Stage 4 Maths: Every NSW Syllabus Outcome, Explained

Stage 4 Mathematics in NSW is 15 outcomes, MA4-ALG-C-01 through MA4-VOL-C-01, covering Year 7 and Year 8 in one syllabus stage. Fifteen looks small. Across the same two years the national curriculum publishes 57 content descriptions, so a single NSW outcome carries, on average, close to four of them. MA4-ALG-C-01 alone covers everything from meeting a variable for the first time through to factorising, which nationally is spread across two full school years.

That coarse grain is the defining feature of Stage 4, and it changes how you plan. This guide covers all 15 outcomes by focus area, why every one of them is a Core outcome and what that means for Stage 5, the three outcomes that decide whether Stage 5 goes well, a term-by-term order across both years, and five checks before the pathways split.

What changes from Stage 3

Stage 3 was the end of primary maths: percentages of quantities, the order of operations, area by rearrangement. Stage 4 is where the letter arrives, where the number line opens properly in both directions, and where a maths answer starts needing a justification attached to it.

Algebra becomes a focus area of its own. Stage 3 had multiplicative relations, where students completed number sentences with a missing value. MA4-ALG-C-01 asks them to generalise number properties and operate with algebraic expressions, which is a different activity: the missing value stops being a puzzle to solve and becomes a quantity to manipulate while it is still unknown. Almost every difficulty in Stage 5 traces back to this outcome.

Integers become operable. Stage 3 located negatives on a number line. MA4-INT-C-01 asks students to compare, order and calculate with them, which is where the two jobs of the minus sign collide in one expression for the first time.

Geometry becomes deductive. MA4-ANG-C-01 covers angle relationships including transversals across parallel lines, and MA4-GEO-C-01 covers the properties of triangles and quadrilaterals. Both are written as reasoning outcomes. A correct number with no reason does not meet them, which is the single most common gap when students move up from a primary programme that rewarded the answer.

And Pythagoras arrives, in its own focus area. MA4-PYT-C-01 gives Pythagoras the whole of one outcome, which is a strong signal about the weight NSW puts on it. It is also worth knowing if you are cross-referencing frameworks: nationally Pythagoras is a Year 8 descriptor, so a Year 7 NSW student has a Stage 4 outcome open in front of them that a Year 7 student elsewhere has not met at all.

Every Stage 4 outcome is Core, and that is the point

Look at the middle letter of every code: MA4-ALG-C-01, MA4-PYT-C-01. All 15 Stage 4 outcomes are Core. There is no Path outcome anywhere in the stage.

That matters because Stage 5 is not built the same way. From Stage 5 the syllabus splits into Core outcomes and Path outcomes, and the Path outcomes are tagged for particular senior directions: Standard, Advanced and Extension. So Stage 4 is the last stage every NSW student does in full, and performance across it is what schools use to place students into a Stage 5 pathway. There is no streaming inside Stage 4, but Stage 4 is where the streaming decision gets made.

The planning consequence is direct. A Stage 4 topic that gets quietly dropped because there was no time is not a gap in one unit, it is a gap in the evidence a placement decision runs on. That is a stronger argument for covering all 15 than any of them carry individually. For the wider structure of NSW syllabuses, including how stages relate to school years, see the NSW syllabuses explained.

The stage at a glance

Fifteen focus areas, fifteen outcomes, exactly one each. That one-to-one structure is worth noticing because it does not survive into Stage 5, where several focus areas carry an A, a B and sometimes a C outcome. In Stage 4 the focus area name and the outcome are effectively the same object.

Reading the codes

NSW outcome codes run learning area, stage, focus area, type, number: MA4-PYT-C-01 is Mathematics, Stage 4, Right-angled triangles, Core, outcome 1. The C is the piece that is easy to skim past, and it is the piece that changes at Stage 5, where you will start seeing P for Path in the same slot. Two focus area codes are worth memorising because they are not obvious from the letters: FRC is fractions, decimals and percentages, and MAG, which you will meet at Stage 5, is numbers of any magnitude.

Focus area by focus area

Number: MA4-INT-C-01, MA4-FRC-C-01, MA4-IND-C-01, MA4-RAT-C-01

These four carry all the number work of two years, and they are best read as a build. MA4-INT-C-01 opens the number line downward and asks for calculation, not just position. MA4-FRC-C-01 is the largest of the four in practice: it covers representing and operating with fractions, decimals and percentages, which folds in multiplying and dividing fractions, converting between the three forms, and percentage problems in both directions. Nationally that content occupies four or five separate descriptors, so treat MA4-FRC-C-01 as a term of work rather than a unit.

MA4-IND-C-01 spans two years by itself. Primes and roots are early Stage 4 material, while establishing the index laws sits naturally in the second year once exponent notation is comfortable. Do not attempt the laws in the same unit as first meeting a square root. Rather than being a rule to learn, the index laws should be something a student notices: writing out 2³ × 2⁴ in full and counting the twos is the whole derivation.

MA4-RAT-C-01 bundles three topics that are usually taught apart: ratio, rate, and distance-time graphs. The bundling is deliberate and it is good pedagogy, because a distance-time graph is a rate made visible, and its gradient is the rate. If you teach the graphs as a data-interpretation activity divorced from the rate work, the outcome is met on paper and the connection Stage 5 needs is not there.

Algebra: MA4-ALG-C-01, MA4-LIN-C-01

MA4-ALG-C-01 is the single widest outcome in the stage. It runs from generalising number properties, which is where variables are introduced, through operating with expressions, and all the way to expansion and factorisation. Nationally that is the span of Year 7 Algebra plus most of Year 8 Algebra. It cannot be taught as one unit and it should not be reported on as if a student who can collect like terms has met it. Split it deliberately across the two years and record which half you have covered.

MA4-LIN-C-01 creates and displays number patterns and finds graphical solutions to problems involving linear relationships. Read the word graphical, because it is doing more work than it looks like it is: there is no Equations focus area at Stage 4 at all. Equations first appears in NSW as MA5-EQU-C-01, which covers solving linear equations of up to three steps. At Stage 4 a linear relationship is something you plot and read, and solving it from the graph is the intended method rather than a fallback.

This is one of the sharpest divergences between NSW and the national frameworks and it is easy to miss. Nationally, solving a one-variable linear equation algebraically and verifying the answer by substitution is a Year 7 descriptor (AC9M7A03, VC2M7A03). In NSW it is a Stage 5 outcome. That does not mean NSW students never rearrange anything at Stage 4, since MA4-ALG-C-01 covers operating with expressions, but it does mean that a Year 7 NSW programme built from national-curriculum resources will front-load a topic the syllabus places two years later, and will do it at the cost of the graphical work the syllabus actually asks for.

Measurement: MA4-LEN-C-01, MA4-ARE-C-01, MA4-VOL-C-01

These three build in that order and should be taught in it. MA4-LEN-C-01 covers perimeter and the circumference of circles. MA4-ARE-C-01 covers area and composite area across triangles, quadrilaterals and circles, so the circle appears in both, and circumference should come first so that π is already familiar when the area formula arrives. MA4-VOL-C-01 covers the volume and capacity of right prisms and cylinders, which depends on area because a prism volume is a cross-sectional area multiplied by a height. A student who cannot find the area of a triangle cannot find the volume of a triangular prism, and the failure will present as a volume problem.

Worth flagging for anyone comparing frameworks: cylinders are Stage 4 in NSW, while nationally the volume of a cylinder waits until Year 9. If you are supplementing with national-curriculum resources, Year 8 material will not cover it.

Space: MA4-ANG-C-01, MA4-GEO-C-01, MA4-PYT-C-01

MA4-ANG-C-01 covers angle relationships and, explicitly, transversals across sets of parallel lines. MA4-GEO-C-01 covers the properties of triangles and quadrilaterals applied to problems. The pairing is intentional: the angle sum of a triangle is an angle relationship and a triangle property at once, and teaching the two focus areas in the same term saves genuine repetition. MA4-PYT-C-01 then applies Pythagoras’ theorem in a range of contexts, and it depends on MA4-IND-C-01 for square roots. It is covered in detail below.

Statistics and Probability: MA4-DAT-C-01, MA4-DAT-C-02, MA4-PRO-C-01

MA4-DAT-C-01 classifies data and displays it in a variety of graphical representations, which includes the categorical and numerical, discrete and continuous vocabulary that Stage 5 and the senior courses assume without ever reintroducing. MA4-DAT-C-02 analyses datasets using measures of centre, range and shape. The two are separate outcomes because they are separate skills, and the split is a useful corrective to programmes that treat statistics as one graph-drawing unit. MA4-PRO-C-01 solves problems involving the probabilities of simple chance experiments, and it depends on MA4-FRC-C-01, because a probability at Stage 4 is written as a fraction, decimal or percentage.

The three outcomes that decide Stage 5

MA4-ALG-C-01: 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. It produces a second, longer-lived error: that unlike terms can be combined, because if a is a thing then 3a + 2 must be five of something.

What you will see: asked to simplify 3a + 2, a student writes 5a. Asked to write an expression for “5 more than a number n”, they write 5n. Asked to write “there are 6 times as many students as teachers”, they write 6s = t, parking the 6 beside the thing there is more of.

The fix: substitution before manipulation, without exception. Substituting three or four values into the same expression inside one minute makes the letter visibly a slot rather than a fixed thing, and it also settles the like-terms question empirically: 3a + 2 and 5a disagree for every value of a except 1, and a student who has checked that will not write it again. Require a written sentence naming what the variable counts (“n is the number of students”) before any expression is accepted, because “the number of students” cannot be multiplied by 6 to produce a teacher. Because this outcome spans two years, keep the substitution habit running into the expansion and factorisation work as a check, not just as an introduction.

MA4-INT-C-01: 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. Stage 3 built negatives as positions 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 the two minus signs as a cancellation. The same student usually gets “the temperature was −3 and dropped 5 degrees” right, which is the diagnostic: the context supplies the reasoning 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 arithmetic: subtracting is going left, adding is going right, and the sign in front tells you where you started. Say “negative three” and “take away five” aloud so the two roles sound different even when they look identical. This outcome sits underneath MA4-ALG-C-01 rather than beside it, because a negative value substituted into an expression is standard from the first week of algebra, and a student who is shaky here will read that as an algebra failure.

MA4-PYT-C-01: the theorem is not always an addition

The misconception: that Pythagoras’ theorem is the instruction “square both, add, square root”, applied regardless of which side is missing. The theorem is a statement about which side is the hypotenuse, and the procedure changes when the unknown is a shorter side.

What you will see: a right-angled triangle with a hypotenuse of 13 and one side of 5, asked for the third side, answered as roughly 13.9, because both given numbers were squared and added. The tell is that the answer is longer than the hypotenuse, which is geometrically impossible, and a student who has been taught to sanity-check will catch it without being told the method was wrong. The second version shows up in applied questions, where the right angle is not drawn at the bottom of the page and the student picks the longest-looking side rather than the one opposite the right angle.

The fix: make identifying the hypotenuse a separate, marked step before any calculation, and define it as the side opposite the right angle rather than the longest or the sloped one. Then require a one-line prediction before every calculation: is the answer going to be bigger or smaller than the numbers given? Missing hypotenuse means bigger, missing shorter side means smaller. That single question converts the two cases into something a student reasons about rather than two procedures they try to remember apart. Rotate the triangles on the page deliberately, including some where the right angle is at the top, because a student who has only ever seen one orientation has learned a picture rather than a theorem.

What students need to arrive with

Stage 4 leans on three Stage 3 outcomes hard enough that a gap will surface in the first term. MA3-RN-03 (percentages of quantities and benchmark equivalents) is the prerequisite for MA4-FRC-C-01 and, through it, for MA4-PRO-C-01 and MA4-RAT-C-01. MA3-MR-02 (the order of operations) is the prerequisite for MA4-ALG-C-01, because the convention is not retaught once letters arrive and a misremembered mnemonic produces wrong answers that are far harder to see in algebra than in arithmetic. MA3-2DS-03 (area of parallelograms and triangles by combining, splitting and rearranging) is the prerequisite for MA4-ARE-C-01 and then MA4-VOL-C-01.

Where any of these is shaky, a deliberate three-week return to Stage 3’s percentage, order-of-operations and area work at the start of Year 7 costs less than rebuilding under pressure in Year 8. 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 stage sets up

• MA4-ALG-C-01 becomes MA5-ALG-C-01, simplifying algebraic fractions with numerical denominators and expanding expressions, and then the Path outcomes MA5-ALG-P-01 and MA5-ALG-P-02 for students heading toward Advanced.
• MA4-LIN-C-01 becomes MA5-LIN-C-01 and MA5-LIN-C-02, midpoint, gradient and length of an interval and the gradient-intercept form, which is where the distance-time gradient work from MA4-RAT-C-01 pays off.
• MA4-IND-C-01 becomes MA5-IND-C-01, negative indices, and the Path outcomes covering surds and fractional indices.
• MA4-PYT-C-01 becomes MA5-TRG-C-01 and MA5-TRG-C-02, the trigonometric ratios in right-angled triangles, bearings and angles of elevation and depression. Trigonometry is a right-angled triangle topic before it is anything else, so a student who is unsure which side is the hypotenuse will not get started.
• MA4-ARE-C-01 and MA4-VOL-C-01 become MA5-ARE-C-01 surface area of right prisms and composite shapes, and MA5-VOL-C-01 composite solids.
• MA4-DAT-C-01 and MA4-DAT-C-02 become MA5-DAT-C-01 summary statistics and MA5-DAT-C-02 bivariate data.
• MA4-PRO-C-01 becomes MA5-PRO-C-01, multistage chance experiments and simulations.

If you are cross-referencing with the national frameworks, Stage 4 spans Year 7 and Year 8. Our guides to Year 7 Maths under the Australian Curriculum and Year 7 Maths under the Victorian Curriculum cover roughly the first half of this stage in much finer grain, which is useful when you want a checklist of subskills that an NSW outcome bundles into one line. If you have moved states recently, which curriculum your state uses sorts out which code set applies.

A term-by-term order across two years

1. Year 7, Terms 1–2: rebuild number for secondary. MA4-INT-C-01 computation with integers, then the first half of MA4-IND-C-01 covering primes, square numbers and roots, then MA4-FRC-C-01, which is a term of work in its own right and where multiplying and dividing fractions belongs.
2. Year 7, Terms 3–4: the first half of algebra, then reasoning. The introductory half of MA4-ALG-C-01, variables, substitution and collecting like terms, then MA4-LIN-C-01 number patterns and graphical solutions while the plane is fresh, then MA4-ANG-C-01 and MA4-GEO-C-01 taught together as one reasoning unit.
3. Year 8, Terms 1–2: measurement, in dependency order. MA4-LEN-C-01 perimeter and circumference, MA4-ARE-C-01 area and composite area including circles, MA4-VOL-C-01 volume of prisms and cylinders, and then MA4-PYT-C-01, which needs the square root work from Year 7 to be automatic.
4. Year 8, Terms 3–4: finish algebra, then proportion and data. The second half of MA4-ALG-C-01, expansion and factorisation, alongside the index laws that complete MA4-IND-C-01. Then MA4-RAT-C-01 ratios, rates and distance-time graphs as one connected unit, MA4-PRO-C-01 probability, and MA4-DAT-C-01 and MA4-DAT-C-02 to finish.

This is a suggested split, not a NSW requirement, because the syllabus deliberately does not assign outcomes to a year within the stage. Four orderings hold whichever way you split it. MA4-INT-C-01 comes before MA4-ALG-C-01, because substituting a negative value turns up immediately and a student shaky on −3 − 5 will read that as an algebra failure. MA4-FRC-C-01 comes before MA4-PRO-C-01 and MA4-RAT-C-01, both of which express their answers as fractions, decimals or percentages. MA4-LEN-C-01 comes before MA4-ARE-C-01, so π is familiar from circumference before the circle area formula arrives, and MA4-ARE-C-01 comes before MA4-VOL-C-01, because a prism volume is a cross-sectional area times a height. And MA4-IND-C-01’s root work comes before MA4-PYT-C-01.

Five checks before Stage 5

• Computation with integers: ask for −3 − 5. An answer of −8 confirms MA4-INT-C-01; −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.
• Algebraic techniques: ask them to simplify 3a + 2, then to write an expression for “5 more than a number n”. “It is already simplified” and n + 5 confirm MA4-ALG-C-01; 5a and 5n mean the letter is still a label, and Stage 5 algebraic fractions will be unreachable until that is fixed.
• Right-angled triangles: give a right-angled triangle with a hypotenuse of 13 and one side of 5, and ask for the third side. An answer of 12, ideally with the hypotenuse identified before any calculation, confirms MA4-PYT-C-01; roughly 13.9 means the theorem is being applied as a single procedure regardless of which side is missing.
• Fractions, decimals and percentages: ask for 15% of 80, then ask what percentage 12 out of 80 is. Both correct confirms MA4-FRC-C-01; the first right and the second stalled means only one direction has been taught, and Stage 5 financial mathematics assumes both.
• Data analysis: 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 MA4-DAT-C-02; “the mean, because that is the average” means the shape of the data is not being read, only calculated.

Recording the alignment

Whether you are programming for a class or building evidence for a NESA home education review, record the outcome code on the activity as you go, and at Stage 4 record which part of the outcome as well. That second half matters more here than at any primary stage, because outcomes this coarse are routinely half-met. “MA4-ALG-C-01” on its own does not tell a reviewer, or you in eighteen months, whether factorisation happened. “MA4-ALG-C-01, substitution and collecting like terms, Year 7 Term 3” does, and it leaves an honest record of what is still open. Our guides to state-by-state registration requirements and the NSW syllabuses cover what NSW reviewers ask for, and teaching maths through interests covers wrapping these outcomes around whatever your student is currently into, which matters more at Stage 4 than it did at Stage 2.

Sprout Lessons builds a full interactive lesson from any of these 15 outcomes, pitched at Stage 4 and wrapped in whatever your student is into, with self-checking practice that hints rather than just marking wrong, and the exact NSW outcome code recorded in the lesson footer. That is particularly useful for the wide outcomes: because MA4-ALG-C-01 and MA4-FRC-C-01 each carry a year or more of content, generating a lesson for one specific slice of them is often more useful than looking for a resource labelled with the whole outcome. Try it free and generate a Stage 4 Maths lesson in about a minute.

Outcome codes reference NSW syllabuses © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, accessed via curriculum.nsw.edu.au. NESA does not endorse this product. Always verify against the current syllabus outcomes and content.

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