Topics · Primary Maths · Addition & Subtraction
Adding and subtracting: columns, regrouping and choosing
Both work column by column, and both depend on place value. The two hard parts are regrouping across a zero, and deciding which of the two a word problem is actually asking for.
- 382 exam papers analysed
- appears in 70% of P3 Maths papers
- ~4 min read
01 Columns, because of place value
Written methods work down the columns — ones under ones, tens under tens — because you can only add things of the same size. Ten ones are worth one ten, and that is the only rule the whole method needs.
Line up the columns, not the ends of the numbers. With decimals that means lining up the points; 3.25 + 0.7 puts the 7 under the 2, because both are tenths.
02 Regrouping, and the zero problem
Adding: when a column reaches ten, carry one into the next column left. Ten ones become one ten; ten tens become one hundred.
Subtracting: when the top digit is too small, take one from the column to its left, which arrives as ten.
The hard case is subtracting across a zero, because there is nothing in the next column to take. Go on to the column after it: in 4,005 − 8, the tens are empty, so borrow from the hundreds — the 0 tens becomes 9 tens and the 5 ones becomes 15. It is the same rule twice, not a special case.
- Start from the right, in the ones, and work leftwards.
- One column at a time. Deal with a carry or a borrow before moving on.
- Across a zero, keep going left until you find a column with something in it. Every column you pass becomes a 9.
- Check by adding back. The answer plus what you took away should give what you started with — a check worth the ten seconds it costs.
03 Which operation is the question asking for?
From P3 the arithmetic stops being the difficulty and the choice starts being it. A bar model settles the choice without any keyword-guessing.
Missing whole → add. Missing part → subtract. That is the entire rule, and the picture tells you which you have.
04 Estimating first
Round each number to something easy and add or subtract those. It takes seconds and catches the answers that are wildly wrong — a misplaced digit, a forgotten carry, a subtraction done the wrong way round.
4,507 + 2,896 is roughly 4,500 + 2,900 = 7,400. If your careful answer comes out as 1,611 or 74,030, the estimate has already told you to look again.
05 How to say them
These are words most children have never said out loud, and a word you cannot say is a word you avoid using. Capitals mark the syllable you lean on. Tap the speaker to hear it.
- summore than onesums
The answer to an addition. The sum of 4 and 5 is 9.
- differencesayDIF-uh-runssmore than onedifferences
The answer to a subtraction — how much bigger one number is than another.
- regroupmore than one—
To exchange ten of one column for one of the next, or one of a column for ten of the one below. Also called carrying and borrowing.
- estimatesayES-ti-maytmore than oneestimates
A rough answer from rounded numbers, used to check a careful one is sensible.
- inversesayIN-verss
The opposite operation. Subtraction is the inverse of addition, which is why adding back checks a subtraction.
06 What each level is tested on
The same topic, asked differently as it goes up. The percentage is the share of papers at that level in which it appears.
- P2
Adding and subtracting within 1,000, with regrouping in one column.
Practise P2 Addition & Subtraction — 10 questions →62% of P2 papers
- P3
Four-digit numbers, regrouping more than once, and two-step word problems.
Practise P3 Addition & Subtraction — 10 questions →70% of P3 papers
- P4
Larger numbers, subtracting across zeros, and estimating to check.
Practise P4 Addition & Subtraction — 10 questions →56% of P4 papers
- P5
Adding and subtracting decimals and fractions, and problems where both appear.
Practise P5 Addition & Subtraction — 10 questions →45% of P5 papers
- P6
Addition and subtraction inside multi-step problems, ratio and before-and-after models.
Practise P6 Addition & Subtraction — 10 questions →67% of P6 papers
07 Mistakes worth knowing about
Each of these is wrong. Decide why before you open it.
“4,005 − 8: I cannot borrow from the zero, so I made it 4,005 − 8 = 4,003.”
Keep going left. The tens are empty, so borrow from the hundreds: the tens become 9 and the ones become 15. 15 − 8 = 7, giving 3,997.
“3.25 + 0.7 = 3.32.”
Line up the points. The 7 is tenths, so it goes under the 2: 3.25 + 0.70 = 3.95.
“The question said ‘left’, so I subtracted.”
Usually, but not always — “He had some, spent $8, and has $12 left. How much had he?” says “left” and needs an addition. The bar model decides it; the keyword does not.
“I subtracted the smaller digit from the bigger one in each column.”
The order is fixed by the question, not by which digit is larger. If the top digit is smaller, regroup — do not quietly flip them.
“I forgot to write the carry.”
Write it down every time, small, above the next column. Holding carries in your head is the commonest source of a near-miss answer.
Now try it
50 questions across 5 levels, marked as you go with the working shown.