
Operations: Fractions, Decimals and Percentages

Operations: Addition and Subtraction

Operations: Multiplication and Division
Operations: Fractions, Decimals and Percentages
Outcomes
A student:

 MALS1WM
responds to and uses mathematical language to demonstrate understanding

 MALS2WM
applies mathematical strategies to solve problems

 MALS3WM
uses reasoning to recognise mathematical relationships

 MALS9NA
represents and operates with fractions, decimals or percentages in everyday contexts
Related Stage 4/5 outcome: MA45NA
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 quarterslices of pizza are equal to \(1\!\tfrac{1}{4}\) pizzas
 subtract a fraction from one whole using concrete materials, eg subtract threequarters 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)
 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 threequarters of an hour, first find onequarter of an hour and then multiply by 3 (Understanding, Fluency)
 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)
 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)
 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)
 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 5cent and/or 10cent pieces, eg round $5.02 to $5.00, round $2.03 to $2.05 (Communicating, Reasoning, Understanding, Fluency)
 Percentages
 read the symbol % as 'percent'
 recognise the use of the % symbol in a variety of contexts, eg advertising, discounts (Communicating, Understanding)
 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)
 decide which is the best interest rate offered for a loan using online calculators (Communicating, Reasoning, Fluency)
 calculate simple percentages of quantities, eg 10% off a $50 item, 10% GST on a bill
 recognise calculations as the same, eg finding 50% of a quantity is the same as dividing a quantity by 2 (Understanding, Fluency)
Operations: Addition and Subtraction
Outcomes
A student:

 MALS1WM
responds to and uses mathematical language to demonstrate understanding

 MALS2WM
applies mathematical strategies to solve problems

 MALS3WM
uses reasoning to recognise mathematical relationships

 MALS10NA
selects and uses strategies for addition and subtraction
Related Stage 4/5 outcome: MA44NA
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)
 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
 recognise terms in a range of situations, eg the difference between scores in a computer game (Understanding)
 use terms in a range of situations, eg 'My allowance plus birthday money equals $50' (Communicating, Understanding)
 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 =
 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)
 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)
 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
 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)
 calculate the change when purchasing items, eg the change from $10 when purchases total $3.50 (Problem Solving, Fluency)
Operations: Multiplication and Division
Outcomes
A student:

 MALS2WM
applies mathematical strategies to solve problems

 MALS3WM
uses reasoning to recognise mathematical relationships

 MALS11NA
selects and uses strategies for multiplication and division
Related Stage 4/5 outcome: MA44NA
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)
 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
 recognise terms in a range of situations, eg 'Two groups of football supporters were at the game' (Understanding)
 use terms in a range of situations, eg 'My share of the money is $10' (Communicating, Understanding)
 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)
 recognise and use the symbols ×, ÷ and =
 multiply two numbers using mental strategies, written processes and/or calculator strategies

multiply numbers using an array of equal rows, eg
(Fluency)  determine the quantities needed when preparing a meal for several people using a recipe based on ingredients for one person (Problem Solving)
 estimate the product of two numbers and check by performing the calculation or using a calculator (Problem Solving, Fluency)
 divide two numbers using mental strategies, written processes and/or calculator strategies

divide numbers using an array of equal rows, eg
(Fluency)  determine the quantities needed when preparing a meal for one person using a recipe based on ingredients for four people (Problem Solving)
 calculate the cost of a single item when given the price of a pack containing several items (Problem Solving, Fluency)
 estimate the result when dividing two numbers and check by performing the calculation or using a calculator (Problem Solving, Fluency)
 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
 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)
 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)