Rectangles and FactorsDate: 09/09/98 at 22:27:56 From: danny johnson Subject: rectangles How many rectangles could you make if someone gave you 10 small squares? 5 small squares? 12 small squares? I do not understand how to do this. Please help me. Date: 09/10/98 at 16:35:33 From: Doctor Rick Subject: Re: rectangles Hello, Danny! Do you have a Scrabble game at home, or another game that has lots of square tiles? I think you will understand this a lot more easily if you really do it. It's fun, too. Whatever number of tiles you have, you can always make a long, skinny rectangle: +---+---+---+---+---+---+---+---+---+---+ | | | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+ This rectangle is 1 square high and 10 squares wide. Can you make a taller rectangle? Let's try making a rectangle two squares high: +---+---+---+---+---+ | | | | | | +---+---+---+---+---+ | | | | | | +---+---+---+---+---+ Well, that worked. It is 2 squares high and 5 wide. So far, so good. Let's try making one 3 squares high: +---+---+---+ | | | | +---+---+---+ | | | | +---+---+---+---+ | | | | | +---+---+---+---+ That's not a rectangle. Did you notice something about the sizes of the rectangles? They were 1 by 10 and 2 by 5. And 1 times 10 is 10, and 2 times 5 is 10. In fact, the rectangle problem is just the same as this one: How many ways can you make 10 by multiplying two whole numbers together? Keep working with 10 tiles until you're sure that there are only 2 kinds of rectangles you can make. (You can also make them standing tall instead of lying flat, but they still have the same shape.) Then try other numbers of tiles. Try using all the tiles you have. See what discoveries you can make. - Doctor Rick, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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