GCSE Maths: Mastering Number Skills

Overview of Number Skills in GCSE Maths

The Number topic in GCSE Mathematics covers a wide range of numerical concepts and techniques that are essential for further study in mathematics and various other disciplines. The key areas within this topic include:

Types of Numbers

• Natural numbers (1, 2, 3, ...)
• Integers (..., -2, -1, 0, 1, 2, ...)
• Rational numbers (fractions, decimals)
• Irrational numbers (π, √2, etc.)

Arithmetic Operations

Performing calculations involving addition, subtraction, multiplication, and division, with proper order of operations (BODMAS/BIDMAS).

Fractions

Understanding fractions, equivalent fractions, simplifying fractions, adding/subtracting/multiplying/dividing fractions, and converting between fractions and decimals.

Decimals

Representing numbers using decimal notation, rounding decimals, arithmetic operations with decimals, and converting between decimals and fractions.

Percentages

Calculating percentages of a quantity, expressing fractions and decimals as percentages, solving problems involving percentages (e.g., interest, profit, and loss).

Worked Example: Percentages

Problem: A shirt originally priced at £40 is discounted by 20%. Find the sale price.

Solution:

• 20% of £40 = 0.2 × £40 = £8
• Sale price = Original price - Discount = £40 - £8 = £32

Ratio and Proportion

Understanding ratios, expressing ratios in simplest form, solving problems involving direct and inverse proportion.

Standard Form

Representing numbers using standard form notation (e.g., 2.5 × 104), converting between standard and decimal forms.

Other Topics

• Rounding and estimating
• Upper and lower bounds
• Highest common factor (HCF) and lowest common multiple (LCM)
• Prime factorisation
• Introduction to surds (square roots)

Mastering these fundamental number skills in GCSE Maths is crucial for success in higher-level mathematics and many other subjects that rely on quantitative reasoning.