Mathematics Version 2.0

Number

1. interpret, compare and order numbers with more than 2 decimal places, including numbers greater than one, using place value understanding; represent these on a number line (VC2M5N01)

   Elaborations

   1. making models of decimals including tenths, hundredths and thousandths by subdividing materials or grids, and explaining the multiplicative relationship between consecutive places; for example, explaining that thousandths are 10 times smaller than hundredths, or writing numbers into a place value chart to compare and order them
   2. renaming decimals to assist with mental computation; for example, when asked to solve 0.6 ÷ 10 they rename 6 tenths as 60 hundredths and say, ‘If I divide 60 hundredths by 10, I get 6 hundredths’ and write 0.6 ÷ 10 = 0.06
   3. using a number line or number track to represent and locate decimals with varying numbers of decimal places and numbers greater than one and justifying the placement; for example, 2.335 is halfway between 2.33 and 2.34, that is, 2.33 < 2.335 < 2.34, and 5.283 is between 5.28 and 5.29 but closer to 5.28
   4. interpreting and comparing the digits in decimal measures, for example, the length or mass of animals or plants, such as a baby echidna weighing 1.78 kilograms and a platypus weighing 1.708 kilograms
   5. interpreting plans or diagrams showing length measures as decimals, placing the numbers into a decimal place value chart to connect the digits to their value
2. express natural numbers as products of their factors, recognise multiples and determine if one number is divisible by another (VC2M5N02)

   Elaborations

   1. 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 × 12, 2 × 6 and 3 × 4
   2. 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
   3. using divisibility tests to determine if larger numbers are multiples of one-digit numbers; for example, testing if 89 472 is divisible by 3 using 8 + 9 + 4 + 7 + 2 = 30, as 30 is divisible by 3 then 89 472 is a multiple of 3
   4. 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 × 7 = 3 × 2 + 3 × 5, and 4 × 7 = 4 × 2 + 4 × 5
3. 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 (VC2M5N03)

   Elaborations

   1. 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
   2. 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
   3. 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
   4. 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
   5. converting between mixed numerals and improper fractions to assist with locating them on a number line
4. recognise that 100% represents the complete whole and use percentages to describe, represent and compare relative size; connect familiar percentages to their decimal and fraction equivalents (VC2M5N04)

   Elaborations

   1. recognising applications of percentages used in everyday contexts, for example, the bar model used for charging devices indicating the percentage of power remaining, and advertising in retail contexts relating to discounts or sales
   2. creating a model by subdividing a whole (for example, using 10 × 10 grids to represent various percentage amounts) and recognising complementary percentages (such as 30% and 70%) combine to make 100%
   3. creating a model by subdividing a collection of materials, such as blocks or money, to connect decimals and percentage equivalents of tenths and the commonly used fractions 12, 14 and 34; for example, connecting that one-tenth or 0.1 represents 10% and one-half or 0.5 represents 50%, and recognising that 60% of a whole is 10% more of the whole than 50%
   4. 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%
5. solve problems involving addition and subtraction of fractions with the same or related denominators, using different strategies (VC2M5N05)

   Elaborations

   1. 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 34 cup of flour and a 14 cup of flour, subtracting 34 of a metre from 2 14 metres
   2. representing and solving addition and subtraction problems involving fractions by using jumps on a number line, or bar models, or making diagrams of fractions as parts of shapes
   3. 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, 12+14 is the same as 24+14 
6. solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient mental and written calculation strategies and using digital tools where appropriate; check the reasonableness of answers (VC2M5N06)

   Elaborations

   1. solving multiplication problems such as 253 × 4 using a doubling strategy, for example, 2 × 253 = 506 and 2 × 506 = 1012
   2. solving multiplication problems like 15 × 16 by thinking of factors of both numbers, 15 = 3 × 5, 16 = 2 × 8, and rearranging the factors to make the calculation easier, 5 × 2 = 10, 3 × 8 = 24 and 10 × 24 = 240
   3. using an array to show place value partitioning to solve multiplication, such as 324 × 8, thinking 300 × 8 = 2400, 20 × 8 = 160, 4 × 8 = 32 then adding the parts, 2400 + 160 + 32 = 2592; and connecting the parts of the array to a standard written algorithm
   4. using different strategies used to multiply numbers, and explaining how they work and if they have any limitations; for example, discussing how the Japanese visual method for multiplication is not effective for multiplying larger numbers
7. solve problems involving division, choosing efficient mental and written strategies and using digital tools where appropriate; interpret any remainder according to the context and express results as a whole number, decimal or fraction (VC2M5N07)

   Elaborations

   1. interpreting and solving everyday division problems such as ‘How many buses are needed if there are 436 passengers and each bus carries 50 people?’, deciding whether to round up or down in order to accommodate the remainder and justifying choices
   2. solving division problems mentally, such as 72 divided by 9, 72 ÷ 9, by thinking, ‘How many nines make 72?’, □ × 9 = 72, or ‘Share 72 equally 9 ways’
   3. using the fact that equivalent division calculations result if both numbers are divided by the same factor
8. check and explain the reasonableness of solutions to problems, including financial contexts using estimation strategies appropriate to the context (VC2M5N08)

   Elaborations

   1. interpreting a series of contextual problems to decide whether an exact answer or an approximate calculation is appropriate, and explaining their reasoning in relation to the context and the numbers involved
   2. recognising the effect of rounding addition, subtraction, multiplication and division calculations, and rounding both numbers up, both numbers down, and one number up and one number down; and explaining which estimation is the best approximation and why
   3. considering the type of rounding that is appropriate when estimating the amount of money required; for example, rounding up or rounding down when buying one item from a store using cash, compared to rounding up the cost of every item when buying groceries to estimate the total cost and not rounding when the financial transactions are digital
9. use mathematical modelling to solve practical problems involving additive and multiplicative situations, including simple financial planning contexts; formulate the problems, choosing operations and efficient mental and written calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation (VC2M5N09)

   Elaborations

   1. 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
   2. modelling a series of contextual problems, deciding whether an exact answer or an approximate calculation is appropriate, and explaining their reasoning in relation to the context and the numbers involved
   3. 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
   4. investigating how mathematical models involving combinations of operations can be used to represent songs, stories and/or dances of Aboriginal and Torres Strait Islander Peoples
10. follow a mathematical algorithm involving branching and repetition (iteration); create and use algorithms involving a sequence of steps and decisions and digital tools to experiment with factors, multiples and divisibility; identify, interpret and describe emerging patterns (VC2M5N10)

    Elaborations

    1. simulating a simple random walk
    2. manipulating sets of numbers using a given rule, for example, if a number is even, halve it; or if a number is odd, subtract 1 then halve it
    3. creating algorithms that use multiplication and division facts to determine if a number is a multiple or factor of another number; for example, using a flow chart that determines whether numbers are factors or multiples of other numbers using branching, such as yes/no decisions
    4. identifying lowest common multiples and highest common factors of pairs or triples of natural numbers; for example, the lowest common multiple of {6, 9} is 18, and the highest common factor is 3, and the lowest common multiple of {3, 4, 5} is 60 and the highest common factor is 1
    5. using the ‘fill down’ function of a spreadsheet and a multiplication formula to generate a sequence of numbers that represent the multiples of any number you enter into the cell, and describing and explaining the emerging patterns