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Using Money to Subtract

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Introduction - Money, the Great Motivator__

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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.

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That was the reason I gave the kids when we launched into a bit of 3-digit subtraction work.

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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.

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Though when I was young I did see a 3c coin made by putting a 1c and 2c together on a railway track.

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And blow me down - there was a 3c coin made in the USA from 1851 to 1889!

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Setting Them Up

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Kids were divided into small groups. Each group was given an amount of "cash":

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10 x $100 notes

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18 x $10 notes

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18 x $1 coins

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The sample question that we were going to investigate was:

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** $255 - $178 = ________**

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So, I have $255.

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My greedy friend wants $178.

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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.

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Phew! Now I have $15 in coins and can give my greedy friend the $8 in coins that he wants.

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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.

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Done. Now I can give my greedy friend $70 in notes. And he wants the $100 from my stack.

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I give him the $100 note I have left. Now he has the $178 he wanted. I have $77 left.

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Conclusion - $255 - $178 = $77

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And using our money we can reinforce the process of subtracting with regrouping without needing to get involved in writing anything down. Yet.

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__Something to Ponder__

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With all the trips to the bank and back, I ended up with $100 x 1, $10 x 15 and $1 x 15

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but

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the amount of money I had __never changed__ (until I gave it to my greedy friend)

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$255 __is the same as__ ($100 x 1) + ($10 x 15) + ($1 x 15)

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__Going Further__

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A question to leave the kids with....

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....why did we get 18 each of the $1 coins and $10 notes?

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