## The proficiency strands *understanding, fluency, problem-solving* and *reasoning* are an integral part of mathematics content across the three content strands: number and algebra, measurement and geometry, and statistics and probability.

**Year 7**

*Understanding*

Students will be describing patterns in uses of indices with whole numbers, recognising equivalences between fractions, decimal, percentages and ratios, plotting points on the Cartesian plane, identifying angles formed by a transversal crossing a pair of lines, and connecting the laws and properties of numbers to algebraic terms and expressions.

**Fluency**

Students will be calculating accurately with integers, representing fractions and decimals in various ways, investigating best buys, finding measures of central tendency and calculating areas of shapes and volumes of prisms.

**Problem Solving**

Students will be formulating and solving authentic problems using numbers and measurements, working with transformations and identifying symmetry, calculating angles and interpreting sets of data collected through chance experiments.

**Reasoning**

Students will be applying the number laws to calculations, applying known geometric facts to draw conclusions about shapes, applying an understanding of ratio and interpreting data displays.

**Year 8**

**Understanding**

Students will be describing patterns involving indices and recurring decimals, identifying commonalities between operations with algebra and arithmetic, connecting rules for linear relations with their graphs, explaining the purpose of statistical measures and explaining measurements of perimeter and area.

**Fluency**

Students will be calculating accurately with simple decimals, indices and integers, recognising equivalence of common decimals, factorising and simplifying basic algebraic expressions, and evaluating perimeters and areas of common shapes and volumes of three-dimensional objects.

**Problem-solving**

Students will be formulating and modelling practical situations involving ratios, profit and loss, areas and perimeters of common shapes and using two-way tables and Venn diagrams to calculate probabilities.

**Reasoning**

Students will be justifying the result of a calculation or estimation as reasonable, deriving probability from its complement, using congruence to deduce properties of triangles, finding estimates of means and proportions of populations.

## Year 9

**Understanding**

Students will be describing the relationship between graphs and equations, simplifying a range of algebraic expressions and explaining the use of relative frequencies to estimate probabilities and of the trigonometric ratios for right-angle triangles.

*Fluency*

Students will be applying the index laws to expressions with integer indices, expressing numbers in scientific notation, listing outcomes for experiments, developing familiarity with calculations involving the Cartesian plane and calculating areas of shapes and surface areas of prisms.

**Problem-solving**

Students will be formulating and modelling practical situations involving surface areas and volumes of right prisms, applying ratio and scale factors to similar figures, solving problems involving right-angle trigonometry and collecting data from secondary sources to investigate an issue.

**Reasoning**

Students will be following mathematical arguments, evaluating media reports and using statistical knowledge to clarify situations, developing strategies in investigating similarity and sketching linear graphs.