Multi-digit subtraction
When one number has several digits, how do you take another away when a place on top does not have enough?
Where you are 7 inside
What this area is about
Subtracting big numbers takes like places from like places: hundreds from hundreds, tens from tens, ones from ones. Trouble starts when a place on top is smaller than the place below it. Then one ten is opened up into ten ones (or one hundred into ten tens), and the subtraction goes on. Every lesson here leads up to that trade, uses it, or goes around it.
How these fit together
No trades needed. Subtracting multiples of ten treats 80 - 50 as 8 tens take away 5 tens. Subtracting two-digit numbers without regrouping works when each place has enough.
The trade. Regrouping in subtraction breaks a ten into ten ones when a place runs short. Subtracting three-digit numbers uses it with hundreds too.
Written methods. The standard algorithm works column by column from the right for numbers of any length. Subtracting across zeros handles a trade when the next places hold nothing, as in 7{,}006 - 2{,}849.
Another way. Counting up starts at the smaller number and adds on to the larger one, which often skips the trade altogether.
A path through it
Start with multiples of ten and two-digit problems with no trade. Then learn regrouping, and take three-digit subtraction and the standard algorithm, then subtracting across zeros. Counting up fits in at any point after that.
Next come subtracting decimals and, later, elapsed time, both built on this.