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# Mathematics and statistics

## Achievement objectives  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:

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. 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:

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. 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. 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. 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. 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.

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.

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