This module is about working well when a calculator is not available: choosing short methods, keeping values exact, checking that an answer is the right size, laying out long working clearly and having a second route in reserve. The arithmetic is usually light. The marks depend on the decisions you make before you start.
Check the current Cambridge IGCSE Mathematics 0580 syllabus and your paper instructions to see which papers allow a calculator in your exam year. The habits here stay useful either way, because they also help you spot a mistyped calculator entry. Our Mathematics learning guide shows where this module sits among the others.
What should you already know?
You should be able to add, subtract, multiply and divide fractions, find a percentage of an amount, and round to one significant figure. If any of these are shaky, revisit number sense and exact arithmetic and percentages and changing bases first.
One orienting example
Work out 3/4 ÷ 2/5 without a calculator.
The decision comes first: division by a fraction means multiply by its reciprocal, so the working is 3/4 × 5/2. No numbers cancel, so multiply across to get 15/8, which is 1 7/8.
Now check the size.
3/4 is 0.75 and 2/5 is 0.4, so 0.75 ÷ 0.4 is about 1.9. That matches 1 7/8, so the answer is plausible. Choosing a method, working exactly, and checking the size took four short lines.
In what order should you study the lessons?
- Choose an efficient fraction method: start here, because picking the shortest route saves time on every other skill.
- Use exact values instead of premature decimals: learn to carry fractions and π through the working and convert only at the end.
- Estimate to reject an impossible answer: add a ten-second size check to every answer.
- Organise working for a multi-operation task: keep long questions readable by splitting them into labelled stages.
- Compare two valid mental strategies: learn a second route for when one method does not fit, or as an independent check.
Then try the non-calculator strategy practice set, which mixes all five skills. The non-calculator working trainer and the percentage-base explorer give extra step-by-step tasks.
What are the common traps?
- Flipping the wrong fraction. Only the fraction you divide by is turned over.
- Rounding too early. A small rounding in the first line grows by the last line.
- Skipping the size check. An answer that is ten times too big often looks fine until you estimate.
- Piling everything into one line. A long line hides the one step that is wrong.
- Applying a second percentage to the original amount. Each change works on the new amount, not the start.
How should you use the practice set?
Do it on paper with no calculator, and write your full working before opening any answer. Compare your method as well as your result, because a correct answer from a long route is a warning for timed papers.
If you get a question wrong, use the table at the end of the set to route the error back to the right lesson. Retry a fresh question a few days later rather than the same one.
If you have worked through the lessons and non-calculator questions still run away from you, our teachers can look at your working directly in online one-to-one Mathematics tuition.