Arithmetika Australian Curriculum practice tasks

Years 7 to 10

Year 7

By the end of Year 7, students interpret integers in real world contexts. They make connections between whole numbers and index. notation. They move flexibly between representations of fractions, decimals and percentages. Students generalise using variables, solve simple linear equations and identify points on the Cartesian plane. They compare costs of items to make financial decisions.

Students investigate questions involving the collection of a range of data. They calculate mean, mode, median and range for sets of data and describe the relationship between median and mode in data displays.

Students classify triangles and quadrilaterals and establish the formulas for the area and perimeter of rectangles. They calculate the volume of rectangular prisms and draw and build three dimensionalobjects. They identify angles formed by a transversal through parallel lines and describe transformations on the Cartesian plane.

Year 8

By the end of Year 8 students use efficient mental and written strategies to carry out the four operations with integers. They round decimals and solve problems involving percentages. Students recognise the index laws and apply them to whole numbers and variables.

They simplify a variety of algebraic expressions and solve linear equations. They graph linear relationships on the Cartesian plane. They solve a range of everyday problems involving rates and ratios.

Students determine complementary events and use the sum of probabilities to solve problems. They understand the challenges of collecting representative data and the effect on medians and means of outliers.

Students choose appropriate units of measurement for area and volume and solve problems. They recognise the features of circles and solve problems involving circumference and area.

Students identify conditions for congruence of plane shapes and establish properties of quadrilaterals and solve related numerical problems. They solve problems involving time duration.

Year 9

By the end of Year 9, students express numbers in scientific notation and apply the index laws to numbers. They expand and factorise algebraic expressions .and solve problems involving simple interest.

Students solve linear equations using graphical and algebraic techniques. Students list outcomes, assign and determine probabilities for events. They construct displays and investigate the position of the mean and median and describe the shape of the distribution.

Students calculate areas of shapes and volume and surface area of right prisms. They investigate similar and congruent triangles and problems involving Pythagoras’ theorem.

Students recognise the connection between similarity and the trigonometric ratios and use trigonometry to solve right-angled triangle problems.

Year 10

By the end of Year 10, students expand and factorise monic quadratic expressions and find unknown values after substitution into formulas. They represent relations on the Cartesian plane and solve linear and quadratic equations. They make connections between simple and compound interest.

Students list outcomes, assign and determine probabilities for chance experiments and investigate independent events. They construct box-plots and compare data sets. Students investigate and describe statistical relationships and evaluate statistical reports.

Students solve problems involving volume and surface area of a range of prisms and apply reasoning to proofs and numerical exercises. They apply trigonometry to solve right-angled triangle problems.

Sample tasks

Example tasks