Year 8 Mathematics

Year 8 Mathematics

Semester 1 Overview

Students will use efficient mental and written strategies to make estimates and carry out the four operations with integers, and apply the index laws to whole numbers. Rational and irrational numbers will be investigated, identified and described in context and problems involving rates and ratios will be discussed. Procedures for solving everyday problems involving profit, loss, rates and percentages will be discussed, with and without the use of digital technology. They will simplify a variety of algebraic expressions and connect the expansion and factorisation of linear expressions. Students will investigate angle properties, and solve related numerical problems using reasoning. The solutions of linear equations will be investigated using algebraic and graphical techniques.

Number and Algebra

Students will:

• Evaluate numbers expressed as powers of positive integers and use patterns to assist in finding rules for the multiplication and division of integers.
• Use the number line to develop strategies for adding and subtracting rational numbers.
• Recognise terminating, recurring and non-terminating decimals and choose their appropriate representations as well as extend their knowledge of the real number system to include irrational numbers.
• Use percentages to solve problems, including those involving mark-ups, discounts and population increases and decreases.
• Investigate the methods used in retail stores to express discounts and express profit and loss as a percentage of the cost or selling price.
• Understand that rate and ratio problems can be solved using fractions or percentages and will choose the most efficient form to solve a particular problem
• Apply the distributive law to the expansion of algebraic expressions using strategies such as the area model
• Recognise the relationship between factorising and expanding. They will also identify the highest common factor of numeric and algebraic expressions and use a range of strategies to factorise algebraic expressions.

Measurement and Geometry

Students will:

• Identify properties related to side lengths, parallel sides, angles, diagonals and symmetry.
• Investigate properties of triangles and quadrilaterals
• Explore angles present at a point and those found within parallel lines and transversals

Semester 2 Overview

Students will solve linear equations using algebraic and graphical techniques. They will apply correct procedures to solve linear equations and plot linear relationships on the Cartesian plane with and without the use of digital technologies. Students will find the perimeter and area of parallelograms, rhombuses and kites. They will investigate the features of circles, calculate circumference and area, and solve problems relating to the volume of prisms. Students will use tools, including digital technology, to construct congruent shapes leading to the establishment and the use of the conditions for congruence for solving problems. Students will model situations with Venn diagrams and two-way tables and explain the use of ‘not’, ‘and’ and ‘or’. They will choose appropriate language to describe events and experiments and determine complementary events and calculate the sum of probabilities. Problems involving rates and ratios will be discussed, as well as the process of finding solutions with and without technology. Transformations of plane shapes and the properties that determine the congruence of triangles will be investigated.

Number and Algebra

Students will:

• Solve real-life problems by using variables to represent unknowns.
• Use algorithms and related testing procedures
• Complete a table of values, plot the resulting points and determine whether the relationship is linear. They will also investigate procedures for finding the rule for a linear relationship.

Measurement and Geometry

Students will:

• Establish and use formulas for areas such as trapeziums, rhombuses and kites
• Investigate the circumference and area of circles to establish an understanding of formulas
• Understand the properties that determine the congruence of triangles and recognise which transformations create congruent figures.
• Establish that two figures are congruent after one or more transformations and recognise that the matching sides and the matching angles are equal.
• Solve problems using the properties of congruent figures

Statistics and Probability

Students will:

• Understand that probabilities range between 0 and 1 and that calculating the probability of an event allows the probability of its complement to be found.
• Pose ‘and’, ‘or’ and ‘not’ probability questions about objects or people.
• Use Venn diagrams and two-way tables to calculate probabilities for events, satisfying ‘and’, ‘or’ and ‘not’ conditions as well as understanding that represent data in this way facilitates the calculation of probabilities.
• Collect data to answer the questions using Venn diagrams or two-way tables.

Year 8 Accelerated and Enhanced Mathematics

Semester 1 Overview

Students will solve problems involving linear equations and inequalities as well as pairs of simultaneous linear equations. They will substitute into formulas, find unknown values and manipulate linear algebraic expressions. Whilst investigating these concepts, students will become familiar with the procedures involved, with and without the use of digital technology. Students will solve problems involving simple interest and investigate the use of percentages, ratios and rates in the area of financial mathematics. They will investigate the distributive law and its application to algebraic expressions as well as numbers. Students will apply Pythagoras’ theorem and trigonometric ratios to solve problems involving angles and lengths in right-angled triangles. They will apply the index laws using integer indices to variables and numbers and express numbers in scientific notation.

Number and Algebra

Students will:

• Apply correct procedures to solve equations arising from formulas and those derived from worded problems.
• Solve linear simultaneous equations, using algebraic and graphical techniques, including the use of digital and CAS technology.
• Simplify and evaluate the numerical expression, using both positive and negative integer indices.
• Represent large and small numbers in scientific notation and numbers expressed in scientific notation as whole numbers or decimals.
• Understand that financial decisions can be assisted by mathematical calculations.
• Recognise that the distributive law can be applied to algebraic expressions as well as numbers.
• Solve a wide range of linear equations and check solutions by substitution

Measurement and Geometry

Students will:

• Investigate Pythagoras’ theorem as a useful tool in determining unknown lengths in right-angled triangles and has widespread applications.
• Recognise that right-angled triangle calculations will generate results that can be integers, fractions or irrational numbers.
• Understand the terms ‘adjacent’ and 'opposite’ sides in a right-angled triangle.
• Select and accurately use the correct trigonometric ratio to find unknown sides in right-angled triangles

Semester 2 Overview

Students will use the distributive law to expand algebraic expressions, including binomial expressions, and simplify a range of algebraic expressions. They will find the distance between two points on the Cartesian plane and the gradient and midpoint of a line segment using a range of strategies. Students will sketch and draw linear relations, solve simple related equations and explain the relationship between the graphical and symbolic forms, with and without the use of digital technology. They will calculate relative frequencies to estimate probabilities and list outcomes for two-step experiments and assign probabilities for those outcomes and related events.

Number and Algebra

Students will:

• Investigate the relationship between expansion and factorisation and identify algebraic factors in algebraic expressions.
• Use Pythagoras’ theorem to calculate the distance between two points on the Cartesian plane.
• Investigate graphical and algebraic techniques for finding the midpoint of line segments and gradients of straight lines.
• Learn and apply a range of procedures when solving problems involving parallel and perpendicular lines.
• Determine linear rules from suitable diagrams, tables of values and graphs and describe them using both words and algebraic expressions. 

Statistics and Probability

Students will:

• Use systematic methods to list outcomes of experiments and list outcomes favourable to an event.
• Compare experiments which differ by being undertaken with replacement or without replacement.
• Use Venn diagrams or two-way tables to calculate relative frequencies of events involving ‘and’, ‘or’ outcomes.