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• VC2M4N09

  use mathematical modelling to solve practical problems that involve 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...

  Elaborations

  • modelling and solving a range of practical additive problems using materials, part-part-whole diagrams and/or a bar model, and writing addition and/or subtraction number sentences, based on whether a part or the whole is missing; and explaining how each number in their number sentence is connected to the situation
  • modelling practical problems with division, interpreting and representing the situation using a diagram or array to represent what is unknown (the number of groups, or the number per group); and writing a division number sentence to represent the situation and choosing an efficient calculation strategy
  • modelling practical problems involving money (such as a budget for a large event) that require either addition, subtraction, multiplication or division and justifying the choice of operation in relation to the situation
  • 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 × $4 = $20, so 5 × $96 is the same as 5 × $100 less $20, giving the answer $500 − $20 = $480
  • 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 × 16 and using place value partitioning, basic facts and an array, thinking 4 × 10 = 40 and 4 × 6 = 24, so 4 × 16 can be written as 40 + 24 = 64

  VC2M4N09 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VC2M7N10

  use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts such as ‘best buys’; formulate problems, choosing representations and efficient calculation strategies, designing algorithms and using digital tools as appropriate; interpret...

  Elaborations

  • 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, or in geography when determining altitude above and below sea level
  • modelling contexts involving proportion, such as the proportion of students attending the school disco, proportion of the bottle cost to the recycling refund, proportion of the 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; and interpreting and communicating answers in terms of the context of the situation
  • modelling financial problems involving profit and loss, credits and debits, gains and losses; for example, holding a fundraising sausage sizzle and determining whether the event made a percentage profit or loss
  • finding the sum of a set of consecutive numbers using a loop structure
  • constructing geometric patterns such as a honeycomb, using dynamic geometry functionality
  • using mathematical modelling to investigate the proportion of land mass/area of Aboriginal Peoples’ traditional grain belt compared with Australia’s current grain belt

  VC2M7N10 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M5ST01

  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

  Elaborations

  • recognising that ordinal data is a form of categorical data even though the data being collected might be numbers, for example, a rating scale using numbers 1–5 to represent the categories people can choose from when asked, ‘What rating would you give this film out of 5?’
  • determining the mode for a set of data and discussing that there may be more than one mode
  • identifying the best methods of presenting data to illustrate the results of investigations and justifying the choice of representations
  • acquiring data through chance experiments, discussing and reporting on the distribution of outcomes and how this relates to equal and unequal outcomes
  • using digital systems to validate data; for example, recognising the difference between numerical, text and date formats in spreadsheets, and setting data types in a spreadsheet to make sure a date is input correctly
  • investigating data relating to the reconciliation process between Aboriginal and Torres Strait Islander Peoples and non-Indigenous Australians, posing questions, discussing and reporting on findings

  VC2M5ST01 | Mathematics | Mathematics Version 2.0 | Level 5 | Statistics

• VC2M4SP03

  create and interpret grid reference systems using grid references and directions to locate and describe positions and pathways

  Elaborations

  • interpreting a grid reference map of a familiar location of interest, such as a map of the showgrounds, a food festival, botanical garden, a park in the local area or a train station, and writing instructions using grid references for a friend to find them at a specified location
  • 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
  • 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; and noticing how the grid helps to pinpoint things quickly and easily
  • using different-sized grids as a tool to enlarge an image or artwork

  VC2M4SP03 | Mathematics | Mathematics Version 2.0 | Level 4 | Space

• VCMNA103

  Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences

  Elaborations

  • developing fluency and confidence with numbers and calculations by saying number sequences
  • recognising that the natural numbers with zero form an ordered infinite set {0, 1, 2, 3 … } with a first element but no last element
  • recognising patterns in number sequences, such as adding 10 always results in the same final digit

  VCMNA103 | Mathematics | Level 2 | Number and Algebra | Number and place value

• VC2M3M01

  identify which metric units are used to measure everyday items; use measurements of familiar items and known units to make estimates

  Elaborations

  • examining the packaging on supermarket items to determine the metric unit used to describe the mass or volume of the contents
  • identifying items that have a mass of one kilogram or 500 grams, or a capacity of one litre or 500 millilitres, and using these benchmarks to estimate the mass or capacity of other things, explaining their reasoning
  • estimating the height of a tree by comparing it to the height of their friend and quoting the result as ‘The tree is about 3 times as tall’; and estimating the capacity of a fish tank by using a litre milk carton as a benchmark
  • choosing and using metres to estimate the dimensions of the classroom

  VC2M3M01 | Mathematics | Mathematics Version 2.0 | Level 3 | Measurement

• VC2M10AA06

  apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation

  Elaborations

  • investigating the features of graphs of polynomials including axes intercepts and the effect of repeated factors

  VC2M10AA06 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra

• VCMMG142

  Make models of three-dimensional objects and describe key features

  Elaborations

  • exploring the creation of three-dimensional objects, including prisms and pyramids, using origami

  VCMMG142 | Mathematics | Level 3 | Measurement and Geometry | Shape

• VCMNA361

  Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation

  Elaborations

  • investigating the features of graphs of polynomials including axes intercepts and the effect of repeated factors

  VCMNA361 | Mathematics | Level 10A | Number and Algebra | Linear and non-linear relationships

• Mathematics Version 2.0: Level 3 achievement standards

  By the end of Level 3, students order and represent natural numbers beyond 10 000, classify numbers as either odd or even, and use the properties of odd and even numbers. They partition, rearrange and regroup two- and three-digit numbers in different ways to assist in calculations. Students...

  Level description | Mathematics | Mathematics Version 2.0 | Level 3

• Mathematics Version 2.0: Level 4 achievement standards

  By the end of Level 4, students use their understanding of place value to represent tenths and hundredths in decimal form and to multiply natural numbers by multiples of 10. Students use mathematical modelling to solve financial and other practical problems, formulating the problem using...

  Level description | Mathematics | Mathematics Version 2.0 | Level 4

• Mathematics Version 2.0: Level 5 description

  In Level 5, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of mathematics that develop their understanding of and fluency with concepts, procedures and processes by making connections...

  Level description | Mathematics | Mathematics Version 2.0

• VC2M9ST03

  represent the distribution of multiple data sets for numerical variables using comparative representations such as back-to-back stem-and-leaf plots and histograms; describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi-modal’; compare data distributions using mean, median and range...

  Elaborations

  • describing the shape of the distribution of data using terms such as ‘positive skew’, ‘negative skew’, ‘symmetric’ and ‘bi-modal’
  • 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
  • constructing grouped histograms that show trends in health issues such as lung cancer, leukaemia, stroke and diabetes, and using the graph to justify, verify or invalidate claims
  • exploring comparative data presented in reports by the 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’ 
  • comparing means, medians and ranges of 2 sets of numerical data that have been displayed using histograms, dot plots or stem-and-leaf plots

  VC2M9ST03 | Mathematics | Mathematics Version 2.0 | Level 9 | Statistics

• VC2M2M05

  identify, describe and demonstrate quarter, half, three-quarter and full measures of turn in everyday situations

  Elaborations

  • identifying things that turn in the school environment, for example, the handle on a tap or a door, or the dial or switch on a piece of equipment; and identifying a half turn and a full turn, drawing a diagram and labelling it with arrows to show the direction and amount of turn
  • giving and following instructions to move during an activity; for example, demonstrating and describing half, quarter and full turns in a choreographed dance
  • investigating hands turning on a clock and relating quarter, half and full hours to angles and the language of clockwise or anticlockwise
  • giving or following directions to locate an object in the room or to provide a pathway through a grid, such as programming a robot, referring to quarter, half, three-quarter and full turns

  VC2M2M05 | Mathematics | Mathematics Version 2.0 | Level 2 | Measurement

• VCMMG166

  Compare objects using familiar metric units of area and volume

  Elaborations

  • comparing areas using grid paper
  • comparing volume using centicubes
  • recognising that metric units are not the only units used throughout the world, for example measuring the area of floor space using tatami mats (Japan), using squares for room and house area (Australia)

  VCMMG166 | Mathematics | Level 4 | Measurement and Geometry | Using units of measurement

• Mathematics Version 2.0: Level 8 achievement standards

  By the end of Level 8, students recognise irrational numbers as numbers that cannot develop from the division of integer values by natural numbers and terminating or recurring decimals. They apply the exponent laws to calculations with numbers involving positive integer exponents. Students...

  Level description | Mathematics | Mathematics Version 2.0 | Level 8

• VC2M10A12

  solve linear equations involving simple algebraic fractions

  Elaborations

  • solving a wide range of linear equations, including those involving one or 2 simple algebraic fractions, and checking solutions by substitution
  • representing word problems, including those involving fractions, as equations and solving them to answer the question

  VC2M10A12 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VCMNA340

  Solve linear equations involving simple algebraic fractions

  Elaborations

  • solving a wide range of linear equations, including those involving one or two simple algebraic fractions, and checking solutions by substitution
  • representing word problems, including those involving fractions, as equations and solving them to answer the question

  VCMNA340 | Mathematics | Level 10 | Number and Algebra | Linear and non-linear relationships

• Mathematics: Level 10A description

  Level 10A provides optional, additional content for students to be extended in their mathematical studies.

  Students could extend work in number and algebra to investigate the structure and properties of number systems, with further analysis of order relations and inequalities. They could extend...

  Level description | Mathematics

• Mathematics: Level 8 achievement standards

  Number and Algebra

  Students use efficient mental and written strategies to make estimates and carry out the four operations with integers, and apply the index laws to whole numbers. They identify and describe rational and irrational numbers in context. Students estimate answers and solve everyday...

  Level description | Mathematics | Level 8