L7 · Standard algorithm: adding big numbers in context

Learning goal

“I can add large whole numbers, money amounts, and metric measurements with the standard column algorithm - lining up place values (and decimal points), and regrouping whenever a column reaches ten.”

Standard algorithm — the column method: write numbers in place-value columns, add right to left, one column at a time.

Regroup (carry) — when a column totals 10 or more, trade 10 of that place for 1 of the next place: 13 ones = 1 ten and 3 ones.

Addend — any number being added. In 348 + 96, both 348 and 96 are addends.

Align — to line up digits by place value. With decimals, aligning the decimal points aligns every place at once.

Worked example

8,476 + 5,389. Step 1: Write the addends in columns - ones under ones, tens under tens. Step 2: Ones: 6 + 9 = 15. Write 5, carry 1 ten. Tens: 7 + 8 + 1 = 16. Write 6, carry 1 hundred. Hundreds: 4 + 3 + 1 = 8. Thousands: 8 + 5 = 13. Write 13. Step 3: 8,476 + 5,389 = 13,865. Sanity check by rounding: about 8,500 + 5,400 = 13,900 - close to 13,865, so the size is right. Model both ways, side by side: the column grid with carries written small above, AND base-ten blocks trading 10 ones for 1 ten rod at the first regroup. Regrouping is just trading - 10 of a place for 1 of the next place. Nothing is "carried away"; the value is conserved.

Check yourself — explain it

When the ones column gives 15, we write 5 and carry 1 because...

Paired problem — example still visible

6,295 + 3,478 = 9,773 (ones 13: write 3 carry 1; tens 9+7+1=17: write 7 carry 1; hundreds 2+4+1=7; thousands 6+3=9)

Faded completion — last step is yours

"4,568 + 2,795: ones 8+5=13, write 3 carry 1; tens 6+9+1=16, write 6 carry 1; hundreds 5+7+1=13, write ___ carry ___; thousands 4+2+1 = ___." -> 3; 1; 7 - total 7,363

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

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