Australian Mathematics Curriculum Awfulnesses

This is our post for noting local nonsense in the new Australian Mathematics Curriculum (downloads here). It is a list of the content descriptions and the elaborations that appear to be deficient/wrong/misplaced/weird/whatever. It includes anything that has come to our attention and has sufficiently annoyed us and/or others. (This post supersedes a previous post, and the suggestions already made have been incorporated below.) There is no intention to be comprehensive, which would probably entail transcribing 80% of the thing. We’ll just keep adding over time, as awfulnesses come to our attention. Of course criticisms and suggestions and discussion are always welcome, and can be made in the comments.

Note that this post is for the identification of local awfulnesses only. Capturing the global, systemic awfulness of the Curriculum, including the many appalling delays and omissions, would require a massive effort, which we have no intention of doing again, and which is also not required: most of the posts listed here still apply in large part, and often in full. The Curriculum excerpts are also not accompanied by any discussion of the awfulness; we’ll update with links to comments and other sources as seems worthwhile.

The (ostensibly mandatory) content descriptions are flush, and the (ostensibly optional) elaborations are indented. The content description linked to a given elaboration is only included if the content is there on its own demerit.

Foundation: Number, Algebra
Year 1: Number, Algebra
Year 2: Number, Algebra
Year 3: Number, Algebra
Year 4: Number
Year 5: Number
Year 6: Number
Year 7: Number
Year 8: Number
Year 9: Number, Space
Year 10: Number
Year 10 Optional: Number

Foundation Number

name, represent and order numbers including zero to at least 20, using physical and virtual materials and numerals (AC9MFN01) (Link)(Link)

establishing the language and process of counting, understanding that each object must be counted only once, that the arrangement of objects does not affect how many there are, and that the last number counted answers the question of “How many?”; for example, saying numbers in sequence while playing and performing actions (AC9MFN03) (11/09/22)

partitioning collections of up to 10 objects in different ways and saying the part-part-whole relationship; for example, partitioning a collection of 6 counters into 4 counters and 2 counters and saying, “6 is 4 and 2 more, it’s 2 and 4””, then partitioning the same collection into 5 and one or 3 and 3 (AC9MFN04) (11/09/22)

represent practical situations involving addition, subtraction and quantification with physical and virtual materials and use counting or subitising strategies (AC9MFN05)

representing addition and subtraction situations found in leaf games involving sets of objects used to tell stories, such as games from the Warlpiri Peoples of Yuendumu in the Northern Territory (AC9MFN05) (11/09/22)

represent practical situations involving equal sharing and grouping with physical and virtual materials and use counting or subitising strategies (AC9MFN06)

representing situations expressed in First Nations Australians’ stories, such as “Tiddalick, the greedy frog”, that describe additive situations and their connections to Country/Place (AC9MFN05) (11/09/22)

exploring instructive games of First Nations Australians that involve sharing; for example, playing Yangamini of the Tiwi Peoples of Bathurst Island to investigate and discuss equal sharing (AC9MFN06) (11/09/22)

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Foundation Algebra

recognise, copy and continue repeating patterns represented in different ways (AC9MFA01) (22/09/22)

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) (22/09/22)

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Year 1 Number

recognise, represent and order numbers to at least 120 using physical and virtual materials, numerals, number lines and charts (AC9M1N01) (14/09/22)

partition one- and two-digit numbers in different ways using physical and virtual materials, including partitioning two-digit numbers into tens and ones (AC9M1N02) (14/09/22)

building knowledge and understanding of the part-part-whole facts to 10, using physical and virtual materials; for example, using virtual ten-frames through a digital app or website to identify pairs of numbers that combine to make 10 (AC9M1N02) (14/09/22)

using physical and virtual materials to partition numbers into counts of tens and ones; for example, recognise 35 as 3 tens and 5 ones or as 2 tens and 15 ones (AC9M1N02) (14/09/22)

using part-part-whole reasoning and physical or virtual materials to represent 24, then partitioning 24 in different ways and recording the partitions using numbers; for example, 10, 10 and 4 combine to make 24 or 10 and 14 combine to make 24 (AC9M1N02) (14/09/22)

add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies (AC9M1N04) (14/09/22)

developing and using strategies for one-digit addition and subtraction based on part-part-whole relationships for each of the numbers to 10 and subitising with physical and virtual materials; for example, 8 and 6 is the same as 8 and 2 and 4 (AC9M1N04) (14/09/22)

creating and performing addition and subtraction stories told through First Nations Australians’ dances (AC9M1N04) (14/09/22)

use mathematical modelling to solve practical problems involving additive situations, including simple money transactions; represent the situations with diagrams, physical and virtual materials, and use calculation strategies to solve the problem (AC9M1N05) (14/09/22)

use mathematical modelling to solve practical problems involving equal sharing and grouping; represent the situations with diagrams, physical and virtual materials, and use calculation strategies to solve the problem (AC9M1N06) (14/09/22)

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Year 1 Algebra

recognise, continue and create repeating patterns with numbers, symbols, shapes and objects, identifying the repeating unit (AC9M1A02) (23/09/22)

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) (23/09/22)

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Year 2 Number

recognise, represent and order numbers to at least 1000 using physical and virtual materials, numerals and number lines (AC9M2N01) (15/09/22)

recognising missing numbers on different number lines; for example, a number line with 1800 on one end and 220 on the other, with every decade numbered (AC9M2N01) (15/09/22)

collecting large quantities of materials for recycling; for example, ring pulls, bottle tops and bread tags, and grouping them into ones, tens and hundreds; using the materials to show different representations of two- and three-digit numbers (AC9M2N01) (15/09/22)

comparing the digits of a number with materials grouped into hundreds, tens and ones, and explaining the meaning of each of the digits in the materials (AC9M2N02) (15/09/22)

add and subtract one- and two-digit numbers, representing problems using number sentences and solve using part-part-whole reasoning and a variety of calculation strategies (AC9M2N04) (15/09/22)

using strategies such as doubles, near doubles, part-part-whole knowledge to 10, bridging tens and partitioning to mentally solve problems involving two-digit numbers; for example, calculating 56 + 37 by thinking 5 tens and 3 tens is 8 tens, 6 + 7 = 6 + 4 + 3 is one 10 and 3, and so the result is 9 tens and 3, 93 (AC9M2N04) (15/09/22)

representing addition and subtraction problems using a bar model and  writing a number sentence, explaining how each number in the sentence is connected to the situation (AC9M2N04) (15/09/22)

using mental strategies and informal written jottings to help keep track of the numbers when solving addition and subtraction problems involving two-digit numbers and recognising that zero added to a number leaves the number unchanged; for example, in calculating 34 + 20 = 54, 3 tens add 2 tens is 5 tens which is 50, and 4 ones add zero ones is 4 ones which is 4, so the result is 50 + 4 = 54 (AC9M2N04) (15/09/22)

using First Nations Australians’ stories and dances to understand the balance and connection between addition and subtraction, representing relationships as number sentences (AC9M2N04) (15/09/22)

multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays, and partitioning to support a variety of calculation strategies (AC9M2N05) (15/09/22)

use mathematical modelling to solve practical problems involving additive and multiplicative situations, including money transactions; represent situations and choose calculation strategies; interpret and communicate solutions in terms of the situation (AC9M2N06) (15/09/22)

modelling practical problems by interpreting an everyday additive or multiplicative situation; for example, making a number of purchases at a store and deciding whether to use addition or subtraction, multiplication or division to solve the problem and justifying the choice of operation; for example, “I used subtraction to solve this problem as I knew the total and one of the parts, so I needed to subtract to find the missing part” (AC9M2N06) (15/09/22)

modelling and solving the problem “How many days are there left in this year?” by using a calendar (AC9M2N06) (15/09/22)

modelling problems involving equal grouping and sharing in First Nations Australian children’s instructive games; for example, Yangamini from the Tiwi Island Peoples, representing relationships  with a number sentence and interpret and communicate solutions in terms of the context (AC9M2N06) (15/09/22)

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Year 2 Algebra

recognising additive patterns in the environment on Country/Place and in First Nations Australians’ material culture; representing them using drawings, coloured counters and numbers (AC9M2A01) (24/09/22)

recall and demonstrate proficiency with multiplication facts for twos; extend and apply facts to develop the related division facts using doubling and halving(AC9M2A03) (24/09/22)

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) (24/09/22) 

recognising and relating terms such as double, twice and multiply by 2, halve and divide by 2 using physical and virtual materials; for example, colouring numbers on a hundreds chart to represent doubles and use to recognise halves; recognising the doubling pattern and applying to find related facts such as for 8 twos think 2 eights(AC9M2A03) (24/09/22)

establishing an understanding of doubles and near doubles using physical or virtual manipulatives; for example, using manipulatives to establish that doubling 5 gives you 10 then extending this doubling fact to respond to the question, “How can you use this fact to double 6 or double 4?” (AC9M2A03) (24/09/22)

develop fluency with doubling and halving numbers within 20 using physical or virtual materials and playing doubling and halving games; for example, using a physical or virtual dice and choosing whether to double or halve to reach a target number (AC9M2A03) (24/09/22)

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Year 3 Number

comparing the Hindu-Arabic numeral system to other numeral systems; for example, investigating the Japanese numeral system,  一、十、百、千、万 (AC9M3N01) (16/09/22)

comparing, reading and writing the numbers involved in the more than 60 000 years of First Peoples of Australia’s presence on the Australian continent through time scales relating to pre-colonisation and post-colonisation (AC9M3N01) (16/09/22)

using partitioning and part-part-whole models and the inverse relationship between addition and subtraction to solve addition or subtraction problems, making informal written “jottings” to keep track of the numbers if necessary (AC9M3N03) (16/09/22)

using physical or virtual grouped materials or diagrams to make proportional models of numbers to assist in calculations; for example, to calculate 214 + 325 representing 214 as 2 groups of 100, one group of 10 and 4 ones and 325 as 3 groups of 100, 2 groups of 10 and 5 ones resulting in 5 groups of 100, 3 groups of 10 and 9 ones which is 539 (AC9M3N03) (16/09/22)

choosing between standard and non-standard place value partitions to assist with calculations; for example, to solve 485 + 365, thinking of 365 as 350 + 15, then adding the parts, 485 + 15 = 500, 500 + 350 = 850 (AC9M3N03) (16/09/22)

solving subtraction problems efficiently by adding or subtracting a constant amount to both numbers to create an easier calculation; for example, 534 – 395 adding 5 to both numbers to make 539 – 400 = 139 (AC9M3N03) (16/09/22)

applying knowledge of place value to assist in calculations when solving problems involving larger numbers; for example, calculating the total crowd numbers for an agricultural show that lasts a week (AC9M3N03) (16/09/22)

multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies (AC9M3N04) (16/09/22)

applying knowledge of numbers and the properties of operations using a variety of ways to represent multiplication or division number sentences; for example, using a Think Board to show different ways of visualising 8 x 4, such as an array, a diagram and as a worded problem (AC9M3N04) (16/09/22)

using part-part-whole and comparative models to visually represent multiplicative relationships and choosing whether to use multiplication or division to solve problems (AC9M3N04) (16/09/22)

formulating connected multiplication and division expressions by representing situations from First Nations Australians’ cultural stories and dances about how they care for Country/Place such as turtle egg gathering using number sentences (AC9M3N04) (16/09/22)

estimate the quantity of objects in collections and make estimates when solving problems to determine the reasonableness of calculations (AC9M3N05) (16/09/22)

estimating how much space a grid paper representation of a large number such as 20 200 will take up on the wall and how much paper will be required (AC9M3N05) (16/09/22)

use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate problems using number sentences and choose calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation (AC9M3N06) (16/09/22)

modelling additive problems using a bar model to represent the problem; for example, “I had 75 tomatoes and then picked some more, now I have 138. How many did I pick?” (AC9M3N06) (16/09/22)

modelling practical multiplicative situations using materials or a diagram to represent the problem; for example, if 4 tomato plants each have 6 tomatoes, deciding whether to use an addition or multiplication number sentence, explaining how each number in their number sentence is connected to the situation (AC9M3N06) (16/09/22)

follow and create algorithms involving a sequence of steps and decisions to investigate numbers; describe any emerging patterns (AC9M3N07) (16/09/22)

following or creating an algorithm to generate number patterns formed by doubling and halving using technology to assist where appropriate; identifying and describing emerging patterns (AC9M3N07) (16/09/22)

following or creating an algorithm that determines whether a given number is a multiple of 2, 5 or 10, identifying and discussing emerging patterns (AC9M3N07) (16/09/22)

creating an algorithm as a set of instructions that a classmate can follow to generate multiples of 3 using the rule “To multiply by 3 you double the number and add on one more of the number”; for example, for 3 threes you double 3 and add on 3 to get 9, for 3 fours you double 4 and add one more 4 to get 12 … (AC9M3N07) (16/09/22)

creating a sorting algorithm that will sort a collection of 5 cent and 10 cent coins and providing the total value of the collection by applying knowledge of multiples of 5 and 10 (AC9M3N07) (16/09/22)

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Year 3 Algebra

recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences (AC9M3A01) (25/09/22)

using the inverse relationship between addition and subtraction to find unknown values with a calculator; for example, representing the problem, “Peter had some money and then spent $375, now he has $158 left. How much did Peter have to start with?” as □ – $375 = $158 and solving the problem using $375 + $158 = $533 ; solving 27 + □ = 63 using subtraction, □ = 63 – 27 or by counting on; 27, 37, 47, 57, 60, 63, so add 3 tens and 6 ones, so □ = 36 (AC9M3A01) (25/09/22)

exploring First Nations Australians’ stories and dances that show the connection between addition and subtraction, representing this as a number sentence and discussing how this conveys important information about balance in processes on Country/Place (AC9M3A01) (25/09/22)

using partitioning to develop and record facts systematically; for example, “How many ways can 12 monkeys be spread among 2 trees?”, 12 = 12 + 0, 12 = 11 + 1, 12 = 10 + 2, 12 = 9 + 3, …; explaining how they know they have found all possible partitions (AC9M3A02) (25/09/22)

understanding basic addition and related subtraction facts and using extensions to these facts; for example, 6 + 6 = 12, 16 + 6 = 22, 6 + 7 = 13, 16 + 7 = 23, and 60 + 60 = 120, 600 + 600 = 1200 (AC9M3A02) (25/09/22)

recall and demonstrate proficiency with multiplication facts for 3, 4, 5 and 10; extend and apply facts to develop the related division facts (AC9M3A03) (25/09/22)

using concrete or virtual materials, groups and repeated addition to recognise patterns and establish the  3, 4, 5 and 10 multiplication facts; using the language of “3 groups of 2 equals 6” to develop into “3 twos are 6” and extend to establish the 3 x 10 multiplication facts and related division facts (AC9M3A03) (25/09/22)

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) (25/09/22)

practising calculating and deriving multiplication facts for 3, 4, 5 and 10, explaining and recalling the patterns in them and using them to derive related division facts (AC9M3A03) (25/09/22)

systematically exploring algorithms used for repeated addition, comparing and describing what is happening, and using them to establish the multiplication facts for3, 4, 5 and 10; for example, following the sequence of steps, the decisions being made and the resulting solution, recognising and generalising any emerging patterns (AC9M3A03) (25/09/22)

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Year 4 Number

recognising that one is the same as ten-tenths and one-tenth is the same as 10 hundredths and using this relationship to rename decimals; for example, renaming 0.25 as two-tenths and five-hundredths or twenty-five-hundredths (AC9M4N01) (17/09/22)

making models of measurement attributes to show the relationship between the base unit and parts of the unit; for example, 1.5 metres is one metre and five-tenths of the next metre; 1.75 units is one unit and seventy-five hundredths of the next unit (AC9M4N01) (17/09/22)

following an algorithm consisting of a flow chart with a series of instructions and decisions to determine whether a number is even or odd; using the algorithm to identify which elements of a set of numbers are divisible by 2 (AC9M4N02) (17/09/22)

cutting objects such as oranges or sandwiches into quarters and counting by quarters to find the total number, and saying the counting sequence: one-quarter, two-quarters, three-quarters, four-quarters or one-whole, five-quarters or one-and-one-quarter, six-quarters or one-and-two-quarters… eight-quarters or two-wholes… (AC9M4N04) (17/09/22)

using a number line to represent and count in tenths, recognising that 10 tenths is equivalent to one (AC9M4N04) (17/09/22)

using physical or virtual materials to demonstrate the multiplicative relationship between the places (AC9M4N05) (17/09/22)

using a calculator or other digital tools to recognise and develop an understanding of the effect of multiplying or dividing numbers by 10s, 100s and 1,000s, recording sequences in a place value chart, in a table or spreadsheet, generalising the patterns noticed and applying them to solve multiplicative problems without a calculator (AC9M4N05) (17/09/22)

develop efficient strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder (AC9M4N06) (17/09/22)

using and choosing efficient calculation strategies for addition and subtraction problems involving larger numbers; for example, place value partitioning, inverse relationship, compatible numbers, jump strategies, bridging tens, splitting one or more numbers, extensions to basic facts, algorithms and digital tools where appropriate (AC9M4N06) (17/09/22)

using physical or virtual materials to demonstrate doubling and halving strategies for solving multiplication problems; for example, for 5 x 18, using the fact that double 5 is 10 and half of 18 is 9; or using 10 x 18 = 180 and halve 180 is 90; applying the associative property of multiplication, where 5 x 18 becomes 5 x 2 x 9, then 5 x 2 x 9 = 10 x 9 = 90 so that 5 x 18 = 90 (AC9M4N06) (17/09/22)

using an array to represent a multiplication problem, connecting the idea of how many groups and how many in each group with the rows and columns of the array, and writing an associated number sentence (AC9M4N06) (17/09/22)

using materials or a diagram to solve a multiplication or division problem, by writing a number sentence, and explaining what each of the numbers within the number sentence refers to (AC9M4N06) (17/09/22)

representing a multiplicative situation using materials, array diagrams and/or a bar model, and writing multiplication and/or division number sentences, based on whether the number of groups, the number per group or the total is missing, and explaining how each number in their number sentence is connected to the situation (AC9M4N06) (17/09/22)

using place value partitioning, basic facts and an area or region model to represent and solve multiplication problems, such as 16 × 4, thinking 10 × 4 and 6 × 4, 40 + 24 = 64 or a double, double strategy where double 16 is 32, double this is 64, so 16 x 4 is 64 (AC9M4N06) (17/09/22)

using materials or diagrams to develop and explain division strategies; for example, finding thirds, using the inverse relationship to turn division into a multiplication (AC9M4N06) (17/09/22)

using proficiency with basic facts to estimate the result of a calculation and say what amounts the answer will be between; for example, 5 packets of biscuits at $2.60 each will cost between $10 and $15 as 5 x $2 = $10 and 5 x $3 = $15 (AC9M4N07) (17/09/22)

recognising the effect of rounding in addition and multiplication calculations; rounding both numbers up, both numbers down and one number up and one number down, and explaining which is the best approximation and why (AC9M4N07) (17/09/22)

use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems using number sentences and choose efficient calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation (AC9M4N08) (17/09/22)

modelling and solving multiplication problems involving money, such as buying 5 toy scooters for $96 each, using efficient mental strategies and written jottings to keep track if needed; for example, rounding $96 up to $100 and subtracting 5 x $4 = $20, so 5 x $96 is the same as 5 x $100 less $20, giving the answer $500 – $20 = $480 (AC9M4N08) (17/09/22)

modelling situations by formulating comparison problems using number sentences, comparison models and arrays; for example, “Ariana read 16 books for the readathon; Maryam read 4 times as many books. How many books did Maryam read?” using the expression 4 x 16 and using place value partitioning, basic facts and an array, thinking 4 x 10 = 40 and 4 x 6 = 24, so 4 x 16 can be written as 40 + 24 = 64 (AC9M4N08) (17/09/22)

follow and create algorithms involving a sequence of steps and decisions that use addition or multiplication to generate sets of numbers; identify and describe any emerging patterns (AC9M4N09) (17/09/22)

creating an algorithm that will generate number sequences involving multiples of one to 10 using digital tools to assist, identifying and explaining emerging patterns, recognising that number sequences can be extended indefinitely (AC9M4N09) (17/09/22)

creating a basic flow chart that represents an algorithm that will generate a sequence of numbers using multiplication by a constant term; using a calculator to model and follow the algorithm, and record the sequence of numbers generated; checking results and describing any emerging patterns (AC9M4N09) (17/09/22)

using a multiplication formula in a spreadsheet and the “fill down” function to generate a sequence of numbers; for example, entering the number one in the cell A1, using “fill down” to cell A100, entering the formula “ = A1*4 “ in the cell B1 and using the “fill down” function to generate a sequence of 100 numbers; describing emerging patterns (AC9M4N09) (17/09/22)

creating an algorithm that will generate number sequences involving multiples of one to 10 using digital tools to assist, identifying and explaining emerging patterns, recognising that number sequences can be extended indefinitely (AC9M4N09) (17/09/22)

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Year 5 Number

using a certain number of blocks to form different rectangles and using these to list all possible factors for that number; for example, 12 blocks can form the following rectangles: 1 x 12, 2 x 6, and 3 x 4 (AC9M5N02) (18/02/22)

researching divisibility tests and explaining each rule using materials; for example, using base-10 blocks to test if numbers are divisible by 2, 5 and 10 (AC9M5N02) (18/02/22)

demonstrating and reasoning that all multiples can be formed by combining or regrouping; for example, multiples of 7 can be formed by combining a multiple of 2 with the corresponding multiple of 5; 3 x 7 = 3 x 2 + 3 x 5, and 4 x 7 = 4 x 2 + 4 x 5 (AC9M5N02) (18/02/22)

using pattern blocks to represent equivalent fractions; selecting one block or a combination of blocks to represent one whole, and making a design with shapes; recording the fractions to justify the total (AC9M5N03) (18/02/22)

creating a fraction wall from paper tape to model and compare a range of different fractions with related denominators; using the model to play fraction wall games (AC9M5N03) (18/02/22)

connecting a fraction wall model and a number line model of fractions to say how they are the same and how they are different; for example, explaining \boldsymbol{\color{OliveGreen} \frac14} on a fraction wall represents the area of one-quarter of the whole while on the number line \boldsymbol{\color{OliveGreen} \frac14} is identified as a point that is one-quarter of the distance between zero and one (AC9M5N03) (18/02/22)

using an understanding of factors and multiples as well as equivalence to recognise efficient methods for the location of fractions with related denominators on parallel number lines; for example, explaining on parallel number lines that \boldsymbol{\color{OliveGreen} \frac2{10}} is located at the same position on a parallel number line as \boldsymbol{\color{OliveGreen} \frac15} because \boldsymbol{\color{OliveGreen} \frac15} is equivalent to \boldsymbol{\color{OliveGreen} \frac2{10}} (AC9M5N03) (18/02/22)

creating a model by subdividing a collection of materials, such as blocks or money, to connect decimals and percentage equivalents of tenths and commonly used fractions \boldsymbol{\color{OliveGreen} \frac12}, \boldsymbol{\color{OliveGreen} \frac13} and \boldsymbol{\color{OliveGreen} \frac34}; for example, one-tenth or 0.1 represents 10% and one half or 0.5 represents 50%; recognising that 60% is 10% more than 50% (AC9M5N04) (18/02/22)

using physical and virtual materials to represent the relationship between decimal notation and percentages; for example, 0.3 is 3 out of every 10, which is 30 out of every 100, which is 30 (AC9M5N04) (18/02/22)

solve problems involving addition and subtraction of fractions with the same or related denominators, using different strategies (AC9M5N05) (18/02/22)

using different ways to add and subtract fractional amounts by subdividing different models of measurement attributes; for example, adding half an hour and three-quarters of an hour using a clock face, adding a \boldsymbol{\color{OliveGreen} \frac34} cup of flour and a \boldsymbol{\color{OliveGreen} \frac14} cup of flour, subtracting \boldsymbol{\color{OliveGreen} \frac34} of a metre from \boldsymbol{\color{OliveGreen} 2\frac14}  metres (AC9M5N05) (18/02/22)

representing and solving addition and subtraction problems involving fractions by using jumps on a number line, bar models or making diagrams of fractions as parts of shapes (AC9M5N05) (18/02/22)

using materials, diagrams, number lines or arrays to show and explain that fraction number sentences can be rewritten in equivalent forms without changing the quantity; for example, \boldsymbol{\color{OliveGreen} \frac12 + \frac14} is the same as \boldsymbol{\color{OliveGreen} \frac24 + \frac14} (AC9M5N05) (18/02/22)

solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient calculation strategies and using digital tools where appropriate; check the reasonableness of answers (AC9M5N06) (18/02/22)

solving multiplication problems such as 253 x 4 using a doubling strategy; for example, 2 x 253 = 506 and 2 x 506 = 1012 (AC9M5N06) (18/02/22)

solving multiplication problems like 15 x 16 by thinking of factors of both numbers, 5 = 3 x 5, 16 = 2 x 8; rearranging the factors to make the calculation easier, 5 x 2 = 10, 3 x 8 = 24 and 10 x 24 = 240 (AC9M5N06) (18/02/22)

solve problems involving division, choosing efficient strategies and using digital tools where appropriate; interpret any remainder according to the context and express results as a whole number, decimal or fraction (AC9M5N07) (18/02/22)

solving division problems mentally like 72 divided by 9, 72 ÷ 9, by thinking, “how many 9s make 72”, ? x 9 = 72 or “share 72 equally 9 ways” (AC9M5N07) (18/02/22)

using the fact that equivalent division calculations result if both numbers are divided by the same factor (AC9M5N07) (18/02/22)

check and explain the reasonableness of solutions to problems including financial contexts using estimation strategies appropriate to the context (AC9M5N08) (18/02/22)

recognising the effect of rounding addition, subtraction, multiplication and division calculations, rounding both numbers up, both numbers down, and one number up and one number down; explaining which estimation is the best approximation and why (AC9M5N08) (18/02/22)

use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems, choosing operations and efficient calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation (AC9M5N09) (18/02/22)

modelling an everyday situation and determining which operations can be used to solve it using materials, diagrams, arrays and/or bar models to represent the problem ; formulating the situation as a number sentence and justifying their choice of operations in relation to the situation (AC9M5N09) (18/02/22)

modelling a series of contextual problems, deciding whether an exact answer or an approximate calculation is appropriate; explaining their reasoning in relation to the context and the numbers involved (AC9M5N09) (18/02/22)

modelling financial situations such as creating financial plans; for example, creating a budget for a class fundraising event, using a spreadsheet to tabulate data and perform calculations (AC9M5N09) (18/02/22)

investigating mathematical models involving combinations of operations can be used to represent songs, stories and/or dances of First Nations Australians (AC9M5N09) (18/02/22)

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Year 6 Number

recognise situations, including financial contexts, that use integers; locate and represent integers on a number line and as coordinates on the Cartesian plane (AC9M6N01) (Link) (09/09/22)

using the definition of a prime number to explain why one is not a prime number (AC9M6N02) (Link)(Link)

representing composite numbers as a product of their factors, including prime factors when necessary and using this form to simplify calculations involving multiplication such as 15 x 16 as 5 x 3 x 4 x 4 which can be rearranged to simplify calculation to 5 x 4 x 3 x 4 = 20 x 12 (AC9M6N02) (Link)

using spreadsheets to list all the numbers that have up to 3 factors, using combinations of only the first 3 prime numbers, recognise any emerging patterns, making conjectures and experimenting with other combinations (AC9M6N02) (Link)

apply knowledge of equivalence to compare, order and represent common fractions including halves, thirds and quarters on the same number line and justify their order (AC9M6N03) (09/09/22)

representing fractions on the same number line, paying attention to relative position, and using this to explain relationships between denominators (AC9M6N03) (09/09/22)

explaining equivalence and order between fractions using number lines, drawings and models (AC9M6N03) (09/09/22)

comparing and ordering fractions by placing cards on a string line across the room and referring to benchmark fractions to justify their position; for example, \boldsymbol{\color{OliveGreen} \frac58} is greater than \boldsymbol{\color{OliveGreen} \frac12} can be written as \boldsymbol{\color{OliveGreen} \frac58 > \frac12}, because half of 8 is 4; \boldsymbol{\color{OliveGreen} \frac16} is less than \boldsymbol{\color{OliveGreen} \frac14}, because 6>4 and can be written as \boldsymbol{\color{OliveGreen} \frac16 < \frac14} (AC9M6N03) (09/09/22)

apply knowledge of place value to add and subtract decimals, using digital tools where appropriate; use estimation and rounding to check the reasonableness of answers (AC9M6N04) (09/09/22)

applying whole-number strategies; for example, using basic facts, place value, partitioning and the inverse relationship between addition and subtraction, and properties of operations to develop meaningful mental strategies for addition and subtraction of decimal numbers to at least hundredth (AC9M6N04) (09/09/22)

deciding to use a calculator as a calculation strategy for solving additive problems involving decimals that vary in their number of decimal places beyond hundredths; for example, 1.0 – 0.0035 or 2.345 + 1.4999 (AC9M6N04) (09/09/22)

solve problems involving addition and subtraction of fractions using knowledge of equivalent fractions (AC9M6N05) (09/09/22)

representing addition and subtraction of fractions, using an understanding of equivalent fractions and methods such as jumps on a number line, or diagrams of fractions as parts of shapes (AC9M6N05) (09/09/22)

understanding the processes for adding and subtracting fractions with related denominators and fractions as an operator, in preparation for calculating with all fractions; for example, using fraction overlays and number lines to give meaning to adding and subtracting fractions with related and unrelated denominators (AC9M6N05) (09/09/22)

multiply and divide decimals by multiples of powers of 10 without a calculator, applying knowledge of place value and proficiency with multiplication facts; using estimation and rounding to check the reasonableness of answers (AC9M6N06) (09/09/22)

applying and explaining estimation strategies in multiplicative situations involving a decimal greater than one that is multiplied by a two- or three-digit number, using a multiple of 10 or 100 when the situation requires just an estimation (AC9M6N06) (09/09/22)

explaining the effect of multiplying or dividing a decimal by 10, 100, 1000 … in terms of place value and not the decimal point shifting (AC9M6N06) (09/09/22)

solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies and using digital tools where appropriate (AC9M6N07) (09/09/22)

representing a situation with a mathematical expression; for example, numbers and symbols such as \boldsymbol{\color{OliveGreen} \frac14 \times 24}, that involve finding a familiar fraction or percentage of a quantity; using mental strategies or a calculator and explaining the result in terms of the situation in question (AC9M6N07) (09/09/22)

approximate numerical solutions to problems involving rational numbers and percentages, including financial contexts, using appropriate estimation strategies (AC9M6N08) (09/09/22)

using familiar fractions, decimals and percentages to approximate calculations, such as, 0.3 of 180 is about a \boldsymbol{\color{OliveGreen} \frac13} of 180 or 52% is about a \boldsymbol{\color{OliveGreen} \frac12} (AC9M6N08) (09/09/22)

recognising the effect of rounding on calculations involving fractions or decimals and saying what numbers the answer will be between (AC9M6N08) (09/09/22)

investigating estimation strategies to make decisions about steam cooking in ground ovens by First Nations Australians, including catering for different numbers of people and resources needed for cooking (AC9M6N08) (09/09/22)

use mathematical modelling to solve practical problems, involving rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and efficient calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, justifying the choices made (AC9M6N09) (09/09/22)

modelling practical situations involving percentages using efficient calculation strategies to find solutions, such as mental calculations, spreadsheets, calculators or a variety of informal jottings, and interpreting the results in terms of the situation; for example, purchasing items during a sale (AC9M6N09) (09/09/22)

modelling and solving the problem of creating a budget for a class excursion or family holiday, using the internet to research costs and expenses, and representing the budget in a spreadsheet, creating and using formulas to calculate totals (AC9M6N09) (09/09/22)

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Year 7 Number

describe the relationship between perfect square numbers and square roots, and use squares of numbers and square roots of perfect square numbers to solve problems (AC9M7N01) (12/09/22)

using the relationship between perfect square numbers and their square roots to determine the perimeter of a square tiled floor using square tiles; for example, an area of floor with 144 square tiles has a perimeter of 48 tile lengths (AC9M7N01) (12/09/22)

solving problems involving lowest common multiples and greatest common divisors (highest common factors) for pairs of natural numbers by comparing their prime factorisation (AC9M7N02) (12/09/22)

investigating equivalence of fractions using common multiples and a fraction wall, diagrams or a number line to show that a fraction such as \boldsymbol{\color{OliveGreen}\frac23} is equivalent to \boldsymbol{\color{OliveGreen}\frac46} and \boldsymbol{\color{OliveGreen}\frac69} and therefore \boldsymbol{\color{OliveGreen}\frac23< \frac56} (AC9M7N04) (12/09/22)

applying and explaining the equivalence between fraction, decimal and percentage representations of rational numbers; for example, 16%, 0.16, \boldsymbol{\color{OliveGreen}\frac{16}{100}} and \boldsymbol{\color{OliveGreen}\frac{4}{25}}, using manipulatives, number lines or diagrams (AC9M7N04) (12/09/22)

use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies (AC9M7N06) (12/09/22)

solving addition and subtraction problems involving fractions and decimals; for example, using rectangular arrays with dimensions equal to the denominators, algebra tiles, digital tools or informal jottings (AC9M7N06) (12/09/22)

developing efficient strategies with appropriate use of the commutative and associative properties, place value, patterning, and multiplication facts to solve multiplication and division problems involving fractions and decimals; for example, using the commutative property to calculate \boldsymbol{\color{OliveGreen}\frac23} of \boldsymbol{\color{OliveGreen}\frac12} giving \boldsymbol{\color{OliveGreen}\frac12} of \boldsymbol{\color{OliveGreen}\frac23=\frac13} (AC9M7N06) (12/09/22)

solving multiplicative problems involving fractions and decimals using fraction walls, rectangular arrays, algebra tiles, calculators or informal jottings (AC9M7N06) (12/09/22)

developing efficient strategies with appropriate use of the commutative and associative properties, regrouping or partitioning to solve additive problems involving fractions and decimals (AC9M7N06) (12/09/22)

carry out calculations to solve problems using the representation that makes computations efficient such as 12.5% of 96 is more efficiently calculated as \boldsymbol{\color{OliveGreen}\frac18} of 96, including contexts such as comparing land-use by calculating the total local municipal area set aside for parkland or manufacturing and retail, the amount of protein in daily food intake across several days, or increases/decreases in energy accounts each account cycle (AC9M7N06) (12/09/22)

compare, order and solve problems involving addition and subtraction of integers (AC9M7N07) (Link)

ordering, adding and subtracting integers using a number line (AC9M7N07) (12/09/22)

using diagrams, physical or virtual materials to represent ratios, recognising that ratios express the quantitative relationship between 2 or more groups; for example, using counters or coloured beads to show the ratios 1:4 and 1:1:2 (AC9M7N08) (12/09/22)

use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts; formulate problems, choosing representations and efficient calculation strategies, using digital tools as appropriate; interpret and communicate solutions in terms of the situation, justifying choices made about the representation (AC9M7N09) (Link)

modelling additive situations involving positive and negative quantities; for example, a lift travelling up and down floors in a high-rise apartment where the ground floor is interpreted as zero; in geography when determining altitude above and below sea level (AC9M7N09) (12/09/22)

modelling contexts involving proportion, such as the proportion of students attending the school disco, proportion of bottle cost to recycling refund, proportion of school site that is green space, 55% of Year 7 students attended the end of term function or 23% of the school population voted yes to a change of school uniform; interpreting and communicating answers in terms of the context of the situation (AC9M7N09) (12/09/22)

using mathematical modelling to investigate the proportion of land mass/area of Australian First Nations Peoples’ traditional grain belt compared with Australia’s current grain belt (AC9M7N09) (12/09/22)

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Year 8 Number

recognise irrational numbers in applied contexts, including square roots and π (AC9M8N01) (Link)

using digital tools to systematically explore contexts or situations that use irrational numbers, such as finding the length of the hypotenuse in a right-angled triangle with the other 2 sides having lengths of one metre or 2 metres and one metre; or given the area of a square, finding the length of the side where the result is irrational; or finding ratios involved with the side lengths of paper sizes A0, A1, A2, A3 and A4 (AC9M8N01) (Link)(Link)

investigating the golden ratio in art and design, and historical approximations to π in different societies (AC9M8N01) (Link)

connecting the ratio between the circumference and diameter of any circle to the irrational value of π using circular objects and string or dynamic drawing software (AC9M8N01) (Link)

establish and apply the exponent laws with positive integer exponents and the zero-exponent, using exponent notation with numbers (AC9M8N02) (Link)

using digital tools to systematically explore the application of the exponent laws; observing that the bases need to be the same (AC9M8N02)

using examples such as \boldsymbol{\color{OliveGreen}\frac{3^{4}}{3^4}=1} and \boldsymbol{\color{OliveGreen} 3^{4-4} = 3^0} to illustrate the necessity that for any non-zero natural number \boldsymbol{\color{OliveGreen} n}, \boldsymbol{\color{OliveGreen} n^0 = 1} (AC9M8N02) (Link)

recognise terminating and recurring decimals, using digital tools as appropriate (AC9M8N03) (Link)

identifying terminating, recurring and non-terminating decimals and choosing their appropriate representations such as \boldsymbol{\color{OliveGreen} \frac13} is represented as \boldsymbol{\color{OliveGreen} 0.\overline{3}} (AC9M8N03) (13/09/22)

use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate (AC9M8N04) (13/09/22)

using patterns to assist in establishing the rules for the multiplication and division of integers (AC9M8N04) (13/09/22)

applying and explaining efficient strategies such as using the commutative or associative property for regrouping, partitioning, place value, patterning, multiplication or division facts to solve problems involving positive and negative integers, fractions and decimals (AC9M8N04) (13/09/22)

use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts; formulate problems, choosing efficient calculation strategies and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model (AC9M8N05) (13/09/22)

modelling situations involving weather and environmental contexts including temperature or sea depths by applying operations to positive and negative rational numbers; for example, involving average temperature increases and decreases (AC9M8N05) (13/09/22)

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Year 9 Number

recognise that the real number system includes the rational numbers and the irrational numbers, and solve problems involving real numbers using digital tools (AC9M9N01) (19/09/22)

investigating the real number system by representing the relationships between irrationals, rationals, integers and natural numbers and discussing the difference between exact representations and approximate decimal representations of irrational numbers (AC9M9N01) (19/09/22)

using a real number line to indicate the solution interval for inequalities of the form ax + b < 7 ;
for example, 2x + 7 < 0, or of the form ax = b > c ; for example, 1.2x – 5.4 > 10.8 (AC9M9N01) (19/09/22)

using positive and negative rational numbers to solve problems; for example, for financial planning such as budgeting (AC9M9N01) (19/09/22)

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Year 9 Space

investigating patterns to reason about nested similar triangles that are aligned on a coordinate plane, connecting ideas of parallel sides and identifying the constancy of ratios of corresponding sides for a given angle (AC9M9SP01) (10/09/22)

apply the enlargement transformation to shapes and objects using dynamic geometry software as appropriate; identify and explain aspects that remain the same and those that change (AC9M9SP02)

using the properties of similarity to solve problems involving enlargement (AC9M9SP02) (10/09/22)

investigating and generalising patterns in length, angle, area and volume when side lengths of shapes and objects are enlarged or dilated by whole and rational numbers; for example, comparing an enlargement of a square and a cube of side length 2 units by a factor of 3 increases the area of the square, \boldsymbol{\color{OliveGreen}2^2} to \boldsymbol{\color{OliveGreen}(3\times 2)^2=9\times 2^2=9}
times the original area and the volume of the cube, \boldsymbol{\color{OliveGreen}2^3} to \boldsymbol{\color{OliveGreen}(3\times 2)^3=27\times 2^3=27}
times the volume 
(AC9M9SP02) (10/09/22)

design, test and refine algorithms involving a sequence of steps and decisions based on geometric constructions and theorems; discuss and evaluate refinements (AC9M9SP03) (Link)

creating an algorithm using pseudocode or flow charts to apply the triangle inequality, or an algorithm to generate Pythagorean triples (AC9M9SP03) (10/09/22)

creating and testing algorithms designed to construct or bisect angles, using pseudocode or flow charts (AC9M9SP03) (10/09/22)

developing an algorithm for an animation of a geometric construction, or a visual proof, evaluating the algorithm using test cases (AC9M9SP03) (10/09/22)

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Year 10 Number

recognise the effect of using approximations of real numbers in repeated calculations and compare the results when using exact representations (AC9M10N01) (20/09/22)

comparing and contrasting the effect of truncation or rounding on the final result of calculations when using approximations of real numbers rather than exact representations (AC9M10N01) (20/09/22)

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Year 10 Optional Number

explaining that \boldsymbol{\color{OliveGreen}\sqrt{a}= a^{\frac12}=a^{0.5}} for \boldsymbol{\color{OliveGreen}a\geq 0}, generalizing to \boldsymbol{\color{OliveGreen}\sqrt[n]{a}= a^{\frac1{n}}}, and evaluating corresponding expressions; for example, \boldsymbol{\color{OliveGreen}\sqrt{10}= 10^{0.5}\approx 3.162} , \boldsymbol{\color{OliveGreen}2^5=32} so \boldsymbol{\color{OliveGreen}32^{\frac15}=2} (Link)

explaining that \boldsymbol{ \color{OliveGreen} a^{\frac{m}{n}}=\left(a^{\frac{1}{n}}\right)^m  =\left(\sqrt[n]{a}\right)^m = \sqrt[n]{a^m}  } and evaluating corresponding expressions; for example, \boldsymbol{ \color{OliveGreen} 8^{\frac{2}{3}}=\left(\sqrt[3]8\right)^2  = 2^2 = 4} and \boldsymbol{ \color{OliveGreen} 8^{\frac{2}{3}}=\sqrt[3]{8^2}  = \sqrt[3]{64} = 4}

showing that \boldsymbol{\color{OliveGreen}\sqrt{a+b}\neq\sqrt{a} + \sqrt{b}} and \boldsymbol{\color{OliveGreen}\sqrt{a-b}\neq\sqrt{a} - \sqrt{b}} for \boldsymbol{\color{OliveGreen}a,b > 0}, for example, \boldsymbol{\color{OliveGreen}\sqrt{16 + 9}=5} but \boldsymbol{\color{OliveGreen}\sqrt{16}+\sqrt{9}=4+3=7}, and \boldsymbol{\color{OliveGreen}\sqrt{16 - 9}=7\approx 2.646}, but \boldsymbol{\color{OliveGreen}\sqrt{16}-\sqrt{9}=4-3=1} (Link)

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32 Replies to “Australian Mathematics Curriculum Awfulnesses”

  1. These examples are suitably horrible to compel one shun the light and become a hermit but I have to wonder what the point of all of this is?
    I have seen time and again the forces of “curriculum reform” and in particular mathematics education reformers beaten back, only to return once again with a vengeance. They wait until the people naysaying (their pet projects) are gone and then they come back with promises of improved performance. You really have to be impressed with their persistence and their ability to take advantage of opportunities ( a new minister of education or a new state head of a board of studies). And time and again their edu-fads and teacher training reforms fail with each TIMMS or PISA ( yes Marty I know your take on PISA but people use it as a metric nonetheless) report. And what do they tell their masters when the dismal results come? That we need to go further down the path of reform! And if I see another bogus response quoting the wonders of Finland again I’ll do an injury to someone.

    But once again I ask, what is the point of all of this? Is it to improve education? I find that hard to believe given the entropic decay that we have witnessed at all levels. Is it gender equality? I was at an education conference that I actually heard a talk in which a speaker proudly proclaimed that at VCE level girls now outperformed boys across all subjects except physics and specialist maths . The fact that this indicates a looming catastrophe with half of the student population educationally underperforming was lost on this ideologue as she queried why physics and specialist maths were such misogynist holdouts (physics has been denuded of any difficult material i.e. advanced maths since).
    Or is it equity that the educrats seek? I recall your recent republishing of Tony Guttman’s letter in which he declared that to him it was irrelevant where someone came from, but it was of prime importance that equality of opportunity be given and that ability be recognised and fostered.

    Equity might come on several forms.

    1. It can come from identifying talent and fostering interest with resources being allocated where they are needed. But this is a high energy path with well trained and resourced teachers; materials that are correct and yet engaging; assessments that actually have meaning (not testing every damn thing every week for the sake of it). It takes a hell of a lot of money, commitment and energy to run this.
    2. The more depressing from of equity is what we appear to be aiming at-as amply demonstrated by ACARA here. Uniform mediocrity that disables differentiation between those who can and those who cannot. It is a lower energy system in that it is easiest to deny opportunity of high performance. Who hasn’t heard “the smart ones will be OK because they can look after themselves”? By lowering what is expected in order to achieve an agreed educational standard the universities and employers won’t know what a person is able to achieve….a perfect utopia of equity
    And the worst thing: it’s a spiral downwards

  2. It’s … err … awful, isn’t it? One hardly knows where to start, as almost every sentence or statement has some hideousness in it. I might just pick out one – not quite at random – “using spreadsheets” in Year 6 Number. This is a WTF moment. Now I am a technophile: I love technology, I love using it, and I love teaching with it (at university). I love playing with it and fiddling, and wondering what might happen if I change something. But – I have the advantage of a solid mathematics education behind me: 12 years of school (we all went from Prep to Grade 2 at my school); four years of tertiary mathematics, two research degrees. I believe that in all that time the most technology I used was a set of Cuisenaire rods in Grade 2.

    Spreadsheets? Grade 6? And to list numbers with up to three factors? I’m just gobsmacked. At that level students will be just using the spreadsheet as a sort of electronic table to enter their numbers in. Irrespective of whether the task is or is not useful in any way (I’m leaning towards the latter), adding technology purely for its own sake has a negative pedagogical value. Time which could be spent actually, you know, doing mathematics, firming up basic arithmetic skills, is wasted in a meaningless add-on.

    And this is really just a detail in an ocean of horror. Every comment quoted above by Marty could be equally so attacked. What is clear – and has been so for some time – is that the creators of this thing have no conception of mathematics, what it is, how it can be used, where its power and beauty lie. It’s a race to the bottom, with the idiots in charge.

  3. Terry and Marty – indeed that was my point. Year 6 students know as much about spreadsheets as they do about forklifts, and both have about the same level of usefulness in a school mathematics classroom.

    Also, given some of the spreadsheets I’ve seen in my professional life (and a university is driven by spreadsheets) I think forklift drivers probably do more good, or at least, less harm.

    1. Spreadsheets are important and useful in many areas. Students could learn the basics of these at school, not necessarily in a mathematics classroom.

      1. Terry, I’m happy for you to play Idiots’ Advocate on this blog, and if you want to try to defend the Year 6 elaboration that is being discussed, then do so. But try to stick to the topic.

  4. “using digital tools to systematically explore contexts or situations that use irrational numbers, such as finding the length of the hypotenuse in a right-angled triangle with the other 2 sides having lengths of one metre or 2 metres and one metre; or given the area of a square, finding the length of the side where the result is irrational; or finding ratios involved with the side lengths of paper sizes A0, A1, A2, A3 and A4 (AC9M8N01)”

    Don’t see at all how digital tools are relevant here, especially for the “systematic exploration” of Pythagoras’ theorem. I thought it was a joke as a student when we had to do “experimental verification” of Pythagoras’ theorem on tests, but I presume it’ll be even more of a joke if the measurement is done digitally.

    I could imagine a conversation going as follows:

    Jimmy: Teacher, how does the computer measure the hypotenuse?

    Teacher: Jimmy, it uses Pythagoras’ theorem.

    Jimmy: How do we know Pythagoras’ theorem is true?

    Teacher: Jimmy, well look here, if you measure the hypotenuse using your calculator, you can see its square is the sum of the squares of the other sides!

    “using examples such as \boldsymbol{\color{OliveGreen}\frac{3^{4}}{3^4}=1} and \boldsymbol{\color{OliveGreen} 3^{4-4} = 3^0} to illustrate the necessity that for any non-zero natural number \boldsymbol{\color{OliveGreen} n}, \boldsymbol{\color{OliveGreen} n^0 = 1} (AC9M8N02)”

    I don’t see how this illustrates “necessity” in any way. Proof by example is not an example of proof.

    You could also just as well define a^b such that a^0 = 7, or whatever, changing the other rules as you see fit. I wonder what a teacher following the curriculum would say to that.

  5. This one is interesting (as in I’m genuinely interested in whether or not any school will bother with this because I cannot make much sense of it from an “actually teaching this crap” perspective)

    “design, test and refine algorithms involving a sequence of steps and decisions based on geometric constructions and theorems; discuss and evaluate refinements”

  6. This one caught my eye:

    “comparing and ordering fractions by placing cards on a string line across the room”

    Who thinks of these things? Another supreme WTF moment. Imaging a teacher teaching fractions by not using a string across the room – could the school then be sued because of improper teaching? But really, this is absurdity of a high order. Where are Spike Milligan, John Cleese, when you need them?

    Teacher: “So, children, I’m going to compare fractions 5/8 and 1/2 by marking them on these cards, and putting the cards on this string with the other cards.”
    Marko: “Why are you using a string?”
    Teacher: “So I can show you how to compare fractions.”
    Julie: “Why are you putting the cards there?”
    Teacher: “Because – RILEY: STOP PULLING THE STRING, YOU MADE ALL THE CARDS MOVE!”
    Benji: “Does it matter?”
    Teacher “Of course it matters! … now I’ve got to put them all back in place again.”
    Riley: “I don’t understand any of this. Can I go to the toilet?”
    Teacher: “No! You went half an hour ago.”
    Riley: “But I need to go AGAIN!” [Pulls string]
    Teacher (defeated): “OK, go.”

    1. Very funny!

      To be fair, that is an elaboration and so it is optional (just like least common multiples and highest common factors). But I agree: who the hell thinks up these ridiculous options? Who proofreads them and says “Yep, that works”?

  7. Such an embarrassment of riches for the critic! But here’s one: “investigating the golden ratio in art and design”.

    This shows that the creators of this document are non-mathematicians who have been led astray by crack-pottery that has all the shrill nonsense of a conspiracy theory. The fact is that aside from a very few people who have used it deliberately (Le Corbusier did, I believe), it is no more special or particular or wonderful than any other ratio. Most “uses” of the golden ratio are just wishful thinking, or a sort of geometric pareidolia. In other words, crap.

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