FOUR MOVES THAT COVER ALMOST EVERY ADDITION YOU'LL DO IN YOUR HEAD
Nobody adds in their head the way they were taught to add on paper. The paper method works right-to-left, one column at a time, holding carries. That's a procedure built for a pencil — it needs somewhere to put the digits you aren't looking at yet.
In your head you do something else. You reshape the problem into one that's easier, then solve the easy one. There are really only four reshaping moves in common use, and between them they handle nearly everything.
1. BRIDGE THROUGH TEN
Step up to the nearest ten, then add whatever's left.
8 + 7 → 8 + 2 = 10, 10 + 5 = 15
You split the 7 into 2 and 5, because 2 is what the 8 needed. Both halves are then trivial: completing a ten, and adding a single digit to a round number.
It scales without changing at all. 47 + 8 → 47 + 3 = 50, then 50 + 5 = 55. 380 + 70 → 380 + 20 = 400, then 400 + 50 = 450. Same move, bigger join.
The whole thing rests on knowing what each number needs to reach ten without working it out — which is what number bonds are. If you have to count to find that the 8 needed 2, the shortcut costs more than it saves.
2. COMPENSATE — ROUND UP, THEN GIVE IT BACK
When a number is just short of a round one, round it and subtract the difference afterwards.
56 + 39 → 56 + 40 = 96, 96 − 1 = 95
Adding 40 is barely harder than adding 4. The cost is remembering one small debt and settling it at the end.
This is the best of the four when a number ends in 8 or 9, and the worst when it ends in 4 or 5 — the debt gets big enough that you've just moved the difficulty rather than removed it. 56 + 34 as 56 + 40 − 6 is no easier than splitting.
The classic failure is settling the debt the wrong way. You rounded up, so you owe a subtraction. Doing it in the wrong direction is the single most common mental-arithmetic slip there is, and it's worth being deliberate about for a while before you trust it.
3. SPLIT INTO PLACE VALUES
Break both numbers into tens and units, add the parts, recombine.
34 + 52 → 30 + 50 = 80, 4 + 2 = 6, 80 + 6 = 86
Unlike the paper method this runs left to right, biggest part first. That matters more than it sounds: you get an approximate answer immediately and refine it, so you notice a wild result straight away instead of at the end.
Splitting is the reliable fallback. It always works and it never surprises you. It's also the slowest, because you're holding two partial answers at once, and it gets awkward the moment the units carry — 38 + 47 as 70 and 15 means a second addition you didn't want.
4. USE A DOUBLE YOU ALREADY KNOW
Doubles get remembered whether you try or not. 6 + 6, 7 + 7, 8 + 8 tend to sit in memory as single facts. So when two numbers are close, reach for the double and adjust.
7 + 8 → 7 + 7 = 14, 14 + 1 = 15
Only useful for near-neighbours — a gap of one or two. Past that the adjustment is its own problem. But within that range it's the fastest of the four, because half the work is already recall rather than calculation.
WHICH ONE TO USE
Fluent people don't pick consciously. They see the shape of the numbers and the move suggests itself, which is a thing you can only get by doing it a lot. If you want a rough guide while that's still forming:
- Something ends in 8 or 9 → compensate.
- The two numbers are within one or two of each other → double and adjust.
- Crossing a ten with small numbers → bridge.
- None of the above, or you're tired → split. It always works.
Worth saying plainly: none of this makes you better at maths in any broad sense. It makes you quicker at arithmetic, which is a narrow and genuinely useful skill — splitting a bill, checking change, sanity-checking a number someone just told you. Don't expect more from it than that.
WHERE THE PRACTICE COMES FROM
All four moves depend on the bonds to ten being instant. That's the bottleneck, and it's the one part that's pure memory rather than technique.
Make10 drills exactly that, without asking you a single question. Numbered tiles fall, any straight line of them adding to ten clears, and finding those lines is the only way to play. The recall gets repeated a few hundred times a session because you're chasing a score, not an answer.