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, Measurement, Space, Statistics

**Year 1:** Number, Algebra, Measurement, Space, Statistics

**Year 2:** Number, Algebra, Measurement, Space, Statistics

**Year 3: Number**, Algebra, Measurement, Space, Statistics, Probability*

**Year 4: Number**, Algebra, Measurement, Space, Statistics, Probability

**Year 5: Number**, Algebra, Measurement, Space, Statistics, Probability

**Year 6:** Number, Algebra, Measurement, Space, Statistics, Probability

**Year 7:** Number, Algebra, Measurement, Space, Statistics, Probability

**Year 8:** Number, Algebra, Measurement, Space, Statistics, Probability

**Year 9: Number, Algebra**, Measurement, Space, Statistics, Probability

**Year 10: Number**, Algebra, Measurement, Space, Statistics, Probability

**Year 10 Optional:** Number, Algebra, Measurement, Space, Measurement, Statistics, Probability

*) The Probability strand begins in Year 3.

## 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)

## 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)

## Foundation Measurement

*identify and compare attributes of objects and events, including length, capacity, mass and duration, using direct comparisons and communicating reasoning* (AC9MFM01) (07/10/22)

*starting 2 events at the same time to decide which takes longer; for example, putting on a pair of sandals with buckles or Velcro, describing the duration using familiar terms and reasoning, “I took a longer time because I’m still learning to do up my buckles” * (AC9MFM01) (07/10/22)

*directly comparing pairs of everyday objects from the kitchen pantry to say which is heavier/lighter; for example, hefting a tin of baked beans and a packet of marshmallows; comparing the same pair of objects to say which is longer/shorter and discussing comparisons *(AC9MFM01) (07/10/22)

## Foundation Space

*describing and naming shapes within objects that can be observed on Country/Place, recreating and sorting into groups based on their shape* (AC9MFSP01) (20/10/22)

*describe the position and location of themselves and objects in relation to other people and objects within a familiar space* (AC9MFSP02) (20/10/22)

*describing where they have moved themselves and items in relation to other items within a space, using familiar terms; for example, playing a hiding game and when asked “Where did you hide the ball?”, responding, “I hid it behind the garbage bin over there near the bench”* (AC9MFSP02) (20/10/22)

*exploring First Nations Australians’ instructive games; for example, Thapumpan from the Wik-Mungkan Peoples of Cape Bedford in north Queensland, describing position and movement of self in relation to other participants, objects or locations* (AC9MFSP02) (20/10/22)

## Foundation Statistics

*collect, sort and compare data represented by objects and images in response to given investigative questions that relate to familiar situations* (AC9MFST01) (03/11/22)

*creating classroom charts and rosters using stickers to represent data; comparing and interpreting representations* (AC9MFST01) (03/11/22)

*exploring what and how information from the environment is collected and used by First Nations Australians to predict weather events* (AC9MFST01) (03/11/22)

## 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)

## 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)

## Year 1 Measurement

*investigating situations where First Nations Australians estimate, compare and communicate measurements; for example, the duration of seasons; understanding animal behaviour using the length of animal tracks; investigating capacity through water management techniques of First Nations Australians, such as traditional water carrying vessels and rock holes* (AC9M1M01) (08/10/22)

*measure the length of shapes and objects using informal units, recognising that units need to be uniform and used end-to-end* (AC9M1M02) (08/10/22)

*comparing the length of 2 objects such as a desk and a bookshelf by laying multiple copies of a unit and counting to say which is longer and how much longer; explaining why they shouldn’t have gaps or overlaps between the units as this will change the length of the unit** * (AC9M1M02) (08/10/22)

## Year 1 Space

*selecting a shape from a small collection of shapes inside a bag and describing the shape by feel, so that others can name the shape and give reasons for their choice* (AC9M1SP01) (21/10/22)

*comparing the different objects that can be built out of the same number of blocks or centi-cubes and discussing the differences between them* (AC9M1SP01) (21/10/22)

*exploring string games used in story telling by First Nations Australians; for example, Karda from the Yandruwandha Peoples of north-east South Australia, recognising, comparing, describing and classifying the shapes made by the string and their relationship to shapes and objects on Country/Place* (AC9M1SP01) (21/10/22)

*give and follow directions to move people and objects to different locations within a space* (AC9M1SP02) (21/10/22)

*creating and following an algorithm consisting of a set of instructions to move an object to a different location; for example, role-playing being a robot and following step-by-step instructions given by another classmate to move from one place to another, only moving as instructed* (AC9M1SP02) (21/10/22)

*following directions to move people into different positions within a line using both ordinal and positional language to describe their position; for example, directly comparing heights and following directions using ordinal and positional language to line up in height order* (AC9M1SP02) (21/10/22)

*describing a familiar journey across Country/Place using directional language* (AC9M1SP02) (21/10/22)

## Year 1 Statistics

*discussing methods of collecting data to answer a question, such as “What types of rubbish are found in the playground?”, sharing ideas and trying out some of the suggested methods; reviewing the data collected and explaining how they might change the way they collect data next time* (AC9M1ST01) (04/11/22)

*exploring ways of representing, sharing and communicating data through stories and symbols used by First Nations Australians* (AC9M1ST01) (04/11/22)

*represent collected data for a categorical variable using one-to-one displays and digital tools where appropriate; compare the data using frequencies and discuss the findings* (AC9M1ST02) (04/11/22)

*translating data from a list or pictorial display into a tally chart to make counting easier; describing what the tally chart is showing, by referring to the categories; using skip counting by fives to compare the numbers within each category and explaining how the tally chart answers the question* (AC9M1ST02) (04/11/22)

*representing data with objects and drawings where one object or drawing represents one data value; describing the displays and explaining patterns that have been created using counting strategies to determine the frequency of responses* (AC9M1ST02) (04/11/22)

*exploring First Nations Australian children’s instructive games; for example, Kolap from Mer Island in the Torres Strait region, recording the outcomes, representing and discussing the results* (AC9M1ST02) (04/11/22)

## 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)

## 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)

## Year 2 Measurement

*measure and compare objects based on length, capacity and mass using appropriate uniform informal units and smaller units for accuracy when necessary* (AC9M2M01) (09/10/22)

*recognising that the same informal unit needs to be used when measuring; for example, demonstrating and discussing why using different shoe lengths to measure the same distance could result in the measures being different; discussing why a smaller sized informal unit may result in a larger number of units compared to a larger informal unit* (AC9M2M02) (09/10/22)

*recognising that halves and quarters can be used to describe lengths, positions and distances; for example, describing the halfway point in a race or instructing someone to stand halfway between the 2 chairs* (AC9M2M02) (09/10/22)

*using addition and a calendar to model and solve the problem “How many days there are in left in this year?” by identifying the number days left in this month and in each of the remaining months, and using addition to model and solve the problem* (AC9M2M03) (09/10/22)

*creating an analog clock from a paper plate, showing the placement of the numbers and the 2 hands; explaining how long it takes for the 2 hands to move around the clock face and what time unit each is showing *(AC9M2M04) (09/10/22)

## Year 2 Space

*sorting a collection of shapes in different ways based on their features such as number of sides, whether all sides are equal, whether pairs of opposite sides are parallel; for example, collections of triangles and other polygons* (AC9M2SP01) (22/10/22)

*manipulating shapes and recognising that different orientations do not change the shape; for example, cutting out pictures of various shapes, recognising they are they are still classified as the same shape even if they are upside down or on their side* (AC9M2SP01) (22/10/22)

*creating regular shapes using digital tools, describing and observing what happens when you manipulate them; for example, dragging or pushing vertices to produce irregular shapes, moving or rotating a shape* (AC9M2SP01) (22/10/22)

*locate positions in two-dimensional representations of a familiar space; move positions by following directions and pathways* (AC9M2SP02) (22/10/22)

*understanding that we use maps, to receive and give directions and to describe place and spatial relationships between places* (AC9M2SP02) (22/10/22)

*using a classroom seating plan to locate a new seating position and giving directions to other classmates to find their seats* (AC9M2SP02) (22/10/22)

*following and creating movement instructions that need to be carried out to move through a 4 x 4 grid mat on the classroom floor or on a computer screen; for example, one forward, 2 to the right and one backwards, and so on to reach a target square; using a robotic toy to follow a path on a street scene on a floor mat, adjusting their directions as they consider the order of their instructions, the direction and how far they want the toy to travel* (AC9M2SP02) (22/10/22)

## Year 2 Statistics

*acquire data for categorical variables through surveys, observation, experiment and using digital tools; sort data into relevant categories and display data using lists and tables* (AC9M2ST01) (05/11/22)

*using familiar software to construct a survey to collect class data; sorting and interpreting responses; and considering the questions asked and whether they need to be modified to reuse the survey* (AC9M2ST01) (05/11/22)

*exploring the ways First Nations Australians observe, collect, sort and record data* (AC9M2ST01) (05/11/22)

*create different graphical representations of data using software where appropriate; compare the different representations, identify and describe common and distinctive features in response to questions* (AC9M2ST02) (05/11/22)

*using digital tools to create picture graphs to represent data using one-to-one correspondence, deciding on an appropriate title for the graph and considering whether the categories of data are appropriate for the context* (AC9M2ST02) (05/11/22)

## 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)

## 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 for 3, 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)

## Year 3 Measurement

*estimating how long it would take to read a set passage of text, and sharing this information to demonstrate understanding of formal units of duration of time* (AC9M3M03) (10/10/22)

*exploring how cultural accounts of First Nations Australians explain cycles of time that involve the sun, moon and stars* (AC9M3M03) (10/10/22)

*describe the relationship between the hours and minutes on analog and digital clocks, and read the time to the nearest minute* (AC9M3M04) (10/10/22)

*using quarter, half and three-quarter turns and comparing them to a right angle; for example, a quarter turn is the same as a right angle; a half a turn is greater than a right angle and is the same as 2 right angles; a three-quarter turn is greater than a right angle and is the same as 3 right angles* (AC9M3M05) (10/10/22)

*exploring First Nations Australian children’s instructive games to investigate angles as measures of turn; for example, the game Waayin from the Datiwuy People in the northern part of the Northern Territory* (AC9M3M05) (10/10/22)

*investigating the relationship between dollars and cents, using physical or virtual materials to make different combinations of the same amount of money* (AC9M3M06) (10/10/22)

## Year 3 Space

*make, compare and classify objects, identifying key features and explaining why these features make them suited to their uses *(AC9M3SP01) (23/10/22)

*making and comparing objects built out of cubic blocks and discussing key features; for example, comparing the amount of space objects occupy by counting how many blocks it takes to build different rectangular prisms that have the same height but different bases* (AC9M3SP01) (23/10/22)

*making geometric objects in solid form out of connecting cubes, in skeleton form with straws, and constructing objects using dynamic geometric software, recognising, comparing and discussing the features of the objects using the different representations* (AC9M3SP01) (23/10/22)

*using familiar shapes and objects to build or construct models and compare the suitability of different shapes and objects for aspects of the model; for example, building rectangular towers out of connecting cubes and recognising that the taller the tower, the less stable it becomes unless the base is increased; building bridges out of straws bent into different shapes and comparing the strength of different designs* (AC9M3SP01) (23/10/22)

*identifying, classifying and comparing common objects found on Country/Place as cubes, rectangular prisms, cylinders, cones and spheres* (AC9M3SP01) (23/10/22)

*investigating and explaining how First Nations Australians’ dwellings are oriented in the environment to accommodate climatic conditions* (AC9M3SP01) (23/10/22)

*interpret and create two-dimensional representations of familiar environments, locating key landmarks and objects relative to each other* (AC9M3SP02) (23/10/22)

*sketching a map within the classroom indicating where they have hidden an object, swapping maps with partners and then providing feedback about what was helpful and what was confusing in the map* (AC9M3SP02) (23/10/22)

*exploring land maps or cultural maps used by First Nations Australians to locate, identify and position important landmarks such as waterholes* (AC9M3SP02) (23/10/22)

## Year 3 Statistics

*acquire data for categorical and discrete numerical variables to address a question of interest or purpose by observing, collecting and accessing data sets; record the data using appropriate methods including frequency tables and spreadsheets* (AC9M3ST01) (06/11/22)

*using efficient ways to collect and record data; for example, written surveys, online surveys, polling the class using interactive digital mediums, and representing and reporting the results of investigations* (AC9M3ST01) (06/11/22)

*using lists, tallies, symbols and digital data tables to record and display data collected during a chance experiment for interpretation* (AC9M3ST01) (06/11/22)

*using different online sources to access data; for example, using online query interfaces to select and retrieve data from an online database such as weather records, Google Trends or the World Health Organization* (AC9M3ST01) (06/11/22)

*using software to sort and calculate data when solving problems; for example, sorting discrete numerical and categorical data in ascending or descending order and automating simple arithmetic calculations using nearby cells and the Sum function in spreadsheets to calculate total frequencies of collected data* (AC9M3ST01) (06/11/22)

*create and compare different graphical representations of data sets including using software where appropriate; interpret the data in terms of the context (AC9M3ST02create and compare different graphical representations of data sets including using software where appropriate; interpret the data in terms of the context* (AC9M3ST02) (06/11/22)

*using digital tools and graphing software to construct graphs of data acquired through experiments or observation and interpreting the data and making inferences; for example, graphing data from a science experiment and interpreting the results* (AC9M3ST03) (06/11/22)

*conducting a whole class statistical investigation into the best day to hold an open day for parents by creating a simple survey; collecting the data by asking the parents, representing and interpreting the results, and deciding as a class which day would be best* (AC9M3ST03) (06/11/22)

*investigating seasonal calendars of First Nations Australians by collecting data and creating frequency tables and spreadsheets based on environmental indicators; creating one-to-one data displays about frequency of environmental indicators for the current season* (AC9M3ST03) (06/11/22)

## Year 3 Probability

*identify practical activities and everyday events involving chance; describe possible outcomes and events as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ explaining reasoning* (AC9M3P01) (20/10/22)

*classifying a list of everyday events or sorting a set of event cards according to how likely they are to happen, using the language of chance and giving reasons for classifications; discussing how impossible outcomes cannot ever happen, uncertain outcomes are affected by chance as they may or may not happen whereas certain events must always happen, so they are not affected by chance *(AC9M3P01) (20/10/22)

*making predictions and testing what would happen; for example, if 10 names were put in a box, and names were then drawn out one at a time and replaced after each selection, discussing how likely it would be after 10 selections that all 10 names were drawn from the box or that one name was drawn multiple times *(AC9M3P01) (20/10/22)

*conduct repeated chance experiments; identify and describe possible outcomes, record the results, recognise and discuss the variation *(AC9M3P02) (20/10/22)

*identifying the possible outcomes of a chance experiment, creating a tally chart to record results carrying out a few trials, and tallying the results for each trial; responding to the questions: “How did your results vary for each trial?” and “How do the results vary across the class?” (*AC9M3P02) (20/10/22)

*conducting repeated trials of chance experiments such as tossing a coin, throwing a dice, drawing a coloured or numbered ball from a bag, using a coloured spinner with equal partitions, and identifying the variation in the number of heads/fives/reds between trials *(AC9M3P02) (20/10/22)

## 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)

## Year 4 Algebra

*find unknown values in numerical equations involving addition and subtraction, using the properties of numbers and operations* (AC9M4A01) (26/09/22)

*demonstrating the commutative properties of addition using materials, diagrams and number lines; for example, using number lines to demonstrate that 5 + 2 = 2 + 5, demonstrating that 2 + 2 + 3 = 7 and 2 + 3 + 2 = 7 and 3 + 2 + 2 = 7* (AC9M4A01) (26/09/22)

*using balance scales and informal uniform units to create addition or subtraction number sentences showing equivalence, such as 7 + 8 = 6 + 9, and to find unknowns in equivalent number sentences, such as 6 + 8 = □ + 10* (AC9M4A01) (26/09/22)

*using relational thinking and knowledge of equivalent number sentences to explain whether equations involving addition or subtraction are true; for example, explaining that 27 – 14 = 17 – 4 is true and using a number line to show the common difference is 13* (AC9M4A01) (26/09/22)

*using part-part-whole diagrams or bar models to recognise and explain the inverse relationship between addition and subtraction, using this to make calculations easier; for example, solving 27 + □ = 63 using subtraction, □ = 63 – 27* (AC9M4A01) (26/09/22)

*using arrays on grid paper or created with blocks or counters to develop, represent and explain patterns in the 10 x 10 multiplication facts; using the arrays to explain the related division facts *(AC9M4A02) (26/09/22)

*using materials or diagrams to develop and record multiplication strategies such as doubling, halving, commutativity, and adding one more or subtracting from a group to reach a known fact; for example, creating multiples of 3 on grid paper and doubling to find multiples of 6; recording and explaining the connections to the x3 and x6 multiplication facts: 3, 6, 9, … doubled is 6, 12, 18, …* (AC9M4A02) (26/09/22)

*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)* *(26/09/22)

*using arrays and known multiplication facts for twos and fives to develop the multiplication facts for sevens, applying the distributive property of multiplication; for example, when finding 6 x 7, knowing that 7 is made up of 2 and 5, and using an array to show that 6 x 7 is the same as 6 x 2 + 6 x 5 = 12 + 30 which is 42 *(AC9M4A02)* *(26/09/22)

## Year 4 Measurement

*recognise ways of measuring and approximating the perimeter and area of shapes and enclosed spaces, using appropriate formal and informal units *(AC9M4M02) (11/10/22)

*creating a range of rectangles representing “paddocks” on grid paper and establishing different methods of working out the length of the boundary fences; explaining that the more efficient methods involve adding the side lengths rather than counting squares* (AC9M4M02) (11/10/22)

*recognising that area is the space enclosed by the boundary of a shape or the surface of an object; measuring and comparing the area of shapes, using an array of paper tiles or mosaic squares, including part units to fill gaps at the edge of the shapes; comparing the total areas by combining the fractional parts to make whole units* (AC9M4M02) (11/10/22)

*investigating the ways First Nations Ranger Groups and other groups measure areas of land to make decisions about fire burns to care for Country/Place* (AC9M4M02) (11/10/22)

*estimate and compare angles using angle names including acute, obtuse, straight angle, reflex and revolution, and recognise their relationship to a right angle* (AC9M4M04) (11/10/22)

## Year 4 Space

*represent and approximate composite shapes and objects in the environment, using combinations of familiar shapes and objects* (AC9M4SP01) (24/10/22)

*identifying common shapes that form part of a composite shape by re-creating these shapes using physical or virtual materials* (AC9M4SP01) (24/10/22)

*physically or virtually using cubes to make three-dimensional models that approximate real objects; for example, building a virtual environment by using a computer software program to construct objects out of cubes* (AC9M4SP01) (24/10/22)

*recognising that a spreadsheet uses a grid reference system, locating and entering data in cells and using a spreadsheet to record data collected through observations or experiments *(AC9M4SP02) (24/10/22)

*comparing and contrasting, describing and locating landmarks, people or things in a bird’s eye picture of a busy scene, such as people in a park, initially without a transparent grid reference system overlaid on the picture, and then with the grid overlaid; noticing how the grid helps to pinpoint things quickly and easily* (AC9M4SP02) (24/10/22)

*recognise line and rotational symmetry of shapes and create symmetrical patterns and pictures, using dynamic geometric software where appropriate* (AC9M4SP03) (24/10/22)

*using dynamic geometric software to manipulate shapes and create symmetrical patterns; for example, creating tessellation patterns that are symmetrical* (AC9M4SP03) (24/10/22)

*exploring the natural environment on Country/Place to investigate and discuss patterns and symmetry of shapes and objects such as in flowers, plants and landscapes* (AC9M4SP03) (24/10/22)

## Year 4 Statistics

*acquire data for categorical and discrete numerical variables to address a question of interest or purpose using digital tools; represent data using many-to-one pictographs, column graphs and other displays or visualisations; interpret and discuss the information that has been created* (AC9M4ST01) (07/11/22)

*investigating many-to-one data displays using digital tools and graphical software, interpreting and discussing key features* (AC9M4ST01) (07/11/22)

*acquiring samples of data using practical activities, observations or repeated chance experiments, recording data using tally charts, digital tables or spread sheets, graphing, discussing and comparing the results using a column graph* (AC9M4ST01) (07/11/22)

*using secondary data of fire burns to construct data displays that assist First Nations Ranger Groups and other groups to care for Country/Place* (AC9M4ST01) (07/11/22)

*interpreting data representations in the media and other forums where symbols represent one-to-many relationships and how this can be challenging when the representations use part-whole representations* (AC9M4ST02) (07/11/22)

*conduct statistical investigations, collecting data through survey responses and other methods; record and display data using digital tools; interpret the data and communicate the results* (AC9M4ST03) (07/11/22)

*creating a survey to collect class responses to a preferred movie choice, and recording data responses using spreadsheets; graphing data using a column graph or other appropriate representations and interpreting the results of the survey reporting findings back to the class* (AC9M4ST03) (07/11/22)

*investigating different contexts in which statistical investigations can take place and the types of questions to ask to collect data relevant to the context; for example, investigating supermarket customer complaints that breakfast cereals with the most sugar are positioned at children’s eye level, discussing what questions they would need to ask and answer* (AC9M4ST03) (07/11/22)

## Year 4 Probability

*using lists of events familiar to students and ordering them from “least likely” to “most likely” to occur; considering and discussing why the order of some events might be different for different students* (AC9M4P01) (19/11/22)

*predicting the outcome of a coin toss after 5 heads have been flipped in a row, discussing the assertion that because so many heads came up, it is more likely that a tail rather than a head will come up next; discussing with reasons why the assumption is correct or incorrect* (AC9M4P01) (19/11/22)

*predicting how likely , from least likely to most likely, of selecting a red ball from a bag containing 10 red balls and 5 white balls, a bag containing 20 of each, or one that has 25 red balls and 20 white balls, justifying their decision *(AC9M4P01) (19/11/22)

*identifying school activities where the chance of them taking place is affected by the chance of other events occurring; for example, given that there is a high chance of a storm on Friday, there is only a small chance that the coastal dune planting project will go ahead *(AC9M4P01) (19/11/22)

*listing the outcomes of everyday chance situations and identifying where one cannot happen if the other happens; for example, discussing that it cannot be hot and cold at the same time; selecting a card from a deck and discussing if it is red it cannot be a spade or a club *(AC9M4P01) (19/11/22)

*conduct repeated chance experiments to observe relationships between outcomes; identify and describe the variation in results* (AC9M4P02) (19/11/22)

*playing games such as Noughts and Crosses or First to 20 and deciding if it makes a difference who goes first and whether you can use a particular strategy to increase your chances of winning* (AC9M4P02) (19/11/22)

*recording and ordering the outcomes of experiments using different physical or virtual random generators such as coins, dice and a variety of spinners (*AC9M4P02) (19/11/22)

*experimenting with tossing 2 coins at the same time, recording and commenting on the chance of outcomes after a number of tosses *(AC9M4P02) (19/11/22)

*shuffling a set of cards, drawing a card at random, and recording whether it was a spade, club, diamond or heart, picture card or numbered; repeating the experiment a number of times and discussing the results *(AC9M4P02) (19/11/22)

## 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 on a fraction wall represents the area of one-quarter of the whole while on the number line 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 is located at the same position on a parallel number line as because is equivalent to ** *(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 , and ; 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* cup of flour and a cup of flour, subtracting of a metre from * 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, is the same as* (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)

## Year 5 Algebra

*using materials or diagrams to develop and explain division strategies, such as halving, using the inverse relationship to turn division into a multiplication* (AC9M5A01) (27/09/22)

*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) (27/09/22)

*demonstrating multiplicative partitioning using materials, diagrams or arrays and recording 2 multiplication and 2 division facts for each grouping; 4 x 6 = 24, 6 x 4 = 24, 24 ÷ 4 = 6 and 24 ÷ 6 = 4; explaining how each is different from and connected to groups in the materials, diagrams or arrays* (AC9M5A01) (27/09/22)

*using materials, diagrams or arrays to recognise and explain the inverse relationship between multiplication and division; for example, solving 240 ÷ 20 = □ by thinking 20 x □ = 240; using the inverse to make calculations easier; for example, solving 17 x □ = 221 using division, □ = 221 ÷ 17* (AC9M5A01) (27/09/22)

*find unknown values in numerical equations involving multiplication and division using the properties of numbers and operations* (AC9M5A02) (27/09/22)

*using knowledge of equivalent number sentences to form and find unknown values in numerical equations; for example, given that 3 x 5 = 15 and 30 ÷ 2 = 15 then 3 x 5 = 30 ÷ 2 therefore the solution to 3 x 5 = 30 ÷ □ is 2* (AC9M5A02) (27/09/22)

*using relational thinking, an understanding of equivalence and number properties to determine and reason about numerical equations; for example, explaining whether an equation involving equivalent multiplication number sentences is true, such as 15 ÷ 3 = 30 ÷ 6* (AC9M5A02) (27/09/22)

*using materials, diagrams and arrays to demonstrate that multiplication is associative and commutative but division is not; for example, using arrays to demonstrate that 2 x 3 = 3 x 2 but 6 ÷ 3 does not equal 3 ÷ 6; demonstrating that 2 x 2 x 3 = 12 and 2 x 3 x 2 = 12 and 3 x 2 x 2 = 12; understanding that 8 ÷ 2 ÷ 2 = (8 ÷ 2) ÷ 2 = 2 but 8 ÷ (2 ÷ 2) = 8 ÷ 1 = 8* (AC9M5A02) (27/09/22)

*constructing equivalent number sentences involving multiplication to form a numerical equation, and applying knowledge of factors, multiples and the associative property to find unknown values in numerical equations; for example, considering 3 x 4 = 12 and knowing 2 x 2 = 4 then 3 x 4 can be written as 3 x (2 x 2) and using the associative property (3 x 2) x 2 so 3 x 4 = 6 x 2 and so 6 is the solution to 3 x 4 = □ x 2* (AC9M5A02) (27/09/22)

## Year 5 Measurement

*choose appropriate metric units when measuring the length, mass and capacity of objects; use smaller units or a combination of units to obtain a more accurate measure* (AC9M5M01) (12/10/22)

*recognising that some units of measurement are better suited to some tasks than others; for example, kilometres are more appropriate than metres to measure the distance between 2 towns* (AC9M5M01) (12/10/22)

*deciding on the unit required to estimate the amount of paint or carpet for a room or a whole building; justifying the choice of unit in relation to the context and the degree of accuracy required* (AC9M5M01) (12/10/22)

*using a physical or a virtual “geoboard app” to recognise the relationship between area and perimeter and solve problems; for example, investigating what is the largest and what is the smallest area that has the same perimeter* (AC9M5M02) (12/10/22)

*exploring the designs of fishing nets and dwellings of First Nations Australians, investigating the perimeter, area and purpose of the shapes within the designs* (AC9M5M02) (12/10/22)

*recognising the size of angles within shapes that do and do not tesselate, measuring the angles and using the sum of angles to explain why some shapes will tesselate and other shapes do not* (AC9M5M04) (12/10/22)

## Year 5 Space

*connect objects to their nets and build objects from their nets using spatial and geometric reasoning* (AC9M5SP01) (25/10/22)

*designing and constructing exact nets for packaging particular shaped items or collections of interest, taking into consideration how the faces will be joined and how the package will be opened* (AC9M5SP01) (25/10/22)

*visualising folding some possible nets for a range of prisms and pyramids, predicating *[sic] *which will work and which cannot work, and justifying their choices, based on the number, size and position of particular shapes in each diagram* (AC9M5SP01) (25/10/22)

*investigating objects designed and developed by First Nations Australians, such as those used in fish traps and instructive toys, identifying the shape and relative position of each face to determine the net of the object* (AC9M5SP01) (25/10/22)

*construct a grid coordinate system that uses coordinates to locate positions within a space; use coordinates and directional language to describe position and movement* (AC9M5SP02) (25/10/22)

*comparing a grid reference system to a grid coordinate system (first quadrant only) by using both to play strategy games involving location; for example, “Quadrant Commander”, deducing that in a grid coordinate system the lines are numbered (starting from zero), not the spaces* (AC9M5SP02) (25/10/22)

*placing a coordinate grid over a contour line, drawing and listing the coordinates of each point in the picture, asking a peer to re-create the drawing using only the list of coordinates, and discussing the reasons for the potential similarities and differences between the 2 drawings* (AC9M5SP02) (25/10/22)

*describe and perform translations, reflections and rotations of shapes, using dynamic geometric software where appropriate; recognise what changes and what remains the same, and identify any symmetries* (AC9M5SP03) (25/10/22)

*understanding and explaining that translations, rotations and reflections can change the position and orientation of a shape but not the shape or size* (AC9M5SP03) (25/10/22)

*investigating how animal tracks can be interpreted by First Nations Australians using the transformation of their shapes to help determine and understand animal behaviour* (AC9M5SP03) (25/10/22)

## Year 5 Statistics

*acquire, validate and represent data for nominal and ordinal categorical and discrete numerical variables to address a question of interest or purpose using software including spreadsheets; discuss and report on data distributions in terms of highest frequency (mode) and shape, in the context of the data* (AC9M5ST01) (08/11/22)

*using digital systems to validate data; for example, recognising the difference between numerical, text and date formats in spreadsheets; setting data types in a spreadsheet to make sure a date is input correctly* (AC9M5ST01) (08/11/22)

*investigating data relating to Australia’s reconciliation process with First Nations Australians, posing questions, discussing and reporting on findings* (AC9M5ST01) (08/11/22)

*interpret line graphs representing change over time; discuss the relationships that are represented and conclusions that can be made* (AC9M5ST02) (08/11/22)

*reading and interpreting different line graphs, discussing how the horizontal axis represents measures of time such as days of the week or times of the day, and the vertical axis represents numerical quantities or ordinal categorical variables such as percentages, money, measurements or ratings such as fire hazard ratings* (AC9M5ST02) (08/11/22)

*matching unlabelled line graphs to the context they represent based on the stories of the different contexts* (AC9M5ST02) (08/11/22)

*developing survey questions that are objective, without opinion and have a balanced set of answer choices without bias* (AC9M5ST03) (08/11/22)

*exploring First Nations Ranger Groups’ and other groups’ biodiversity detection techniques to care for Country/Place, posing investigative questions, collecting and interpreting related data to represent and communicate findings* (AC9M5ST03) (08/11/22)

## Year 5 Probability

*list the possible outcomes of chance experiments involving equally likely outcomes and compare to those which are not equally likely* (AC9M5P01) (21/11/22)

*discussing what it means for outcomes to be equally likely and comparing the number of possible and equally likely outcomes of chance events; for example, when drawing a card from a standard deck of cards there are 4 possible outcomes if you are interested in the suit, 2 possible outcomes if you are interested in the colour or 52 outcomes if you are interested in the exact card *(AC9M5P01) (21/11/22)

*discussing how chance experiments that have equally likely outcomes can be referred to as random chance events; for example, if all the names of students in a class are placed in a hat and one is drawn at random, each person has an equally likely chance of being drawn *(AC9M5P01) (21/11/22)

*commenting on the chance of winning games by considering the number of possible outcomes and the consequent chance of winning* (AC9M5P01) (21/11/22)

*investigating why some games are fair and others are not; for example, drawing a track game to resemble a running race and taking it in turns to roll 2 dice, where the first runner moves a square if the difference between the 2 dice is zero, one or 2 and the second runner moves a square if the difference is 3, 4 or 5; responding to the questions, “Is this game fair?”, “Are some differences more likely to come up than others?” and “How can you work that out?” *(AC9M5P01) (21/11/22)

*comparing the chance of a head or a tail when a coin is tossed, whether some numbers on a dice are more likely to be facing up when the dice is rolled, or the chance of getting a 1, 2 or 3 on a spinner with uneven regions for the numbers *(AC9M5P01) (21/11/22)

*discussing supermarket promotions such as collecting stickers or objects and whether there is an equal chance of getting each of them *(AC9M5P01) (21/11/22)

*conduct repeated chance experiments including those with and without equally likely outcomes, observe and record the results ; use frequency to compare outcomes and estimate their likelihoods *(AC9M5P02) (22/11/22)

*discussing and listing all the possible outcomes of an activity and conducting experiments to estimate the probabilities; for example, using coloured cards in a card game and experimenting with shuffling the deck and turning over one card at a time, recording and discussing the result *(AC9M5P02) (22/11/22)

*conducting experiments, recording the outcomes and the number of times the outcomes occur, describing the relative frequency of each outcome; for example, using “I threw the coin 10 times, and the results were 3 times for a head, so that is 3 out of 10, and 7 times for a tail, so that is 7 out of 10” *(AC9M5P02) (22/11/22)

*experimenting with and comparing the outcomes of spinners with equal-coloured regions compared to unequal regions; responding to questions such as “How does this spinner differ to one where each of the colours has an equal chance of occurring?”, giving reasons *(AC9M5P02) (22/11/22)

*comparing the results of experiments using a fair dice and one that has numbers represented on faces more than once, explaining how this affects the likelihood of outcomes *(AC9M5P02) (22/11/22)

*using spreadsheets to record the outcomes of an activity and calculate the total frequencies of different outcomes, representing these as a fraction; for example, using coloured balls in a bag, drawing one out at a time and recording the colour, replacing them in the bag after each draw *(AC9M5P02) (22/11/22)

*investigating First Nations Australian children’s instructive games; for example, Diyari koolchee from the Diyari Peoples near Lake Eyre in South Australia, to conduct repeated trials and explore predictable patterns, using digital tools where appropriate *(AC9M5P02) (22/11/22)

## 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, is greater than can be written as , because half of 8 is 4; is less than , because 6>4 and can be written as * (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 , 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 of 180 or 52% is about a *(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)

## Year 6 Algebra

*recognise and use rules that generate visually growing patterns and number patterns involving rational numbers* (AC9M6A01) (28/09/22)

*using a calculator or spreadsheet to experiment with number patterns that result from multiplying or dividing; for example, 1 ÷ 9, 2 ÷ 9, 3 ÷ 9…, 210 x 11, 211 x 11, 212 x 11…, 111 x 11, 222 x 11, 333 x 11…, or 100 ÷ 99, 101 ÷ 99, 102 ÷ 99…* (AC9M6A01) (28/09/22)

*investigating the number of regions created by successive folds of a sheet of paper: one fold, 2 regions; 2 folds, 4 regions; 3 folds, 8 regions, and describing the pattern using everyday language* (AC9M6A01) (28/09/22)

*find unknown values in numerical equations involving brackets and combinations of arithmetic operations, using the properties of numbers and operations* (AC9M6A02) (28/09/22)

*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) (28/09/22)

*finding pairs of unknown values in numerical equations that make the equation hold true; for example, listing possible combinations of natural numbers that make this statement true: 6 + 4 x 8 = 6 x Δ + □* (AC9M6A02) (28/09/22)

*applying knowledge of inverse operations and number properties to create equivalent number sentences; removing one of the numbers and replacing it with a symbol, then swapping with a classmate to find the unknown values* (AC9M6A02) (28/09/22)

*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) (28/09/22)

*using an algorithm to create extended number sequences involving rational numbers, using a rule and digital tools, explaining any emerging patterns* (AC9M6A03) (28/09/22)

*designing an algorithm to model operations, using the concept of input and output, describing and explaining relationships and any emerging patterns; *for example, using function machines to model operations and *recognising and comparing additive and multiplicative relationships* (AC9M6A03) (28/09/22)

*designing an algorithm or writing a simple program to generate a sequence of numbers based on the user’s input and a chosen operation, discussing any emerging patterns; for example, generating a sequence of numbers and comparing how quickly the sequences are growing in comparison to each other using the rule adding 2 to the input number compared to multiplying the input number by 2* (AC9M6A03) (28/09/22)

## Year 6 Measurement

*convert between common metric units of length, mass and capacity; choose and use decimal representations of metric measurements relevant to the context of a problem* (AC9M6M01) (13/10/22)

*establish the formula for the area of a rectangle and use it to solve practical problems* (AC9M6M02) (13/10/22)

*using the relationship between the length and area of square units and the array structure to derive a formula for calculating the area of a rectangle from the lengths of its sides *(AC9M6M02) (13/10/22)

*using one centimetre grid paper to construct a variety of rectangles, recording the side lengths and the related areas of the rectangles in a table to establish the formula for the area of a rectangle by recognising the relationship between the length of the sides and its calculated area* (AC9M6M02) (13/10/22)

*solving problems involving the comparison of lengths and areas using appropriate units* (AC9M6M02) (13/10/22)

*investigating the connection between the perimeters of different rectangles with the same area and between the areas of rectangles with the same perimeter* (AC9M6M02) (13/10/22)

*using protractors or dynamic geometry software to measure and generalise about the size of angles formed when lines are crossed, and combinations of angles that meet at a point, including combinations that form right or straight angles* (AC9M6M03) (13/10/22)

*demonstrating the meaning of language associated with properties of angles, including right, complementary, complement, straight, supplement, vertically opposite, and angles at a point* (AC9M6M03) (13/10/22)

*using the properties of supplementary and complementary angles to represent spatial situations with number sentences and solving to find the size of unknown angles* (AC9M6M03) (13/10/22)

## Year 6 Space

*using different pieces of fruit, slicing across different cross-sections, drawing the cross-section; reporting back to the class the results of the investigation* (AC9M6SP01) (26/10/22)

*investigating the design of First Nations Australians’ dwellings, exploring the relationship between the cross-sections and the dwellings’ construction* (AC9M6SP01) (26/10/22)

*locate points in the 4 quadrants of a Cartesian plane; describe changes to the coordinates when a point is moved to a different position in the plane* (AC9M6SP02) (26/10/22)

*understanding that the Cartesian plane provides a graphical or visual way of describing location with respect to a fixed origin* (AC9M6SP02) (26/10/22)

*understanding that the axes are number lines that can have different scales, including fractions and decimals, depending on purpose* (AC9M6SP02) (26/10/22)

*using the Cartesian plane to draw lines and polygons, listing co-ordinates in the correct order to complete a polygon *(AC9M6SP02) (10/12/22)

*investigating and connecting land or star maps used by First Nations Australians with the Cartesian plane through a graphical or visual way of describing location* (AC9M6SP02) (26/10/22)

*recognise and use combinations of transformations to create tessellations and other geometric patterns, using dynamic geometric software where appropriate* (AC9M6SP03) (26/10/22)

*using digital tools to create tessellations of shapes, including paver and tiling patterns, describing the transformations used and discussing why these shapes tessellate; identifying shapes or combinations of shapes that will or will not tessellate, answering questions such as, “Do all triangles tessellate?”* (AC9M6SP03) (26/10/22)

*designing a school or brand logo using the transformation of one or more shapes and describing the transformations used* (AC9M6SP03) (26/10/22)

*using dynamic geometric software and digital tools to experiment with transformations; for example, to demonstrate when the order of transformations produces different results; experimenting with transformations and their application to fractals* (AC9M6SP03) (26/10/22)

*designing an algorithm as set of instructions to transform a shape, including getting back to where you started from; for example, programming a robot to move around the plane using instructions for movements, such as 2 down, 3 to the right, and combinations of these to transform shapes* (AC9M6SP03) (26/10/22)

*investigating symmetry, transformation and tessellation in different shapes on Country/Place, including rock formations, insects, and land and sea animals, discussing the purpose or role symmetry plays in their physical structure* (AC9M6SP03) (26/10/22)

## Year 6 Statistics

*interpret and compare data sets for ordinal and nominal categorical, discrete and continuous numerical variables using comparative displays or visualisations and digital tools; compare distributions in terms of mode, range and shape* (AC9M6ST01) (09/11/22)

*using technology to access data sets and graphing software to construct side-by-side column graphs or stacked line graphs; comparing data sets that are grouped by gender, year level, age group or other variables and discussing findings* (AC9M6ST01) (09/11/22)

*selecting and using appropriate peripherals; for example, using a scientific probe to collect data about changing soil moisture for plants, interpreting the data and sharing the results as a digital chart* (AC9M6ST03) (09/11/22)

*using a spreadsheet to record and analyse data, recognising the difference between cell formats in spreadsheets; for example, changing the default general format to numerical, text or date as needed* (AC9M6ST03) (09/11/22)

## Year 6 Probability

*listing the different possible outcomes for rolling a dice and using a scale to locate the relative probability by considering the chance of more or less than for each possible event ; for example, the probability of getting a number greater than 4* (AC9M6P01) (22/11/22)

*exploring First Nations Australian children’s instructive games, such as Weme from the Warlpiri Peoples of Central Australia, to investigate and assign probabilities that events will occur, indicating their estimated likelihood* (AC9M6P01) (22/11/22)

*conduct repeated chance experiments and run simulations with an increasing number of trials using digital tools; compare observations with expected results and discuss the effect on variation of increasing the number of trials* (AC9M6P02) (22/11/22)

*using digital tools to simulate multiple tosses of a coin or dice and comparing the relative frequency of an outcome as the number of trials increases; identifying the variation between trials and realising that the results tend to the prediction with larger numbers of trials* (AC9M6P02) (22/11/22)

*using online simulations of repeated random events to recognise emerging patterns, discussing and comparing expected results to the actual results* (AC9M6P02) (22/11/22)

## 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 is equivalent to and and therefore *(AC9M7N04) (12/09/22)

*applying and explaining the equivalence between fraction, decimal and percentage representations of rational numbers; for example, 16%, 0.16, and , 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 of giving of *(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 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)

## Year 7 Algebra

*recognise and use variables to represent everyday formulas algebraically and substitute values into formulas to determine an unknown* (AC9M7A01) (28/09/22)

*linking variables to attributes and measures being modelled when using formulas, such as the area of a rectangle is equal to the length x width as A = l x w; using p = 6g + b to describe a total of points expressed as goals (worth 6 points) and behinds (worth one point)* (AC9M7A01) (28/09/22)

*using **everyday formulas and their application to contexts on Country/Place, investigating the relationships between variables* (AC9M7A01) (28/09/22)

*formulate algebraic expressions using constants, variables, operations and brackets* (AC9M7A02) (28/09/22)

*recognising and applying the concept of variable as something that can change in value, investigating the relationships between variables, and the application to processes on Country/Place, including how cultural expressions of First Nations Australians, such as storytelling, communicate mathematical relationships that can be represented as mathematical expressions* (AC9M7A02) (28/09/22)

*solve one-variable linear equations with natural number solutions; verify the solution by substitution* (AC9M7A03) (29/09/22)

*solving equations using concrete materials, the balance model, and backtracking, explaining the process* (AC9M7A03) (29/09/22)

*describe relationships between variables represented in graphs of functions from authentic data* (AC9M7A04) (29/09/22)

*using graphs to analyse a building’s electricity or gas usage over a period of time, the value of shares on a stock market, or the temperature during a day, interpreting and discussing the relationships they represent* (AC9M7A04) (29/09/22)

using travel graphs to compare the distance travelled to and from school, interpreting and discussing features of travel graphs such as the slope of lines and the meaning of horizontal line segments (AC9M7A04) (29/09/22)

*using graphs of evaporation rates to explore and discuss First Nations Australians’ methods of water resource management* (AC9M7A04) (29/09/22)

## Year 7 Measurement

*solve problems involving the area of triangles and parallelograms using established formulas and appropriate units* (AC9M7M01) (14/10/22)

*using the formula for the area of a rectangle and the array structure to derive the formula for the area of a triangle and the area of a parallelogram, given their perpendicular heights; for example, establish that the area of a triangle is half the area of an appropriate rectangle by using the spatial relationship between rectangles and different types of triangle*s (AC9M7M01) (14/10/22)

*using dynamic geometry software to demonstrate how the sliding of the vertex of a triangle at a fixed altitude opposite a side leaves the area of the triangle unchanged* (AC9M7M01) (14/10/22)

*solve problems involving the volume of right prisms including rectangular and triangular prisms, using established formulas and appropriate units* (AC9M7M02) (14/10/22)

*building a rectangular prism out of unit cubes and showing that the measure of volume is the same as would be found by multiplying the 3 edge lengths or by multiplying the area of the base by the height/length* (AC9M7M02) (14/10/22)

*connecting the area of the floor space and the number of floors of a high-rise building to calculate the volume of a building* (AC9M7M02) (14/10/22)

*using dynamic geometry software, spatial reasoning and prediction to derive the formula for the volume of prisms* (AC9M7M02) (14/10/22)

*describe the relationship between π and the features of circles including the circumference, radius and diameter* (AC9M7M03) (14/10/22)

*recognising the features of circles and their relationships to one another; for example, labelling the parts of a circle including centre, radius, diameter, circumference and using one of radius, diameter or circumference to determine the measure of the other 2; understanding that the diameter of a circle is twice the radius, or that the radius is the circumference divided by 2π* (AC9M7M03) (14/10/22)

*investigating the applications and significance of circles in everyday life of First Nations Australians such as in basketry, symbols and architecture, recognising the relationships between the centre, radius, diameter and circumference* (AC9M7M03) (14/10/22)

*constructing a pair of parallel lines and a pair of perpendicular lines using their properties, a pair of compasses and a ruler, set squares or using dynamic geometry software* (AC9M7M04) (14/10/22)

*using dynamic geometry software to identify relationships between alternate, corresponding and co-interior angles for a pair of parallel lines cut by a transversal* (AC9M7M04) (14/10/22)

*using dynamic geometry software to demonstrate how angles and their properties are involved in the design and construction of scissor lifts, folding umbrellas, toolboxes and cherry pickers* (AC9M7M04) (14/10/22)

*using geometric reasoning of angle properties to generalise the angle relationships of parallel lines and transversals, and related properties such as the size of an exterior angle of a triangle is equal to the sum of the sizes of opposite and non-adjacent interior angles, and the sum of the sizes of interior angles in a triangle in the plane is equal to the size of 2 right angles or 180° *(AC9M7M04) (14/10/22)

*use mathematical modelling to solve practical problems involving ratios; formulate problems, interpret and communicate solutions in terms of the situation, justifying choices made about the representation* (AC9M7M06) (14/10/22)

*using fractions to model and solve ratio problems involving comparison of quantities, and considering part-part and part-whole relations* (AC9M7M06) (14/10/22)

*modelling and solving practical problems involving ratios of length, capacity or mass, such as in construction, design, food or textile production; for example, mixing concrete, the golden ratio in design, mixing a salad dressing* (AC9M7M06) (14/10/22)

*modelling the situation using manipulatives, diagrams and/or mathematical discussion; for example, mixing primary colours in a variety of ratios to investigate how new colours are created and the strength of those colours* (AC9M7M06) (14/10/22)

*investigating commercialised substances founded on First Nations Australians’ knowledges of substances including pharmaceuticals and toxins, understanding how ratios are used in their development* (AC9M7M06) (14/10/22)

## Year 7 Space

*represent objects in 2 dimensions; discuss and reason about the advantages and disadvantages of different representations* (AC9M7SP01) (27/10/22)

*using different nets to construct prisms and determining which nets will make a cube, rectangular prism, triangular prism or pyramid* (AC9M7SP01) (27/10/22)

*using aerial views of buildings and other three-dimensional structures to visualise the footprint made by the building or structure, identifying prisms that could approximate the structure* (AC9M7SP01) (27/10/22)

*building objects by interpreting isometric and perspective drawings* (AC9M7SP01) (27/10/22)

*exploring different two-dimensional representations of objects in First Nations Australians’ artworks or cultural maps of Country/Place* (AC9M7SP01) (27/10/22)

*classify triangles, quadrilaterals and other polygons according to their side and angle properties; identify and reason about relationships* (AC9M7SP02) (27/10/22)

*using strips of paper with parallel sides to make triangles and quadrilaterals, and contrasting the rigidity of triangles with the flexibility of quadrilaterals* (AC9M7SP02) (27/10/22)

*constructing triangles with 3 given side lengths and discussing the question, “Can any 3 lengths be used to form the sides of a triangle?”* (AC9M7SP02) (27/10/22)

*describe transformations of a set of points using coordinates in the Cartesian plane, translations and reflections on an axis, and rotations about a given point* (AC9M7SP03) (27/10/22)

*using digital tools to transform shapes in the Cartesian plane, describing and recording the transformations* (AC9M7SP03) (27/10/22)

*describing patterns and investigating different ways to produce the same transformation, such as using 2 successive reflections to provide the same result as a translation* (AC9M7SP03) (27/10/22)

*experimenting with, creating and re-creating patterns using combinations of translations, reflections and rotations, using digital tools* (AC9M7SP03) (27/10/22)

*design and create algorithms involving a sequence of steps and decisions that will sort and classify sets of shapes according to their attributes, and describe how the algorithms work* (AC9M7SP04) (27/10/22)

*creating a classification scheme for triangles based on sides and angles, using a flow chart using sequences and decisions* (AC9M7SP04) (27/10/22)

*creating a classification scheme for regular, irregular, concave or convex polygons that are sorted according to the number of sides* (AC9M7SP04) (27/10/22)

## Year 7 Statistics

*create different types of numerical data displays including stem-and-leaf plots using software where appropriate; describe and compare the distribution of data, commenting on the shape, centre and spread including outliers and determining the range, median, mean and mode* (AC9M7ST02) (10/11/22)

*comparing variation in attributes by category using split stem-and-leaf plots or dot plots; interpreting the shape of the distribution using qualitative terms to describe symmetry or skewness, “average” in terms of the mean, median and mode, and the amount of variation based on qualitative descriptions of the spread of the data* (AC9M7ST02) (10/11/22)

*connecting features of the data display; for example, highest frequency, clusters, gaps, symmetry or skewness, to the mode, range and median, and the question in context; describing the shape of distributions using terms such as “positive skew”, “negative skew”, “symmetric” and “bi-modal” and discussing the location of the median and mean on these distributions* (AC9M7ST02) (10/11/22)

*conducting an investigation to draw conclusions about whether teenagers have faster reaction times than adults* (AC9M7ST03) (10/11/22)

*conducting an investigation to support claims that a modification of a Science, Technology, Engineering and Mathematics (STEM) related design has improved performance* (AC9M7ST03) (10/11/22)

*using secondary data from the Reconciliation Barometer to conduct and report on statistical investigations relating to First Nations Australians* (AC9M7ST03) (10/11/22)

## Year 7 Probability

*identify the sample space for single-stage events; assign probabilities to the outcomes of these events and predict relative frequencies for related events* (AC9M7P01) (23/11/22)

*assigning the probability for throwing a 6 on a dice and using this to predict the number of times a 6 will occur when a dice is thrown multiple times* (AC9M7P01) (23/11/22)

*conduct repeated chance experiments and run simulations with a large number of trials using digital tools; compare predictions about outcomes with observed results, explaining the differences* (AC9M7P02) (23/11/22)

*developing an understanding of the law of large numbers through using experiments and simulations to conduct large numbers of trials for seemingly random events and discussing findings *(AC9M7P02) (23/11/22)

*conducting simulations using online simulation tools and comparing the combined results of a large number of trials to predicted results *(AC9M7P02) (23/11/22)

*exploring and observing First Nations Australian children’s instructive games; for example, Koara from the Jawi and Bardi Peoples of Sunday Island in Western Australia, to investigate probability, predicting outcomes for an event and comparing with increasingly larger numbers of trials, and between observed and expected results *(AC9M7P02) (23/11/22)

## 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 and to illustrate the necessity that for any non-zero natural number , *(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 is represented as *(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)

## Year 8 Algebra

*create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties* (AC9M8A01) (30/09/22)

*rearranging and simplifying linear expressions involving variables with integer coefficients and constants; using manipulatives such as algebra tiles to support calculations; for example, using manipulatives to demonstrate that 2x + 4 = 2(x + 2), 3(a – b) = 3a – 3b, or 5(m + 2n) + 3m – 4n = 5m **+ 10n + 3m – 4n = 8m + 6n* (AC9M8A01) (30/09/22)

*demonstrating the relationship between factorising and expanding linear expressions using manipulatives, such as algebra tiles or area models, and describing with mathematical language** *(AC9M8A01) (30/09/22)

*using the distributive, associative, commutative, identity and inverse properties to expand and factorise algebraic expressions using strategies such as the area model* (AC9M8A01) (30/09/22)

*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) (30/09/22)

*completing a table of values, plotting the resulting points on the Cartesian plane and determining whether the relationship is linear** *(AC9M8A02) (30/09/22)

*graphing the linear relationship ax + b = c for given values of a, b and c and identifying from the graph where ax + b < c or where ax + b > c* (AC9M8A02) (30/09/22)

*solving linear equations of the form ax + b = c and one-variable inequalities of the form ax + b < c or ax + b > c where a > 0 using inverse operations and digital tools, and checking solutions by substitution *(AC9M8A02) (30/09/22)

*solving linear equations such as 3x + 7 = 6x – 9, representing these graphically, and verifying solutions by substitution** *(AC9M8A02) (30/09/22)

*use mathematical modelling to solve applied problems involving linear relations , including financial contexts; formulate problems with linear functions, choosing a representation; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model* (AC9M8A03) (30/09/22)

*modelling patterns on Country/Place and exploring their connections and meaning to linear equations, using the model as a predictive tool and critiquing results by connecting back to Country/Place* (AC9M8A03) (30/09/22)

*experiment with linear functions and relations using digital tools, making and testing conjectures and generalising emerging patterns* (AC9M8A04) (30/09/22)

*using graphing software to investigate the effect of systematically varying parameters of linear functions on the corresponding graphs, making and testing conjectures; for example, making a conjecture that if the co-efficient of x is negative, then the line will slope down from left to right* (AC9M8A04) (30/09/22)

*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) (30/09/22)

*using digital tools to investigate integer solutions to equations such as 2x + 3y = 48 *(AC9M8A04) (30/09/22)

## Year 8 Measurement

*solve problems involving the volume and capacity of right prisms using appropriate units* (AC9M8M02) (15/10/22)

*solving practical problems involving volume and capacity; for example, optimal packaging and production* (AC9M8M02) (15/10/22)

*choosing which measurements are useful to consider when solving practical problems in context; for example, when purchasing a new washing machine, the dimensions are useful when determining whether it will fit in the available space in the laundry and its capacity is useful when considering the maximum washing load it can carry* (AC9M8M02) (15/10/22)

*solve problems involving the circumference and area of a circle using formulas and appropriate units* (AC9M8M03) (15/10/22)

*deducing that the area of a circle is between 2 radius squares and 4 radius squares, and using 3 × radius ^{2} as a rough estimate for the area of a circle* (AC9M8M03) (15/10/22)

*investigating the area of circles using a square grid or by rearranging a circle divided into smaller and smaller sectors or slices to resemble a close approximation of a rectangle* (AC9M8M03) (15/10/22)

*exploring traditional weaving designs by First Nations Australians and investigating the significance and use of circles* (AC9M8M03) (15/10/22)

*using digital tools to investigate time zones around the world and convert from one zone to another, such as time in Perth, Western Australia compared to Suva in Fiji or Toronto in Canada* (AC9M8M04) (15/10/22)

*recognise and use rates to solve problems involving the comparison of 2 related quantities of different units of measure* (AC9M8M05) (15/10/22)

*investigating the application of rates in First Nation Australians’ land management practices, including the rate of fire spread under different environmental conditions such as fuel types, wind speed, temperature and relative humidity; the conservation of water by First Nations Australians by estimating rates of water evaporation based on surface area and climatic conditions* (AC9M8M05) (15/10/22)

*discussing and comparing different applications, demonstrations and proofs of Pythagoras’ theorem, from Egypt and Mesopotamia, Greece, India and China with other historical and contemporary applications and proofs* (AC9M8M06) (15/10/22)

*use mathematical modelling to solve practical problems involving ratios and rates, including financial contexts; formulate problems; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model* (AC9M8M07) (15/10/22)

*modelling situations involving ratio and its application in the making of string and cordage by First Nations Australians, including the ratio of length to the mass of a rope, the strength of the ply in proportion to a rope’s pulling force, and the proportion of fibre for the length of string required* (AC9M8M07) (15/10/22)

## Year 8 Space

*using the enlargement transformation and digital tools to develop sets of similar shapes* (AC9M8SP01) (28/10/22)

*investigating sufficient conditions to establish that 2 triangles are congruent* (AC9M8SP01) (28/10/22)

*applying logical reasoning and tests for congruence and similarity, to problems and proofs involving plane shapes* (AC9M8SP01) (28/10/22)

*establishing that 2 shapes are congruent if one lies exactly on top of the other after one or more transformations including translations, reflections and rotations, and recognising that the matching sides and the matching angles are equal* (AC9M8SP01) (28/10/22)

*establish properties of quadrilaterals using congruent triangles and angle properties, and solve related problems explaining reasoning* (AC9M8SP02) (28/10/22)

*establishing the properties of squares, rectangles, parallelograms, rhombuses, trapeziums and kites using geometric properties and proof, such as the sum of the exterior angles of a polygon is equal to a complete turn or 360°* (AC9M8SP02) (28/10/22)

*applying the properties of triangles and quadrilaterals to construction designs such as car jacks, scissor lifts, folding umbrellas, toolboxes and cherry pickers* (AC9M8SP02) (28/10/22)

*describe the position and location of objects in 3 dimensions in different ways, including using a three-dimensional coordinate system with the use of dynamic geometric software and other digital tools* (AC9M8SP03) (28/10/22)

*constructing three-dimensional objects using 3D printers or designing software that uses a three-dimensional coordinate system* (AC9M8SP03) (28/10/22)

*comparing and contrasting two-dimensional and three-dimensional coordinate systems by highlighting what is the same and what is different, including virtual maps versus street views* (AC9M8SP03) (28/10/22)

*using dynamic geometry software to construct shapes and objects within the first quadrant of a three-dimensional coordinate system* (AC9M8SP03) (28/10/22)

*exploring position and transformation through geospatial technologies used by First Nations Australians’ communities* (AC9M8SP03) (28/10/22)

*design, create and test algorithms involving a sequence of steps and decisions that identify congruency or similarity of shapes, and describe how the algorithm works* (AC9M8SP04) (28/10/22)

*listing the properties or criteria necessary to determine if shapes are similar or congruent* (AC9M8SP04) (28/10/22)

*using the conditions for congruence of triangles and similarity of triangles to develop a sorting algorithm; for example, creating a flow chart* (AC9M8SP04) (28/10/22)

*evaluating algorithms for accuracy in classifying and distinguishing between similar and congruent triangles* (AC9M8SP04) (28/10/22)

## Year 8 Statistics

*using digital tools such as simulations and digital measuring devices to observe, measure and record qualitative and quantitative data, discussing precision and the implications of error* (AC9M8ST01) (11/11/22)

*comparing the sampling methods of simple random, systematic, stratified, quota, clustered or convenience, or judgement, and discussing the reliability of conclusions about the context that could be drawn *(AC9M8ST02) (11/11/22)

*investigating primary and secondary data sources relating to reconciliation between First Nations Australians and non-Indigenous Australians, analysing and reporting on findings *(AC9M8ST02) (11/11/22)

*using digital tools to simulate repeated sampling of the same population, such as heights or arm spans of students, recording and comparing means, median and range of data between samples* (AC9M8ST03) (11/11/22)

*investigating the effect that adding or removing data from a data set has on measures of central tendency and spread* (AC9M8ST03) (11/11/22)

*plan and conduct statistical investigations involving samples of a population; use ethical and fair methods to make inferences about the population and report findings, acknowledging uncertainty* (AC9M8ST04) (11/11/22)

*exploring progress in reconciliation between First Nations Australians and non-Indigenous Australians, investigating and evaluating sampling techniques and methods to gather relevant data to measure progress* (AC9M8ST04) (11/11/22)

## Year 8 Probability

*recognise that complementary events have a combined probability of one; use this relationship to calculate probabilities in applied contexts* (AC9M8P01) (24/11/22)

*understanding that knowing the probability of an event allows the probability of its complement to be found, including for those events that are not equally likely, such as getting a specific novelty toy in a supermarket promotion *(AC9M8P01) (24/11/22)

*using the relationship that for a single event A, Pr(A) + Pr(not A) = 1; for example, if the probability that it rains on a particular day is 80%, the probability that it does not rain on that day is 20%, or the probability of not getting a 6 on a single roll of a fair dice is *(AC9M8P01) (24/11/22)

*using the sum of probabilities to solve problems, such as the probability of starting a game by throwing a 5 or 6 on a dice is and probability of not throwing a 5 or 6 is *(AC9M8P01) (24/11/22)

*determine all possible combinations for 2 events, using two-way tables, tree diagrams and Venn diagrams, and use these to determine probabilities of specific outcomes in practical situations* (AC9M8P02) (24/11/22)

*describing events using language of “at least”, exclusive “or” (A or B but not both), inclusive “or” (A or B or both) and “and” *(AC9M8P02) (24/11/22)

*using the relation Pr(A and B) + Pr(A and not B) + Pr(not A and B) + Pr(not A and not B) = 1 to calculate probabilities, including the special case of mutually exclusive events where Pr(A and B) = 0 *(AC9M8P02) (24/11/22)

*exploring First Nations Australian children’s instructive games; for example, Battendi from the Ngarrindjeri Peoples of Lake Murray and Lake Albert in southern Australia, applying possible combinations and relationships and calculating probabilities using two-way tables and Venn diagrams *(AC9M8P02) (24/11/22)

*conduct repeated chance experiments and simulations, using digital tools to determine probabilities for compound events, and describe results* (AC9M8P03) (24/11/22)

*using digital tools to conduct probability simulations involving compound events *(AC9M8P03) (24/11/22)

*using a random number generator and digital tools to simulate rolling 2 dice and calculating the difference between them, investigating what difference is likely to occur more often *(AC9M8P03) (24/11/22)

*using online simulation software to conduct probability simulations to determine in the long run if events are complementary *(AC9M8P03) (24/11/22)

## 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)

## Year 9 Algebra

*apply the exponent laws to numerical expressions with integer exponents and extend to variables* (AC9M9A01) (01/10/22)

*simplifying and evaluating numerical expressions, involving both positive and negative integer exponents, explaining why; for example, and connecting terms of the sequence to terms of the sequence *(AC9M9A01) (01/10/22)

*recognising exponents in algebraic expressions and applying the relevant exponent laws and conventions; for example, for any non-zero natural number a, , , , , , and* * *(AC9M9A01) (01/10/22)

*simplify algebraic expressions, expand binomial products and factorise monic quadratic expressions* (AC9M9A02) (01/10/22)

*expanding combinations of binomials such as , , , , to identify expansion and factorisation patterns related to , where a and b are integers* (AC9M9A02) (01/10/22)

*using manipulatives such as algebra tiles or area models to expand or factorise algebraic expressions with readily identifiable binomial factors; for example, , or ** *(AC9M9A02) (01/10/22)

*recognising the relationship between expansion and factorisation, and using digital tools to systematically explore the factorisation of where m and n are integers** *(AC9M9A02) (01/10/22)

*find the gradient of** a line segment, the midpoint of the line interval and the distance between 2 distinct points on the Cartesian plane* (AC9M9A03) (01/10/22)

*using digital tools and transformations to illustrate that parallel lines in the Cartesian plane have the same gradient and that the relationship between the gradients of pairs of perpendicular lines is that their product is (-1)* (AC9M9A03) (01/10/22)

*investigating graphical and algebraic techniques for finding the midpoint and gradient of the line segment between 2 points** *(AC9M9A03) (01/10/22)

*using dynamic graphing software and superimposed images; for example, playground equipment, ramps and escalators, to investigate gradients in context and their relationship to rule of a linear function, and interpret gradient as a constant rate of change in linear modelling contexts *(*AC9M9A03)* (01/10/22)

*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) (01/10/22)

*recognising that in a table of values, if the second difference between consecutive values of the dependent variable is constant, then it is a quadratic* (AC9M9A04) (01/10/22)

*graphing quadratic functions using digital tools and comparing what is the same and what is different between these different functions and their respective graphs; interpreting features of the graphs such as symmetry, turning point, maximum and minimum values, and determining when values of the quadratic function lie within a given range* (AC9M9A04) (01/10/22)

*solving quadratic equations algebraically and comparing these to graphical solutions *(AC9M9A04) (01/10/22)

*recognising that the equation , where , has 2 solutions, and ; for example, if then correct to 3 decimal places, or correct to 3 decimal places, and representing these graphically *(AC9M9A04) (01/10/22)

*graphing percentages of illumination of moon phases in relation to First Nations Australians’ understandings that describe the different phases of the moon* (AC9M9A04) (01/10/22)

*use mathematical modelling to solve applied problems involving change including financial contexts; formulate problems, choosing to use either linear or quadratic functions; interpret solutions in terms of the situation; evaluate the model and report methods and findings* (AC9M9A05) (01/10/22)

*modelling measurement situations and determining the perimeter and areas of rectangles where the length, l, of the rectangle is a linear function of its width, w, for example, ** *(AC9M9A05) (01/10/22)

*modelling practical contexts using simple quadratic functions, tables and graphs (hand drawn or using digital tools) and algebraically, interpreting features of the graphs such as the turning point and intercepts in context; for example, area, paths of projectiles, parabolic mirrors, satellite dishes *(AC9M9A05) (01/10/22)

*modelling the hunting techniques of First Nations Australians using quadratic functions and exploring the effect of increasing the number of hunters to catch more prey *(AC9M9A05) (01/10/22)

*experiment with the effects of the variation of parameters on graphs of related functions, using digital tools, making connections between graphical and algebraic representations, and generalising emerging patterns *(AC9M9A06) (01/10/22)

*investigating transformations of the graph of to the graph of by systematic variation of a and b and interpreting the effects of these transformations using digital tools; for example, **(vertical enlargement as a>1) (vertical translation) and **(vertical compression as a<1) (reflection in the horizontal axis) (vertical translation) *(AC9M9A06) (01/10/22)

*investigating transformations of the parabola in the Cartesian plane using digital tools to determine the relationship between graphical and algebraic representations of quadratic functions, including the completed square form; for example, **(vertical compression as a<1) (horizontal translation) (vertical translation) or (vertical enlargement as a>1) (reflection in the horizontal axis) (horizontal translation) (vertical translation)* (AC9M9A06) (01/10/22)

*experimenting with digital tools by applying transformations to the graphs of functions, such as reciprocal , square root , cube and exponential functions, , identifying patterns* (AC9M9A06) (01/10/22)

## Year 9 Measurement

*investigating objects and technologies of First Nations Australians**, analysing and connecting surface area and volume, and exploring their relationship to their capacity* (AC9M9M01) (16/10/22)

*solve spatial problems, applying angle properties, scale, similarity, Pythagoras’ theorem and trigonometry in right-angled triangles* (AC9M9M03) (16/10/22)

*applying the formula for calculation of distances between points on the Cartesian plane from their coordinates, emphasising the connection to vertical and horizontal displacements between the points* (AC9M9M03) (16/10/22)

*using dynamic graphing software and superimposed images; for example, playground equipment, ramps and escalators, to investigate gradients in context and their relationship to rule of a linear function, and interpret gradient as a constant rate of change in linear modelling contexts* (AC9M9M03) (16/10/22)

*use mathematical modelling to solve practical problems involving direct proportion, rates, ratio and scale, including financial contexts; formulate the problems and interpret solutions in terms of the situation; evaluate the model and report methods and findings* (AC9M9M05) (16/10/22)

*modelling situations that impact on image editing used in social media and how proportion may not be maintained and can result in distorted images* (AC9M9M05) (16/10/22)

*exploring fire techniques in land management practices used by First Nations Australians that use proportion relationships, including the rate of fire spread in different fuel types to wind speed, temperature and relative humidity* (AC9M9M05) (16/10/22)

## Top

## 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)

*relating the tangent of an angle to the altitude and base of nested similar right-angled triangles, and connecting the tangent of the angle at which the graph of a straight line meets the positive direction of the horizontal coordinate axis to the gradient of the straight line* (AC9M9SP01) (29/10/22)

*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)

*comparing the ratio of lengths of corresponding sides of similar triangles and angles* (AC9M9SP02) (29/10/22)

*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, to
times the original area and the volume of the cube, to
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)

## Year 9 Statistics

*exploring potential cultural bias relating to First Nations Australians** by critically analysing sampling techniques in statistical reports* (AC9M9ST02) (12/11/22)

*represent the distribution of multiple data sets for numerical variables using comparative representations; compare data distributions with consideration of centre, spread and shape, and the effect of outliers on these measures* (AC9M9ST03) (12/11/22)

*using stem-and-leaf plots to compare 2 like sets of data such as the heights of girls and the heights of boys in a class* (AC9M9ST03) (12/11/22)

*exploring comparative data presented in reports by National Indigenous Australians Agency in regard to “Closing the Gap”, discussing the comparative distributions within the context of the data; for example, comparative data presented in the “Closing the Gap – Prime Minister’s Report” *(AC9M9ST03) (12/11/22)

*choose appropriate forms of display or visualisation for a given type of data; justify selections and interpret displays for a given context* (AC9M9ST04) (12/11/22)

*comparing data displays using mean, median and range to describe and interpret numerical data sets in terms of centre and spread using histograms, dot plots, or stem-and-leaf plots* (AC9M9ST04) (12/11/22)

*planning and conducting an investigation relating to consumer spending habits; modelling market research on what teenagers are prepared to spend on technology compared to clothing, with consideration of sample techniques and potential sources of bias* (AC9M9ST05) (12/11/22)

*investigating where would be the best location for a tropical fruit plantation by conducting a statistical investigation comparing different variables such as the annual rainfall in various parts of Australia, Indonesia, New Guinea and Malaysia, land prices and associated farming costs* (AC9M9ST05) (12/11/22)

*posing statistical questions, collecting, representing and interpreting data from different sources in relation to reconciliation, considering the relationships between variables* (AC9M9ST05) (12/11/22)

## Year 9 Probability

*list all outcomes for compound events both with and without replacement, using lists, tree diagrams, tables or arrays; assign probabilities to outcomes* (AC9M9P01) (25/11/22)

*discussing two-step chance experiments, such as the game of Heads and tails, describing the different outcomes and their related probabilities* (AC9M9P01) (25/11/22)

*using systematic methods such as lists or arrays to record outcomes and assign probabilities, such as drawing the names of students from a bag to appoint 2 team leaders *(AC9M9P01) (25/11/22)

*using a tree diagram to represent a three-stage event and assigning probabilities to these events; for example, selecting 3 cards from a deck, assigning the probability of drawing an ace, then a king, then a queen of the same suit, with and without replacing the cards after every draw *(AC9M9P01) (25/11/22)

*assigning probabilities to compound events involving the random selection of people from a given population; for example, selecting 2 names at random from all of the students at a high school and assigning the probability that they are both in Year 9 *(AC9M9P01) (25/11/22)

*design and conduct repeated chance experiments and simulations, using digital tools to compare probabilities of simple events to related compound events, and describe results* (AC9M9P03) (25/11/22)

*using digital tools to conduct probability simulations that demonstrate the relationship between the probability of compound events and the individual probabilities *(AC9M9P03) (25/11/22)

*conducting two-step chance experiments using systematic methods to list outcomes of experiments and to list outcomes favourable to an event *(AC9M9P03) (25/11/22)

*using repeated trials of First Nations Australian children’s instructive games; for example, Gorri from all parts of Australia, to calculate the probabilities of winning and not winning *(AC9M9P03) (25/11/22)

## 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)

## Year 10 Algebra

*expand, factorise and simplify expressions and solve equations algebraically, applying exponent laws involving products, quotients and powers of variables, and the distributive property* (AC9M10A01) (02/10/22)

*applying knowledge of exponent laws to algebraic terms and using both positive and negative integral exponents to simplifying algebraic expressions and solve equations algebraically* (AC9M10A01) (02/10/22)

*solve linear inequalities and simultaneous linear equations in 2 variables; interpret solutions graphically and communicate solutions in terms of the situation* (AC9M10A02) (02/10/22)

*describing the solution of simultaneous equations within the context of the situation* (AC9M10A02) (02/10/22)

*testing when a circle of a specified radius has a corresponding area greater than a given value, or whether a point satisfies an inequality; for example, whether the point (3, 5) satisfies* * *(AC9M10A02) (02/10/22)

*investigating the strategies inherent in First Nations Australian children’s instructive games; for example, Weme from the Warlpiri Peoples of central Australia, and their connection to strategies to solve simultaneous linear equations in 2 variables* (AC9M10A02) (02/10/22)

*recognise the connection between algebraic and graphical representations of exponential relations and solve related exponential equations, using digital tools where appropriate* (AC9M10A03) (02/10/22)

*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) (02/10/22)

*investigating the links between algebraic and graphical representations of exponential functions using graphing software* (AC9M10A03) (02/10/22)

*using digital tools with symbolic manipulation functionality to systematically explore exponential relations* (AC9M10A03) (02/10/22)

*investigating First Nations Australian Ranger groups’ and other groups’ programs that attempt to eradicate feral animals for survival of native animals on Country/Place, exploring the competition between feral and native animals and their impact on natural resources by formulating exponential equations for population growth for each animal species* (AC9M10A03) (02/10/22)

*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) (02/10/22)

*modelling situations that involve working with authentic information, data and interest rates to calculate compound interest and solve related problems* (AC9M10A04) (02/10/22)

*modelling and formulating situations involving population growths of native animals on Country/Place with varying reproductive behaviour, using exponential equations and critiquing their applicability to real-world situations* (AC9M10A04) (02/10/22)

*experiment with functions and relations using digital tools, making and testing conjectures and generalising emerging patterns* (AC9M10A05) (02/10/22)

applying the graphing zoom functionality of digital tools and systematically refining intervals to identify approximate location of points of intersection of the graphs of 2 functions, such as * *(AC9M10A05) (02/10/22)

*applying transformations to the graph of* * *(AC9M10A05) (02/10/22)

## Year 10 Measurement

*using mathematical modelling to provide solutions to problems involving surface area and volume; for example, ascertaining the rainfall that can be saved from a roof top and the optimal shape and dimensions for rainwater storage based on where it will be located on a property; determining whether to hire extra freezer space for the amount of ice cream required at a fundraising event for the school or community* (AC9M10M01) (17/10/22)

*interpret and use logarithmic scales in applied contexts involving small and large quantities and change* (AC9M10M02) (17/10/22)

*applying Pythagoras’ theorem and trigonometry to problems in surveying and design, where three-dimensional problems are decomposed into two-dimensional problems; for example, investigating the dimensions of the smallest box needed to package an object of a particular length* (AC9M10M03) (17/10/22)

*using a clinometer to measure angles of inclination, and applying trigonometry, and proportional reasoning to determine the height of buildings in practical contexts* (AC9M10M03) (17/10/22)

*applying Pythagoras’ theorem and trigonometry, and using dynamic geometric software, to design three-dimensional models of practical situations involving angles of elevation and depression; for example, modelling a crime scene *(AC9M10M03) (17/10/22)

*exploring navigation, design of technologies or surveying by First Nations Australians, investigating geometric and spatial reasoning, and how these connect to trigonometry* (AC9M10M03) (17/10/22)

*investigating scientific measuring techniques, including dating methods and genetic sequencing, applied to First Peoples of Australia and their artefacts, and the social impact of measurement errors* (AC9M10M04) (17/10/22)

*use mathematical modelling to solve practical problems involving proportion and scaling of objects; formulate problems and interpret solutions in terms of the situation; evaluate and modify models as necessary, and report assumptions, methods and findings* (AC9M10M05) (17/10/22)

*analysing and applying scale and ratios in situations such as production prototypes and 3D printing; for example, using a 3D printer to produce scaled versions of actual objects *(AC9M10M05) (17/10/22)

*investigating compliance with building codes and standards in design and construction, such as for escalators in shopping centres *(AC9M10M05) (17/10/22)

## Top

## Year 10 Space

*apply deductive reasoning to proofs involving shapes in the plane and use theorems to solve spatial problems* (AC9M10SP01) (29/10/22)

*investigating proofs of geometric theorems and using them to solve spatial problems; for example, applying logical reasoning and similarity to proofs and numerical exercises involving plane shapes; using visual proofs to justify solutions* (AC9M10SP01) (29/10/22)

*using dynamic geometric software to investigate the shortest path that touches 3 sides of a rectangle, starting and finishing at the same point and proving that the path forms a parallelogram* (AC9M10SP01) (29/10/22)

*interpret networks and network diagrams used to represent relationships in practical situations and describe connectedness (*AC9M10SP02) (29/10/22)

*investigating how polyhedra can be represented as a network using edges, vertices, interior and exterior faces; representing the number of edges, vertices and faces in a table and demonstrating how Euler’s formula F + V = E + 2 applies* (AC9M10SP02) (29/10/22)

*design, test and refine solutions to spatial problems using algorithms and digital tools; communicate and justify solutions* (AC9M10SP03) (29/10/22)

*designing and making scale models of three-dimensional objects using digital tools; for example, making components of a puzzle using a three-dimensional printer, planning and designing the puzzle using principles of tessellations* (AC9M10SP03) (29/10/22)

*applying a computational thinking approach to solving problems involving networks; for example, connectedness, coverage and weighted measures; taking different routes and choosing the most efficient route to take when travelling by car using virtual map software* (AC9M10SP03) (29/10/22)

*defining and decomposing spatial problems, creating and applying algorithms to generate solutions, evaluating and communicating solutions in terms of the problem; for example, designing a floor plan for a department store that limits congestion at key areas such as checkouts, changing rooms and popular sale items *(AC9M10SP03) (29/10/22)

*designing, creating and testing algorithms using pseudocode or flow charts for producing self-similar patterns; validating algorithms using a range of test cases to compare their output *(AC9M10SP03) (29/10/22)

*exploring geospatial technologies used by First Nations Australians’ communities to consider spatial problems including position and transformation* (AC9M10SP03) (29/10/22)

## Year 10 Statistics

*investigating population rates and discussing potential ethical considerations when presenting statistical data involving infection rates, and the number of cases per head of population *(AC9M10ST01) (15/11/22)

*using secondary data to predict the number of people likely to be infected with a strain of flu or experience side effects with a certain medication, discussing the ethical considerations of reporting of such data to the wider public, considering validity claims and samples sizes *(AC9M10ST01) (15/11/22)

*using the concept of Indigenous data sovereignty to critique and evaluate the Australian Government’s “Closing the Gap” report *(AC9M10ST01) (15/11/22)

*using digital tools to compare boxplots and histograms as displays of the same data in the light of the statistical questions being addressed and the effectiveness of the display in helping to answer the question *(AC9M10ST02) (15/11/22)

*comparing the information that can be extracted and the stories that can be told about continuous and discrete numerical data sets that have been displayed in different ways, including histograms, dot plots, box plots and cumulative frequency graphs *(AC9M10ST02) (15/11/22)

*construct scatterplots and comment on the association between the 2 numerical variables in terms of strength, direction and linearity* (AC9M10ST03) (15/11/22)

*discussing the difference between association and cause and effect, and relating this to situations such as health, diversity of species and climate control *(AC9M10ST03) (15/11/22)

*using statistical evidence to make, justify and critique claims about association between variables, such as in contexts of climate change, migration, online shopping and social media *(AC9M10ST03) (15/11/22)

*investigating the relationship between 2 variables of spear throwers used by Australian First Nations Peoples by using data to construct scatterplots, make comparisons and draw conclusions* (AC9M10ST03) (15/11/22)

*using two-way tables to investigate and comparing the survey responses to questions involving five-point Likert scale against 2 different categories of respondents; for example, junior compared to senior students’ responses to a survey question *(AC9M10ST04) (15/11/22)

*conducting a litter survey around the school, considering the relationship between different categorical variables such as the day of the week as canteen specials might lead to different types of litter or the weather due to hot days leading to more ice blocks and cold drinks being sold *(AC9M10ST04) (15/11/22)

*investigating biodiversity changes in Australia before and after colonisation by comparing related bivariate numerical data, discussing and reporting on associations* (AC9M10ST05) (15/11/22)

## Year 10 Probability

*design and conduct repeated chance experiments and simulations using digital tools to model conditional probability and interpret results* (AC9M10P02) (26/11/22)

*using samples of different sizes with and without replacement from a population to identify when the difference in methods becomes negligible *(AC9M10P02) (26/11/22)

*recognising that an event can be dependent on another event and that this will affect the way its probability is calculated *(AC9M10P02) (26/11/22)

*using simulations to gather data on frequencies for situations involving chance that appear to be counter-intuitive, such as the three-door problem or the birthday problem* (AC9M10P02) (26/11/22)

*using simulation to predict the number of people likely to be infected with a strain of flu or virus *(AC9M10P02) (26/11/22)

## Year 10 Optional Number

*operations on numbers involving fractional exponents and surds *(06/10/22)

*explaining that for , generalizing to , and evaluating corresponding expressions; for example,* * , so *(Link)

*explaining that and evaluating corresponding expressions; for example, and *

*showing that and for , for example, but , and , but *(Link)

## Year 10 Optional Algebra

*simplification of combinations of linear expressions with rational coefficients and the solution of related equations* (03/10/22)

*algebraic representations of quadratic functions of the form * (03/10/22)

*where*a, b, *and *c *are non-zero integers, and their transformation to the form **, where *h *and *k *are non-zero rational numbers, and the solution of related equations* (03/10/22)

*exploring the use of the unit circle and animations to show the periodic, symmetric, and complementary nature of the sine and cosine functions *(03/10/22)

*establishing relationships between Pythagoras’ theorem, the unit circle, trigonometric ratios, and angles in half-square triangles and equilateral triangles* (03/10/22)

*approximating values of the sine and cosine functions from a suitably scaled diagram of the unit circle, and solving equations of the form and **over a specified interval graphically* (03/10/22)

## Year 10 Optional Measurement

*the effect of increasingly small changes in the value of variables on the average rate of change and in relation to limiting values* (18/10/22)

*using the gradient of the line segment between two distinct points as a measure of rate of change to obtain numerical approximations to instantaneous speed and interpreting ‘tell me a story’ piecewise linear position-time graphs *(18/10/22)

## Year 10 Optional Space

*relationships between angles and various lines associated with circles (radii, diameters, chords, tangents) *(30/10/22)

*identifying relationships, angles between tangents and chords, angles subtended by a chord with respect to the centre of a circle, and with respect to a point on the circumference of a circle, including using dynamic geometric software* (30/10/22)

*exploring how deductive reasoning and diagrams are used in proving geometric theorems related to circles* (30/10/22)

## Year 10 Optional Statistics

*measures of spread, their interpretation and usefulness with respect to different data distributions *(14/11/22)

*comparing the use of quantiles, percentiles, and cumulative frequency to analyse the distribution of data* (14/11/22)

*comparing measures of spread for different data distributions, such as mean or median absolute deviations with standard deviations, and exploring the effect of outliers* (14/11/22)

## Year 10 Optional Probability

*counting principles, and factorial notation as a representation that provides efficient counting in multiplicative contexts, including calculations of probabilities* (27/11/22)

*understanding that a set with n elements has 2 ^{n} different subsets formed by considering each element for inclusion or not in combination, and that these can be systematically listed using a tree diagram or a table, for example, the set {a, b, c} has 2^{3} = 8 subsets which are {ø, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}. *(27/11/22)

*using the definition of n! to represent and calculate in contexts that involve choices from a set for example, how many different combinations of 3 playing cards from a pack? How many if the suits are ignored? How many with and without replacement? *(27/11/22)

*performing calculations on numbers expressed in factorial form, such as to evaluate the number of possible arrangements of n objects in a row, r of which are identical, for example 5 objects, 3 of which are identical, can be arranged in a row in *

*different ways*(27/11/22)

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

I hadn’t noticed the spiral.

The reports from TIMMS and PISA paint quite different pictures.

They both indicate that Australia sucks, one accurately.

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.

@Alasdair: In my experience, few students at school know much about spreadsheets.

They also know little about driving a forklift. What’s your point?

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.

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

Terry, I’m happy for you to play Idiots’ Advocate on this blog, and if you want to try to defend the

Year 6elaboration that is being discussed, then do so. But try to stick to the topic.I’ve added a bunch of stuff from Year 6 Number.. Lord spare us, and me in particular.

“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 and to illustrate the necessity that for any non-zero natural number (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.

Thanks, Anon. I’ve fixed up the LaTex in your comment.

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”

I’ve added a bunch of stuff from Year 9 Space.

I’ve added a bunch of stuff from Foundation Number.

I’ve added a bunch of stuff from Year 7 Number.

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.”

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”?

I’ve added a bunch of stuff from Year 8 Number.

I’ve added a section with stuff from Year 1 Number

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.

I’ve added a section with stuff from Year 2 Number.

I’ve added a section with stuff from Year 3 Number

I’ve added a section with stuff from Year 4 Number.

I’ve added a section with stuff from Year 5 Number.

I’ve added a section with stuff from Year 9 Number.

I’ve added a section with stuff from Year 10 Number.

On we go. I’ve added a section with stuff from Foundation Algebra (sic).

I’ve added a section with stuff from Year 1 Algebra.

I’ve added a section with stuff from Year 2 Algebra.

I’ve added a section with stuff from Year 3 Algebra.

I’ve added a section with stuff from Year 4 Algebra.

I’ve added a section with stuff from Year 5 Algebra.

I’ve added a section with stuff from Year 6 Algebra.

I’ve added a section with stuff from Year 7 Algebra.

I’ve added a section with stuff from Year 8 Algebra.

I’ve added a section with stuff from Year 9 Algebra. (Hoo boy.)

I’ve added a section with stuff from Year 10 Algebra.

I’ve added a section with stuff from Year 10 Optional Algebra.

I’ve added a section with stuff from Foundation Measurement.

I’ve added a section with stuff from Year 1 Measurement.

I’ve added a section with stuff from Year 2 Measurement.

I’ve added a section with stuff from Year 3 Measurement.

I’ve added a section with stuff from Year 4 Measurement.

I’ve added a section with stuff from Year 5 Measurement.

I’ve added a section with stuff from Year 6 Measurement.

I’ve added a section with stuff from Year 7 Measurement.

I’ve added a section with stuff from Year 8 Measurement.

I’ve added a section with stuff from Year 9 Measurement.

I’ve added a section with stuff from Year 10 Measurement.

I’ve added a section with stuff from Year 10 Optional Measurement.

I’ve added a section with stuff from Foundation Space (ugh!).

I’ve added a section with stuff from Year 1 Space.

I have just gone through the entire curriculum trying to map it for the company I work for.

I have no idea how you singled out these “awful” examples – as they all seem about as awful as the ones you haven’t included!

I think one of my favourite parts is the year 4 outcome ” choose and use estimation and rounding to check and explain the reasonableness of calculations including the results of financial transactions” and then the year 5 outcome “check and explain the reasonableness of solutions to problems including financial contexts using estimation strategies appropriate to the context”.

Maybe if we just swap the order of the sentence around nobody will notice they’re the same!

Hi jono, I hope your company paid you appropriately for pain and suffering.

Of course you are correct, that it is all awful. Even the rare, not-totally-awful line is just phrased badly. Your outcome example is hilarious. There’s tons of examples of infinitesimal change from Year N to Year N +1, but I hadn’t previously seen an example of zero change.

Also, if anyone could tell me when inequality symbols are introduced, or say naming and identifying quadrilaterals, that’d be great!

Oh Jesus. Have they done another cone job? I’ll look.

Elaboration for AC9M1SP01 “classifying a collection of shapes, including different circles, ovals, regular and irregular shapes, triangles and quadrilaterals, saying what is the same about the shapes in a group and what is different between the groups” is the only mention of “quadrilateral” in F-6. Not a single mention of rhombus, parallelogram, kite, trapezium, etc.

AC9M5N01 is the first time an inequality symbol appears (in an elaboration) on comparing and ordering decimal numbers but of course there isn’t a single outcome that mentions teaching inequality symbols, especially not in any of the outcomes about comparing things.

Thanks, jono. I have little doubt you are correct. I’ll check it out for myself soon and then post. (Trying to get another ACARA post done as we speak …)

Hi, jono. I checked and of course you are correct. In brief, the Year 6 stuff on quadrilaterals has been moved to Year 7 (and stupidified). Presumably, that was to make way for the flakier stuff now included in Year 6.

I’ll try to post on it at some point soon.

Hi jono. The (non) treatment of inequality symbols in the new currciulum is hilarious, but is it better in the current curriculum?

I’ve added a section with stuff from Year 2 Space.

I’ve added a section with stuff from Year 3 Space.

I’ve added a section with stuff from Year 4 Space.

I’ve added a section with stuff from Year 5 Space.

I’ve added a section with stuff from Year 6 Space.

I’ve added a section with stuff from Year 7 Space.

I’ve added a section with stuff from Year 8 Space.

I’ve added a section with stuff from Year 10 Space, and added a couple things to Year 9 Space.

I’ve added a section with stuff from Year 10 Optional Space.

I’ve added a section with stuff from Foundation Statistics (ha ha ha).

I’ve added a section with stuff from Year 1 Statistics.

I’ve added a section with stuff from Year 2 Statistics.

I’ve added sections with stuff from Year 3 Statistics and Year 4 Statistics

I’ve added a section with stuff from Year 5 Statistics.

I’ve added a section with stuff from Year 6 Statistics.

I’ve added a section with stuff from Year 7 Statistics.

I’ve added a section with stuff from Year 8 Statistics.

I’ve added a section with stuff from Year 9 Statistics.

I’ve added a section with stuff from Year 10 Statistics.

I’ve added a section with stuff from Year 10 Optional Statistics.

I’ve added a section with stuff from Year 3 Probability.

I’ve added a section with stuff from Year 3 Probability (and moved the Year 4 Probability to the correct spot).

I’ve added a section with everything from Year 5 Probability.

I’ve added a section with stuff from Year 6 Probability.

I’ve added a section with stuff from Year 8 Probability.

I’ve added a section with stuff from Year 9 Probability.

I’ve added a section with stuff from Year 10 Probability.

And, we’re done.

I’ve added a section with stuff from Year 10 Optional Probability.