lesson
Keep a rule true after every operation
1 · Learn
Program state is the information currently held. An invariant is a condition intended to remain true at defined points, such as an inventory count never becoming negative. Each operation must preserve it or reject an invalid request.
Checking only when a screen first opens is insufficient if later actions can break the rule. Identify where state changes occur.
2 · Worked example
If stock is 3, a request to remove 5 must not simply leave -2 when the invariant forbids negative stock.
3 · Your turn
Starting at stock 3, what should happen to a request to remove 5 under that invariant?
Check your answer
Reject the request or otherwise handle it explicitly without storing a negative count.
4 · Apply your learning
Trace add and remove operations, including boundary cases, and verify the invariant after each.
Adult guidance and safety
Work in an approved local sandbox with invented records and test accounts. Do not access other people's systems or collect real credentials. Practical project evidence is required in addition to these explanations; this is not a specified GCSE Computer Science course.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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