## Number and Algebra of Year 8 Mathematics

### Number and Place Value

Use index notation with numbers to establish the index laws with positive integral indices and the zero index.

Carry out the four operations with integers, using efficient mental and written strategies and appropriate digital technologies of Year 8 Mathematics.

### Real Numbers

Compare fractions using equivalence. Locate and represent fractions and mixed numerals on a number line.

Solve problems involving addition and subtraction of fractions, including those with unrelated denominators.

Multiply and divide fractions and decimals using efficient written strategies and digital technologies.

Express one quantity as a fraction of another, with and without the use of digital technologies

Round decimals to a specified number of decimal places.

Investigate terminating and recurring decimals.

Investigate the concept of irrational numbers, including \( \pi \).

Solve problems including the use of percentages, including percentage increases and decreases, with and without digital technologies.

Solve a range of problems involving rates and ratios, with and without digital technologies.

### Money and Financial Mathematics

Solve problems involving profit and loss, with and without digital technologies.

### Patterns and Algebra

Extend and apply the distributive law to the expansion of algebraic expressions.

Factorise algebraic expressions involving the four operations.

Extend and apply the index law to variables, using positive integral indices and the zero index.

### Linear and Non-Linear Relationships

Plot linear relationships on the Cartesian plane with and without the use of digital technologies.

Solve linear equations using algebraic and graphical techniques. Verify solutions by substitution.

Solve simple quadratic equations.

## Measurement and Geometry of Year 8 Mathematics

### Using Units of Measurement

Choose appropriate units of measurement for area and volume and convert from one unit to another.

Find perimeters and area of parallelograms, rhombus and kites.

Investigate the relationship between the features of circles such as circumference, are, radius and diameter. use formulas to solve problems involving circumference and area.

Develop the formulas for volumes of rectangular and triangular prisms in general. Use formulas to solve propblems involving circumstance and area.

Develop the formulas for volumes of rectangular and triangular prisms and Solve problems involving duration, including using 12- and 24-hour time within a single time zone.

Solve Problems involving international time zones.

### Geometric Reasoning

Define congruence of plane shapes using transformations.

Develop the conditions for congruence of triangles.

Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related problems using reasoning.

Apply the result for the interior angle sum of a triangle to find, by discussion, the interior angle sum of polygons with more than three sides.

### Pythagoras and Trigonometry

Investigate Pythagoras’ theorem and its application to solving simple problems right-angled triangles.

## Statistics and Probability of Year 8 Mathematics

### Chance

Identify complementary events and use the sum of probabilities to solve problems.

Describe events using languages of ‘at least’, exclusive ‘or’, inclusive ‘or’ and ‘and’.

Represent such events in two-way tables and Venn diagrams and solve related problems.

### Data Representation and Interpretation

Explore the practicalities and implications of obtaining representative data using a variety of investigative processes.

Investigate the effect of individual data values, including outliers, on the mean and median.

Explore the variation of means and proportions in representative data.

#### Course Materials

#### Volume

- Metric Units for Volume
- Cross-section of a Prism
- Volume of a Prism
- Volume of a Prism by Finding the area of Cross-Sections
- Volume of a Composite Prism
- Volume of a Cylinder
- Volume of a Composite Cylinder
- Volume and Capacity
- Conversion of Capacity
- Conversion from Capacity to Volume
- Conversion from Volume to Capacity

#### Fractions

- Conversion from Improper Fractions to Mixed Numbers
- Conversion from Mixed Numerals to Improper Fractions
- Comparing Fractions
- Simplifying Fractions
- Adding Fractions
- Solving Equations by Adding Fractions
- Subtracting Fractions
- Solving Equations by Subtracting Fractions
- Multiplying Fractions
- Solving Equations by Multiplying Fractions
- Dividing Fractions
- Complex Fractions
- Solving Equations by Dividing Fractions
- Applications of Fractions

#### Percentages

- Converting Percentage to Fractions
- Converting Fractions to Decimal
- Converting Fractions to Percentages
- Converting Decimals to Percentages
- Arrangements in Order
- Fraction of a Quantity
- Percentage of a Quantity
- Expression Amounts as Fractions
- Expressions Amounts as a Percentage
- Percentage Increase
- Percentage Decrease
- Applications of Percentage Increase
- Applications of Percentage Decrease
- Unitary Method for Finding Amount
- Unitary Method for the Rest