skip to main content
NSW Syllabuses

Mathematics K–10 - Life Skills - Number and Algebra Operations

Operations: Fractions, Decimals and Percentages

Outcomes

A student:

  • MALS-1WM

    responds to and uses mathematical language to demonstrate understanding

  • MALS-2WM

    applies mathematical strategies to solve problems

  • MALS-3WM

    uses reasoning to recognise mathematical relationships

  • MALS-9NA

    represents and operates with fractions, decimals or percentages in everyday contexts

Related Stage 4/5 outcome: MA4-5NA

Content

  • Students:
  • Fractions
  • use fraction notation to represent parts of a whole, eg \(\frac{1}{2}, \; \frac{1}{4},\; \frac{2}{4},\; \frac{3}{4},\; \frac{1}{3},\; \frac{2}{3}\)
  • interpret the denominator as the number of equal parts a whole has been divided into (Understanding)
  • interpret the numerator as the number of equal fractional parts, eg \(\frac{3}{4}\) means 3 equal parts of 4 (Understanding)
  • add a fraction to a whole number using concrete materials and record the result as a mixed numeral, eg \(3+\frac{3}{4} = 3\!\tfrac{3}{4}\)
  • add a fraction to another fraction, using concrete materials, so that the total is no more than one whole
  • add a fraction to another fraction, using concrete materials, so that the total is more than one whole and represent this as a mixed numeral, eg five quarter-slices of pizza are equal to \(1\!\tfrac{1}{4}\) pizzas
  • subtract a fraction from one whole using concrete materials, eg subtract three-quarters of a pizza from one whole pizza and find the fraction remaining
  • find a unit fraction of a quantity, eg \(\frac{1}{2}\) of $30, \(\frac{1}{3}\) of 300 g, \(\frac{1}{4}\) of 100 cm
  • recognise that finding a unit fraction of a quantity is related to division, eg half of $60 is the same as $60 divided by 2 (Understanding, Fluency) CCT
  • find any fraction of a quantity, eg \(\frac{2}{3}\) of $30, \(\frac{3}{4}\) of 100 cm
  • recognise the relationship between finding a unit fraction of a quantity and finding any fraction of a quantity, eg to find three-quarters of an hour, first find one-quarter of an hour and then multiply by 3 (Understanding, Fluency) CCT
  • Decimals
  • read numbers as decimals, eg 3.5 is read as 'three point five', 3.12 is read as 'three point one two'
  • recognise the use of decimals in the community, eg advertisements for interest rates (Reasoning, Understanding) PSC
  • recognise the use of decimals for recording measurements, eg 3.5 metres means three and a half metres, timing swimming races to tenths and hundredths of a second (Communicating, Reasoning, Understanding) PSC
  • recognise decimal notation for commonly used fractions, eg \(\frac{1}{2}\) = 0.5, \(\frac{1}{4}\) = 0.25
  • add and subtract numbers correct to two decimal places in the context of money, eg $2.25 + $1.25
  • relate fractions to decimals in the context of parts of one dollar, eg 10 cents = \(\frac{10}{100}\) of $1 = $0.10, 50 cents = \(\frac{50}{100}\) of $1 = $0.50
  • interpret decimal notation for tenths and hundredths, eg 0.1 is the same as \(\frac{1}{10}\), 0.01 is the same as \(\frac{1}{100}\)
  • interpret calculator displays involving decimals (Communicating, Reasoning, Understanding) L
  • compare decimals with the same number of decimal places, eg 0.3 is less than 0.5
  • use a number line to position decimals between 0 and 1 (Communicating, Understanding, Fluency)
  • round decimals in the context of money, eg round $4.99 to $5.00
  • explain the result of rounding when purchasing goods where the total number of cents involved cannot be made up using 5-cent and/or 10-cent pieces, eg round $5.02 to $5.00, round $2.03 to $2.05 (Communicating, Reasoning, Understanding, Fluency) CCTPSC
  • Percentages
  • read the symbol % as 'percent' L
  • recognise the use of the % symbol in a variety of contexts, eg advertising, discounts (Communicating, Understanding) L
  • recognise the fraction equivalent for commonly used percentages, eg \(50\% = \frac{1}{2}\), \(25\% = \frac{1}{4}\), \(10\% = \frac{1}{10}\)
  • recognise that percentages are parts of 100, eg \(50\% = \frac{50}{100}\)
  • interpret the use of percentages in everyday contexts
  • interpret advertising and media reports involving percentages, eg 90% success rate for goal kicking, 25% more chocolate (Communicating, Reasoning, Understanding) CCTPSC
  • decide which is the best interest rate offered for a loan using online calculators (Communicating, Reasoning, Fluency) CCTWE
  • calculate simple percentages of quantities, eg 10% off a $50 item, 10% GST on a bill WE
  • recognise calculations as the same, eg finding 50% of a quantity is the same as dividing a quantity by 2 (Understanding, Fluency) CCT

Operations: Addition and Subtraction

Outcomes

A student:

  • MALS-1WM

    responds to and uses mathematical language to demonstrate understanding

  • MALS-2WM

    applies mathematical strategies to solve problems

  • MALS-3WM

    uses reasoning to recognise mathematical relationships

  • MALS-10NA

    selects and uses strategies for addition and subtraction

Related Stage 4/5 outcome: MA4-4NA

Content

  • Students:
  • model addition using concrete materials
  • combine two or more groups of objects (Fluency, Understanding)
  • compare two groups of objects to determine how many more are in the larger group (Reasoning, Understanding) CCT
  • model subtraction using concrete materials
  • separate and take away part of a group of objects to model subtraction (Understanding, Fluency)
  • respond to and use the language of addition and subtraction in everyday contexts, eg add, plus, take away, minus, the difference between L
  • recognise terms in a range of situations, eg the difference between scores in a computer game (Understanding) L
  • use terms in a range of situations, eg 'My allowance plus birthday money equals $50' (Communicating, Understanding) L
  • add two numbers using concrete materials and/or mental strategies
  • count on from the larger number to find the total of two numbers (Communicating, Fluency)
  • subtract a number from a given number using concrete materials and/or mental strategies
  • count back from a number to find the number remaining (Communicating, Fluency)
  • recognise and use the symbols +, – and = L
  • add two numbers using mental strategies, written processes and/or calculator strategies
  • create combinations for numbers to at least 10, eg 'How many more to make 10?' (Understanding, Fluency)
  • estimate the sum of two numbers and check by performing the calculation or using a calculator (Problem Solving, Fluency) CCT
  • subtract a number from a given number using mental strategies, written processes and/or calculator strategies
  • estimate how much will be left over when one number is subtracted from another and check by performing the calculation or using a calculator (Fluency, Problem Solving) CCT
  • add more than two numbers, eg 6 + 2 + 5, using mental strategies, written processes and/or calculator strategies
  • subtract more than two numbers, eg 6 – 4 – 2, using mental strategies, written processes and/or calculator strategies
  • select and apply appropriate mental strategies, written processes and/or calculator strategies for addition and subtraction to solve problems in a range of contexts CCT
  • calculate the total cost when purchasing more than one item, eg the total cost of a $2.50 juice and a $4.50 sandwich (Problem Solving, Fluency) PSC
  • calculate the change when purchasing items, eg the change from $10 when purchases total $3.50 (Problem Solving, Fluency) PSC

Operations: Multiplication and Division

Outcomes

A student:

  • MALS-2WM

    applies mathematical strategies to solve problems

  • MALS-3WM

    uses reasoning to recognise mathematical relationships

  • MALS-11NA

    selects and uses strategies for multiplication and division

Related Stage 4/5 outcome: MA4-4NA

Content

  • Students:
  • model multiplication using concrete materials
  • combine equal groups of objects, eg three boxes each containing four pencils (Understanding, Fluency)
  • model division using concrete materials
  • share a group of objects equally among people, eg 12 balls among 3 students (Understanding, Fluency) PSC
  • use repeated subtraction with concrete materials, eg determine how many bags of golf balls can be created by placing 5 golf balls into each bag (Understanding, Fluency)
  • respond to and use the language of multiplication and division in everyday contexts, eg lots of, groups of, shares, equal groups L
  • recognise terms in a range of situations, eg 'Two groups of football supporters were at the game' (Understanding) L
  • use terms in a range of situations, eg 'My share of the money is $10' (Communicating, Understanding) L
  • multiply two numbers using concrete materials and/or mental strategies
  • collect groups of items from two or more people and determine how many items there are altogether (Understanding, Fluency)
  • divide two numbers using concrete materials and/or mental strategies
  • share a number of items between two or more people using concrete materials (Understanding, Fluency) PSC
  • recognise and use the symbols ×, ÷ and = L
  • multiply two numbers using mental strategies, written processes and/or calculator strategies
  • multiply numbers using an array of equal rows, eg 
    The equation 3 times 4 equals 12 is represented by an array of 3 rows of 4 dots.    (Fluency) 
  • determine the quantities needed when preparing a meal for several people using a recipe based on ingredients for one person (Problem Solving) CCTPSC
  • estimate the product of two numbers and check by performing the calculation or using a calculator (Problem Solving, Fluency) CCT
  • divide two numbers using mental strategies, written processes and/or calculator strategies
  • divide numbers using an array of equal rows, eg 
    The equation 12 divided by 3 equals 4 is represented by an array of 3 rows of 4 dots.(Fluency)
  • determine the quantities needed when preparing a meal for one person using a recipe based on ingredients for four people (Problem Solving) CCTPSC
  • calculate the cost of a single item when given the price of a pack containing several items (Problem Solving, Fluency) CCTPSC
  • estimate the result when dividing two numbers and check by performing the calculation or using a calculator (Problem Solving, Fluency) CCT
  • multiply more than two numbers, eg 3 × 5 × 2, using mental strategies, written processes and/or calculator strategies
  • divide by one number followed by another, eg 20 ÷ 5 ÷ 2, using mental strategies, written processes and/or calculator strategies
  • select and apply appropriate mental strategies, written processes and/or calculator strategies for multiplication and division to solve problems in a range of contexts CCTWE
  • determine the total cost of a number of items, given the price of one, eg calculate the combined cost of train travel over two or more days for two or more people (Problem Solving, Fluency) CCTPSC
  • determine the unit cost of an item or service when sold as a group, eg calculate the daily cost of shared accommodation over a set period of time for two or more people (Problem Solving, Fluency) CCTPSC