Probing Questions
Five types of rich questions for every topic to develop reasoning, communication, and deep mathematical understanding.
The Five Question Types
🧠 Convince me — construct a mathematical argument to show why a statement is true
💡 Give an example — generate examples, boundary cases, and plausible non-examples
⚖️ Always, sometimes, never — decide and justify with examples and reasoning
🔍 Odd one out — identify and argue a case for each option
❌ Explain the mistake — find and explain the error targeting a common misconception
How to Use Probing Questions
👩🏫
Teachers
Use after students have consolidated the basics, as an extension activity, as an alternative to traditional homework, as a final assessment question, or as a retrieval activity.
Tip: Try “Explain the mistake” as a mini-plenary — it reveals misconceptions instantly.
📚
Students
Use these probing questions to test and expand your knowledge of key maths topics. Try to answer each one, then compare your answers to mine.
Tip: Don’t just say “sometimes” — always try to find a specific example and a counter-example.
👨👩👧
Parents
Use these probing questions to engage in meaningful, stimulating mathematical discussions with your child — no preparation needed.
Tip: Ask your child to explain their thinking out loud — the conversation matters more than the answer.
Jump to Topic
Number
Number basics
Integer skills
Factors, multiples and primes
Negative numbers
Rounding and estimating
Decimals
Fractions
FDP equivalence
Algebra
Brackets
Geometry
Shape properties
Statistics
I’m adding new topics regularly — keep checking back for more! 🚀