The Worked Example You Improvised on the Whiteboard Is Costing You

Here's the uncomfortable bit: the example you make up on the spot is almost always the wrong one. It's either too clean — no messy numbers, no awkward wording — or you accidentally pick the edge case and spend eight minutes untangling something that wasn't the point.

Worked examples are one of the highest-leverage things we do. They're also the thing we prepare the least, because writing a good sequence of them takes longer than the lesson does.

This is exactly the kind of grunt work AI is good at. Not deciding what to model — that's your call — but generating the variations once you've made it.

Start with the sequence, not the examples

The mistake is asking for "five examples of X." You'll get five near-identical problems that teach students to pattern-match instead of think.

Ask for a faded sequence instead:

I'm teaching [topic] to [year level]. Build me a sequence of four worked examples that fade the support: Example 1 fully worked with every step shown and explained, Example 2 fully worked but with the reasoning statements removed, Example 3 with the first two steps done and the rest blank, Example 4 as an independent problem. Keep the underlying structure identical across all four so the only thing changing is the level of support.

That "keep the structure identical" line matters. Without it you'll get four different problem types and the fading does nothing.

Then change one thing at a time

Once the sequence works, build the variation set:

Now give me three more problems based on Example 4. In each one, change exactly one surface feature — the numbers, the context, or the wording of the question — but keep the underlying method the same. Tell me which feature you changed in each.

This is what separates students who understand from students who've memorised a shape. If they can do it with a decimal instead of a whole number, or dressed up in a different context, they've got it.

Ask for the broken ones

The most useful prompt in this whole workflow, and the one nobody uses:

Write two worked solutions to this problem that contain a realistic student error — the kind a [year level] student actually makes, not a careless arithmetic slip. Don't label the error. Then, separately, tell me where each one goes wrong and what misconception it reveals.

Hand students the wrong solutions and ask them to find the break. It takes thirty seconds to set up and produces better discussion than almost anything else you can do with the same time.

The "not a careless slip" instruction is doing real work here. Left alone, AI writes errors like "they added instead of multiplied" — which nobody learns anything from.

Get your live commentary written for you

For Example 1, write the exact sentences I'd say aloud while working through it — including the question I'd ask the class at each decision point. Under 15 words per sentence. No jargon.

Read it once before the lesson. You won't use it word for word, but you'll stop rambling at step three.

Two checks before you use any of it

Do the maths yourself. AI gets arithmetic wrong, confidently, especially with negatives and fractions. Work Example 4 through on paper. If that one's right, the sequence usually is.

Check the context is real. AI defaults to American shopping malls and baseball. Add "use New Zealand contexts and everyday situations a Year 9 here would recognise" to any prompt and it improves immediately.

Ten minutes of prep, four examples that actually build on each other, and two broken ones to argue about. That beats improvising at the whiteboard every time.

TeachSmarterAI helps New Zealand teachers use AI tools effectively. New posts every week.