The idea, step by step
Give instructions in the right order
An algorithm is a set of steps that solves a task. Steps need an order, a starting point and a clear stopping point. Start at 3, add 2, then multiply by 4 gives 20. Swapping the operations gives a different answer.
Make it bigger is not a precise instruction. Say add 2 or multiply by 4. When a step repeats, say how many times to repeat it or what condition will stop it.
Make one decision at a time
A decision has a question with clear answers, often yes or no. Decide whether the starting number is even. Follow only the matching branch in the flowchart. Both branches finish at Stop.
Test an algorithm with more than one input. Include an input for each branch. Trace the steps and record results. If an instruction is missing or never stops, change it and test again.
A common trap
I added 4 and then 1 because both are in the flowchart.
Instead: A yes/no decision chooses one branch. Follow only the branch matching the input.
See the thinking
Trace ordered operations
Start at 6. Add 3. Multiply the result by 5.
- Start with 6.
- 6 + 3 = 9.
- 9 × 5 = 45.
Follow a decision
Use the flowchart with inputs 8 and 7.
- 8 is even: follow Yes, so 8 + 4 = 12.
- 7 is odd: follow No, so 7 + 1 = 8.
- Stop after the chosen operation; do not follow both branches.
Check your understanding
Start at 10. Subtract 2, then double. What is the output?
Show answer
16
10 − 2 = 8, then 8 × 2 = 16.
Your turn
6 questions · 11 marks · Work at your own pace.
Read the questions online
- Start at 5. Multiply by 3, then add 2.2 marks
- Start at 5. Add 2, then multiply by 3.2 marks
- Start at 4. Repeat add 3 exactly three times.1 mark
- If the input is greater than 20, subtract 5; otherwise add 5. Find the outputs for 25 and 20.2 marks
- Start at 6. Add 2 until the result is greater than 10, then stop. Write every number reached.2 marks
- An instruction says: start at 1 and keep adding 1. What is needed to make it finish?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Start at 5. Multiply by 3, then add 2.2 marks
5 × 3 = 15.
15 + 2 = 17.
17 - Start at 5. Add 2, then multiply by 3.2 marks
5 + 2 = 7.
7 × 3 = 21.
21 - Start at 4. Repeat add 3 exactly three times.1 mark
4 → 7 → 10 → 13.
13 - If the input is greater than 20, subtract 5; otherwise add 5. Find the outputs for 25 and 20.2 marks
25 is greater than 20, so 25 − 5 = 20.
20 is not greater than 20, so 20 + 5 = 25.
20 and 25 - Start at 6. Add 2 until the result is greater than 10, then stop. Write every number reached.2 marks
10 equals 10; it is not greater.
The first number greater than 10 is 12.
6, 8, 10, 12 - An instruction says: start at 1 and keep adding 1. What is needed to make it finish?2 marks
Without a stopping condition the additions continue.
Any clear reachable stopping condition is acceptable.
A stopping instruction, such as stop when you reach 10.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics 2026
Additive/multiplicative rules; steps/decisions; predicting and explaining patterns.
Official curriculum source ↗