Stage 3
Outcomes
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Numbers and Algebra
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Whole Numbers
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MA3-4NA
Orders, reads and represents integers of any size and describes properties of whole numbers
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Whole Numbers 1
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Recognise, represent and order numbers to at least tens of millions
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Apply an understanding of place value and the role of zero to read and write numbers of any size
Play Activities 104Examples
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State the place value of digits in numbers of any size
Examples
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Arrange numbers of any size in ascending and descending order
Examples
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Partition numbers of any size in non-standard 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
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Use numbers of any size in real-life situations, including in money problems
Examples
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Round numbers to a specified place value, eg round 5 461 883 to the nearest million
Examples
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Apply an understanding of place value and the role of zero to read and write numbers of any size
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Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098)
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Determine all 'factors' of a given whole number, eg 36 has factors 1, 2, 3, 4, 6, 9, 12, 18 and 36
Examples
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Determine the 'highest common factor' (HCF) of two whole numbers, eg the HCF of 16 and 24 is 8
Examples
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Determine 'multiples' of a given whole number, eg multiples of 7 are 7, 14, 21, 28, ...
Examples
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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
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Determine all 'factors' of a given whole number, eg 36 has factors 1, 2, 3, 4, 6, 9, 12, 18 and 36
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Recognise, represent and order numbers to at least tens of millions
- Whole Numbers 2
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Whole Numbers 1
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MA3-4NA
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Addition and Subtraction
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MA3-5NA
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Addition and Subtraction 1
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Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)
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Add three or more numbers with different numbers of digits, with and without the use of digital technologies, eg 42 000 + 5123 + 246
Examples
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Select and apply efficient mental, written and calculator strategies to solve addition and subtraction word problems, including problems involving money
Play Activities 193Examples
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Record the strategy used to solve addition and subtraction word problems
Examples
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Check solutions to problems, including by using the inverse operation
Play Activities 165Examples
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Add three or more numbers with different numbers of digits, with and without the use of digital technologies, eg 42 000 + 5123 + 246
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Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)
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Addition and Subtraction 2
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Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)
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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
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Record the strategy used to solve addition and subtraction word problems
Examples
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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
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Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)
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Addition and Subtraction 1
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MA3-5NA
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Multiplication and Division
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MA3-6NA
Selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation
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Multiplication and Division 1
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Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental and written strategies and appropriate digital technologies (ACMNA100)
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Use mental and written strategies to multiply three- and four-digit numbers by one-digit numbers, including:multiplying the thousands, then the hundreds, then the tens and then the ones, using an area model, using the formal algorithm
Examples
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Use mental and written strategies to multiply two- and three-digit numbers by two-digit numbers, including: using an area model for two-digit by two-digit multiplication, factorising the numbers, using the extended form (long multiplication) of the formal
Examples
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Apply appropriate mental and written strategies, and digital technologies, to solve multiplication word problems
Examples
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Record the strategy used to solve multiplication word problems
Examples
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Use mental and written strategies to multiply three- and four-digit numbers by one-digit numbers, including:multiplying the thousands, then the hundreds, then the tens and then the ones, using an area model, using the formal algorithm
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Solve problems involving division by a one-digit number, including those that result in a remainder (ACMNA101)
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Use the term 'quotient' to describe the result of a division calculation, eg 'The quotient when 30 is divided by 6 is 5'
Examples
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Recognise and use different notations to indicate division
Examples
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Use mental and written strategies to divide a number with three or more digits by a one-digit divisor where there is no remainder, including: dividing the hundreds, then the tens, and then the ones, using the formal algorithm
Examples
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Use mental and written strategies to divide a number with three or more digits by a one-digit divisor where there is a remainder, including: dividing the tens and then the ones, using the formal algorithm
Examples
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Apply appropriate mental and written strategies, and digital technologies, to solve division word problems
Examples
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Use and interpret remainders in solutions to division problems, eg recognise when it is appropriate to round up an answer, such as 'How many 5-seater cars are required to take 47 people to the beach?'
Examples
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Record the strategy used to solve division word problems
Examples
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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)
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Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental and written strategies and appropriate digital technologies (ACMNA100)
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Multiplication and Division 2
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Select and apply efficient mental and written strategies, and appropriate digital technologies, to solve problems involving multiplication and division with whole numbers (ACMNA123)
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Select and use efficient mental and written strategies, and digital technologies, to multiply whole numbers of up to four digits by one- and two-digit numbers
Examples
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Select and use efficient mental and written strategies, and digital technologies, to divide whole numbers of up to four digits by a one-digit divisor, including where there is a remainder
Examples
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Use mental strategies to multiply and divide numbers by 10, 100, 1000 and their multiples
Examples
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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
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Select and use efficient mental and written strategies, and digital technologies, to multiply whole numbers of up to four digits by one- and two-digit numbers
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Explore the use of brackets and the order of operations to write number sentences (ACMNA134)
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Investigate and establish the order of operations using real-life 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
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Apply the order of operations to perform calculations involving mixed operations and grouping symbols, without the use of digital technologies
Examples
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Investigate and establish the order of operations using real-life 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
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Select and apply efficient mental and written strategies, and appropriate digital technologies, to solve problems involving multiplication and division with whole numbers (ACMNA123)
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Multiplication and Division 1
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MA3-6NA
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Fractions and Decimals
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MA3-7NA
Compares, orders and calculates with fractions, decimals and percentages
- Fractions and Decimals 1
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Fractions and Decimals 2
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Compare fractions with related denominators and locate and represent them on a number line (ACMNA125)
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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
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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
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Find equivalent fractions by re-dividing the whole, using diagrams and number lines
Examples
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Record equivalent fractions using diagrams and numerals
Examples
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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)
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Add and subtract decimals, with and without the use of digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128)
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Add and subtract decimals with the same number of decimal places, with and without the use of digital technologies
Play Activities 159Examples
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Add and subtract decimals with a different number of decimal places, with and without the use of digital technologies
Examples
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Round a number of up to three decimal places to the nearest whole number
Examples
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Add and subtract decimals with the same number of decimal places, with and without the use of digital technologies
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Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without the use of digital technologies (ACMNA129)
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Use mental strategies to multiply simple decimals by single-digit numbers, eg 3.5 x 2
Examples
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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
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Divide decimals by a one-digit whole number where the result is a terminating decimal, eg 5.25 / 5 = 1.05
Examples
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Solve word problems involving the multiplication and division of decimals, including those involving money, eg determine the 'best buy' for different-sized cartons of cans of soft drink
Examples
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Use mental strategies to multiply simple decimals by single-digit numbers, eg 3.5 x 2
- Multiply and divide decimals by powers of 10 (ACMNA130)
- Make connections between equivalent fractions, decimals and percentages (ACMNA131)
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Compare fractions with related denominators and locate and represent them on a number line (ACMNA125)
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MA3-7NA
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Patterns and Algebra
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MA3-8NA
Analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane
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Patterns and Algebra 1
- Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction (ACMNA107)
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Use equivalent number sentences involving multiplication and division to find unknown quantities (ACMNA121)
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Identify and use inverse operations to assist with the solution of number sentences, eg 125 / 5 = ( ) becomes ( ) x 5 = 125
Play Activities 141Examples
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Complete number sentences involving multiplication and division, including those involving simple fractions or decimals, eg 7 x ( ) = 7.7
Examples
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Write number sentences to match word problems that require finding a missing number, eg 'I am thinking of a number that when I double it and add 5, the answer is 13. What is the number?
Examples
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Identify and use inverse operations to assist with the solution of number sentences, eg 125 / 5 = ( ) becomes ( ) x 5 = 125
- Patterns and Algebra 2
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Patterns and Algebra 1
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MA3-8NA
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Whole Numbers
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Measurement and Geometry
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Length
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MA3-9MG
Selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length
- Length 1
- Length 2
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MA3-9MG
- Area
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Volume and Capacity
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MA3-11MG
Selects and uses the appropriate unit to estimate, measure and calculate volumes and capacities, and converts between units of capacity
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MA3-11MG
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Mass
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MA3-12MG
Selects and uses the appropriate unit and device to measure the masses of objects, and converts between units of mass
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MA3-12MG
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Time
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MA3-13MG
Uses 24-hour time and am and pm notation in real-life situations, and constructs timelines
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MA3-13MG
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Three-Dimensional Space
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MA3-14MG
Identifies three-dimensional objects, including prisms and pyramids, on the basis of their properties, and visualises, sketches and constructs them given drawings of different views
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Three-Dimensional Space 1
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Compare, describe and name prisms and pyramids
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Identify and determine the number of pairs of parallel faces of three-dimensional objects, eg 'A rectangular prism has three pairs of parallel faces'
Examples
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Recognise that prisms have a 'uniform cross-section' when the section is parallel to the base
Examples
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Identify, describe and compare the properties of prisms and pyramids, including: number of faces, shape of faces, number and type of identical faces, number of vertices, number of edges
Examples
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Identify and determine the number of pairs of parallel faces of three-dimensional objects, eg 'A rectangular prism has three pairs of parallel faces'
- Connect three-dimensional objects with their nets and other two-dimensional representations (ACMMG111)
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Compare, describe and name prisms and pyramids
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Three-Dimensional Space 1
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MA3-14MG
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Two-Dimensional Space
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MA3-15MG
Manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties
- Two-Dimensional Space 1
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Two-Dimensional Space 2
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Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142)
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Identify whether a two-dimensional shape has been translated, reflected or rotated, or has undergone a number of transformations, eg 'The parallelogram has been rotated clockwise through 90 degrees once and then reflected once'
Examples
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Construct patterns of two-dimensional shapes that involve translations, reflections and rotations using computer software
Examples
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Identify whether a two-dimensional shape has been translated, reflected or rotated, or has undergone a number of transformations, eg 'The parallelogram has been rotated clockwise through 90 degrees once and then reflected once'
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Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142)
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MA3-15MG
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Angles
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MA3-16MG
Measures and constructs angles, and applies angle relationships to find unknown angles
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Angles 1
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Construct angles using a protractor (ACMMG112)
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Identify that a right angle is 90 degrees, a straight angle is 180 degrees and an angle of revolution is 360 degrees
Examples
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Identify and describe angle size in degrees for each of the classifications acute, obtuse and reflex
Examples
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Compare the sizes of two or more angles in degrees, eg compare angles in different two-dimensional shapes
Examples
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Identify that a right angle is 90 degrees, a straight angle is 180 degrees and an angle of revolution is 360 degrees
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Construct angles using a protractor (ACMMG112)
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Angles 2
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Investigate, with and without the use of digital technologies, angles on a straight line, angles at a point, and vertically opposite angles; use the results to find unknown angles (ACMMG141)
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Identify and name angle types formed by the intersection of straight lines, including right angles, 'angles on a straight line', 'angles at a point' that form an angle of revolution, and 'vertically opposite angles'
Examples
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Investigate, with and without the use of digital technologies, angles at a point and establish that they form an angle of revolution and add to 360 degrees
Examples
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Identify and name angle types formed by the intersection of straight lines, including right angles, 'angles on a straight line', 'angles at a point' that form an angle of revolution, and 'vertically opposite angles'
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Investigate, with and without the use of digital technologies, angles on a straight line, angles at a point, and vertically opposite angles; use the results to find unknown angles (ACMMG141)
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Angles 1
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MA3-16MG
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Position
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MA3-17MG
Locates and describes position on maps using a grid-reference system
- Use a grid-reference system to describe locations (ACMMG113)
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Describe routes using landmarks and directional language (ACMMG113)
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Find a location on a map that is in a given direction from a town or landmark, eg locate a town that is north-east of Broken Hill
Examples
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Describe the direction of one location relative to another, eg 'Darwin is north-west of Sydney'
Examples
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Follow a sequence of two or more directions, including compass directions, to find and identify a particular location on a map
Examples
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Describe a route taken on a map using landmarks and directional language, including compass directions, eg 'Start at the post office, go west to the supermarket and then go south-west to the park'
Examples
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Find a location on a map that is in a given direction from a town or landmark, eg locate a town that is north-east of Broken Hill
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MA3-17MG
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Length
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Statistics and Probability
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Data
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MA3-18SP
Uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two-way tables
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MA3-18SP
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Chance
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MA3-19SP
Conducts chance experiments and assigns probabilities as values between 0 and 1 to describe their outcomes
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MA3-19SP
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Data