Mental maths isn't a written method done in your head. It's a genuinely different set of strategies — here's how to build them.
25 August 2026 · 5 min read
A common misconception about mental maths is that it means doing a written method without the paper — carrying digits and exchanging, purely in your head. That's genuinely difficult and rarely how strong mental mathematicians actually work. Good mental maths uses different strategies from written methods entirely, chosen because they're easier to hold in your head, not because they're a paper method done invisibly.
Take 47 + 29. Adding those exactly as written, in your head, means tracking two separate carries — awkward without paper. Compensation instead rounds 29 up to 30 (an easy number to add), giving 47 + 30 = 77, then adjusts back by subtracting the 1 that was added: 77 − 1 = 76. Two easy steps replace one awkward one, and the whole thing is far easier to hold in working memory.
Mental maths leans heavily on connections between facts rather than calculating everything from first principles. Knowing 8 + 8 = 16 means 8 + 9 is just one more, without needing to add fresh. This is the same "known fact to new fact" strategy that underpins strong times-table recall, applied to addition and subtraction as well.
Multiplying 23 × 4 mentally is easier split into (20 × 4) + (3 × 4) — 80 + 12 = 92 — than attempted as one unbroken calculation. Breaking a number into its place value parts (tens and ones) and dealing with each separately is one of the most generally useful mental strategies across addition, subtraction and multiplication alike.
Doubling and halving are unusually fast mental operations for most people once practised, and a lot of calculations can be reshaped to use them. Multiplying by 4 is doubling twice; multiplying by 5 is often easier as "multiply by 10, then halve" (23 × 5 becomes 230, halved to 115). Spotting when a calculation can be reframed this way is a genuine skill worth building deliberately.
A rough estimate before the exact calculation — knowing 47 + 29 should land somewhere around 75 — gives a mental checkpoint to catch an error, and it's a habit that's useful for both mental and written calculations alike.
These strategies genuinely need to be taught and practised, not left to develop on their own — a child left purely to written methods often never discovers compensation or partitioning independently. Short, regular practice specifically aimed at choosing and applying a mental strategy (not just getting a right answer by any means) tends to build this far more reliably than general calculation practice alone.
Grasp Maths practises mental strategies explicitly, not just calculation accuracy, so a child builds a genuine toolkit of approaches — compensation, partitioning, known-fact bridging — rather than relying on one slow method for everything.
Try a free Grasp Maths practice session and see mental strategies practised explicitly, not left to chance.