The Awfullest Australian Curriculum Algebra Lines

We’ve now gone through all the algebra – more accurately, “algebra” – sections of ACARA’s new mathematics curriculum. Parallel to our Worst Number Lines post, the following is our list of the worst algebra lines. Once again, it is important to note that these few lines do not begin to convey the unrelenting stupidity and triviality of the curriculum.


recognise, copy and continue repeating patterns represented in different ways (AC9MFA01)

recognising repeating patterns used at home and in daily activities to help make tasks easier or to solve problems; for example, setting the table to eat (AC9MFA01)


recognise, continue and create repeating patterns with numbers, symbols, shapes and objects, identifying the repeating unit (AC9M1A02)

considering how the making of shell or seed necklaces by First Nations Australians includes practices such as sorting shells and beads based on colour, size and shape, and creating a repeating pattern sequence (AC9M1A02)


recall and demonstrate proficiency with multiplication facts for twos; extend and apply facts to develop the related division facts using doubling and halving(AC9M2A03) 

using ten-frames or materials such as connecting cubes to develop and record addition and subtraction strategies including doubles, near doubles, counting on, combinations to 10 and bridging to 10, explaining patterns and connections noticed within the facts(AC9M2A03)


recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences (AC9M3A01)

recognising that when they multiply a number by 5, the resulting number will either end in a 5 or a zero; using a calculator or spreadsheet to generate a list of the multiples of 5 to develop the multiplication and related division facts for fives (AC9M3A03)


find unknown values in numerical equations involving addition and subtraction, using the properties of numbers and operations (AC9M4A01) 

using known multiplication facts for 2, 3, 5 and 10 to establish multiplication facts for 4, 6, 7, 8 and 9 in different ways; for example, using multiples of 10 to establish the multiples of 9 as “to multiply a number by 9 you multiply by 10 then take the number away”; 9 x 4 = 10 x 4 – 4, so 9 x 4 is 40 – 4 = 36; using multiple of 3 as “to multiply a number by 9 you multiply by 3, and then multiply the result by 3 again” (AC9M4A02)


using arrays, multiplication tables, and physical and virtual materials to develop families of facts; for example, 3 x 4 = 12, 4 x 3 = 12, 12 ÷ 3 = 4 and 12 ÷ 4 = 3 (AC9M5A01)

find unknown values in numerical equations involving multiplication and division using the properties of numbers and operations (AC9M5A02)


using brackets and the order of operations to write number sentences and appreciating the need for an agreed set of rules to complete multiple operations within the same number sentence; for example, for 40 ÷ 2 x (4 + 6) = □, you solve what is in the brackets first then complete the number sentence from left to right as there is no hierarchy between division and multiplication (AC9M6A02)

create and use algorithms involving a sequence of steps and decisions that use rules to generate sets of numbers; identify, interpret and explain emerging patterns (AC9M6A03)


describe relationships between variables represented in graphs of functions from authentic data (AC9M7A04)

solving equations using concrete materials, the balance model, and backtracking, explaining the process (AC9M7A03)


graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution (AC9M8A02)

using graphing software to systematically contrast the graphs of y = 2x, -y = 2x, y = -2x and -y = -2x with those of y < 2x, -y < 2x, y < -2x and -y < -2x and those of y > 2x, -y > 2x, y > -2x and -y > -2x, making and testing conjectures about sign and direction of the inequality (AC9M8A04)


simplifying and evaluating numerical expressions, involving both positive and negative integer exponents, explaining why; for example, \boldsymbol{\color{OliveGreen}5^{-3}=\frac1{5^3}=\left(\frac15\right)^3=\frac1{125}} and connecting terms of the sequence \boldsymbol{\color{OliveGreen}125, 25, 5, 1, \frac15, \frac1{25}, \frac1{125}\dots} to terms of the sequence \boldsymbol{\color{OliveGreen}5^3, 5^2, 5^1, 5^0, 5^{-1}, 5^{-2}, 5^{-3} \dots} (AC9M9A01)

identify and graph quadratic functions, solve quadratic equations graphically and numerically, and solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate (AC9M9A04)


recognising that in a table of values, if the ratio between consecutive values of the dependent variable is constant, then it is an exponential relation (AC9M10A03)

use mathematical modelling to solve applied problems involving growth and decay, including financial contexts; formulate problems, choosing to apply linear, quadratic or exponential models; interpret solutions in terms of the situation; evaluate and modify models as necessary and report assumptions, methods and findings (AC9M10A04)


wherea, b, and c are non-zero integers, and their transformation to the form \boldsymbol{\color{blue} f(x) =a(x+h)^2 + k}, where and are non-zero rational numbers, and the solution of related equations [sic]

approximating values of the sine and cosine functions from a suitably scaled diagram of the unit circle, and solving equations of the form \boldsymbol{\color{OliveGreen}sin(x)=\frac1{\sqrt2} } and \boldsymbol{\color{OliveGreen}cos(x)=-0.73} over a specified interval graphically

11 Replies to “The Awfullest Australian Curriculum Algebra Lines”

  1. I cannot comment on the Australian curriculum in general, but one can’t help feeling that curriculum drafters would do much better if they (and we) could only admit that writing maths curriculum documents is surprisingly hard! Yet it matters: the final version guides (or curses) the daily lives of tens of thousands of teachers (and kids).
    Of course, some of the infelicities may be deliberate; but others may simply reflect ignorance.

    To take one example:
    “using brackets and the order of operations […]; for example, for 40 ÷ 2 x (4 + 6)”

    Anyone who understands anything would realise that resolving difficulties by “appealing to rules” fosters precisely the opposite of what should guide us in teaching elementary mathematics. (So “using brackets and the order of operations to …” is worse than saying “using astronomy and astrology to …”. “Using brackets” is important for a mathematical reason; “order of operations” is just a way of declaring that reason plays no part.) Hence “order of operations” has no obvious place as curriculum content (though it must arise as a discussion point (a) to highlight the importance of brackets, and the fact that use of brackets removes the problem; and (b) to alert students to the different rule-based world of calculators).

    So the the paragraph needs to read something like:
    “using brackets to write number sentences with a clear meaning: for example, “40 ÷ 2 x (4 + 6)” is like a sentence with such bad grammar and poor spelling that it has no clear meaning; hence we need to sort out what is intended, and then write either “(40 ÷ 2) x (4 + 6)” or “40 ÷ (2 x (4 + 6))””

      1. The only snag is that there \displaystyle are people like Tony already in Australia. ACARA does not want them involved. ACARA wants it’s own like-minded, woke flunkies calling the shots. Tony would simply be another name on a petition.

        Personally, I think the ACARA curriculum is part of a plot by either:
        1) an unfriendly nation to conquer Australia. Dumbing down the curriculum (and hence dumbing down the population over time) will make the country ripe for invasion, or
        2) a secret ruling elite that wants to make the country dumber and dumber to maintain control.

        Although Occam’s Razor would suggest that it’s simply due to incompetents being put in charge who recruit in their own image.

  2. Two questions:

    1 (for any Primary teachers who may be reading this). What is a “number sentence”?
    I’m asking genuinely. Secondary teachers (as far as I know) do not use this phrase.

    2 (for everyone). What is meant by “related equations”? (appears in a few places, but quoted here in Year 10 Optional)

    I’m genuinely curious on both.

    1. Hi, RF. A number sentence is a sentence with numbers. For example,

      ACARA employs 17 idiots, each with an IQ of 43.

      More curriculumly, “8 + 5 = 8 + 2 + 3” is an example of a number sentence.

      As for “related equations”, in the above context it means the equation p(x) = 0 associated to a polynomial p. In other contexts, the use of “related” and/or “equivalent” is usually clear enough in each context if you squint, but is invariably a slovenly and pompous manner of expressing some idea that could be, and should be, expressed much more clearly.

      1. Right… so it is VCAA-speak for “equations that are somewhat related to other equations”.

        Think I’ll just ignore and move on.

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