Chain of thought and step-by-step instructions

Short answer: when AI gets a word problem wrong, it is usually not because it cannot do the maths. It is because you let it start writing the answer with its very first word. Ask for the working first and both accuracy and reviewability improve.

One Secondary 3 question, two ways of asking

A Secondary 3 Mathematics teacher is checking the answer key for her own test:

An item costs $480. The price rises by 20%, then falls by 20%. What is the final price?

Back comes "$480 — the 20% increase and 20% decrease cancel out." That is the classic intuition trap and it is wrong; the answer is $460.80. If she is in a hurry, the wrong figure goes onto the answer sheet.

Asked differently:

You are a proofreading assistant for a Hong Kong secondary Mathematics teacher.
Task: work out the answer to the question below for a Secondary 3 test answer key.
Question: an item costs $480. The price rises by 20%, then falls by 20%. What is the final price?
Output format: first the working, one step per line, each line saying what that step does; then a separate paragraph, one sentence, on the step where students most often go wrong; the final answer only on the last line.
Constraints: do not state the answer before the working; if the question itself is ambiguous — for example if the base for the 20% reduction is unclear — say so and mark it "teacher to verify" rather than assuming.

This time the model actually computes: 480 × 1.2 = 576, then 576 × 0.8 = 460.8, and names the common misconception as believing the two percentages cancel. That sentence goes straight into the misconceptions box of the lesson plan.

Why this works

A model generates one token at a time. If the first token is the answer, that answer was produced with almost no computation behind it — it reflects what answers to questions like this tend to look like. Ask for the working and each step becomes context for the next, so the computation genuinely happens in the text.

An analogy: tell a student to do it in their head and they will announce a number that feels right. Tell them to show the working and the act of writing slows them down, and you can see the step where it went wrong. The student did not get cleverer; the thinking became visible.

Current reasoning models already do this internally without being asked. In a teaching context, though, written-out steps keep two irreplaceable advantages: the steps themselves are teaching material, and a teacher needs to see the reasoning before trusting the result. For how reasoning models work, see the LLM Classroom.

Template 1: steps before conclusion

Useful in any subject that needs verification or a visible process.

You are a proofreading assistant for a Hong Kong secondary [subject] teacher.
Task: solve the question below and produce a worked solution suitable for showing students.
Context: [year level]. The learning focus of this unit is [focus]. Students have already covered [prior knowledge] and have not yet met [later content].
Output format: three parts — (1) the working, one step per line, each naming the concept or rule it uses; (2) one sentence identifying the step students most often get wrong and why; (3) the final answer on its own line.
Constraints: do not give the answer until part 1 is complete; use only methods students have already been taught; if the question is ambiguous or missing data, say so and mark it "teacher to verify" rather than filling in an assumption.

Question: [paste the question]

Template 2: check it in a different role

The second pass is the cheapest accuracy gain available. Paste the first output into a fresh turn and do not mention that AI produced it.

You are an experienced marker for Hong Kong secondary [subject].
Task: check the solution below against the marking scheme, item by item, for correctness and completeness.
Context: this is a draft answer key for a [year level] [unit] test that will be handed to students, so accuracy matters more than fluency.
Marking scheme: [paste it, or list the marks for each step]
Output format: a three-column table — step number, verdict (correct / incorrect / unclear), and what the problem is if there is one. After the table, three sentences at most on whether the key is fit to issue.
Constraints: check item by item, not as a general impression; if you cannot determine whether a step is correct, mark it "teacher to verify" rather than guessing; do not rewrite the solution, only identify problems.

Solution: [paste the output from the first pass]

Template 3: splitting a long task into four

A Primary 5 General Studies teacher is planning a six-lesson inquiry unit. Asking for all of it at once guarantees that every part is shallow.

You are a unit planning assistant for a Hong Kong primary General Studies teacher. We will work in four steps. Do step one only and wait for my confirmation.
Task (step one): design the overall structure of a six-lesson Primary 5 inquiry unit on waste management in Hong Kong.
Context: 35-minute lessons, a class of 30 working in six groups. The learning focus is comparing the costs and effects of different waste-handling methods, with group presentations in lesson six.
Output format: a table of six rows, one per lesson, with four columns — lesson, focus question, student activity, output. After the table, three bullet points on how the six lessons build on each other.
Constraints: one focus question per lesson only; do not write worksheets or rubrics yet, those are steps three and four; where recycling figures or policy details are involved, mark them "teacher to verify" so the teacher can supply current data.

Step two asks for the slide outline, step three the worksheets, step four the rubric, each using the previous output as context. Lesson 6, lesson planning prompts demonstrates the full sequence.

Common mistakes

• Asking for steps and brevity in the same sentence. "Explain step by step but keep it short" is contradictory, the model picks short, and you lose the steps. If you want brevity, ask for a one-line summary after the working.
• Checking with "are you sure?" The most common effect is that the model changes a correct answer to please you. To check properly, change the role, supply a rubric and demand an item-by-item verdict.
• Splitting the task but dropping the context. Four prompts in four fresh conversations produce a worksheet in step three that does not match the structure from step one. Stay in one thread, or paste the previous output forward.
• Printing the chain of thought for students. Model working often contains self-corrections and padding. To use it as material, add a format instruction: "rewrite this solution in language a [year level] student can follow, no more than two sentences per step."

Going further

• A different subject: in Chinese Language, use it to unpack classical Chinese — gloss each character, then translate each clause, and only then state the meaning of the passage. In Liberal Studies / Citizenship and Social Development, use it for argument — list three points on each side with their supporting reasons, then evaluate which side is stronger and state the criteria used.
• A different year level: primary steps must be shorter. Add to constraints "one sentence per step, no more than 12 words, numbered with a tick box".
• SEN adaptation: for students with attention or executive-function difficulties, step decomposition is the adaptation. Ask for "one instruction per step, each with a completion indicator so the student knows that step is finished".
• As a diagnostic tool: paste a student's incorrect answer and ask it to identify the step where the reasoning first goes astray and infer the underlying misconception — with the constraint "do not rewrite the student's answer". Lesson 9 develops this.

The next lesson fixes all of this in place as a school-wide default: lesson 5, system prompts and school-based personas.