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Mathematics and statistics

Achievement objectives

Mathematics and statistics learning area title.

Level 1

 

Maths bubbles level one and two- Number and algebra, geometry and measurement, statistics.

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

Maths bubbles level one and two- Number and algebra, geometry and measurement, statistics.

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

Maths bubbles level 3- Number and Algebra, Geometry and Measurement, Statsitics.

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

Maths Bubbles Level 4- Number and Algebra, Geometry and Measurement, Statsitics.

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

Maths Bubbles Level 5- Number and Algebra, Geometry and Measurement, Statsitics.

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

Maths Bubbles Level 6- Number and Algebra, Geometry and Measurement, Statsitics.

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


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