Problem first, prompt second

arqiv✳

Lesson · Logic & problem solving

Problem first, prompt second

Students solve a real problem on paper using a four-step method, estimate the answer, and then perform an “autopsy” on an AI solution that sounds right but isn’t.

Level 1 AI after thinkingGrades 6–1245 minutesMath · SciencePaper only (AI sample provided)

The big idea

If you can’t estimate the answer, you can’t tell when a machine gets it wrong.

Students will be able to, without AI:

  • Use a four-step problem-solving method
  • Estimate before calculating
  • Find and explain an error in a confident-sounding solution
  • Explain a solution so a younger student could follow it

Lesson flow · the 5 P’s

Think first. Then the tool.

Most of the lesson happens on paper. AI appears for one short, structured phase, and the teacher can run it from a single projector screen. How the 5 P’s work →

1

Ponder

12 min○ Screens off · paper only

Students meet the problem with pencils only. They use George Pólya’s classic four steps from How to Solve It (1945): understand, plan, solve, look back.

  1. The problem: A school has 600 students. Three-quarters ride the bus. Each bus holds 54 students. How many buses does the school need?
  2. Understand: What do you know? What are you asked? Circle the trap words.
  3. Estimate: Before calculating, about how many buses? Write it down.
  4. Solve: Work it out on paper.
  5. Look back: Does your answer make sense in the real world?
Say to students“Calculators didn’t make math class pointless; they made checking more important. AI is the same.”
2

Plan

5 min○ Screens off · paper only

Students write what a correct answer must look like before seeing the AI’s.

  1. A correct answer must be about ___ because ___.
  2. List one mistake you think is easy to make here.
3

Partner

8 min● AI on · teacher screen or lab

Students receive an AI-written solution (printed on the worksheet, or shown by the teacher). It is fluent, confident and wrong.

  1. Optional: on the teacher’s screen, ask a current AI the same problem and compare. (Today’s AI often gets this right. That’s fine: the skill is checking.)
“First, 3/4 of 600 is 450 students who ride the bus. Next, divide 450 by 54 seats per bus: 450 ÷ 54 = 8.33. Since you can’t have part of a bus, round to the nearest whole number. The school needs 8 buses.”
4

Probe

12 min○ Screens off · paper only

Screens off. Students do an answer autopsy.

  1. Check each step. Which steps are correct?
  2. Find the error. (8 buses only carry 432 students, leaving 18 behind. You must round up to 9.)
  3. Compare the AI’s answer with your estimate. Would your estimate have caught it?
  4. Write the rule the AI broke in your own words.
5

Prove

8 min○ Screens off · paper only

Students show they own the skill without any help.

  1. Solve the twin problem on the worksheet with no help.
  2. Explain the bus problem so a 5th grader could understand it.
  3. Exit ticket: “The best way to check an AI’s math is…”
  4. Teacher key (twin problem): 920 ÷ 15 = 61.33, so 62 vans. 61 vans carry only 915 people and leave 5 behind.

Printable

Student worksheet

Print one per student. Everything students hand in is handwritten, so their thinking is visible.

Answer autopsy

Solve it yourself first. Then check the AI.

Name:Date:Class:
1 · Understand: what do I know and what am I asked?
2 · My estimate before calculating
3 · My solution
4 · The AI’s solution
3/4 of 600 = 450 students ride the bus. 450 ÷ 54 = 8.33 You can’t have part of a bus, so round to the nearest whole number. Answer: 8 buses.
5 · Where is the error, and what rule did the AI break?
6 · Twin problem: 920 people attend a game. Vans hold 15 people. How many vans to bring everyone home?
7 · Explain the bus problem to a 5th grader

Assessment

Grade the thinking, not the output

Every row scores something students did themselves. An AI can produce a product; it can’t produce a student’s reasons.

Criteria4 · Excellent3 · Solid2 · Developing1 · Beginning
Understanding & estimateIdentifies key info and a reasonable estimate with reasoningReasonable estimateEstimate off or unexplainedNo estimate
Own solutionCorrect with clear steps and correct roundingCorrect with minor gapsPartially correctIncorrect
Answer autopsyFinds the error, explains why it matters in the real worldFinds the errorSenses something wrong but can’t locate itAccepts the AI answer
ExplanationA younger student could follow itMostly clearConfusing in partsMissing

Why this is hard to cheat

The AI answer is supplied, so there’s nothing to gain by looking one up. The twin problem and the “explain it to a 5th grader” task are done in class on paper.

Adjust it

Younger students: Use smaller numbers (60 students, buses of 25) and pictures of buses to count.

Older students: Have students write their own “trap” problem and a fluent but wrong AI-style solution for a classmate to autopsy.

No devices at all? Already device-free. The AI solution is printed on the worksheet.

Discussion questions

  • Why does a wrong answer feel more believable when it’s written confidently?
  • When is a small error dangerous in real life? (Medicine doses, bridge loads, budgets.)
  • Should you trust a calculator? An AI? What’s the difference?
  • What habits help you catch your own mistakes?

Extensions & connections

  • Science version: give an AI-style lab conclusion that ignores a variable and have students find it.
  • Connect to how AI can be confidently wrong: how transformers predict words.
  • Careers: engineers, pharmacists and accountants all check numbers for a living.

Put curiosity to work

Read it. Try it. Question it.

Explore new AI research, or take a paper-first investigation into your classroom.

Classroom starter pack →Research explained →