In this Australian Curriculum Mathematics course students will solve problems involving the comparison, addition and subtraction of integers in the Number strand. They will also learn to solve problems involving percentages and all four operations with fractions and decimals. In the Measurement and Geometry strand students will classify triangles and quadrilaterals and describe different views of three-dimensional objects. They will represent transformations in the Cartesian plane, and assign ordered pairs to given points on the Cartesian plane. In the Probability and Statistics strand, students will determine the sample space for simple experiments with equally likely outcomes and assign probabilities to those outcomes.
Within the Number and Algebra strand, students will consolidate their knowledge of integers and make connections between whole numbers and index notation and the relationship between perfect squares and square roots. They will learn to represent numbers using variables and connect the laws and properties for number to algebra and solve simple linear equations. In Measurement and Geometry students will learn the names and relationships between angles and use formula to calculate the area, perimeter and volume of shapes and simple objects. In the Statistics strand students will collect data and display these in stem-and-leaf and dot-plots. They will build on their knowledge of “averages” to calculate the mean, mode and median of data sets.
Students will increase their understandings in all strands of maths – number and algebra, geometry and measurement and chance. In Number and Algebra students will consolidate their understanding and skills in operating with integers, apply the concept of percentages to real life situations in financial contexts and use rates and ratios to solve problems. Students will also consolidate their understandings of the units of time and identify various time zones within Australia and around the world. Students will compare the features of linear and non-linear equations and plot these on Cartesian Planes. In Probability they will learn how to represent data in Venn diagrams and two way tables, as well as consider complementary events in probability. In Measurement the concepts of perimeter and area in simple and more complex shapes including parallelograms, kites, trapezia and circles will be studied.
In the Number and Algebra strand students will describe rational and irrational numbers and apply index laws to simplify expressions. They will study distributive law (expansion and factorisation of algebraic expressions), solve linear equations and graph linear relationships on the Cartesian plane. In the Measurement and Geometry strand students will identify the conditions for congruence of triangles and deduce the properties of quadrilaterals, solve problems relating to the volume of prisms and convert units of measurement. In Statistics students will consolidate on their understanding of measures of central tendencies and study the effects of outliers on these.
Students will consolidate their understandings in all strands of maths – number and algebra, geometry and measurement and chance. In Number students will build on their understanding and skills in using index laws to simplify expressions using both numerals and variables and use scientific notation to represent very large and very small numbers. In Algebra they will apply the distributive law to the expansion of algebraic expressions. In Measurement and Geometry students will use Pythagoras’ Theorem to find the length of an unknown side in right angled triangles and apply this to a variety of real life situations. They will investigate problems involving proportion and solve problems using ratio and scale figures. Students will apply the four similarity tests to solve problems and investigate conditions of similarity in real life situations. In Chance they will calculate relative frequencies, determine the outcomes of two-step chance experiments using tree diagrams and arrays and organise data into Venn diagrams and two-way tables to solve problems.
Students will solve real life problems involving simple interest, find the distance between two points on the Cartesian plane and the gradient and midpoint of a line segment in the Number strand. They will also investigate the properties of linear and non-linear graphs. In the Measurement and Geometry use Pythagoras’ Theorem and trigonometry to find unknown sides of right- angled triangles. Students will calculate the volume and surface area of right prisms and cylinders. In Statistics students will learn to make sense of the position of the mean and median in skewed, symmetric and bi-modal displays, and display data in histograms and back-to-back stem-and-leaf plots.