Using AI to Create Problem Solving Practice Problems
AI creates effective problem solving practice problems when you distinguish mathematical problem solving — which requires students to select, connect, and apply strategies without being told which one — from calculation exercises, which require students to execute a known procedure. The key prompt instruction is: "Students should not know which strategy to apply from reading the problem." Without this, AI generates sophisticated-looking word problems that are solved by applying the most recently taught formula — calculation exercises in word problem clothing.
Quick Answer: Specify in the prompt that the problem should not telegraph the solution strategy; require students to plan before calculating; include at least two valid solution paths; and request a worked solution showing the problem-solving process (understand → plan → execute → check), not just the final answer. These four specifications produce genuine problem solving practice rather than dressed-up computation tasks.
Problem Solving vs. Calculation: A Distinction That Changes Everything
Problem solving practice is one of the most frequently requested and least effectively executed genres in AI-generated mathematics content. Teachers ask for "problem solving practice" and receive word problems. Students complete the word problems by identifying which recent topic is being tested, applying that formula, and reaching an answer — with no genuine problem solving having occurred.
Genuine mathematical problem solving, as defined by NCTM (2025), is the process of engaging with a non-routine task: one where the path to solution is not immediately apparent, where multiple strategies might apply, and where the student must make decisions rather than execute a predetermined sequence. George Pólya's four-phase framework — Understand the Problem, Plan an Approach, Execute the Plan, Look Back — describes not a procedure but a flexible thinking disposition.
The diagnostic question for distinguishing problem solving from calculation:
"If the student removed the word problem wrapper, would they still need to think?"
Compare two versions of the same recipe scenario:
- Calculation version: "A recipe calls for 2½ cups of flour and you want to make 1.6 times the recipe — how much flour do you need?" This is a multiplication-of-fractions calculation problem. The word problem adds context but not cognitive demand — the student knows immediately to multiply 2½ by 1.6.
- Problem solving version: "You have 3 cups of flour and want to make as large a batch as possible. The original recipe uses 2½ cups for 12 cookies. How many cookies can you make?" Now the student must identify that they need to find what fraction of the recipe the available flour allows — a reasoning step that precedes the calculation.
According to EdWeek Research Center (2024), problem solving performance is one of the most significant predictors of student readiness for high school mathematics, yet traditional instruction produces students who are competent calculators but struggle with non-routine problems. AI can generate the non-routine problems that effective problem solving instruction requires — but only with the right specifications.
The Four Problem Solving Types and How to Prompt for Each
Mathematical problem solving problems fall into four structurally distinct types. Each requires different planning approaches and produces different types of mathematical thinking.
| Problem Type | What Students Must Do | Grade Range | Key Prompt Phrase |
|---|---|---|---|
| Find-the-strategy | Identify which approach applies (draw a diagram, work backwards, list systematically) | Grade 3–9 | "Students must choose their own strategy — do not suggest one" |
| Multi-context integration | Apply one mathematical skill in an unfamiliar real-world context | Grade 5–9 | "The context should not immediately reveal that [specific operation] is needed" |
| Optimisation | Find the best solution among multiple valid possibilities | Grade 6–9 | "There are multiple possible answers; students must determine which is best and justify it" |
| Non-routine open-ended | Problems with multiple valid approaches and multiple valid answers | Grade 5–9 | "This problem has more than one correct answer; students must explore and justify their answer" |
Build problem sets that include all four types. Single-type problem sets produce students who are proficient at one problem solving approach while remaining strategy-rigid.
Type 1: Find-the-Strategy Problems
Find-the-strategy problems present a mathematical situation where the productive path forward is not obvious. Students must consider several approaches — and choose the most efficient one.
AI prompt:
"Write 4 find-the-strategy problems for Grade 6. Each problem can be solved using at least two of these strategies: draw a diagram, work backwards, use a table, find a pattern, solve a simpler problem first. The problem should not suggest which strategy to use. Answer key shows two different valid solution approaches for each problem, explaining why each works. Problems should not be solvable by applying the most recently taught formula alone."
Example output:
"A staircase pattern is made from blocks. Staircase 1 needs 1 block. Staircase 2 needs 3 blocks. Staircase 3 needs 6 blocks. How many blocks does Staircase 8 need? How did you figure this out?"
This problem can be solved by: extending the table (identify the pattern: each staircase adds one more block than the previous added), drawing the staircase and counting, or recognising the triangular number formula. The problem does not specify any of these approaches. Students who extend the table are using a valid strategy; students who spot the n(n+1)/2 pattern are using a more elegant one — both produce correct answers through genuine problem solving.
Type 2: Multi-Context Integration Problems
Multi-context integration problems embed a familiar mathematical skill in an unfamiliar real-world context that students must first interpret before calculating.
AI prompt:
"Write 4 problem solving problems for Grade 7 where students must apply proportional reasoning in contexts that don't obviously look like proportion problems. The mathematical skill (proportional reasoning) should only become apparent after careful reading. Contexts: one involving cooking and nutrition labels, one involving map scale and actual distance, one involving unit conversion between currencies, one involving rate of work (two people working at different speeds). Worked solution showing: (1) how to identify that proportion applies, (2) setting up the proportion, (3) solving, (4) interpreting the answer in context."
The "how to identify that proportion applies" step in the worked solution is the critical element. Students who only see the calculation step do not develop the strategy-recognition skill that non-routine problem solving requires.
Type 3: Optimisation Problems
Optimisation problems have a definite structure (some solutions are better than others) but require students to reason about what "better" means and to explore the solution space rather than apply a formula.
AI prompt:
"Write 3 optimisation problems for Grade 7–8. Each problem has multiple possible numerical solutions, but one (or a small class) is optimal. Example structure: 'A farmer has 40 metres of fencing for a rectangular garden. What dimensions give the largest area?' Students must: (a) identify that multiple configurations are possible, (b) systematically explore several configurations, (c) identify the optimal one, (d) explain why it is optimal. Worked solution shows the systematic exploration and the identification of the pattern — not just the formula answer."
The most common teacher error with optimisation problems is providing the formula immediately in the worked example, eliminating the discovery component. Request "systematic exploration" explicitly in the prompt to ensure the worked solution models the problem solving process.
Type 4: Non-Routine Open-Ended Problems
Non-routine open-ended problems have multiple valid answers and require students to make and justify mathematical decisions.
AI prompt:
"Write 3 non-routine open-ended problems for Grade 8 that have multiple valid answers. Each problem should: (a) have a clear mathematical structure, (b) require students to make a decision and justify it with mathematics, (c) be genuinely open (not a disguised single-answer problem). Example: 'Design a rectangular room with an area of 24 m². Give three different sets of dimensions. Which would you choose if the room is a bedroom? Justify your choice using mathematics.' Include teacher notes on what constitutes a well-justified response."
The "teacher notes on what constitutes a well-justified response" addition produces the rubric guidance that open-ended problems require. Without it, teachers receive problems they cannot mark consistently.
A Classroom Example: A Grade 6 Class Working With Area
Say you teach Grade 6 and your class has completed the topic of areas and perimeters. Standard assessment results show high accuracy on formula application. But when you assign a non-routine area problem, you notice that students apply length × width to shapes where this is incorrect and freeze when no formula is obviously applicable.
You could generate a problem solving practice set focused on spatial reasoning with area, without specifying which formula applies.
Prompt:
"Write 6 problem solving problems for Grade 6 involving area, where students cannot immediately identify the correct formula from reading the problem. Include: 2 problems requiring decomposition of a composite shape without labelling the sub-shapes; 2 problems that require reasoning about what information is missing before calculating; 2 optimisation problems ('which of these shapes has the largest area?' or 'create the largest possible shape with a given perimeter'). Worked solutions showing the problem solving process: understand → identify what's unknown → plan (which strategy to use and why) → calculate → check. Do not provide formulas in the problem statements."
You receive 6 problems. Read each and verify that none of them telegraphs the solution strategy — all require planning before calculating. Verify all area calculations in Wolfram Alpha before printing.
In the lesson itself, students work in pairs on the problem set for 25 minutes. With problems that don't telegraph a formula, you can expect more discussion and planning than during formula-practice lessons — students reading problems twice and debating which strategy to use before beginning. Over time, students who struggled to plan before calculating may begin writing brief "what do I need to find?" notes before solving.
Structuring the Worked Solution for Problem Solving Practice
The worked solution in a problem solving practice set serves a different purpose than an answer key for calculation practice. An answer key for calculation shows the correct procedure. A problem solving worked solution models the cognitive process that leads to a solution — it is the most valuable teaching tool in the problem set.
Effective worked solutions for problem solving problems show:
- Understand — what is given, what is unknown, what constraints apply
- Plan — which strategy is being selected and why (acknowledging that other strategies also exist)
- Execute — the calculation or reasoning step, shown clearly
- Check — verify the answer makes sense in the context, not just numerically
AI prompt for worked solutions: "For each problem, write a four-step worked solution using the headings: Understand / Plan / Execute / Check. Under 'Plan', name the strategy selected AND briefly mention one alternative strategy that would also work. Under 'Check', verify the answer by a method different from the one used in Execute (e.g., if the problem was solved using multiplication, verify using division)."
The "mention one alternative strategy" instruction in the Plan section is the difference between a worked solution that produces problem solving skill and one that produces a single-strategy habit.
Problem Solving Problems for Different Mathematical Strands
Problem solving practice should span all mathematical strands — not just the strand currently being taught. Students who only encounter problem solving problems within a single topic cannot transfer problem solving skills to new contexts, which is the essential assessment of problem solving capacity.
Cross-strand problem prompt:
"Write 5 problem solving problems for Grade 7 that draw on more than one mathematical strand simultaneously. Each problem should require skills from at least two of: number sense, algebra, geometry, data and probability, measurement. The mathematical connections should be genuine — not two separate calculations in the same word problem. Worked solution shows which strands are being integrated and why."
Cross-strand problems are the most authentic problem solving format because real-world problems do not come labelled by mathematical strand. They are also the most difficult to generate well — most AI attempts produce two single-strand problems joined by "and." Specify "the mathematical connections should be genuine" explicitly to reduce this failure mode.
Tools for Generating Problem Solving Practice
Claude for Worked Solutions
Claude is the strongest AI tool for genuine problem solving problem generation because it produces worked solutions that articulate the reasoning process. The "four-step worked solution" format (Understand/Plan/Execute/Check) is implemented more consistently and precisely by Claude than by ChatGPT for open-ended and multi-context problem types.
ChatGPT for High-Volume Generation
ChatGPT generates adequate find-the-strategy and single-context problems quickly. For high-volume generation of Type 1 and Type 2 problems, ChatGPT with explicit strategy specifications is efficient.
EduGenius for Bloom's-Aligned Problem Sets
EduGenius generates problem solving problem sets aligned to Bloom's Taxonomy levels — particularly useful for ensuring that a problem set progresses from Tier 3 (Apply) to Tier 4 (Analyse) and Tier 5 (Evaluate) problems, rather than clustering at the application level.
For teachers who want problem solving practice that is explicitly differentiated by Bloom's level (rather than by mathematical difficulty), the Bloom's tagging in EduGenius-generated content provides a structure for that differentiation. The PDF and PPTX export formats make presenting problem solving problems to the whole class efficient — projecting a PPTX version that reveals the worked solution step by step is a practical class demonstration format.
What to Avoid
Avoid Problems That Telegraph the Solution Strategy
If a problem appears immediately after a lesson on proportions and uses the word "ratio" in the problem text, students know to apply proportional reasoning before reading further. This is calculation practice, not problem solving practice. Problem solving requires strategy selection — which requires genuine ambiguity about which approach to apply. Generate problem solving problems at least one week after the relevant topic has been taught, and specify: "Do not mention the mathematical topic the problem is based on in the problem text."
Avoid Open-Ended Problems Without Teacher Guidance on Correct Answers
Non-routine open-ended problems (Type 4) can be justified in multiple ways, and not all justifications are equally strong. Without teacher guidance on what constitutes a complete, well-reasoned response, teachers cannot mark consistently and students do not know what quality to aim for. Every open-ended problem must include teacher notes specifying: what mathematical reasoning is necessary, what level of justification constitutes a "complete" response, and what partial credit looks like. Request these notes explicitly in the prompt.
Avoid Using Worked Solutions That Show Only One Strategy
A worked solution that shows only one strategy for a problem solving problem teaches students that there is one correct approach — which is the opposite of the problem solving disposition. Every worked solution for a genuine problem solving problem should acknowledge that "this is one approach; another approach would be..." and briefly describe the alternative. This single-sentence addition fundamentally changes how students relate to the solution.
Avoid Mixing Routine and Non-Routine Problems in the Same Problem Set Without Labelling
If a problem set includes both routine calculation problems and genuine problem solving problems without distinguishing them, students who solve the routine problems quickly then slow down on the non-routine ones feel confused — they are unsure whether they are missing something or whether the problem genuinely requires more thinking. Label problem sets explicitly: "Problems 1–4 are calculation practice. Problems 5–8 are problem solving — there is no single correct approach." The distinction reduces anxiety and focuses attention.
Pro Tips for AI-Generated Problem Solving Practice
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Generate a context library for problem solving problems. The most engaging problem solving contexts are ones students find genuinely interesting: sports statistics, video game mechanics, food and cooking, architecture, travel planning, environmental data. Generate a list of 10 strong contexts for your class demographic and use them as a recurring resource: "Generate 10 real-world contexts that Grade 7 students in [your city] would find genuinely interesting. These contexts will be used as settings for problem solving problems across the year."
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Use problem solving problems as unit openers, not closers. A non-routine problem at the start of a unit creates a productive puzzle that gives students an authentic reason to learn the upcoming content. At the end of the unit, when students have the tools to solve it, returning to the opening problem provides a concrete sense of mathematical progress. AI generates "unit opening problems" efficiently: "Write a problem that a Grade 7 class cannot yet solve but will be able to after studying linear equations. The problem should be interesting and solvable using the upcoming content."
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Generate problems that require estimation before calculation. A good problem solving habit is estimating the answer range before calculating — students who estimate first catch calculation errors because "that's way bigger than I expected" is a warning signal. Generate problems that specifically require estimation: "Write 4 problem solving problems for Grade 8 where students must first estimate the answer range, then solve precisely, then check whether the precise answer falls within the estimated range. Include contexts where the estimation step reveals useful information." See AI Math Vocabulary Worksheets for Grades 6-8 for how vocabulary precision ("estimate" vs. "calculate") shapes student problem solving behaviour.
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Connect problem solving to math fluency practice. Students who hesitate on the calculation steps of multi-step problems lose the problem solving thread. Math fluency and problem solving practice are complementary — students who are fluent with the component calculations can devote cognitive resources to the strategy selection and planning phases. Assign fluency practice and problem solving practice in the same week, treating them as building distinct but related skills.
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Link to the AI for Math Education guide for how problem solving practice connects to the full K–9 mathematical reasoning strand and why the NCTM (2025) process standards position problem solving as the overarching goal of mathematics education.
Key Takeaways
- The defining characteristic of genuine problem solving practice is that students must select their own strategy — problems that telegraph the approach are calculation exercises in word problem form.
- Four problem solving types serve different cognitive demands: find-the-strategy (strategy selection), multi-context integration (application in unfamiliar contexts), optimisation (exploring the solution space), and non-routine open-ended (multiple valid answers).
- The four-step worked solution (Understand / Plan / Execute / Check) models the problem solving process — not just the calculation — and must always acknowledge alternative approaches in the Plan step.
- Cross-strand problems (drawing on two or more mathematical strands simultaneously) are the most authentic problem solving format and the most difficult to generate without explicit prompt specification.
- Specify problem type and strategy requirements explicitly in the prompt — "students should choose their own strategy," "do not mention the mathematical topic," "include two valid solution approaches in the worked solution."
- Unit-opening problems (non-routine problems presented before students have the tools to solve them) provide authentic motivation for upcoming content learning.
- Teacher notes on justified responses are essential for non-routine open-ended problems — without them, consistent marking and student self-assessment are impossible.
FAQ
How do I use AI to create problem solving practice problems?
Specify the problem solving type (find-the-strategy, multi-context integration, optimisation, or non-routine open-ended), include the instruction "students should not know which strategy to apply from reading the problem," and request a worked solution showing the four-phase process (Understand/Plan/Execute/Check) with two alternative approaches mentioned in the Plan step. Avoid problems generated immediately after the relevant topic is taught — the recency effect converts problem solving to calculation.
What is the difference between a problem solving problem and a word problem?
A word problem describes a calculation in a real-world context; the student's job is to execute the indicated calculation. A problem solving problem presents a situation where the mathematical path forward is not immediately clear; the student's job is to plan before calculating, select a strategy, and make mathematical decisions. The test: if the student knows which operation or formula to apply immediately after reading, it is a word problem. If they must think about which approach to use, it is a problem solving problem.
How do I generate a four-step worked solution for problem solving problems?
Prompt: "Write a worked solution for this problem using four steps: Understand (list what is given and what is unknown), Plan (name the strategy selected — and briefly describe one alternative strategy that would also work), Execute (show the calculation or reasoning), Check (verify the answer by a method different from Execute — not just the same calculation repeated). The worked solution should model the thinking process, not just the correct calculation." Claude implements this format more consistently than other AI tools for non-routine problem types.
How many problem solving problems should students practice per week?
Two to three genuine problem solving problems per week is the effective range. Problem solving problems take significantly more time per problem than calculation practice (10–20 minutes per problem vs. 2–5 minutes). A class that works through three problem solving problems per week — one find-the-strategy, one multi-context, one optimisation — builds problem solving capacity more effectively than a class that completes 15 word problems. See How AI Helps Students Master Factors and Multiples for how targeted practice volume applies to procedural skills that support problem solving.
Related reading: Best AI for Place Value in 2026-2027 — the number sense foundation that underpins problem solving involving quantity and measurement contexts. Best AI Study Guide Generators in 2026 — student-facing strategy reference materials that support independent problem solving practice.