### Rational and irrational numbers

In this lesson, we will explore the concept of rationality and irrationality in numbers, and learn how to classify rational and irrational numbers.

Skip navigation# Unit Overview: Surds and trigonometry

## Lessons:

### Rational and irrational numbers

### Introduction to Surds

### Surds and triangles

### Manipulating surds

### Varying the ratio of side lengths in right angle triangles

### The case of 30 and 60 degrees

### The sine ratio

### The sine and cosine ratios

### The sine and cosine ratios for 30 and 60 degrees

### Finding missing sides using sine and cosine for any angle

### Using inverse sine and cosine to find missing angles

### Sine and cosine graphs

12 lessons

In this lesson, we will explore the concept of rationality and irrationality in numbers, and learn how to classify rational and irrational numbers.

In this lesson, we will learn what a surd is and we will explore how to accurately estimate the value of a surd.

In this lesson, we will recap how to use Pythagorean theorem to find the length of missing sides in triangles leaving the answers is surd form.

In this lesson, we will look at basic surd rules in particular multiplication and division.

In this lesson, we will learn about the the ratio of side lengths in right angle triangles.

In this lesson, we will look at the special cases of 30 and 60 degrees right angled-triangles.

In this lesson, we will develop an understanding of trigonometric ratios focusing on sine.

In this lesson, we will explore trigonometric ratios focusing on sine and cosine.

In this lesson, we will learn how to find missing sides and angles in triangles using sine and cosine for 30 and 60 degrees.

In this lesson, we will learn how to find missing sides using sine and cosine for any angle in a triangle.

In this lesson, we will use inverse sine and cosine to find missing angles in triangles.

In this lesson, we will look at the graphs made by the sine and cosine functions and compare them to highlight similarities and differences.

Units in Maths

- Numbers and numerals
- Axioms and arrays
- Factors and multiples
- Order of operations
- Positive and negative numbers
- Expressions, equations and inequalities
- Angles
- Classifying 2-D shapes
- Constructing triangles and quadrilaterals
- Coordinates
- Area of 2-D shapes
- Transforming 2-D figures
- Prime factor decomposition
- Conceptualising and comparing fractions
- Manipulating and calculating with fractions
- Ratio
- Percentages
- Different number systems
- Sequences
- Forming and solving equations
- Forming and solving inequalities
- Linear graphs
- Accuracy and estimation
- Algebra and problem solving
- Ratio (8.6a)
- Ratio, real life graphs, and rates of change
- Direct and indirect proportion
- Univariate data
- Bivariate data
- Famous maths problems
- Angles and parallel lines
- Angles in polygons
- Bearings
- Volume and surface area of prisms
- Area review
- Circles
- FDP review (9.1a)
- Probability
- Sets and Venn Diagrams
- Solving linear simultaneous equations algebraically
- Solving linear simultaneous equations graphically
- Angle review (9.5a)
- Constructions, congruence, and loci
- Pythagoras's theorem
- Famous maths problems
- Ratio review (9.7a)
- Similarity and enlargement
- Surds and trigonometry
- Quadratic expressions (9.9)
- Quadratic equations (9.10)
- Indices and standard form
- Growth and decay
- Finance

- Doubling and halving
- Addition and subtraction within 10
- Exploring calculation strategies within 20
- Money
- Measures
- 2-D shape, perimeter and area
- Numbers to 50
- Manipulating and calculating with fractions
- Fractions
- Fractions and decimals
- Conceptualising and comparing fractions
- Numbers 50 to 100 and beyond
- Reasoning with large whole numbers
- Converting units of measure
- Numbers to 10
- Solving measure and money problems
- Addition and subtraction within 20
- Addition and subtraction (applying strategies)
- Numbers within 1000
- Place value
- Problem solving with integer addition and subtraction
- Volume
- Positive and negative numbers
- Numbers within 10
- Numbers within 15
- Addition and subtraction within 20
- Measures (1): Length and mass
- Measures (2): Capacity and volume
- Addition and subtraction of 2-digit numbers
- Fractions
- Multiplication and division
- Multiplication and division
- Axioms and arrays
- Prime factor decomposition
- Indices and standard form
- Time
- Addition and subtraction of 2-digit numbers (regrouping and adjusting)
- Area and perimeter
- Numbers and numerals
- Percentages
- Fractions
- Measures: Length
- Numbers beyond 20
- Time
- Securing multiplication facts
- Addition and subtraction within 10
- Measures: Mass
- Number sense and exploring calculation strategies
- Addition and subtraction
- Securing multiplication and division
- Position and Direction
- Pattern and Early Number
- Addition and subtraction word problems
- Fractions
- Decimals
- Multiplication and division: 3 and 4
- Multiplication and division: 2, 5 and 10
- Measures: Capacity and volume
- Addition and subtraction
- Extending calculation strategies and additive reasoning
- Deriving multiplication and division facts
- Calculating with whole numbers and decimals
- Integers & Decimals
- Multiplication and division
- Grouping and Sharing
- Surds and trigonometry
- Numbers within 6
- Numbers within 100
- Exploring calculation strategies
- Time
- Exploring calculation strategies and place value
- Multiplication and division
- Factors and multiples
- Graphs
- Graphs
- Reasoning with 4-digit numbers
- Reasoning with patterns and sequences
- Calculation problems
- Numbers within 20
- Money
- Multiplication and division
- Fractions, decimals and percentages
- Decimals and measures
- Early Mathematical Experiences
- Order of operations
- Depth of numbers within 20
- Numbers to 20
- Addition and subtraction within 20 (comparison)
- Addition and subtraction within 6
- Accuracy and estimation
- Money
- Length and perimeter
- Fractions
- Fractions
- Problem solving with whole numbers and decimals