L1 · Adding with the standard algorithm (including decimals to hundredths)

Learning goal

“I can add whole numbers and decimals within 10 000 using the standard algorithm - lining up place values, regrouping when a place reaches 10 - and check my sum against an estimate.”

Sum — the result of an addition.

Standard algorithm — the conventional step-by-step method for adding or subtracting in columns, place by place, from the right.

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

Estimate — a quick rough calculation with rounded numbers, used to predict and check an answer.

Worked example

4,386 + 2,547. Step 1 (estimate first): 4,386 is about 4,400 and 2,547 is about 2,500, so the answer should be near 6,900. Step 2 (align): ones under ones, tens under tens - the chart does the organizing. Step 3 (add right to left): ones 6 + 7 = 13 - write 3, regroup 1 ten. Tens: 8 + 4 + 1 = 13 - write 3, regroup 1 hundred. Hundreds: 3 + 5 + 1 = 9. Thousands: 4 + 2 = 6. Step 4: Sum = 6,933. The estimate said about 6,900 - reasonable. Say it plainly: regrouping is just trading - 10 ones are 1 ten, 10 tens are 1 hundred. You learned trading in place value; the algorithm is trading while you add.

Check yourself — explain it

We start adding at the ones place because...

Paired problem — example still visible

3,275 + 1,468 -> 4,743 (ones 5+8=13 write 3 carry 1; tens 7+6+1=14 write 4 carry 1; hundreds 2+4+1=7; thousands 3+1=4)

Faded completion — last step is yours

"5,649 + 2,386: ones 9+6=15 write 5 carry 1; tens 4+8+1=13 write 3 carry 1; hundreds 6+3+1=10 write 0 carry 1; thousands 5+2+1 = ___" -> 8 (sum 8,035)

Ready to practise?

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

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