A great reason to be careful and knowledgeable with mathematical calculations is that it might cost you money one day. If you're not sure about how to add and subtract 2- or 3-digit numbers, it might cost you 2- or 3-digits worth of cash.
That was the reason I gave the kids when we launched into a bit of 3-digit subtraction work.
Money is real. People use it every day. And having 1 dollar coins, 10 dollar notes and 100 dollar notes is a great advantage when working in a base-10 number system. Probably why we don't have $6 notes or 17c coins.
Though when I was young I did see a 3c coin made by putting a 1c and 2c together on a railway track.
And blow me down - there was a 3c coin made in the USA from 1851 to 1889!
Setting Them Up
Kids were divided into small groups. Each group was given an amount of "cash":
10 x $100 notes
18 x $10 notes
18 x $1 coins
The sample question that we were going to investigate was:
$255 - $178 = ________
So, I have $255.
My greedy friend wants $178.
Let's start in the units. I have to give my greedy friend $8 - but wait! I only have $5 in coins! I need to get to the bank and change a $10 for some coins.
Phew! Now I have $15 in coins and can give my greedy friend the $8 in coins that he wants.
Now, on to the 10's column. My greedy friend wants $70 but I only have four $10 notes left! Oops - back to the bank! I'll trade a $100 for ten $10 notes.
Done. Now I can give my greedy friend $70 in notes. And he wants the $100 from my stack.
I give him the $100 note I have left. Now he has the $178 he wanted. I have $77 left.
Conclusion - $255 - $178 = $77
And using our money we can reinforce the process of subtracting with regrouping without needing to get involved in writing anything down. Yet.
Something to Ponder
With all the trips to the bank and back, I ended up with $100 x 1, $10 x 15 and $1 x 15
the amount of money I had never changed (until I gave it to my greedy friend)
$255 is the same as ($100 x 1) + ($10 x 15) + ($1 x 15)
A question to leave the kids with....
....why did we get 18 each of the $1 coins and $10 notes?