My kids are seven and a half and frankly I thought they'd have got it by now. Same with "reading the time" and "fractions".
Granted last night* was a bit of a challenge for Grade Two maths.
I owed the kids $4 each which I had pledged in return for tidying their rooms and helping me clean up the house last weekend*, which they had done very well.
After a few days of failing to amass $8 in gold coins, and as I had two ten-dollar notes in my wallet, I suggested this to the kids: I'll give you each a ten-dollar note and you each give me $6 back.
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I didn't expect them to really get this, so I was well prepared with explanations, diagrams and appeals to recent lessons in school on counting money.
M. grasped an opportunity straightaway. "Yes, yes, I want to!" she said and pulled her sister into the hallway for discussion. "Tell her we'll give her the $6 tomorrow and then she'll forget," she whispered - but not out of my earshot as she imagined.
A. was interested but confused. "Why do we have to give you $6?"
"Because I owe you FOUR dollars," I said, "but I don't have four dollars in coins, so how can I give you four dollars? Well, one way is if I give you a TEN-dollar note, and you give me the change. So if I give you TEN dollars, you give me SIX dollars in change. Because TEN minus FOUR is SIX."
"Oh, I get it! Wait. I don't get it."
"Well I have to give you four dollars. Now if I give you ten dollars, that's too much, right? Cos I only owe you four? So if I give you ten dollars, you give me some back. The difference between four dollars (which I owe you) and ten dollars is six dollars. So if I give you ten dollars and you give me six dollars, it's the exact same thing as if I gave you four dollars."
I drew it on a piece of paper in two ways. One was drawing ten dots and then crossing out six of them to leave four. The other was using numbers to show them how the exchange added up. "OK. At the moment you have about $20 in pocket money, right? OK. I have to give you $4 so then you'll have $24. Like this -" I wrote down 20 + 4 = 24. "Now another way to get the same amount of money is like this: 20 + 10 = 30. 30 - 6 = 24. So if I give you $10 then you'll have $30, so you give me $6 and then you'll have $24. So either way we do it, you end up with $24. See?"
"Ohhhhh! I get it, I get it!"
M. grabbed a ten-dollar note and said "I'll give you $6 tomorrow."
I grabbed it back. "No, missy, you give it to me today, or you can wait and I'll give you $4 in coins tomorrow."
M. was suddenly indignant. "But why do we have to give you six dollars?"
I explained it again, and finally they both seemed to get it and agree. A. looked at me admiringly. "You have your smart brain on today," she said. We repaired to the bedrooms to empty out piggy banks.
A. was initially excited, but as she emptied out her coins she changed her mind. "These are all my special gold coins, from birthdays and the tooth fairy. I don't know if I want to change them."
"That's OK," I said. I can give you coins tomorrow instead."
She eyed the $10. "But I do want the $10..."
"Well it's up to you," I said. "Either way it's the same amount of money, right? It's just different ways for me to give you $4. You think about it and let me know."
Five minutes later while cleaning up in the kitchen I heard A sobbing miserably, and went back to find her crying over her pile of coins. "I don't want to spend all my money! You always tell me not to waste it and I don't want to give you all my coins!"
I explained again (a) the concept and (b) that it was voluntary. I showed her how ten dollars in coins and a ten-dollar note were the same amount of money.
"Well, I do want the $10 note..." She eyed the mountain of five-cent pieces on the floor next to her precious gold coins. "Can you make $10 out of these instead?"
Both of my kids have a crap-load of five and ten cent coins. I don't even know where they got them all. There was easily $10 worth in each piggy bank, now that I looked at them.
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"Well that's good thinking," I said. "Let's count them together."
A. wanted to count all her money, so we started counting the coins and I showed her how to first put aside the larger denomination coins, and then count just the fives, putting them in piles of a dollar as we went.
We got to eight dollars in fives with three five-cent coins left over and had just started on the tens when I got distracted by the dog and had to let him outside. When I came back, the coins were strewn everywhere and A. was busy stuffing them into her boots. "I'm hiding my treasure!" she laughed. "Ohhhh, I get it, " I said. "It's your BOOTy!"
(As their dad is not a native English speaker, I have to do all the Dad Jokes in our house).
"But A.," I said, "Now we have to start counting all over again!"
"No we don't," she said. "The five-cent coins made eight dollars and we had three left over, so all you have to do is take those three away and then start counting again from eight."
I did an honest-to-god double-take. "Wow," I said. "Now you've got YOUR smart brain on!"
This from the kid who couldn't compute that ten dollars in coins and a ten dollar note were the same thing.
Also, why hadn't I thought of it?
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Anyway. We counted out six dollars in fives and tens and she gave them to me in exchange for the $10 note.
Then I went through the same exercise with M, but she insisted on swapping ten dollars worth of coins for the ten-dollar note, and then me giving her four dollars. She didn't want $4 in fives and tens, so she gave me six dollars in fives and tens and four dollars in gold coins, which I then gave back to her.
I think it's safe to say there are no math geniuses in our house.
*Not really last night/weekend, I've had this post sitting in drafts a few weeks.