Earlier this week I attended a three-day non-beginner's CGI institute and was thoroughly inspired and motivated to have more conversations with my own children about mathematics. I created a string of true-false statements to see how much my 9-year-old understands about fraction equivalence.
True or False?
5/5 = 1 "True," he says.
8/8 = 1 "True," he says again.
1 = 2/2 "False, because it's backwards."
So I asked him: "What does the equal sign mean?"
As soon as I asked him the question, he changed his mind and decided that the statement 1 = 2/2 is actually true, because "the left side is one, and 'two 2ths' is also 1."
5/5 = 8/5 (Pause for about five seconds) "True," he says.
4/2 - 1/2 = 5/2 - 2/2 "That's true too," he says.
At this point I suspect that he expects every statement to be true, so I wanted to trick him:
5/5 + 5/5 = 10/5 - 1 "False, because there's two on the left side and one on the other side." Darn, it didn't work!
I was somewhat impressed, but I wasn't about to stop yet. I asked: "What can you do to the left side so that it becomes a true statement?"
He writes: 5/5 = 10/5 -1
"What can you do to the right side so that it becomes a true statement?"
He writes: 5/5 + 5/5 = 1 - 0
End of conversation. Back to dinner.
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