The Mathematics Curriculum in Primary and Lower Secondary Grades

At the time of the TIMSS 2015 assessment (which was administered in October to November 2014 in Australia), the curriculum was in a state of flux. The new Australian Curriculum had been implemented in some schools, but others still were using the version authored by the relevant state or territory curriculum body. The description that follows is a summary of the Australian Curriculum based on ACARA materials downloaded from the Australian Curriculum website in 2015.¹⁰ For information on prior versions of the curricula, please refer to earlier editions of the TIMSS Encyclopedia.¹¹

In the Australian Curriculum, mathematics is organized around the interaction of three content strands and four proficiency strands. The content strands are Number and Algebra, Measurement and Geometry, and Statistics and Probability. They describe what is to be taught and learned. The proficiency strands are Understanding, Fluency, Problem Solving, and Reasoning. They describe how content is explored or developed—that is, the thinking and doing of mathematics. They provide language for discussing the developmental aspects of learning mathematics and have been incorporated into the content strand descriptions. This approach has been adopted to ensure students’ proficiency in mathematics develops and that their mathematical skills become increasingly sophisticated over their years of schooling.

The proficiency strands for mathematics in Year 4 may be summarized as follows:

Understanding—Making connections between representations of numbers, partitioning and combining numbers flexibly, extending place value to decimals, using appropriate language to communicate time, and describing properties of symmetrical shapes
Fluency—Recalling multiplication tables, communicating sequences of simple fractions, using instruments to measure accurately, creating patterns with shapes and their transformations, and collecting and recording data
Problem Solving—Formulating, modeling, and recording authentic situations involving operations; comparing large numbers; comparing durations of time; and using properties of numbers to continue patterns
Reasoning—Generalizing from properties of numbers and calculation results, deriving strategies for unfamiliar multiplication and division tasks, comparing angles, communicating information using graphical displays, and evaluating the appropriateness of different displays

The achievement standards for mathematics in Year 4 include the following skills: choosing appropriate strategies for calculations involving multiplication and division; recognizing common equivalent fractions in familiar contexts and making connections between fraction and decimal notations up to two decimal places; solving simple purchasing problems; identifying unknown quantities in number sentences; describing number patterns resulting from multiplication; comparing areas of regular and irregular shapes using informal units; solving time problems; interpreting maps; identifying dependent and independent events; describing different methods of data collection and representation, and evaluating their effectiveness; using properties of odd and even numbers; recalling multiplication facts up to and related division facts; locating familiar fractions on a number line; continuing number sequences involving multiples of single-digit numbers; using scaled instruments to measure temperature, length, shapes, and objects; converting between units of time; creating symmetrical shapes and patterns; classifying angles in relation to a right angle; listing the probabilities of everyday events; and constructing data displays from given or collected data.

The proficiency strands for mathematics in Year 8 may be summarized as follows:

Understanding—Describing patterns involving indices and recurring decimals, identifying commonalities between operations with algebra and arithmetic, connecting rules for linear relations and their graphs, explaining the purpose of statistical measures, and explaining measurements of perimeter and area
Fluency—Calculating accurately with simple decimals, indices, and integers, recognizing equivalence of common decimals and fractions including recurring decimals, factorizing and simplifying basic algebraic expressions, and evaluating perimeters, areas of common shapes and their volumes, and three-dimensional objects
Problem Solving—Formulating and modeling 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—Justifying the result of a calculation or estimation as reasonable, deriving probability from its complement, using congruence to deduce properties of triangles, and estimating means and proportions of populations

The achievement standards for mathematics in Year 8 include the following skills: solving everyday problems involving rates, ratios, and percentages; recognizing index laws and applying them to whole numbers; describing rational and irrational numbers; solving problems involving profit and loss; making connections between expanding and factoring algebraic expressions; solving problems relating to the volume of prisms; making sense of time in real applications; identifying conditions for the congruence of triangles and deducing the properties of quadrilaterals; modeling authentic situations with two-way tables and Venn diagrams; choosing appropriate language to describe events and experiments; explaining issues related to the collection of data and the effect of outliers on means and medians in that data; using efficient mental and written strategies to carry out the four arithmetic operations with integers; simplifying a variety of algebraic expressions; solving linear equations and graphing linear relationships on the Cartesian plane; converting between units of measurement for area and volume; calculating the perimeter and area of parallelograms, rhombuses, and kites; naming the features of circles and calculating their area and circumference; determining complementary events; and calculating the sum of probabilities.