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Achievement objectives

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# Achievement objectives by level

For convenience, all achievement objectives have been given a three-part code consisting of:

1. the strand (NA for number and algebra, GM for geometry and measurement, S for statistics, and M for mathematics)
2. the curriculum level
3. the ordinal position of the achievement objective (1st, 2nd, 3rd, and so on) as listed in the Curriculum.

### 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

• NA 6-1 Apply direct and inverse relationships with linear proportions
• NA 6-2 Extend powers to include integers and fractions
• NA 6-3 Apply everyday compounding rates
• NA 6-4 Find optimal solutions, using numerical approaches
• NA 6-5 Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns
• NA 6-6 Generalise the properties of operations with rational numbers, including the properties of exponents
• NA 6-7 Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns
• NA 6-8 Relate rate of change to the gradient of a graph

#### Geometry and measurement

• GM 6-1 Measure at a level of precision appropriate to the task
• GM 6-2 Apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures
• GM 6-3 Calculate volumes, including prisms, pyramids, cones, and spheres, using formulae
• GM 6-4 Deduce and apply the angle properties related to circles
• GM 6-5 Recognise when shapes are similar and use proportional reasoning to find an unknown length
• GM 6-6 Use trigonometric ratios and Pythagoras’ theorem in two and three dimensions
• GM 6-7 Use a co-ordinate plane or map to show points in common and areas contained by two or more loci
• GM 6-8 Compare and apply single and multiple transformations
• GM 6-9 Analyse symmetrical patterns by the transformations used to create them

#### Statistics

• S 6-1 Plan and conduct investigations using the statistical inquiry cycle:
• A – justifying the variables and measures used
• B – managing sources of variation, including the use of random sampling
• C – identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays
• D – making informal inferences about populations from sample data
• E – justifying findings, using displays and measures
• S 6-2 Evaluate statistical reports in the media by relating the displays, statistics, processes, and probabilities used to the claims made
• S 6-3 Investigate situations that involve elements of chance:
• A – comparing discrete theoretical distributions and experimental distributions, appreciating the role of sample size
• B – 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

• M 7-1 Apply co-ordinate geometry techniques to points and lines
• M 7-2 Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs
• M 7-3 Use arithmetic and geometric sequences and series
• M 7-4 Apply trigonometric relationships, including the sine and cosine rules, in two and three dimensions
• M 7-5 Choose appropriate networks to find optimal solutions
• M 7-6 Manipulate rational, exponential, and logarithmic algebraic expressions
• M 7-7 Form and use linear, quadratic, and simple trigonometric equations
• M 7-8 Form and use pairs of simultaneous equations, one of which may be non-linear
• M 7-9 Sketch the graphs of functions and their gradient functions and describe the relationship between these graphs
• M 7-10 Apply differentiation and anti-differentiation techniques to polynomials

#### Statistics

• S 7-1 Carry out investigations of phenomena, using the statistical inquiry cycle:
• A – conducting surveys that require random sampling techniques, conducting experiments, and using existing data sets
• B – evaluating the choice of measures for variables and the sampling and data collection methods used
• C – using relevant contextual knowledge, exploratory data analysis, and statistical inference
• S 7-2 Make inferences from surveys and experiments:
• A – making informal predictions, interpolations, and extrapolations
• B – using sample statistics to make point estimates of population parameters
• C – recognising the effect of sample size on the variability of an estimate
• S 7-3 Evaluate statistically based reports:
• A – interpreting risk and relative risk
• B – identifying sampling and possible non-sampling errors in surveys, including polls
• S 7-4 Investigate situations that involve elements of chance:
• A – comparing theoretical continuous distributions, such as the normal distribution, with experimental distributions
• B – 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

• M 8-1 Apply the geometry of conic sections
• M 8-2 Display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions
• M 8-3 Use permutations and combinations
• M 8-4 Use curve fitting, log modelling, and linear programming techniques
• M 8-5 Develop network diagrams to find optimal solutions, including critical paths
• M 8-6 Manipulate trigonometric expressions
• M 8-7 Form and use trigonometric, polynomial, and other non-linear equations
• M 8-8 Form and use systems of simultaneous equations, including three linear equations and three variables, and interpret the solutions in context
• M 8-9 Manipulate complex numbers and present them graphically
• M 8-10 Identify discontinuities and limits of functions
• M 8-11 Choose and apply a variety of differentiation, integration, and anti-differentiation techniques to functions and relations, using both analytical and numerical methods
• M 8-12 Form differential equations and interpret the solutions

#### Statistics

• S 8-1 Carry out investigations of phenomena, using the statistical inquiry cycle:
• A – conducting experiments using experimental design principles, conducting surveys, and using existing data sets
• B – finding, using, and assessing appropriate models (including linear regression for bivariate data and additive models for time-series data), seeking explanations, and making predictions
• C – using informed contextual knowledge, exploratory data analysis, and statistical inference
• D – communicating findings and evaluating all stages of the cycle
• S 8-2 Make inferences from surveys and experiments:
• A – determining estimates and confidence intervals for means, proportions, and differences, recognising the relevance of the central limit theorem
• B – using methods such as resampling or randomisation to assess the strength of evidence
• S 8-3 Evaluate a wide range of statistically based reports, including surveys and polls, experiments, and observational studies:
• A – critiquing causal-relationship claims
• B – interpreting margins of error
• S 8-4 Investigate situations that involve elements of chance:
• A – calculating probabilities of independent, combined, and conditional events
• B – calculating and interpreting expected values and standard deviations of discrete random variables
• C – applying distributions such as the Poisson, binomial, and normal

Last updated September 15, 2018