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Formal trace tables and variable state

A trace table records how an algorithm's state changes while it runs. Examiners use traces to check that you can follow sequence, selection and iteration systematically. A trace is evidence, not a guess at the final output.

1. One row records one meaningful step

For an iteration trace, complete one row for each loop pass. Write a variable only when its value changes. Record a condition as True or False when it is tested, and record text in the output column only when print executes. A blank means unchanged; it never means zero.

Fill in the blanks3 marks

A stored value is part of the program's gap 1. Text produced by print is gap 2. An empty trace cell normally means the value is gap 3.

output
state
unchanged
zero

2. Worked trace

total = 0
for value in [2, 5, 1]:
    total = total + value
    if total > 5:
        print(total)

After the three passes, total is 2, then 7, then 8. The condition is false, true, true. Output occurs only on the last two passes: 7 then 8. The final value 8 and the two printed values are related, but they are not the same record.

Multiple choice1 mark

A variable did not change during one loop pass. What belongs in its trace cell when the instructions say blank means unchanged?

A0
BA blank
CThe variable name
DFalse

Written answer2 marks

A student writes 0 in every unused trace cell. Explain why this makes the trace inaccurate.

Refer to assignment and unchanged state.

Students type their answer here.

3. Trace nested selection carefully

For each item, first update count, then test the condition, then update score only if the condition is true. Indentation shows that the if body belongs inside the loop. Never apply the if only once after all iterations.

Trace table5 marks

Complete the trace table for the algorithm.

Use one row per iteration. Leave a cell blank when its value is unchanged.

Use one row for each pass through the loop. Fill in a box only when that value changes on that row, and leave the rest blank.

ProgramPython

score = 1
count = 0
for item in [4, 7, 3]:
count = count + 1
if item > 4:
score = score + item
print(score)

Trace table with 5 columns
Row	score	count	item	item > 4	Output
1
2
3
4
5
6
7

4. Commit to a prediction

Read this code without running it.

value = 3
for step in range(2):
    value = value * 2
print(value)

Multiple choice1 mark

What exact value is printed?

Written answer2 marks

Explain how the program reaches its output.

State the value after each loop pass.

Students type their answer here.

Written answer2 marks

In the worked trace, what value is held in total immediately after the second addition, and what has been printed by that point?

Keep current state and output separate.

Students type their answer here.

Multiple choice1 mark

Which habit gives the most reliable trace?

AGuess the final print and work backwards
BExecute each indented statement in order for every iteration
CPut every variable on every row even when unchanged
DTreat blanks as zero

Route forward

You can now separate state, conditions and output in a formal trace. Next you will use trace evidence, error messages and focused tests to diagnose and repair programs.