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) • 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)
• 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 5-cent and/or 10-cent 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: • 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) • 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:

• 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)
• 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)