L3 · The standard algorithms for addition and subtraction

Learning goal

“I can add and subtract three-digit numbers with the standard algorithms - the column methods the curriculum names. I work right to left, and I regroup in writing, the same trades I made with blocks.”

Standard algorithm — the conventional column procedure: align the places, work right to left, regroup when needed. It works for any natural numbers.

Column — one place written up and down: the ones column, the tens column, the hundreds column.

Regroup — the written form of a block trade (L2): carry a ten or a hundred in addition; borrow ten from the place on the left in subtraction.

Difference — the result of a subtraction.

Worked example

486 + 357. Step 1 (align): ones under ones, tens under tens, hundreds under hundreds. Step 2 (ones): 6 + 7 = 13. Write 3, regroup 1 ten above the tens column. Step 3 (tens): 8 + 5 + 1 = 14. Write 4, regroup 1 hundred. Step 4 (hundreds): 4 + 3 + 1 = 8. Sum = 843. It is L2's block work, written down: two trades, same numbers.

Check yourself — explain it

The standard algorithm works right to left because...

Paired problem — example still visible

579 + 268: ones 9 + 8 = 17 -> write 7, regroup 1; tens 7 + 6 + 1 = 14 -> write 4, regroup 1; hundreds 5 + 2 + 1 -> 847

Faded completion — last step is yours

"694 + 157: ones 4 + 7 = 11 -> write 1, regroup 1; tens 9 + 5 + 1 = 15 -> write 5, regroup 1; hundreds 6 + 1 + 1 = ___" -> 8 (sum 851)

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

Start practice →Take the unit quiz