Pilot Classroom Guided Learning with a source-bound hint ladder

Check the activity entry and account scope

The official update lists Education Fundamentals, Standard and Plus, with admin-enabled Gemini access for teachers and students. Rollout does not mean every school sees the feature now. Check the school account and administrator’s arrangements if it is missing.

The teacher instructions describe creating an Assignment in Classwork, attaching Guided Learning, selecting or uploading sources and choosing Create and preview. Assignment Instructions are for students and are not referenced by Gemini in this activity; put essential exercise conditions in the source itself.

The student instructions describe opening the assignment attachment for a focused conversation and explain teacher visibility for assigned activity chats. Keep student personal information and unrelated private material out of this exercise.

Supply a complete, bounded source

This is an original fictional function-comparison exercise. Amounts are teaching units, not market prices. Put the student material in one source file and keep the teacher answer separate. This does not predict school licensing or policy.

Print the same batch of n teaching cards, where n is a nonnegative integer.
Plan A: fixed preparation fee 18 units plus 4 per card; C_A=18+4n.
Plan B: no fixed fee, 6 per card; C_B=6n.
Task: compare total costs for n=6, 9 and 12; find the equal-cost quantity; explain why comparing only 4 and 6 is insufficient.
Count only the stated costs. Add no taxes, discounts or unstated quality differences.

I think A costs 4 per card versus B’s 6, so I would choose A for n=6. Help me locate the first omission in that reasoning and ask a question so I can continue, without immediately giving the final answer.

Use a hint ladder to expose the missing fixed fee

The first hint can ask what A charges besides its per-card rate. If more support is needed, ask the learner to substitute n=6 into the complete expressions 18+4n and 6n. Do not delete 18. How far to scaffold depends on the learning goal and current response, not a universal number of turns.

The contrasting hints below are editorial examples, not Gemini outputs. If a real preview invents discounts, drops the integer condition or says A is always cheaper, repair the material or teaching arrangement before deciding to assign it.

Independent teacher answer: equal at nine cards

For n=6, A=18+24=42 and B=36, so B is lower by 6. At n=9, both cost 54. At n=12, A=66 and B=72, so A is lower by 6. Solving 18+4n=6n gives 18=2n and n=9. For nonnegative integers, B is lower at 0–8, costs are equal at 9, and A is lower from 10 onward.

The lower per-card rate does not guarantee a lower small-batch total. A needs the accumulated two-unit per-card difference to cover its 18-unit fixed fee. Keep cases on both sides of the equality, not just n=9, so the intersection is not mistaken for equality at every quantity.

After previewing, inspect the learner’s own explanation

Preview three questions: forgetting the fixed fee, requesting only the answer and claiming A is always cheaper. Save actual responses alongside the source version. Check retention of 18, 4, 6 and the nonnegative-integer condition, and whether the response returns to the complete formulas. Without real responses, describe prepared material and reference answers, not a passed product pilot.

Ask the learner to explain why A’s lower unit rate still costs more at n=6, using both expressions. A teacher should consider actual work and conversation; an AI summary is not sufficient evidence for a grade or placement. Use stepwise self-explanation to inspect reasoning and the AI quiz audit for other generated questions.

This article supplies source material, task, prompts, complete reference results and corrections. Account permissions, actual responses, student performance and school data rules still need local confirmation. It promises no attainment gain and does not assign or grade students.