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:
Use a range of counting, grouping, and equal-sharing strategies with whole numbers and fractions.
Know the forward and backward counting sequences of whole numbers to 100.
Know groupings with five, within ten, and with ten.
Communicate and explain counting, grouping, and equal-sharing strategies, using words, numbers, and pictures.
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.
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.
Sort objects by their appearance.
Give and follow instructions for movement that involve distances, directions, and half or quarter turns.
Describe their position relative to a person or object.
Communicate and record the results of translations, reflections, and rotations on plane shapes.
Conduct investigations using the statistical enquiry cycle:
posing and answering questions
gathering, sorting and counting, and displaying category data
discussing the results.
Interpret statements made by others from statistical investigations and probability activities.
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:
Use simple additive strategies with whole numbers and fractions.
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.
Communicate and interpret simple additive strategies, using words, diagrams (pictures), and symbols.
Generalise that whole numbers can be partitioned in many ways.
Find rules for the next member in a sequential pattern.
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.
Sort objects by their spatial features, with justification.
Identify and describe the plane shapes found in objects.
Create and use simple maps to show position and direction.
Describe different views and pathways from locations on a map.
Predict and communicate the results of translations, reflections, and rotations on plane shapes.
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.
Compare statements with the features of simple data displays from statistical investigations or probability activities undertaken by others.
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:
Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.
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.
Record and interpret additive and simple multiplicative strategies, using, words, diagrams, and symbols, with an understanding of equality.
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.
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.
Classify plane shapes and prisms by their spatial features.
Represent objects with drawings and models.
Use a co-ordinate system or the language of direction and distance to specify locations and describe paths.
Describe the transformations (reflection, rotation, translation, or enlargement) that have mapped one object onto another.
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.
Evaluate the effectiveness of different displays in representing the findings of a statistical investigation or probability activity undertaken by others.
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:
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.
Form and solve simple linear equations.
Generalise properties of multiplication and division with whole numbers.
Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns.
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.
Identify classes of two- and three-dimensional shapes by their geometric properties.
Relate three-dimensional models to two-dimensional representations, and vice versa.
Communicate and interpret locations and directions, using compass directions, distances, and grid references.
Use the invariant properties of figures and objects under transformations (reflection, rotation, translation, or enlargement).
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.
Evaluate statements made by others about the findings of statistical investigations and probability activities.
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:
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.
Form and solve linear and simple quadratic equations.
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.
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.
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.
Construct and describe simple loci.
Interpret points and lines on co-ordinate planes, including scales and bearings on maps.
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.
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.
Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings.
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:
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.
Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns.
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.
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.
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.
Use a co-ordinate plane or map to show points in common and areas contained by two or more loci.
Compare and apply single and multiple transformations.
Analyse symmetrical patterns by the transformations used to create them.
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.
Evaluate statistical reports in the media by relating the displays, statistics, processes, and probabilities used to the claims made.
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:
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.
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.
Sketch the graphs of functions and their gradient functions and describe the relationship between these graphs.
Apply differentiation and anti-differentiation techniques to polynomials.
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.
Evaluate statistically based reports:
interpreting risk and relative risk
identifying sampling and possible non-sampling errors in surveys, including polls.
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:
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.
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.
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.
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.
Evaluate a wide range of statistically based reports, including surveys and polls, experiments, and observational studies:
critiquing causal-relationship claims
interpreting margins of error.
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
