Testing conditions at their boundaries

Step 1 Warm-up recall

From M3.L3: which branch runs for age 65?

Your answer

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Step 2 Learning goal

By the end of this lesson you can:

• choose test inputs at boundaries (Foundation);
• find an off-by-one error (Core);
• correct a faulty condition (Core).

Step 3 A familiar example

Most mistakes in rules are not in the middle of a range; they sit exactly on the boundary, where “under 18” and “18 and over” meet.

Step 4 Clear explanation

A boundary is a value at which the answer changes. For each boundary, test the value on each side of it.

An off-by-one error happens when a rule uses < instead of ≤, or > instead of ≥, so the boundary value falls on the wrong side. Consider this faulty chain: under 5 is free; under 17 costs £4; under 64 costs £8; otherwise £5. A 17-year-old gets the adult price of £8 (should be £4), and a 64-year-old gets the senior price of £5 (should be £8). The fix is to change 17 to 18 and 64 to 65. Boundary tests find such errors quickly, because they test exactly the values the rule gets wrong. The same idea applies to any programming language.

Step 5 Worked example (4 marks)

The faulty chain says under 17 costs £4. What does a 16-, 17- and 18-year-old pay, and which is wrong?

1. Age 16: 16 < 17 is true, so £4 (correct). (1 mark)
2. Age 17: 17 < 17 is false; next, 17 < 64 gives £8 (wrong, should be £4). (1 mark)
3. Age 18: £8 (correct). (1 mark)
4. The error is at the boundary: change < 17 to < 18. (1 mark)

Step 6 Learner practice (instant-marked)

Step 7 Recap

• Test the value on each side of every boundary.
• Off-by-one errors come from < versus ≤.
• Fix the comparison, then re-run all the boundary tests.

Step 8 Exit ticket (ungraded)

List six boundary tests for a rule that changes at ages 5, 18 and 65.

Your answer

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Step 9 Go further (Extension)

Write a boundary test table for a password rule of at least 12 characters.