Generating Differentiated Problem Solving Problems With AI

Quick answer: AI generates effective problem-solving tasks when the prompt specifies the reasoning type required (not just the topic), the entry points for different learners, and whether multiple solution strategies should be valid. The most valuable prompt addition is: "there should be more than one valid approach to solving this problem." Without it, AI defaults to single-path computation exercises rather than genuine problem-solving tasks.

"Problem solving" is one of the most overused phrases in mathematics education. In practice, it describes two very different activities. One is applying a known procedure to a familiar situation — "solve these word problems using long multiplication." The other is encountering a situation where the path to a solution is not immediately clear, requiring genuine mathematical reasoning to find a way through.

AI is well-suited to generating the first type without any special prompting, and largely useless for the second without precise instructions. The key difference is in what the prompt demands: a calculation with a story attached, or a situation that requires genuine reasoning to resolve.

Research from the National Council of Teachers of Mathematics (NCTM, 2024) on mathematical problem-solving instruction identifies three features of genuine problem-solving tasks:

• Students cannot immediately identify the solution method from problem surface features
• Multiple solution strategies are valid
• The problem connects to a context that gives the answer meaning

All three can be specified in an AI prompt once you know what to ask for.

What Genuine Problem-Solving Tasks Look Like

The clearest way to distinguish genuine problem-solving tasks from calculation exercises is the "can I see the method immediately?" test. If a student reads the problem and can instantly identify whether to add, subtract, multiply, or divide — without reasoning about the situation — it is a calculation exercise. If the student must think about what the situation requires before identifying an operation, it is a problem-solving task.

Examples across grade levels:

• Grade 3 calculation exercise: "A library has 4 shelves with 18 books on each shelf. How many books are there?" (Student immediately identifies multiplication.)
• Grade 3 problem-solving task: "The school library wants to store 72 books on shelves. How many shelves might they need, and how many books would be on each shelf? Find at least two different arrangements." (Student must understand factors and make decisions; multiple answers are valid.)
• Grade 6 calculation exercise: "A juice bottle holds 1.5 litres. How much juice is in 8 bottles?"
• Grade 6 problem-solving task: "A drinks company makes bottles in three sizes: 250ml, 500ml, and 1.5 litres. A customer wants exactly 3 litres. What combinations of bottles could they buy?" (Multiple solutions, requires systematic reasoning.)

The second versions are not harder in terms of computation — they are harder in terms of reasoning. AI generates both; the prompt determines which type you get.

The Four-Phase Problem-Solving Framework and How AI Fits

Polya's four-step problem-solving model (Understand → Plan → Execute → Review) remains the standard framework for teaching problem-solving process. AI can generate problems structured to practice each phase:

• Understand phase practice: Give students a problem with the solution already provided and ask "What was the problem asking? Write it in your own words without looking at the question again." AI generates these by including a worked solution alongside the problem statement.
• Plan phase practice: Provide a problem and ask students to write their planned approach before calculating. AI generates problems that reward this by including a "strategy first, then calculate" instruction.
• Execute phase practice: Standard computation with the method specified — not genuinely open, but useful for checking calculation accuracy once a plan is made.
• Review phase practice: Provide a problem, a stated answer, and ask "Is this answer reasonable? How can you check it without repeating the full calculation?" AI generates these readily when asked.

Prompt Structure for Genuine Problem-Solving Tasks

Here is a prompt that reliably produces genuine problem-solving tasks rather than calculation exercises:

Generate 6 mathematical problem-solving tasks for Grade 5 students. For each task, ensure:

1. There should be more than one valid approach to solving the problem.
2. The problem should not immediately signal which operation to use from surface features (avoid key words like "total," "left," or "each").
3. Students should need to make at least one mathematical decision (choose an approach, decide what to find first, or determine whether a particular strategy works).
4. Include a "Getting Started" hint that gives a direction without giving the method.

Use varied contexts: building design, cooking, travel planning, sports statistics, and nature/science. Include an answer section showing two different valid approaches for each problem.

The "two different valid approaches" in the answer key is the most important quality check: if AI cannot produce two approaches, the problem was likely a calculation exercise disguised as a problem-solving task.

Three-Tier Differentiation for Problem Solving

Problem-solving differentiation at its best keeps the same core situation but varies the entry point and the required reasoning depth:

Generate a three-tier differentiated problem-solving task for Grade 4 students on the theme of planning a class party. All three tiers describe the same situation:

• Tier 1 (consolidation): students have a fixed budget, fixed prices, and must find the total — partial scaffolding with a table to fill in. All numbers are whole numbers under 100.
• Tier 2 (grade level): students must stay within a budget, choose items from a list with quantities and prices, and maximise the value of what they purchase. No scaffold provided.
• Tier 3 (extension): students must plan the party for two different scenarios (a small class of 20 and a large class of 35), find the minimum cost for each, and decide whether the budget is sufficient — explaining any assumptions they make.

Include full solutions for all three tiers showing the reasoning process, not just the answer.

This structure is different from most differentiation approaches because all three tiers are working on the same mathematical situation, not three separate problems at different difficulty levels. This enables whole-class discussion of the shared context while allowing students to work at different depths.

The same structure applies across topics — data interpretation, geometry, number — and the shared context reduces preparation time because the teacher only explains one situation to the class.

Classroom Scenario: A Wide-Ability Class, One Shared Context

Say you teach Grade 6 and your class has a very wide range of abilities: some students are already working through Grade 8 content independently, while others need significant support with Grade 6 number work. Standard differentiation — three different worksheets on three different topics — can mean you are effectively running three separate lessons simultaneously.

You could shift to shared-context differentiated problem-solving tasks generated with the three-tier prompt structure above. In one session, all students work on a single scenario: planning an outdoor seating area for a school café, with different entry points:

• Tier 1 students find the total cost of a fixed layout
• Tier 2 students maximize seating within a budget
• Tier 3 students design two layouts with different cost and capacity trade-offs and present a recommendation with mathematical justification

All three groups can discuss their work because the situation is identical. You can move between groups asking "what decisions did you make?" — a question that has genuine answers at all three levels. In a session like this, Tier 3 students may find themselves explaining their reasoning to peers who are genuinely interested in the outcome, not just helping with a calculation.

For multi-step calculation problems that serve as the computation layer underneath problem-solving tasks, Best AI for Multi-Step Word Problems in 2026-2027 covers the generation tools that work best for that adjacent need.

Open-Ended Problems vs. Closed Problems

Not all problem-solving tasks should be open-ended. The curriculum balance matters:

• Closed problems (one correct answer, multiple paths): Good for whole-class discussion of strategy efficiency. "There are 24 students in a class. How many ways could they be divided into equal groups?" (Factors of 24: several correct answers, but the set is finite.)
• Open problems (multiple valid answers, student makes choices): Good for higher-order reasoning and differentiation. "Design a rectangular garden that has a perimeter of 40 metres. What could its dimensions be? Which design would give the most growing space?"
• Non-routine problems (no obvious method, strategy exploration required): Good for genuine problem-solving instruction but takes more class time. "A snail climbs 3 metres up a wall during the day and slides 2 metres down at night. The wall is 12 metres tall. When does the snail reach the top?"

AI generates all three when specified. The classroom application determines which type to request. For routine calculation practice that underpins these reasoning tasks, Using AI to Create Mental Math Practice Problems covers the fluency side of the problem-solving equation.

How to Request Non-Routine Problems

Non-routine problems are the hardest to generate with AI because they require genuine structural novelty — the solution method must not be immediately obvious. The prompt needs to specify the "trick" explicitly:

Generate a non-routine problem for Grade 6 students involving a pattern or trick that is not immediately obvious. The problem should appear to require extensive calculation but have a shortcut that rewards systematic thinking. Include a hint that points toward the shortcut without revealing it, and a full solution showing both the long approach and the shortcut. Make sure the shortcut involves mathematical reasoning, not just a formula.

This prompt reliably produces problems in the "working backwards" or "find the pattern" categories. Specifying "the shortcut involves mathematical reasoning, not just a formula" prevents AI from generating problems where the trick is simply knowing a specific formula rather than reasoning to it.

Using EduGenius for Problem-Solving Units

EduGenius generates complete problem-solving units that include a progression of tasks across the three types (closed, open, non-routine), differentiated across three tiers with a shared context, and teacher notes on the reasoning processes to look for and common errors to expect. For teachers running Grades KG–9 classes, the platform calibrates the task complexity to the specified grade level without requiring the teacher to adjust problem structure manually in each prompt.

For companion resources — Best AI Study Guide Generators in 2026 covers tools that produce problem-solving strategy reference cards, useful when students are learning to use Polya's framework or a structured approach like RUCSAC. For statistics and probability reasoning tasks that feed into problem-solving units, AI Probability Worksheets for Grades 6-8 covers the overlap between probability reasoning and mathematical problem solving.