Number Families
Understand natural, whole, integer, rational and irrational numbers.
O LEVEL MATHEMATICS
Real Numbers
Build a solid foundation in the number system by learning how different types of numbers behave, compare and combine.
What Will You Learn?
Build your understanding one clear idea at a time.
Factors and Multiples
Explore prime numbers, divisibility, HCF and LCM.
Fractions and Decimals
Calculate with different forms of parts of a whole.
Percentages and Ratio
Solve comparison, sharing and proportional problems.
Powers and Surds
Work with indices, roots and exact irrational values.
Accuracy and Bounds
Round, estimate and describe possible ranges of values.
Maps and Scale Drawings
Read scales, create drawings and solve distance and area problems.
Why Does This Topic Matter?
Real numbers are the foundation for nearly every branch of mathematics.
Shopping, budgeting and discounts all depend on working with numbers accurately.
Measurement, scale and estimation rely on understanding values and rounding.
Graphs, equations and formulae all use number operations and notation.
Strong number sense makes later topics easier to understand.
CENTRAL IDEA
Numbers make sense when we see how they fit together.
Real numbers bring together whole numbers, fractions, decimals, negatives, roots and other values into one connected system.
Ask what kind of number you are working with before choosing a method.
YOUR LEARNING JOURNEY
Work Through the Lessons Step by Step
Each lesson builds on the ideas introduced before it.
01Available
Types of Numbers
Meet natural, whole, integer, rational and irrational numbers.
Open Lesson โ02Available
Factors, Multiples and Prime Numbers
Identify factors, multiples, prime numbers and prime factorisation.
Open Lesson โ03Available
Highest Common Factor and Lowest Common Multiple
Solve grouping and repeating-event problems using HCF and LCM.
Open Lesson โ04Available
Directed Numbers
Calculate confidently with positive and negative numbers.
Open Lesson โ05Available
Order of Operations
Use BODMAS to perform calculations in the correct order.
Open Lesson โ06Available
Fractions
Simplify, compare and calculate with fractions and mixed numbers.
Open Lesson โ07Available
Decimals
Understand place value and calculate with decimal numbers.
Open Lesson โ08Available
Percentages
Convert, compare and solve percentage problems.
Open Lesson โ09Available
Powers, Squares, Cubes and Roots
Work with powers, square numbers, cube numbers and roots.
Open Lesson โ10Available
Surds
Understand and simplify exact irrational values.
Open Lesson โ11Available
Number Patterns
Recognise, continue and describe numerical patterns.
Open Lesson โ12Available
Introduction to Number Bases
Represent numbers using bases other than base ten.
Open Lesson โ13Available
Calculations in Number Bases
Perform calculations and conversions involving number bases.
Open Lesson โ14Available
Ratio, Rate and Proportion
Compare quantities and solve proportional problems.
Open Lesson โ15Available
Standard Form
Write and calculate with very large and very small numbers.
Open Lesson โ16Available
Estimation and Approximation
Round and estimate values appropriately.
Open Lesson โ17Available
Bounds and Error Intervals
Describe the possible range of rounded or measured values.
Open Lesson โ18Available
Introduction to Scales
Understand what a scale is and use simple statement scales.
Open Lesson โ19Available
Types of Scales
Recognise statement, ratio and line scales.
Open Lesson โ20Available
Measuring Lengths Using Scales
Measure accurately and convert drawing lengths to real lengths.
Open Lesson โ21Available
Scale Drawings
Create accurate drawings from real measurements.
Open Lesson โ22Available
Calculating Distances on Maps
Calculate map and real distances in simple problems.
Open Lesson โ23Available
Representative Fraction (RF)
Interpret and convert representative fractions.
Open Lesson โ24Available
Ratio Scales
Write, simplify and use ratio scales correctly.
Open Lesson โ25Available
Practical Scale Problems
Solve multi-step map and plan problems.
Open Lesson โ26Available
Scale Factor
Calculate and apply linear scale factors.
Open Lesson โ27Available
Area Factor
Connect linear scale factor with area factor.
Open Lesson โ28Available
Distance and Area Using Scales
Use map scales to calculate distances and areas.
Open Lesson โ29Available
Mixed Scale Problems
Combine all scale skills in unfamiliar problems.
Open Lesson โ30Review
Real Numbers Mixed Review
Choose the correct number method without being told.
Open Lesson โ31Checkpoint
Real Numbers Revision Worksheet
Review the full topic through mixed revision questions.
Open Lesson โTHE STUDYNEST METHOD
How We Will Approach Real Numbers
Understand the idea before applying the procedure.
Identify
Decide what the numbers represent.
Choose
Select the correct operation or relationship.
Calculate
Show clear and organised working.
Check
Estimate and confirm the answer makes sense.
Understand the Number Before You Calculate
Real numbers become easier to work with when you first identify what kind of number you are handling.
Ask what each number represents before choosing a method.
YOUR PROGRESS
Real Numbers Journey
Begin with Lesson 1 and build your understanding step by step.
Real Numbers Progress0%
Begin Lesson 1 โ