L1 · Adding with standard algorithms (including decimals)

Learning goal

“I can add whole numbers and decimals up to 1,000,000 with the standard algorithm - aligning places, regrouping when a column reaches ten, and estimating first to check that my sum is reasonable.”

Standard algorithm — the conventional column procedure: align the places, add right to left, regroup when needed. It works for any size of number, which is why the curriculum names it.

Align — to line up digits of the same place value in columns; with decimals, lining up the decimal points aligns everything.

Regroup — to trade 10 of one place for 1 of the next place left (also called carrying in addition).

Sum — the result of an addition.

Worked example

268,415 + 437,286. Step 1 (estimate first): 268,000 + 437,000 is about 705,000. The sum should land near there. Step 2 (align): ones under ones, tens under tens, and so on, commas matching. Step 3 (add right to left, regrouping aloud): ones 5 + 6 = 11 - write 1, regroup 1 ten. Tens: 1 + 8 + 1 = 10 - write 0, regroup 1 hundred. Hundreds: 4 + 2 + 1 = 7. Thousands: 8 + 7 = 15 - write 5, regroup 1 ten-thousand. Ten-thousands: 6 + 3 + 1 = 10 - write 0, regroup 1 hundred-thousand. Hundred-thousands: 2 + 4 + 1 = 7. Step 4 (check): sum = 705,701 - the estimate said about 705,000. Reasonable. Say it plainly: regrouping is not a rule to memorize - 10 ones really ARE 1 ten, so the trade never changes the value, it just moves it to the column where it belongs.

Check yourself — explain it

When the ones column totals 11, we write 1 and regroup 1 because...

Paired problem — example still visible

154,382 + 267,459 = ___ -> 421,841

Faded completion — last step is yours

"375,908 + 248,376: ones 8 + 6 = 14 -> write 4, regroup 1; tens 0 + 7 + 1 = 8; hundreds 9 + 3 = 12 -> write 2, regroup 1; thousands 5 + 8 + 1 = 14 -> write 4, regroup 1; ten-thousands 7 + 4 + 1 = 12 -> write 2, regroup 1; hundred-thousands 3 + 2 + 1 = ___ hundred-thousands" -> 6 (sum 624,284)

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