Number Sense and Operations
What you must understand
Number sense is the ability to see how numbers relate before you calculate. Candidates should be fluent with place value, rounding, order of operations (BIDMAS/PEMDAS), integer arithmetic including negatives, factors, multiples, primes, and divisibility rules. You should also recognise equivalent forms: fractions, decimals, and percentages as different labels for the same quantity, and be able to estimate an answer to check whether a calculated result is plausible.
Traps to watch for
- Negative signs and brackets: in an expression like -3² the exponent applies before the sign, giving -9, whereas (-3)² gives 9.
- Left-to-right rules: multiplication and division rank equally, so 24 ÷ 4 × 3 is 18, not 2.
- Zero and one: zero is even but neither prime nor composite; 1 is not prime.
- Rounding drift: rounding each step of a chain can shift the final answer, so round only at the end.
- Divisibility shortcuts: a number is divisible by 3 if its digit sum is, and by 9 if its digit sum is a multiple of 9.
Worked example
Evaluate 5 + 2 × (8 − 3)² ÷ 5. Brackets first: 8 − 3 = 5. Exponent: 5² = 25. Multiply/divide left to right: 2 × 25 = 50, then 50 ÷ 5 = 10. Add: 5 + 10 = 15.
Rule of thumb: estimate first, compute second, compare third. If your estimate and answer disagree by a factor of ten, look for a place-value or decimal-point slip.