 comes before AC9M7A02, for the reason set out above. And AC9M7N08 comes before AC9M7M06, because the modelling descriptor applies ratio rather than teaching it.

Assessment checkpoints

• Number: ask for 7 squared, and then for the square root of 36. Answers of 49 and 6 confirm AC9M7N01; 14 and 18 mean the small 2 is being read as an instruction to double, and the array work needs redoing before AC9M7N02 goes anywhere.
• Number: ask for −3 − 5. An answer of −8 confirms AC9M7N07; −2 or 2 means the sign and the operation have collided, so return to the number line and to reading the two roles aloud differently.
• Algebra: ask them to write an expression for “5 more than a number n”, then to find its value when n = 4. Answers of n + 5 and 9 confirm AC9M7A01 and AC9M7A02; 5n and 54 mean the letter is still a label, so go back to substitution-only work for a fortnight.
• Measurement: draw two parallel lines cut by a transversal, mark one angle as 65 degrees, and ask for a co-interior angle with a reason. 115 degrees with “co-interior angles on parallel lines add to 180” confirms AC9M7M04; a correct number with no reason, or 65 for every angle on the diagram, means the relationships have not been separated from each other yet.
• Probability: ask for the probability of rolling an even number on a fair six-sided die, and for the sample space first. A written sample space followed by 3/6 or 1/2 confirms AC9M7P01; an answer of 3, or “even chance” with no list, means the sample space step is being skipped and compound events in Year 8 will be unreachable.
• Statistics: give the data set 2, 3, 3, 4, 40 and ask which measure of centre best describes it and why. Median, with a reason naming the outlier, confirms AC9M7ST01; “the mean, because that is the average” means the justification clause has been dropped and only the calculation was taught.

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; “AC9M7A01, substituting into the cost and perimeter formulas, 3 March” answers the question before it is asked, and at Year 7 it also gives you a readable record of which of the six Algebra descriptors have actually been covered, which is harder to reconstruct later than it sounds. 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 matters more at Year 7 than it did at Year 5.

Sprout Lessons builds a full interactive lesson from any of these 30 codes, pitched at Year 7 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. That is particularly useful for AC9M7A01 and AC9M7A02, where the difference between a lesson that works and one that does not is whether the substitution examples come from something the student cares about. Try it free and generate a Year 7 Maths lesson in about a minute.

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