Curriculum+Level+6+Mathematics+and+statistics

=Curriculum levels=

=Level Six Mathematics and 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 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.

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.

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.