NSW Mathematics Syllabus — Stage 3
In the NSW Mathematics K–10 syllabus, Stage 3 covers Level 5 and Level 6. This page shows the whole Stage: open any row to see its e-Text pages and worksheets at each level.
Number and algebra
Represents numbers A
Whole numbers: to 1 billion, place-value roundingLevel 5: 6 · Level 6: 5
Level 5 e-Text pages: 1, 26-30
Level 6 e-Text pages: 1, 25, 75-77
Other resources
- Tests and Answers 4:06 — Multiple choice 1
- Tests and Answers 4:06A — Answers: Multiple choice 1
- Tests and Answers 4:08 — Multiple choice 2
- Tests and Answers 4:08A — Answers: Multiple choice 2
- Tests and Answers 5:03 — Multiple choice 1
- Tests and Answers 5:03A — Answers: Multiple choice 1
- Tests and Answers 5:06 — Multiple choice 2
- Tests and Answers 5:06A — Answers: Multiple choice 2
- Tests and Answers 6:06 — Multiple choice 1
- Tests and Answers 6:06A — Answers: Multiple choice 1
- Tests and Answers 6:08 — Multiple choice 2
- Tests and Answers 6:08A — Answers: Multiple choice 2
- Fun and Games 5:01 — Addition challenge, Number roles/Rock around the clock
- Fun and Games 5:02 — Shape maze/Two-and three-digit reversals
- Fun and Games 5:03 — Building a flat, Colour times/What number am I?
- Fun and Games 5:04 — Name the area/A good deal
- Fun and Games 5:05 — Colour my day/Fraction roll
- Fun and Games 5:06 — High totals/Four in a row
- Fun and Games 5:07 — Find my fleet/5-digit order
- Fun and Games 5:08 — 3D cover up
- Fun and Games 5:09 — Flat out/The sixth sense
- Fun and Games 5:10 — Operations rule, What's the time Mr?/All at sea
- Fun and Games 5:11 — Product choice/Egyptian division
- Fun and Games 5:12 — Pattern play/Match up
- Fun and Games 5:13 — Win a block/Multiple to and fro
- Fun and Games 5:14 — Multiples of 9: dot-to-dot/Fraction knock-out
- Fun and Games 5:15 — Speed limits/Line out
- Fun and Games 5:16 — Number juggle/Triangles, triangles everywhere
- Fun and Games 5:17 — Mystery words/Holiday time
- Fun and Games 6:01 — The order of numbers/Clock symmetry
- Fun and Games 6:02 — Rock around the clock/Line up
- Fun and Games 6:03 — High times/Out in space
- Fun and Games 6:04 — Colour my day/Mixed-up number sentences
- Fun and Games 6:05 — Block out/The end of the line
- Fun and Games 6:06 — Time for a pattern/Estimate and divide
- Fun and Games 6:07 — Mouse race/Shape up
- Fun and Games 6:08 — Product choice/Grid objects
- Fun and Games 6:09 — Number patterns/Prime time
- Fun and Games 6:10 — Circle designs/High shuffle
- Fun and Games 6:11 — 3D favourites/Tangrams
- Fun and Games 6:12 — Circle maze/Make 100, Pascal's triangle
- Fun and Games 6:13 — 3D favourites/Symmetry
- Fun and Games 6:14 — Hidden faces/Phone in
- Fun and Games 6:15 — A fair share/Mixed operator
- Fun and Games 6:16 — Operations search/Piece it together/Mystery words
- Concept Dictionary – Whole Numbers
- Cards and boards 5:01 — Roman numerals cards
- Other resources 5:03 — Place value: 5-digit numbers
- Other resources 5:04 — Place value: 6-digit numbers
- Other resources 6:04 — Representing large numbers
Alan’s note: Naplan practice: (Resources: Tests and Answers 4:06, 4:06A, 4:08, 4:08A, 5:03, 5:03A, 5:06, 5:06A, 6:06, 6:06A, 6:08, 6:08A), Fun and Games: 5:01-5:17, 6:01-6:16, Concept Dictionary: Whole Numbers, Roman numerals: e-Text 5 p 49, Cards and boards: 5:01 (Roman numerals), Other resources: 5:03-5:04 (Place-value: 5-digit numbers/Place-value: 6-digit numbers), Other resources: 6:04 (Representing large numbers)
Fractions/decimals: decimals 3 decimal places, pace-value,Level 5: 5 · Level 6: 8
Level 5 e-Text pages: 8-10, 42-43
Level 6 e-Text pages: 24-31
Other resources
- Language Cards 5:01 — Language cards
- Language Cards 5:02 — Language cards
- Language Cards 5:03 — What will happen tomorrow?
- Language Cards 6:01 — Language cards
- Language Cards 6:02 — Language cards
- Language Cards 6:03 — What will happen tomorrow?
- Charts and Mindmaps 6:08 — Decimals mindmap
- Cards and boards 5:04 — Decimal cards
- Cards and boards 5:05 — Decimal cards
- Cards and boards 5:06 — Decimal place value cards
Alan’s note: Language Cards: 5:01-5:03, 6:01-6:03, Charts and Mindmaps: 6:08 (Decimals), Cards and boards: 5:04-5:06 (Decimal cards),
Compare and order decimalsLevel 5: 2
Level 5 e-Text pages: 9-10
Other resources
Alan’s note: Concept Dictionary: Patterns and Algebra
Represents numbers B
Whole numbers: integers (positive and negative whole numbers), number lineLevel 6: 5
Level 6 e-Text pages: 1, 15-18
Other resources
Alan’s note: Other resources: 6:02 (Number lines: negative numbers)
Fractions/decimals/percentages: convert between fractions, decimals and percentages (1/10, 1/4, 1/2, 3/4)Level 5: 1 · Level 6: 9
Level 5 e-Text pages: 42
Level 6 e-Text pages: 9-14, 24-26
Other resources
- Cards and boards 6:02 — Fraction cards
- Cards and boards 6:03 — Fraction cards
- Other resources 6:21 — Fractions, decimals and percentages
Alan’s note: Cards and boards: 6:02-6:03 (Fraction cards), Other resources: 6:21 (Fractions, decimals and percentages)
Percentage discounts (10%, 25%, 50%)Level 6: 2
Level 6 e-Text pages: 82-83
Additive relations A
Addition/subtraction: mental and written strategiesLevel 5: 17 · Level 6: 6
Level 5 e-Text pages: 1, 3, 12-19, 31-32, 45-47, 64-65
- 5:NA01Mental strategies
- 5:NA03Subtraction
- 5:NA12Thirds, sixths and twelfths
- 5:NA13Mental strategies
- 5:NA14Checking by estimating
- 5:NA15Addition and data
- 5:NA16Addition to 4 digits
- 5:NA17Subtraction to 4 digits
- 5:NA18Subtracting from thousands
- 5:NA19Patterns using whole numbers
- 5:NA31Addition to 5 digits
- 5:NA32Subtraction to 5 digits
- 5:NA455-digit addition and subtraction
- 5:NA46Using large numbers
- 5:NA47Checking: inverse operations
- 5:NA64Addition and subtraction
- 5:NA65Budgeting
Level 6 e-Text pages: 2, 32-36
Other resources
- Concept Dictionary - Addition and Subtraction
- Other resources 5:07 — Addition and subtraction algorithms: 4 digits
- Other resources 5:08 — Addition and subtraction algorithms: 5 digits
Alan’s note: Maths Builder homepage: addition facts (3:plus1 up to 3:plusten, 3:plusA, 3:plusB, 3:S1, 3:S2, 3:S3) These drill addition and subtraction facts to 20.), Concept Dictionary: Addition and Subtraction, Other resources: 5:07-5:08 (Addition and subtraction algorithms: 4 digits/5 digits)
Using rounding and estimationLevel 5: 5 · Level 6: 7
Level 5 e-Text pages: 14, 22, 33, 46-47
Additive relations B
Addition/subtraction: strategies, problemsLevel 5: 11 · Level 6: 5
Level 5 e-Text pages: 1, 3, 13, 16-19, 31-32, 45, 65
Level 6 e-Text pages: 32-36
Other resources: Square and triangular numbers: e-Text 6 pp 53-54
+ and – of six-digit numbers and beyondLevel 6: 3
Level 6 e-Text pages: 73-74, 77
Other resources
Alan’s note: Other resources: 6:09 (Addition and subtraction: larger numbers)
Addition and subtraction of decimals, word problems, strategiesLevel 5: 1 · Level 6: 10
Level 5 e-Text pages: 48
Level 6 e-Text pages: 22-23, 27-31, 51, 71-72
Other resources
Alan’s note: Other resources: 6:06 (Addition and subtraction large numbers)
Multiplicative relations A
Multiplication/division: Products, factors, primes, composites, tablesLevel 5: 4 · Level 6: 8
Level 5 e-Text pages: 4-7
Level 6 e-Text pages: 3, 7-8, 52-55, 93
Other resources
- Concept Dictionary - Multiplication and Division
- Charts and Mindmaps 5:06 — Important things you should know
- Other resources 5:09 — Multiplication tables
- Other resources 5:10 — Multiplication grids
- Other resources 5:11 — Multiplication webs
Alan’s note: Maths Builder homepage: x tables facts (4:x2 up to 4:x11, 4:xa Mixed times tables). These drill multiplication facts. Concept Dictionary: Multiplication and Division, Charts and Mindmaps: 5:06 (Important things you should know), Other resources: 5:09-5:11 (Multiplication tables/grids/webs)
Multiply numbers up to 4 digits by a 1-digit numberLevel 5: 4
Level 5 e-Text pages: 38-40, 58
Other resources
Alan’s note: Other resources: 5:12 (Multiplication algorithms)
Strategies, multiply 2- and 3-digit numbers by 1- and 2-digit numbersLevel 5: 15 · Level 6: 2
Level 5 e-Text pages: 20-22, 33-35, 38, 63, 66-70, 74-75
- 5:NA20Multiplying 10s and 100s numbers
- 5:NA21Multiplication of 2-digit numbers
- 5:NA22Estimating using rounding
- 5:NA33Using known facts to estimate
- 5:NA34Division: 2-digit answers
- 5:NA35Division strategies
- 5:NA38Multiplication using strategies
- 5:NA63Division strategies
- 5:NA66Multiplying by multiples of 10
- 5:NA67Multiplication strategy 1
- 5:NA68Multiplication strategy 2
- 5:NA69Extended multiplication
- 5:NA70Extended multiplication
- 5:NA74Inverse operations
- 5:NA75Equivalent number sentences
Level 6 e-Text pages: 37, 43
Division by a 1-digit number, whole number remaindersLevel 5: 15 · Level 6: 6
Level 5 e-Text pages: 4, 34-37, 53-57, 59-63
- 5:NA04Division
- 5:NA34Division: 2-digit answers
- 5:NA35Division strategies
- 5:NA36Averages
- 5:NA37Division: 2-digit answers
- 5:NA53Division with 2 digits: remainders
- 5:NA54Checking division
- 5:NA55Division: 0 in the answer
- 5:NA56Dividing multiples of ten
- 5:NA57Division using tens numbers
- 5:NA59Dividing 3-digit numbers
- 5:NA60Dividing 3-digit numbers
- 5:NA61Dividing 4-digit numbers
- 5:NA62Estimating division
- 5:NA63Division strategies
Level 6 e-Text pages: 3-8
Other resources
Alan’s note: Other resources: 6:16-6:17 (Division algorithms/Division:larger numbers)
Multiplicative relations B
Multiplication/division: using strategies and word problemsLevel 5: 4 · Level 6: 8
Level 5 e-Text pages: 33-35, 63
Level 6 e-Text pages: 7, 37, 71-72, 90-93
Other resources: Equivalent number sentences, finding missing numbers: e-Text 5 pp 74-75
Multiply numbers up to 4 digits by 1- and 2-digit numbersLevel 5: 5 · Level 6: 7
Level 5 e-Text pages: 66-70
Level 6 e-Text pages: 40-41, 43-47
Other resources
- Other resources 6:14 — Multiplication algorithms: larger numbers
- Other resources 6:15 — Extended multiplication
Alan’s note: Other resources: 6:14-6:15 (Multiplication algorithms: larger numbers/Extended multiplication)
x and ÷ of decimals by powers of 10, x decimals by a single digit number, x decimals by a 2-digit number, estimating, patternsLevel 5: 1 · Level 6: 13
Level 5 e-Text pages: 66
Level 6 e-Text pages: 37-43, 48-51, 68-69
- 6:NA37Multiplication algorithm
- 6:NA38Multiplying decimals
- 6:NA39Multiplying decimals
- 6:NA40Multiplying 4-digit numbers
- 6:NA41Division of decimals
- 6:NA42Division of decimals
- 6:NA43Multiplication strategies
- 6:NA48A decimal times a power of 10
- 6:NA49A decimal times a 2-digit number
- 6:NA50Estimating decimal multiplication
- 6:NA51Estimating with decimals
- 6:NA68Dividing a decimal by a power of 10
- 6:NA69Dividing by multiples of 10
Other resources
Alan’s note: Other resources: 6:13 (Multiplication algorithm)
Number patterns and number sentencesLevel 5: 1 · Level 6: 6
Level 5 e-Text pages: 19
Level 6 e-Text pages: 84-89
Other resources: Prime and composite numbers: e-Text 6 p 52
Order of operationsLevel 6: 3
Level 6 e-Text pages: 19-21
Representing quantity fractions A
Fractions/decimals: fractions to 1, number line, comparing unit fractions, equivalent fractionsLevel 5: 4
Level 5 e-Text pages: 11-12, 41. 51
Other resources
- Concept Dictionary - Fractions, Decimals and Percentages
- Other resources 5:14 — Fractions of a whole
- Other resources 5:15 — Comparing fractions
- Other resources 5:16 — Comparing fractions: blanks
Alan’s note: Concept Dictionary: Fractions, Decimals and Percentages, Other resources: 5:14-5:16 (Fractions of a whole/Comparing fractions/Comparing fractions: blanks)
Fraction and decimal equivalents, mixed numbersLevel 5: 11 · Level 6: 5
Level 5 e-Text pages: 8, 10, 12, 24-25, 41-44, 71-72
- 5:NA08Fractions and decimals
- 5:NA10Fractions and decimals
- 5:NA12Thirds, sixths and twelfths
- 5:NA24Improper fractions/ mixed numerals
- 5:NA25Improper fractions/ mixed numerals
- 5:NA41Decimal patterns
- 5:NA42Thousandths
- 5:NA43Thousandths
- 5:NA44Comparing and ordering decimals
- 5:NA71Addition with mixed numerals
- 5:NA72Subtraction with mixed numbers
Level 6 e-Text pages: 12-14, 58-59
Other resources
- Charts and Mindmaps 5:07 — Decimals mindmap
- Other resources 5:17 — Fractions, decimals and percentages
Alan’s note: Charts and Mindmaps: 5:07 (Decimals), Other resources: 5:17 (Place value of decimals)
+ and – of fractions with the same denominatorLevel 5: 9 · Level 6: 3
Level 5 e-Text pages: 12, 24, 41, 50-52, 71-73
Representing quantity fractions B
Fractions/decimals: comparing fractions with related denominators, equivalent fractionsLevel 5: 5 · Level 6: 3
Level 5 e-Text pages: 9-12, 56
Level 6 e-Text pages: 61-63
Other resources: Percentages: e-Text 6: pp 9-13
+ and – of fractions with different denominatorsLevel 6: 11
Level 6 e-Text pages: (58-62), 63-66, 80-81
- 6:NA58Fractions and mixed numerals
- 6:NA59Mixed numerals, improper fractions
- 6:NA60Fractions, addition and subtraction
- 6:NA61Equivalent fractions
- 6:NA62Simplifying fractions
- 6:NA63Fractions, addition and subtraction
- 6:NA64Addition of fractions
- 6:NA65Subtraction of fractions
- 6:NA66Calculating with mixed numerals
- 6:NA80Multiplying fractions
- 6:NA81Operations with fractions
Other resources
Alan’s note: Charts and Mindmaps: 6:07 (Fractions)
Fractions of whole numbers, remainders using decimals, multiplying a fractionLevel 5: 1 · Level 6: 5
Level 5 e-Text pages: 11
Level 6 e-Text pages: 67, 78-79, 80-81
Measurement and space
Geometric measure A
Position: Cartesian coordinates using first quadrantLevel 5: 3 · Level 6: 4
Level 5 e-Text pages: 104, 125-126
Level 6 e-Text pages: 125-126, 144, 151
Other resources
Alan’s note: Concept Dictionary: Position (Direction and Coordinates)
Length: m, km, cm, mm, perimeters, measuringLevel 5: 6 · Level 6: 2
Level 5 e-Text pages: 81-83, 111-113
Level 6 e-Text pages: 106-107
Other resources
Alan’s note: Concept Dictionary: Length, Charts and Mindmaps: 5:01 (Length)
Angles: angles up to 360º, measure and draw using degrees, estimationLevel 5: 9
Level 5 e-Text pages: 99-101, 108-110, 119, 145-146
Right angle, straight angle revolution, acute angle, obtuse angle, reflex angleLevel 5: 6
Level 5 e-Text pages: 88-90, 108-110
Geometric measure B
Position: Cartesian coordinates using all 4 quadrantsLevel 6: 4
Level 6 e-Text pages: 125-128
Other resources: Maps: e-Text 6 pp145-146
Length: lengths and distances using metric units, conversion between units, problem solvingLevel 5: 1 · Level 6: 9
Level 5 e-Text pages: 83
Level 6 e-Text pages: 71, 94-97, 105-107, 139
Other resources
Alan’s note: Charts and Mindmaps: 6:01 (Length)
Angles: angles on a straight line, angles at a point, vertically opposite anglesLevel 6: 7
Two-dimensional spatial structure A
2D space: 2D shapes, classify and describe properties, types of trianglesLevel 5: 5 · Level 6: 4
Level 5 e-Text pages: 86-87, 117-119
Level 6 e-Text pages: 114-117
Other resources
- Concept Dictionary - 2D Space
- Charts and Mindmaps 6:06 — Polygon flow chart
- Cards and boards 5:09 — 2D shapes cards
- Cards and boards 5:10 — 2D shapes, name cards
- Cards and boards 5:12 — Shapes around the clock
Alan’s note: Concept Dictionary: 2D Space, Charts and Mindmaps: 6:06 (polygon flow chart), Cards and boards: 5:09-5:10, 5:12 (2D shapes)
Area: area of rectangles using hectares (ha) and square kilometres (km2)Level 5: 8 · Level 6: 2
Level 5 e-Text pages: 95-98, 114-116, 132
Level 6 e-Text pages: 94, 108
Other resources
Alan’s note: Concept Dictionary: Area, Charts and Mindmaps: 5:02 (Area)
Two-dimensional spatial structure B
2D space: dissect and rearrange 2D shapes using transformations, reflections, rotationsLevel 5: 5 · Level 6: 2
Level 5 e-Text pages: 133-137
Level 6 e-Text pages: 123-124
Area: area of composite figures, parallelograms and trianglesLevel 6: 5
Level 6 e-Text pages: 108-111, 119
Other resources
Alan’s note: Comparison of perimeter and area: e-Text 6 p 118, Charts and Mindmaps: 6:02 (Area)
Three-dimensional spatial structure A
3D space: name and draw prisms and pyramids, views and netsLevel 5: 9
Level 5 e-Text pages: 91-94. 120-124
Other resources
- Concept Dictionary - 3D Space
- Cards and boards 5:07 — 3D shapes cards
- Cards and boards 5:08 — 3D shapes, name cards
- Cards and boards 5:12 — Shapes around the clock
- Cards and boards 5:14 — Sliding nets
- Other resources 5:24 — Nets of prisms and pyramids
- Other resources 5:25 — Net of a cube
- Other resources 5:26 — Net of a rectangular pyramid
- Other resources 5:30 — Isometric grid paper
- Other resources 5:31 — Isometric dot paper
Alan’s note: Concept Dictionary: 3D Space, Cards and boards: 5:07-5:08, 5:12 (3D shapes), Cards and boards: 5:14 (Sliding nets), Other resources 5:24-5:26 (Nets of prisms and pyramids/Net of a cube/Net of a rectangular pyramid), Other resources: 5:30-5:31 (Isometric grid paper/Isometric dot paper)
Volume/capacity: capacity (mL, L), write litres using 3 decimal placesLevel 5: 2 · Level 6: 3
Level 5 e-Text pages: 80, 132
Level 6 e-Text pages: 94, 139-140
Other resources
Alan’s note: Concept Dictionary: Volume and Capacity, Charts and Mindmaps: 5:02 (Volume and capacity)
Volume/capacity: investigate the volume of solids by displacementLevel 5: 5 · Level 6: 1
Level 5 e-Text pages: 105-107, 128, 132
Level 6 e-Text pages: 142
Other resources: e-Text 4 p135,
Three-dimensional spatial structure B
3D space: construct 3D models of prisms and pyramidsLevel 5: 1 · Level 6: 4
Level 5 e-Text pages: 124
Level 6 e-Text pages: 98-101
Volume/capacity: volumes of rectangular prisms in cm3 and m3Level 5: 5 · Level 6: 6
Level 5 e-Text pages: 105-107, 127-128
Level 6 e-Text pages: 94, 129-131, 141, 143
Non-spatial measure A
Mass: the tonne (t), measure and record mass using decimalsLevel 5: 4 · Level 6: 2
Level 5 e-Text pages: 85, 130-132
Level 6 e-Text pages: 94, 103
Other resources
Alan’s note: Concept Dictionary: Mass, Charts and Mindmaps: 5:04 (Mass)
Time: duration of timeLevel 5: 4 · Level 6: 2
Level 5 e-Text pages: 76, 79, 138-139
Level 6 e-Text pages: 148-149
Other resources
- Concept Dictionary - Time
- Charts and Mindmaps 5:05 — Time chart
- Other resources 5:22 — Calendar blanks
- Other resources 5:23 — Timelines
- Other resources 6:26 — Calendar months
Alan’s note: Concept Dictionary: Time, Charts and Mindmaps: 5:05 (Time), Other resources 5:22-5:23 (Calendar blanks/Timelines), Other resources: 6:26 (Calendar months)
12- and 24-hour time, timetablesLevel 5: 3 · Level 6: 2
Level 5 e-Text pages: 77-79
Level 6 e-Text pages: 112-113
Other resources: Time Zones and Daylight Savings: e-Text 5 pp139-140
Non-spatial measure B
Mass: conversions, grams, kilograms and tonnes, problemsLevel 5: 1 · Level 6: 8
Level 5 e-Text pages: 131
Level 6 e-Text pages: 94, 102-104, 120-122, 139
Time: duration problems using 12- and 24-hour time, elapsed timeLevel 5: 1 · Level 6: 4
Level 5 e-Text pages: 79
Level 6 e-Text pages: 112-113, 148-149
Statistics and probability
Data A
Statistics (Data): Categorical and discrete data, surveysLevel 5: 5
Level 5 e-Text pages: 15, 156, 159, 163, 165
Other resources
Alan’s note: Concept Dictionary: Statistics (Data)
Tables, graphs and timelines, interpret theseLevel 5: 11 · Level 6: 3
Level 5 e-Text pages: 15, 147-151, 156-158, 164-165
Level 6 e-Text pages: 147, 150-151
Data B
Statistics (Data): interpret and compare data displaysLevel 5: 1 · Level 6: 9
Level 5 e-Text pages: 15
Sources of bias and misleading data displaysLevel 6: 4
Level 6 e-Text pages: 160-161, 167-168
Chance A
Probability (Chance): list outcomes and find probabilities, as a numerical value, sum of outcome probabilitiesLevel 5: 7 · Level 6: 4
Level 5 e-Text pages: 152-155, 160-162
Level 6 e-Text pages: 154-155, 162, 164
Other resources
- Concept Dictionary - Chance
- Cards and boards 5:15 — Game spinners and dice stickers
- Other resources 5:19 — Chance materials and language
- Other resources 5:20 — Chance events
Alan’s note: Concept Dictionary: Chance, Cards and boards: 5:15 (Game spinners and dice stickers), 5:19-5:20 (Chance materials and language/Chance events)
Chance B
Probability (Chance): frequency of an outcome, expected results, random generators, chance experiments with small and large numbers of trialsLevel 6: 8
Level 6 e-Text pages: 153-157, 162-164
Other resources
Alan’s note: Cards and boards: 6:13 (Around the clock: chance game)