### Indices and Radicals

In this lesson, we will recap our knowledge of surds. We will rewrite surds in their simplest form and recall how to rationalise the denominator. We will also practise organising surds in order of ascending size.

Skip navigation# Unit Overview: Indices and standard form

## Lessons:

### Indices and Radicals

### Indices and power of 0

### Expressing powers of in different bases

### Laws of indices

### Fractional Indices (Part 1)

### Fractional Indices (Part 2)

### Negative indices

### Powers of 10

### Sorting large numbers

### Multiplying and dividing in standard form

### Addition and Subtraction in standard form

### Mixed problems with standard form

12 lessons

In this lesson, we will recap our knowledge of surds. We will rewrite surds in their simplest form and recall how to rationalise the denominator. We will also practise organising surds in order of ascending size.

In this lesson, we will recap our knowledge of basic indices. We will explore the power of zero, and carry out calculations involving low power values.

In this lesson, we will learn that some powers can be expressed as different powers of different base numbers.

In this lesson, we will investigate some of the laws of indices and how they are derived. We will look specifically at multiplying and dividing numbers with the same base.

In this lesson, we will begin to work with fractional indices and learn how to evaluate calculations with fractional indices.

In this lesson, we will continue working with fractional indices and we will investigate fractional index problems and model their solutions,.

In this lesson, we will build on our knowledge of fractional indices and work with negative indices.

In this lesson, we will work with powers of 10 with both integers and decimal numbers. We will calculate these numbers as a starting point to investigate standard form.

In this lesson, we will learn how to write large numbers in standard form and write numbers given in standard form as an ordinary number.

In this lesson, we will learn how to multiply and divide numbers that are presented in standard form.

In this lesson, we will learn to add and subtract numbers written in standard form, giving your answer as both ordinary numbers and in standard form.

In this lesson, we will recap our knowledge of working with standard form and perform calculations with mixed operations.

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