Numbers and Algebra
Outcomes

Whole Numbers

MA34NA
Orders, reads and represents integers of any size and describes properties of whole numbers

Whole Numbers 1

Recognise, represent and order numbers to at least tens of millions

Apply an understanding of place value and the role of zero to read and write numbers of any size
Play Activities 104Examples

State the place value of digits in numbers of any size
Examples

Arrange numbers of any size in ascending and descending order
Examples

Partition numbers of any size in nonstandard forms to aid mental calculation, eg when adding 163 480 and 150 000, 163 480 could be partitioned as 150 000 + 13 480, so that 150 000 could then be doubled and added to 13 480
Examples

Use numbers of any size in reallife situations, including in money problems
Examples

Round numbers to a specified place value, eg round 5 461 883 to the nearest million
Examples

Apply an understanding of place value and the role of zero to read and write numbers of any size

Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098)

Determine all 'factors' of a given whole number, eg 36 has factors 1, 2, 3, 4, 6, 9, 12, 18 and 36
Examples

Determine the 'highest common factor' (HCF) of two whole numbers, eg the HCF of 16 and 24 is 8
Examples

Determine 'multiples' of a given whole number, eg multiples of 7 are 7, 14, 21, 28, ...
Examples

Solve problems using knowledge of factors and multiples, eg 'There are 48 people at a party. In how many ways can you set up the tables and chairs, so that each table seats the same number of people and there are no empty chairs?'
Examples

Determine all 'factors' of a given whole number, eg 36 has factors 1, 2, 3, 4, 6, 9, 12, 18 and 36

Recognise, represent and order numbers to at least tens of millions
 Whole Numbers 2

Whole Numbers 1

MA34NA

Addition and Subtraction

MA35NA

Addition and Subtraction 1

Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)

Add three or more numbers with different numbers of digits, with and without the use of digital technologies, eg 42 000 + 5123 + 246
Examples

Select and apply efficient mental, written and calculator strategies to solve addition and subtraction word problems, including problems involving money
Play Activities 193Examples

Record the strategy used to solve addition and subtraction word problems
Examples

Check solutions to problems, including by using the inverse operation
Play Activities 165Examples

Add three or more numbers with different numbers of digits, with and without the use of digital technologies, eg 42 000 + 5123 + 246

Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)

Addition and Subtraction 2

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)

Solve addition and subtraction word problems involving whole numbers of any size, including problems that require more than one operation, eg 'I have saved $40 000 to buy a new car. The basic model costs $36 118 and I add tinted windows for $860 and Bluet
Examples

Record the strategy used to solve addition and subtraction word problems
Examples

Solve addition and subtraction word problems involving whole numbers of any size, including problems that require more than one operation, eg 'I have saved $40 000 to buy a new car. The basic model costs $36 118 and I add tinted windows for $860 and Bluet

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)

Addition and Subtraction 1

MA35NA

Multiplication and Division

MA36NA
Selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation

Multiplication and Division 1

Solve problems involving multiplication of large numbers by one or twodigit numbers using efficient mental and written strategies and appropriate digital technologies (ACMNA100)

Use mental and written strategies to multiply three and fourdigit numbers by onedigit numbers, including:multiplying the thousands, then the hundreds, then the tens and then the ones, using an area model, using the formal algorithm
Examples

Use mental and written strategies to multiply two and threedigit numbers by twodigit numbers, including: using an area model for twodigit by twodigit multiplication, factorising the numbers, using the extended form (long multiplication) of the formal
Examples

Apply appropriate mental and written strategies, and digital technologies, to solve multiplication word problems
Examples

Record the strategy used to solve multiplication word problems
Examples

Use mental and written strategies to multiply three and fourdigit numbers by onedigit numbers, including:multiplying the thousands, then the hundreds, then the tens and then the ones, using an area model, using the formal algorithm

Solve problems involving division by a onedigit number, including those that result in a remainder (ACMNA101)

Use the term 'quotient' to describe the result of a division calculation, eg 'The quotient when 30 is divided by 6 is 5'
Examples

Recognise and use different notations to indicate division
Examples

Use mental and written strategies to divide a number with three or more digits by a onedigit divisor where there is no remainder, including: dividing the hundreds, then the tens, and then the ones, using the formal algorithm
Examples

Use mental and written strategies to divide a number with three or more digits by a onedigit divisor where there is a remainder, including: dividing the tens and then the ones, using the formal algorithm
Examples

Apply appropriate mental and written strategies, and digital technologies, to solve division word problems
Examples

Use and interpret remainders in solutions to division problems, eg recognise when it is appropriate to round up an answer, such as 'How many 5seater cars are required to take 47 people to the beach?'
Examples

Record the strategy used to solve division word problems
Examples

Use the term 'quotient' to describe the result of a division calculation, eg 'The quotient when 30 is divided by 6 is 5'
 Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099)

Solve problems involving multiplication of large numbers by one or twodigit numbers using efficient mental and written strategies and appropriate digital technologies (ACMNA100)

Multiplication and Division 2

Select and apply efficient mental and written strategies, and appropriate digital technologies, to solve problems involving multiplication and division with whole numbers (ACMNA123)

Select and use efficient mental and written strategies, and digital technologies, to multiply whole numbers of up to four digits by one and twodigit numbers
Examples

Select and use efficient mental and written strategies, and digital technologies, to divide whole numbers of up to four digits by a onedigit divisor, including where there is a remainder
Examples

Use mental strategies to multiply and divide numbers by 10, 100, 1000 and their multiples
Examples

Solve word problems involving multiplication and division, eg 'A recipe requires 3 cups of flour for 10 people. How many cups of flour are required for 40 people?'
Examples

Select and use efficient mental and written strategies, and digital technologies, to multiply whole numbers of up to four digits by one and twodigit numbers

Explore the use of brackets and the order of operations to write number sentences (ACMNA134)

Investigate and establish the order of operations using reallife contexts, eg 'I buy six goldfish costing $10 each and two water plants costing $4 each. What is the total cost?'; this can be represented by the number sentence 6 x 10 + 2 x 4 but, to obtai
Examples

Apply the order of operations to perform calculations involving mixed operations and grouping symbols, without the use of digital technologies
Examples

Investigate and establish the order of operations using reallife contexts, eg 'I buy six goldfish costing $10 each and two water plants costing $4 each. What is the total cost?'; this can be represented by the number sentence 6 x 10 + 2 x 4 but, to obtai

Select and apply efficient mental and written strategies, and appropriate digital technologies, to solve problems involving multiplication and division with whole numbers (ACMNA123)

Multiplication and Division 1

MA36NA

Fractions and Decimals

MA37NA
Compares, orders and calculates with fractions, decimals and percentages
 Fractions and Decimals 1

Fractions and Decimals 2

Compare fractions with related denominators and locate and represent them on a number line (ACMNA125)

Model, compare and represent fractions with denominator of 2, 3, 4, 5, 6, 8, 10, 12 and 100 of a whole object, a whole shape and a collection of objects
Examples

Compare and order simple fractions with related denominators using strategies such as diagrams, the number line, or equivalent fractions, eg write 3/5, 3/10, 1 1/10, 4/5 and 7/10 in ascending order
Examples

Find equivalent fractions by redividing the whole, using diagrams and number lines
Examples

Record equivalent fractions using diagrams and numerals
Examples

Model, compare and represent fractions with denominator of 2, 3, 4, 5, 6, 8, 10, 12 and 100 of a whole object, a whole shape and a collection of objects
 Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126)
 Find a simple fraction of a quantity where the result is a whole number, with and without the use of digital technologies (ACMNA127)

Add and subtract decimals, with and without the use of digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128)

Add and subtract decimals with the same number of decimal places, with and without the use of digital technologies
Play Activities 159Examples

Add and subtract decimals with a different number of decimal places, with and without the use of digital technologies
Examples

Round a number of up to three decimal places to the nearest whole number
Examples

Add and subtract decimals with the same number of decimal places, with and without the use of digital technologies

Multiply decimals by whole numbers and perform divisions by nonzero whole numbers where the results are terminating decimals, with and without the use of digital technologies (ACMNA129)

Use mental strategies to multiply simple decimals by singledigit numbers, eg 3.5 x 2
Examples

Multiply decimals of up to three decimal places by whole numbers of up to two digits, with and without the use of digital technologies, eg 'I measured three desks. Each desk was 1.25 m in length, so the total length is 3 x 1.25 = 3.75 m'
Examples

Divide decimals by a onedigit whole number where the result is a terminating decimal, eg 5.25 / 5 = 1.05
Examples

Solve word problems involving the multiplication and division of decimals, including those involving money, eg determine the 'best buy' for differentsized cartons of cans of soft drink
Examples

Use mental strategies to multiply simple decimals by singledigit numbers, eg 3.5 x 2
 Multiply and divide decimals by powers of 10 (ACMNA130)
 Make connections between equivalent fractions, decimals and percentages (ACMNA131)

Compare fractions with related denominators and locate and represent them on a number line (ACMNA125)

MA37NA