Probing Questions

Five types of rich questions for every topic to develop reasoning, communication, and deep mathematical understanding.

How Probing Questions work

Each topic has around twenty questions, split across five types. None of them can be answered with a number alone: students have to explain, justify and give examples.

Every question has a worked solution, so you can check answers and spot misconceptions quickly.

The five question types

Every topic has all five. Each one asks students to explain their thinking, not just get an answer.

1
Convince me
Construct a mathematical argument to show why a statement is true.
2
Give an example
Give an example, another example, one no-one else will think of, and a sneaky non-example.
3
Always, sometimes, never
Decide whether a statement is always, sometimes or never true, and justify it with examples.
4
Odd one out
Make a valid mathematical case for each option being the odd one out.
5
Explain the mistake
Find where the reasoning goes wrong and explain why. Each mistake targets a common misconception.

Key stage

No Probing Questions match

Try fewer words, or a different word for the same thing.

Number

12 topics · 48 sets

Mental arithmetic
Mental addition and subtractionKS1KS2
23 questions across the five types.
Mental arithmetic
Times tablesKS1KS2
21 questions across the five types.
Mental arithmetic
Order of operationsKS2KS3
21 questions across the five types.

Factors, multiples and primes

6All resources →

Factors, multiples and primes
FactorsKS2
22 questions across the five types.
Factors, multiples and primes
MultiplesKS2
22 questions across the five types.
Factors, multiples and primes
Prime numbersKS2
21 questions across the five types.
Factors, multiples and primes
Prime factorisationKS2KS3
21 questions across the five types.
Factors, multiples and primes
Highest common factorKS3
22 questions across the five types.
Factors, multiples and primes
Lowest common multipleKS3
21 questions across the five types.

Negative numbers

3All resources →

Negative numbers
Ordering negative numbersKS2KS3
22 questions across the five types.
Negative numbers
Adding and subtracting negative numbersKS3
19 questions across the five types.
Negative numbers
Multiplying and dividing negative numbersKS3
20 questions across the five types.
Also in: Indices, roots and surds

Rounding and estimation

5All resources →

Rounding and estimation
Rounding to the nearest 10, 100, 1000KS2
19 questions across the five types.
Rounding and estimation
Rounding to decimal placesKS2
19 questions across the five types.
Rounding and estimation
Rounding to significant figuresKS3GCSE
19 questions across the five types.
Rounding and estimation
EstimationKS3
22 questions across the five types.
Rounding and estimation
Bounds of errorGCSE
21 questions across the five types.

Fractions

7All resources →

Fractions
Simplifying and equivalent fractionsKS2
20 questions across the five types.
Fractions
Mixed-number and improper fractionsKS2
20 questions across the five types.
Fractions
Ordering fractionsKS2
20 questions across the five types.
Fractions
Fractions of an amountKS1KS2
19 questions across the five types.
Fractions
Adding and subtracting fractionsKS2
21 questions across the five types.
Fractions
Multiplying fractionsKS2
22 questions across the five types.
Fractions
Dividing fractionsKS2KS3
21 questions across the five types.

Decimals

3All resources →

Decimals
Ordering decimalsKS2
21 questions across the five types.
Decimals
Adding and subtracting with decimalsKS2
19 questions across the five types.
Decimals
Multiplying and dividing with decimalsKS2KS3
19 questions across the five types.
Also in: Place value

Percentages

3All resources →

Percentages
Percentage of an amountKS2KS3
21 questions across the five types.
Percentages
Percentage increase and decreaseKS3GCSE
22 questions across the five types.
Percentages
Reverse percentagesKS3GCSE
22 questions across the five types.

Fraction, decimal, percentage equivalence

3All resources →

Fraction, decimal, percentage equivalence
Converting between decimals and percentagesKS2
21 questions across the five types.
Fraction, decimal, percentage equivalence
Converting between fractions and percentagesKS2
21 questions across the five types.
Fraction, decimal, percentage equivalence
Converting between decimals and fractionsKS2KS3GCSE
21 questions across the five types.

Ratio

3All resources →

Ratio
Writing ratiosKS2KS3
19 questions across the five types.
Ratio
Simplifying and equivalent ratiosKS2KS3
19 questions across the five types.
Ratio
Sharing in a ratioKS2KS3
19 questions across the five types.