Mathematics and statistics
- What is mathematics and statistics?
- Why study mathematics and statistics?
- Learning area structure
- Achievement objectives
Achievement objectives
Level 1

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
Number and algebra
Number strategies
- Use a range of counting, grouping, and equal-sharing strategies with whole numbers and fractions.
Number knowledge
- Know the forward and backward counting sequences of whole numbers to 100.
- Know groupings with five, within ten, and with ten.
Equations and expressions
- Communicate and explain counting, grouping, and equal-sharing strategies, using words, numbers, and pictures.
Patterns and relationships
- Generalise that the next counting number gives the result of adding one object to a set and that counting the number of objects in a set tells how many.
- Create and continue sequential patterns.
Geometry and measurement
Measurement
- Order and compare objects or events by length, area, volume and capacity, weight (mass), turn (angle), temperature, and time by direct comparison and/or counting whole numbers of units.
Shape
- Sort objects by their appearance.
Position and orientation
- Give and follow instructions for movement that involve distances, directions, and half or quarter turns.
- Describe their position relative to a person or object.
Transformation
- Communicate and record the results of translations, reflections, and rotations on plane shapes.
Statistics
Statistical investigation
Conduct investigations using the statistical enquiry cycle:
- posing and answering questions
- gathering, sorting and counting, and displaying category data
- discussing the results.
Statistical literacy
- Interpret statements made by others from statistical investigations and probability activities.
Probability
- Investigate situations that involve elements of chance, acknowledging and anticipating possible outcomes.
Level 2

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
Number and algebra
Number strategies
- Use simple additive strategies with whole numbers and fractions.
Number knowledge
- Know forward and backward counting sequences with whole numbers to at least 1000.
- Know the basic addition and subtraction facts.
- Know how many ones, tens, and hundreds are in whole numbers to at least 1000.
- Know simple fractions in everyday use.
Equations and expressions
- Communicate and interpret simple additive strategies, using words, diagrams (pictures), and symbols.
Patterns and relationships
- Generalise that whole numbers can be partitioned in many ways.
- Find rules for the next member in a sequential pattern.
Geometry and measurement
Measurement
- Create and use appropriate units and devices to measure length, area, volume and capacity, weight (mass), turn (angle), temperature, and time.
- Partition and/or combine like measures and communicate them, using numbers and units.
Shape
- Sort objects by their spatial features, with justification.
- Identify and describe the plane shapes found in objects.
Position and orientation
- Create and use simple maps to show position and direction.
- Describe different views and pathways from locations on a map.
Transformation
- Predict and communicate the results of translations, reflections, and rotations on plane shapes.
Statistics
Statistical investigation
Conduct investigations using the statistical enquiry cycle:
- posing and answering questions
- gathering, sorting, and displaying category and whole-number data
- communicating findings based on the data.
Statistical literacy
- Compare statements with the features of simple data displays from statistical investigations or probability activities undertaken by others.
Probability
- Investigate simple situations that involve elements of chance, recognising equal and different likelihoods and acknowledging uncertainty.
Level 3

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
Number and algebra
Number strategies
- Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.
Number knowledge
- Know basic multiplication and division facts.
- Know counting sequences for whole numbers.
- Know how many tenths, tens, hundreds, and thousands are in whole numbers.
- Know fractions and percentages in everyday use.
Equations and expressions
- Record and interpret additive and simple multiplicative strategies, using, words, diagrams, and symbols, with an understanding of equality.
Patterns and relationships
- Generalise the properties of addition and subtraction with whole numbers.
- Connect members of sequential patterns with their ordinal position and use tables, graphs, and diagrams to find relationships between successive elements of number and spatial patterns.
Geometry and measurement
Measurement
- Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time.
- Find areas of rectangles and volumes of cuboids by applying multiplication.
Shape
- Classify plane shapes and prisms by their spatial features.
- Represent objects with drawings and models.
Position and orientation
- Use a co-ordinate system or the language of direction and distance to specify locations and describe paths.
Transformation
- Describe the transformations (reflection, rotation, translation, or enlargement) that have mapped one object onto another.
Statistics
Statistical investigation
Conduct investigations using the statistical enquiry cycle:
- gathering, sorting, and displaying multivariate category and whole-number data and simple time-series data to answer questions
- identifying patterns and trends in context, within and between data sets
- communicating findings, using data displays.
Statistical literacy
- Evaluate the effectiveness of different displays in representing the findings of a statistical investigation or probability activity undertaken by others.
Probability
- Investigate simple situations that involve elements of chance by comparing experimental results with expectations from models of all the outcomes, acknowledging that samples vary.
Level 4

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
Number and algebra
Number strategies and knowledge
- Use a range of multiplicative strategies when operating on whole numbers.
- Understand addition and subtraction of fractions, decimals, and integers.
- Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
- Apply simple linear proportions, including ordering fractions.
- Know the equivalent decimal and percentage forms for everyday fractions.
- Know the relative size and place value structure of positive and negative integers and decimals to three places.
Equations and expressions
- Form and solve simple linear equations.
Patterns and relationships
- Generalise properties of multiplication and division with whole numbers.
- Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns.
Geometry and measurement
Measurement
- Use appropriate scales, devices, and metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time.
- Convert between metric units, using whole numbers and commonly used decimals.
- Use side or edge lengths to find the perimeters and areas of rectangles, parallelograms, and triangles and the volumes of cuboids.
- Interpret and use scales, timetables, and charts.
Shape
- Identify classes of two- and three-dimensional shapes by their geometric properties.
- Relate three-dimensional models to two-dimensional representations, and vice versa.
Position and orientation
- Communicate and interpret locations and directions, using compass directions, distances, and grid references.
Transformation
- Use the invariant properties of figures and objects under transformations (reflection, rotation, translation, or enlargement).
Statistics
Statistical investigation
Plan and conduct investigations using the statistical enquiry cycle:
- determining appropriate variables and data collection methods
- gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends
- comparing distributions visually
- communicating findings, using appropriate displays.
Statistical literacy
- Evaluate statements made by others about the findings of statistical investigations and probability activities.
Probability
- Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging variation and independence.
- Use simple fractions and percentages to describe probabilities.
Level 5

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
Number and algebra
Number strategies and knowledge
- Reason with linear proportions.
- Use prime numbers, common factors and multiples, and powers (including square roots).
- Understand operations on fractions, decimals, percentages, and integers.
- Use rates and ratios.
- Know commonly used fraction, decimal, and percentage conversions.
- Know and apply standard form, significant figures, rounding, and decimal place value.
Equations and expressions
- Form and solve linear and simple quadratic equations.
Patterns and relationships
- Generalise the properties of operations with fractional numbers and integers.
- Relate tables, graphs, and equations to linear and simple quadratic relationships found in number and spatial patterns.
Geometry and measurement
Measurement
- Select and use appropriate metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time, with awareness that measurements are approximate.
- Convert between metric units, using decimals.
- Deduce and use formulae to find the perimeters and areas of polygons and the volumes of prisms.
- Find the perimeters and areas of circles and composite shapes and the volumes of prisms, including cylinders.
Shape
- Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties.
- Create accurate nets for simple polyhedra and connect three-dimensional solids with different two-dimensional representations.
Position and orientation
- Construct and describe simple loci.
- Interpret points and lines on co-ordinate planes, including scales and bearings on maps.
Transformation
- Define and use transformations and describe the invariant properties of figures and objects under these transformations.
- Apply trigonometric ratios and Pythagoras’ theorem in two dimensions.
Statistics
Statistical investigation
Plan and conduct surveys and experiments using the statistical enquiry cycle:
- determining appropriate variables and measures
- considering sources of variation
- gathering and cleaning data
- using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets
- comparing sample distributions visually, using measures of centre, spread, and proportion
- presenting a report of findings.
Statistical literacy
- Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings.
Probability
- Compare and describe the variation between theoretical and experimental distributions in situations that involve elements of chance.
- Calculate probabilities, using fractions, percentages, and ratios.
Level 6

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
Number and algebra
Number strategies and knowledge
- Apply direct and inverse relationships with linear proportions.
- Extend powers to include integers and fractions.
- Apply everyday compounding rates.
- Find optimal solutions, using numerical approaches.
Equations and expressions
- Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns.
Patterns and relationships
- Generalise the properties of operations with rational numbers, including the properties of exponents.
- Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns.
- Relate rate of change to the gradient of a graph.
Geometry and measurement
Measurement
- Measure at a level of precision appropriate to the task.
- Apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures.
- Calculate volumes, including prisms, pyramids, cones, and spheres, using formulae.
Shape
- Deduce and apply the angle properties related to circles.
- Recognise when shapes are similar and use proportional reasoning to find an unknown length.
- Use trigonometric ratios and Pythagoras’ theorem in two and three dimensions.
Position and orientation
- Use a co-ordinate plane or map to show points in common and areas contained by two or more loci.
Transformation
- Compare and apply single and multiple transformations.
- Analyse symmetrical patterns by the transformations used to create them.
Statistics
Statistical investigation
Plan and conduct investigations using the statistical enquiry cycle:
- justifying the variables and measures used
- managing sources of variation, including through the use of random sampling
- identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays
- making informal inferences about populations from sample data
- justifying findings, using displays and measures.
Statistical literacy
- Evaluate statistical reports in the media by relating the displays, statistics, processes, and probabilities used to the claims made.
Probability
Investigate situations that involve elements of chance:
- comparing discrete theoretical distributions and experimental distributions, appreciating the role of sample size
- calculating probabilities in discrete situations.
Level 7
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
Mathematics
Patterns and relationships
- Apply co-ordinate geometry techniques to points and lines.
- Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs.
- Use arithmetic and geometric sequences and series.
- Apply trigonometric relationships, including the sine and cosine rules, in two and three dimensions.
- Choose appropriate networks to find optimal solutions.
Equations and expressions
- Manipulate rational, exponential, and logarithmic algebraic expressions.
- Form and use linear, quadratic, and simple trigonometric equations.
- Form and use pairs of simultaneous equations, one of which may be non-linear.
Calculus
- Sketch the graphs of functions and their gradient functions and describe the relationship between these graphs.
- Apply differentiation and anti-differentiation techniques to polynomials.
Statistics
Statistical investigation
Carry out investigations of phenomena, using the statistical enquiry cycle:
- conducting surveys that require random sampling techniques, conducting experiments, and using existing data sets
- evaluating the choice of measures for variables and the sampling and data collection methods used
- using relevant contextual knowledge, exploratory data analysis, and statistical inference.
Make inferences from surveys and experiments:
- making informal predictions, interpolations, and extrapolations
- using sample statistics to make point estimates of population parameters
- recognising the effect of sample size on the variability of an estimate.
Statistical literacy
Evaluate statistically based reports:
- interpreting risk and relative risk
- identifying sampling and possible non-sampling errors in surveys, including polls.
Probability
Investigate situations that involve elements of chance:
- comparing theoretical continuous distributions, such as the normal distribution, with experimental distributions
- calculating probabilities, using such tools as two-way tables, tree diagrams, simulations, and technology.
Level 8
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
Mathematics
Patterns and relationships
- Apply the geometry of conic sections.
- Display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions.
- Use permutations and combinations.
- Use curve fitting, log modelling, and linear programming techniques.
- Develop network diagrams to find optimal solutions, including critical paths.
Equations and expressions
- Manipulate trigonometric expressions.
- Form and use trigonometric, polynomial, and other non-linear equations.
- Form and use systems of simultaneous equations, including three linear equations and three variables, and interpret the solutions in context.
- Manipulate complex numbers and present them graphically.
Calculus
- Identify discontinuities and limits of functions.
- Choose and apply a variety of differentiation, integration, and anti-differentiation techniques to functions and relations, using both analytical and numerical methods.
- Form differential equations and interpret the solutions.
Statistics
Statistical investigation
Carry out investigations of phenomena, using the statistical enquiry cycle:
- conducting experiments using experimental design principles, conducting surveys, and using existing data sets
- finding, using, and assessing appropriate models (including linear regression for bivariate data and additive models for time-series data), seeking explanations, and making predictions
- using informed contextual knowledge, exploratory data analysis, and statistical inference
- communicating findings and evaluating all stages of the cycle.
Make inferences from surveys and experiments:
- determining estimates and confidence intervals for means, proportions, and differences, recognising the relevance of the central limit theorem
- using methods such as resampling or randomisation to assess the strength of evidence.
Statistical literacy
Evaluate a wide range of statistically based reports, including surveys and polls, experiments, and observational studies:
- critiquing causal-relationship claims
- interpreting margins of error.
Probability
Investigate situations that involve elements of chance:
- calculating probabilities of independent, combined, and conditional events
- calculating and interpreting expected values and standard deviations of discrete random variables
- applying distributions such as the Poisson, binomial, and normal.
Published on: 03 Apr 2014