This module covers the number skills that sit underneath almost every other IGCSE Mathematics topic: ordering signed numbers, using factors, working with fractions exactly, knowing when an answer should be exact or rounded, and applying operations in the correct order. Algebra, ratio, percentages, indices and geometry all borrow from it.
Check the current Cambridge IGCSE Mathematics 0580 syllabus for the exact wording of each content point in your exam year. The habits taught here stay the same across versions. Our Mathematics learning guide shows where this module sits among the others.
What should you already know?
You need the four operations on whole numbers, times tables, and a rough idea of what a fraction and a decimal are. You do not need algebra. If multiplying 7 by 8 still makes you pause, practise that first, because every lesson here assumes it.
An orienting example
Work out 2 + 3 × (1/2 − 1/3), giving the exact answer.
Step 1, brackets: 1/2 − 1/3 = 3/6 − 2/6 = 1/6.
Step 2, multiplication: 3 × 1/6 = 3/6 = 1/2.
Step 3, addition: 2 + 1/2 = 5/2, which is 2 1/2.
Check: with decimals, 0.5 − 0.333 gives 0.167, then × 3 gives 0.501, then + 2 gives 2.501. The decimal route drifts away from 2.5, while the fraction route lands exactly on it.
That one question used four of the five lessons: fractions, operation order, exact versus approximate answers and careful signs. It is a good picture of how the module hangs together.
In which order should you study it?
- Order signed numbers on a number line: the picture that stops sign errors.
- Use factors to simplify a numerical expression: the tool that shrinks big calculations before you start.
- Work with fractions without decimal rounding: keeps answers exact and is the base for algebraic fractions later.
- Compare exact and approximate answers: tells you when to keep π or a fraction and when to round.
- Check operation order in a multi-step calculation: pulls the earlier lessons into longer questions.
Then work through the mixed practice set. If you revise in the evenings, one lesson a day and the practice set on the weekend is a steady pace.
Which traps catch most students here?
- Ignoring the sign when ordering or subtracting negatives.
- Cancelling across addition, for example treating (20 + 8)/4 as 20 + 2.
- Adding fractions by adding tops and bottoms, which turns 2/3 + 3/4 into 5/7.
- Rounding early and carrying the error into the final answer.
- Working left to right and skipping the order of operations.
Each lesson shows one of these slips in full and then corrects it.
How should you use the practice set?
Attempt each question on paper before opening the answer. Write your working as you would in an exam, because the marks in a real paper come from method as well as the final value. The non-calculator working trainer lets you check a fraction step without reaching for a calculator.
When you get something wrong, read the routing notes at the end of the practice set and go back to the lesson it names. Fix the lesson, then retry a fresh question a few days later.
If you want teaching beyond self-study, online one-to-one Mathematics tuition means an experienced teacher looks at your written working and finds which habit is behind the error.