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Result list

• VC2M4N02

  investigate number sequences involving multiples of 3, 4, 6, 7, 8 and 9

  Elaborations

  • recognising that number sequences can be extended indefinitely, and determining any patterns in the sequences

  VC2M4N02 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VC2M8N05

  solve problems involving the use of percentages, including percentage increases and decreases and percentage error, with and without digital tools

  Elaborations

  • using percentages to solve problems, including those involving mark-ups, discounts and Goods and Services Tax (GST)
  • using percentages to calculate population increases and decreases
  • using percentage error to compare the relative size of error in calculations involving a given or actual value, and an estimated or measured value

  VC2M8N05 | Mathematics | Mathematics Version 2.0 | Level 8 | Number

• VC2M1N01

  recognise, represent and order numbers to at least 120 using physical and virtual materials, numerals, number lines and charts

  Elaborations

  • reading, writing and naming numerals and ordering two-digit numbers from zero to at least 120, using patterns within the natural number system, including numbers that look and sound similar, for example, 16, 60, 61 and 66
  • using number tracks or positioning a set of numbered cards in the correct order and relative location by pegging them on an empty number line
  • using hundreds charts to build understanding and fluency with numbers; for example, collaboratively building a hundreds chart using cards numbered from zero to 99, or colour-coding the count of tens in a hundreds chart using one colour to represent the number of tens and another to represent the number of ones
  • recognising that numbers are used in all languages and cultures but may be represented differently in words and symbols (for example, through kanji numbers in Japanese and characters in Chinese) and that there are alternative numeration systems (for example, using special characters for 10 and 100 and other multiples of 10 in Japanese and Chinese numeration)

  VC2M1N01 | Mathematics | Mathematics Version 2.0 | Level 1 | 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

• VC2M8N02

  establish and apply the exponent laws with positive integer exponents and the zero exponent, using exponent notation with numbers

  Elaborations

  • recognising the connection between exponent form and expanded form with the exponent laws of product of powers rule, quotient of powers rule, and power of a power rule, for example, 23×22 can be represented as 2×2×2×2×2=25 , and connecting the result to the addition of exponents
  • applying the exponent laws of the product of powers rule, quotient of powers rule, power of a power rule and zero exponent individually and in combination; for example, using exponents to determine the effect on the volume of a 2 centimetre cube when the cube is enlarged to a 6 centimetre cube, 6323= 23×3323=33, so the volume is increased by a factor of 27
  • using digital tools to systematically explore the application of the exponent laws; observing that the bases need to be the same
  • using examples such as 3434=1, and 34-4=30 to illustrate the necessity that for any non-zero natural number n,  n0=1

  VC2M8N02 | Mathematics | Mathematics Version 2.0 | Level 8 | Number

• VC2M7N05

  multiply and divide fractions and decimals using efficient mental and written strategies, and digital tools

  Elaborations

  • investigating multiplication of fractions and decimals, using strategies including patterning and multiplication as repeated addition, with both concrete materials and digital tools, and identifying the processes for division as the inverse of multiplication

  VC2M7N05 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M1N06

  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

  Elaborations

  • modelling problems involving repeated equal group situations, such as ‘How many wheels are needed for 3 cars?’, using materials and drawing a picture to show what they did, and recording the results with a number
  • modelling practical problems involving equal sharing situations; for example, sharing a set of dominoes between the 2 players in a game, and then counting or subitising to ensure they both have the same number of tiles
  • modelling money problems involving equal sharing; for example, sorting coins from a moneybox according to their denominations, sharing the coins equally between 4 people, and using counting or subitising to ensure they have equal amounts of each denomination

  VC2M1N06 | Mathematics | Mathematics Version 2.0 | Level 1 | Number

• VC2M1N04

  add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies

  Elaborations

  • using drawings, physical and virtual materials, and number combinations within 10 to add and subtract collections to 20
  • adding and subtracting numbers within 20, using a variety of representations and strategies, such as counting on, counting back, partitioning and part-part-whole knowledge of numbers to 10; for example, using partitioning and combining 7+5=7+3+2=10+2=12
  • 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
  • representing story problems involving addition and subtraction of numbers within 20 using a Think Board; recognising and using + and − symbols and the equal sign (=) to represent the operations of addition and subtraction; and showing and explaining the connections between any materials used using the language of plus and minus, and the numbers within the story problem
  • creating and performing addition and subtraction stories told through Aboriginal and/or Torres Strait Islander dances

  VC2M1N04 | Mathematics | Mathematics Version 2.0 | Level 1 | Number

• VC2M7N01

  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

  Elaborations

  • investigating squares of natural numbers from one to 20, and connecting them to visual representations such as dots arranged in a square pattern
  • using the square and square root notation, and the distributive property and area diagrams, to calculate the squares of two-digit numbers; for example, 432=40+32=402+2×40×3+32=1600+240+9=1849
  • determining between which 2 consecutive natural numbers the square root of a given number lies; for example, 43 is between the square numbers 36 and 49 so 43 is between 36 and 49 and therefore between 6 and 7
  • generating a list of perfect square numbers and describing any emerging patterns, for example, the last digit of perfect square numbers, or the difference between consecutive square numbers, and recognising the constant second difference
  • 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

  VC2M7N01 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M6N02

  identify and describe the properties of prime, composite, square and triangular numbers and use these properties to solve problems and simplify calculations

  Elaborations

  • using the definition of a prime number to explain why one is not a prime number
  • testing numbers by using division to distinguish between prime and composite numbers, recording the results on a number chart to identify any patterns
  • 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 × 16 as 5 × 3 × 4 × 4, which can be rearranged to simplify calculation to 5 × 4 × 3 × 4 = 20 × 12
  • identifying and describing the product of a number with itself as square; for example, 3 × 3 is the same as 3²
  • using spreadsheets to list all the numbers that have up to 3 factors, using combinations of only the first 3 prime numbers, recognising any emerging patterns, making conjectures and experimenting with other combinations

  VC2M6N02 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VC2M4N04

  count by multiples of quarters, halves and thirds, including mixed numerals; locate and represent these fractions as numbers on number lines

  Elaborations

  • 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 ...’
  • subdividing the sections between whole numbers on parallel number lines so that one shows halves, another shows quarters and one other shows thirds; and counting the fractions by jumping along the number lines, and noticing when the count is at the same position on the parallel lines
  • converting mixed numerals into improper fractions and vice versa, and representing mixed numerals on a number line
  • using a number line to represent and count in tenths, recognising that 10 tenths is equivalent to one

  VC2M4N04 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VC2M5N03

  compare and order common unit fractions with the same and related denominators, including mixed numerals, applying knowledge of factors and multiples; represent these fractions on a number line

  Elaborations

  • 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; and recording the fractions to justify the total
  • creating a fraction wall from paper tape to model and compare a range of different fractions with related denominators, and using the model to play fraction wall games
  • 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 14 on a fraction wall represents the area of one-quarter of the whole, while on the number line 14 is identified as a point that is one-quarter of the distance between zero and one
  • 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 210 is located at the same position on a parallel number line as 15 because 15 is equivalent to 210
  • converting between mixed numerals and improper fractions to assist with locating them on a number line

  VC2M5N03 | Mathematics | Mathematics Version 2.0 | Level 5 | Number

• VCMNA019

  Correspond ‘one’ with a single object

  Elaborations

  • showing understanding of object permanency, by tracking and finding an object
  • exploring ‘oneness’ and indicate one, for example one clap, experiencing one object, giving out materials one at a time, requesting one, hearing one sound or beat
  • distributing objects and materials with support, using basic one-to-one correspondence

  VCMNA019 | Mathematics | Level B | Number and Algebra | Number and place value

• VCMNA054

  Subitise regular arrangements of objects and arrays up to five

  Elaborations

  • understanding that some numbers are represented by a set pattern or array

  VCMNA054 | Mathematics | Level D | Number and Algebra | Number and place value

• VCMNA039

  Demonstrate in practical situations, ‘adding one more to’ and ‘taking one away from’ in everyday situations

  Elaborations

  • using shared experiences with concrete materials to add one more to or take away one from a group of objects, and count to find a total
    • experiencing addition and subtraction in games
  • communicating using language such as ‘more’ or ‘less’ to describe a change in a group using classroom resources and in practical situations

  VCMNA039 | Mathematics | Level C | Number and Algebra | Number and place value

• VCMNA059

  Sort like objects based on a given classification, and identify and continue a simple repeated pattern with its next element

  Elaborations

  • continuing a simple repeated two-part pattern with given objects, movements or sounds, for example, red, blue, red (set the table with drinking cups), paper, glue (set up equipment), knife and fork (set a table using two implements)
  • making patterns and collections based on objects being the same, different and alike
  • examining and continuing a simple repeated pattern with given objects, movements or sounds, for example, continue a two-beaded pattern (red, blue, red, blue)
  • sorting and grouping objects and communicating attributes such as texture, colour, size, category; for example, sort papers into two colours, sort cutlery into two groups
  • recognising patterns in familiar environments

  VCMNA059 | Mathematics | Level D | Number and Algebra | Patterns and algebra

• VCMNA002

  Respond to situations where counting is involved

  Elaborations

  • experiencing to number name, numerals and quantities in everyday experiences
  • experiencing activities that use number names, numerals and quantities, for example stories, songs, cooking, music
  • attending to and being aware of number as objects are being counted
  • reacting to objects moving, disappearing and re-appearing within the context of everyday situations
  • responding to wanting more or less of an object

  VCMNA002 | Mathematics | Level A | Number and Algebra | Number and place value

• VCMNA052

  Use number names in sequence to count in everyday situations, initially from one to ten

  Elaborations

  • developing fluency with forward counting by communicating number names while counting, initially to 10 and in meaningful contexts such as cooking, collecting equipment, stories and games
  • understanding one-to-one correspondence by knowing that each object is counted only once, by tracking an object while counting in shared and structured counting experiences, for example moving objects once counted, counting objects left to right

  VCMNA052 | Mathematics | Level D | Number and Algebra | Number and place value

• VCMNA022

  Participate in everyday situations involving ‘adding’ and ‘taking away’

  Elaborations

  • combining two groups of objects to make ‘more’ within the context of familiar everyday situations
  • participating in everyday situations that involve moving objects to make ‘less’ or ‘more’, for example dragging an object to or from a group, using a switch to initiate the action or augmentative and alternative communication to communicate the action required

  VCMNA022 | Mathematics | Level B | Number and Algebra | Number and place value

• VCMNA021

  Make comparison between items using appropriate language such as ‘same’ or ‘different’

  Elaborations

  • comparing two collections using one to one correspondence within the context of everyday situations
  • responding to questions about group comparison for example ‘Are they the same?’ ‘Or different?’ verbally or by indicating through augmentative and alternative communication, actions or eye gaze

  VCMNA021 | Mathematics | Level B | Number and Algebra | Number and place value