L8 · Standard algorithm: subtracting in context (money and metric)

Learning goal

“I can subtract large numbers, money amounts, and metric measurements with the standard algorithm - including regrouping across zeros - and give change and differences in context.”

Difference — the result of a subtraction (review from L6 - today it is computed by algorithm, in context).

Regroup (borrow) — trading 1 of a higher place for 10 of the place you need: 1 hundred becomes 10 tens so a column can be subtracted.

Change — in money problems, the money returned after a purchase: change = amount paid - price.

Check by adding — verifying a subtraction with its inverse: if a - b = c, then c + b must equal a.

Worked example

5,203 - 2,847. Step 1: Ones: 3 - 7 won't go. Regroup from the tens - but the tens digit is 0. Keep walking left: the hundreds digit 2 gives 1 hundred to the tens (hundreds 2 becomes 1, tens 0 becomes 10), then the tens give 1 ten to the ones (tens 10 becomes 9, ones 3 becomes 13). Step 2: Ones: 13 - 7 = 6. Tens: 9 - 4 = 5. Hundreds: 1 - 8 won't go: regroup from the thousands (5 becomes 4, hundreds 1 becomes 11): 11 - 8 = 3. Thousands: 4 - 2 = 2. Step 3: 5,203 - 2,847 = 2,356. Check by adding: 2,356 + 2,847 = 5,203. Model both ways, side by side: the column grid with the regrouping written above each digit, AND base-ten blocks physically trading 1 flat (100) for 10 rods (10s), then 1 rod for 10 unit cubes. A zero in the way is not a dead end - you trade from the nearest place that HAS something, one step at a time.

Check yourself — explain it

In 5,203, why did the tens column pass through 10 and end at 9?

Paired problem — example still visible

7,004 - 3,658 = 3,346 (ones: regroup chain thousands to hundreds to tens to ones: 14 - 8 = 6; tens 9 - 5 = 4; hundreds 9 - 6 = 3; thousands 6 - 3 = 3; check: 3,346 + 3,658 = 7,004)

Faded completion — last step is yours

"6,020 - 1,485: ones 10 - 5 = 5; tens 1 - 8 won't go, regroup from hundreds (0 is empty, go to thousands: thousands 6 becomes 5, hundreds 0 becomes 10 then 9, tens 1 becomes 11): 11 - 8 = 3; hundreds 9 - 4 = ___; thousands 5 - 1 = ___." -> 5; 4 - total 4,535

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