Tracing an algorithm by hand

Step 1 Warm-up recall

From M1.L2: list the four properties of an algorithm.

Your answer

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Step 2 Learning goal

By the end of this lesson you can:

• fill in a trace table for a short algorithm (Foundation);
• use a trace to find where an algorithm goes wrong (Core);
• predict the output before running a method (Core).

Step 3 A familiar example

A teacher marks a student’s long division by reading each line and checking what changed. A trace does the same for a method: you act as the machine, one step at a time.

Step 4 Clear explanation

To trace an algorithm, you carry out its steps yourself and record every value that changes. A trace table has one row per step and one column per stored value. It is the main way programmers find mistakes, because it shows what the method really does rather than what you think it does.

Trace the largest-number method on the list 4, 9, 2, 7:

Read the table from top to bottom. “Largest so far” starts with the first item, rises to 9 at step 2 and does not change after that, so the output is 9. If a trace shows a value you did not expect, the fault lies in the step that produced it.

Step 5 Worked example (4 marks)

Trace “add each number to a running total, starting at 0” on the list 3, 5, 2.

1. Start: total = 0. (1 mark)
2. After 3: total = 3. After 5: total = 8. (1 mark)
3. After 2: total = 10. (1 mark)
4. No items remain, so output 10. (1 mark)

Step 6 Learner practice (instant-marked)

Step 7 Recap

• A trace follows the steps by hand and records every changing value.
• A trace table has a row per step and a column per stored value.
• Trace before you trust a method.

Step 8 Exit ticket (ungraded)

Trace “largest so far” on the list 1, 6, 6, 2 and write the final value.

Your answer

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Step 9 Go further (Extension)

Invent a four-item list where the largest item is the last one, and trace the method on it.