Explaining maths to kids
I have just been helping my 6 year old son with his maths homework. One question asked:
“Can you add two odd numbers together to get an odd number? Why?”
There was a single line in the workbook for an answer.
We quickly established that it was impossible to add two odd numbers and get an odd number, but the tricky part was explaining why - especially in such a tiny space.
Luckily, Google came to my aid, and I found this explanation…
“With two odd numbers, each odd number by itself has one left over, but when we add them together, we can combine these two “leftovers” to form another pair.
Any time we add an even number of odd numbers, we’ll be able to pair up the “leftovers” and get an even number for our sum. But if we add an odd number of odd numbers, we’ll get an odd number for a sum. “
Adding Odd Numbers with Dr Maths
So how would you answer the question? More importantly, how would you fit the answer into a single line so that it fits into a six year olds work book?
September 18th, 2007
11:05 pm
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Written in a language EVERY child understands:
The definition of an odd number is that it can be written 2*x+1 (where x is integer), thus if you take two such numbers: 2*a+1 and 2*b+1 and add them together, you get 2*(a+b+1), which clearly is not an odd number, but instead a multiple of 2.
Err.. or maybe not
September 18th, 2007
11:13 pm
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Even numbers of odd numbers added equal an even number, as paired odd remainders even out evenly.
September 19th, 2007
2:50 am
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ODD + ODD = OO DD DD
best illustrated with coloured paper, a thick marker, scissors, glue, snacks, apple juice and a promise to the playground after this odd lesson.
And done in the fashion like http://www.youtube.com/watch?v=eRqUE6IHTEA
September 19th, 2007
3:51 pm
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I think the only answer that would fit is: “because two odds make an even”. It seems redundant, but it does reinforce what has been learned as an easy to remember rule.
September 21st, 2007
12:22 pm
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I can’t resist a try:
Take ONE away from both the odd numbers, and they become even. The two ONEs taken away become a pair (2), which is EVEN. Add all those even numbers together and you’ll still have an even number.
September 21st, 2007
4:04 pm
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Some good suggestions here, thank you all.
Ill post next time BEFORE I try to deal with any sticky maths questions!
September 21st, 2007
7:33 pm
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That is a stupid workbook.
First, what is the significance of knowing that it is impossible to add up two odd numbers to get an odd numbers? Extremely small. It is not important to know that two odd numbers added together is even. You could do a high school level workbook without knowing that two odd numbers added together means even, couldn’t you?
Secondly, as the kids grows up, (s)he’ll realize about it in one way or another, even if the question is never raised. It’ll arise in his/her unconscious mind that two odd numbers added together is even.
Third, by raising this question, you’ll have to feed the kid an explanation, since sometimes concepts like this isn’t easy to be grasped by a kid, this hampers the kids ability to think by himself later in the future, (s)he got too much explanation of difficult concepts, and never allowed to think himself. This approach would better the kids ability to memorize, but severely damage their ability to think. A better approach would be to give the kid easier questions, and let him/her think about the solution.
September 23rd, 2007
12:50 am
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Lie, well.. I remember from when I was a young kid, that exact question came to mind, but no one could offer an explanation - not even one I didn’t understand…
also stuff like why odd*even=even, even*even=even, odd*odd=odd, negative*positive=negative…
While I can easily figure out why this is now, even without having been taught, I remember being severely frustrated with not having explanations for these basic questions about the nature of integers…
I believe that had I been explained just a single of these, I could probably have figured out the others, resulting in much less frustration, and a better understanding of maths and logic…
September 23rd, 2007
2:46 pm
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I guess 6 year olds aren’t on to negative numbers yet. But many of the explanations don’t hold water with negative numbers, but ultimately, the result is the same. Or stated another way, it doesn’t matter if you are adding or subtracting the second odd number, the result will be even.