Arranging Things on a ShelfDate: 05/05/2006 at 15:51:41 From: Amy Subject: word problem about arrangement Lucy is arranging her vases on a shelf. She has a blue vase, a yellow vase, a red vase, and a purple vase. How many ways can she arrange her vases? I am trying to solve this and explain it to my third grade class. Date: 05/05/2006 at 16:45:53 From: Doctor Jeremiah Subject: Re: word problem about arrangement Hi Amy, Let's break it down a bit. Say all the vases are in a box and we are going to arrange them. I am going to explain this at a more mathematical level. I have a suggestion for how to explain it at the end. Say we grab one of the vases out of the box. There are four ways to pick one of the vases (because there are four to choose from). Now we have: total combinations of four items = number of choices for first picked vase (4) x combinations of remaining three vases So we pick the second vase from the remaining three. There are three ways to pick a vase (because there are three to choose from)). Now we have: total combinations of four items = number of choices for first picked vase (4) x number of choices for second picked vase (3) x combinations of remaining two vases Then we pick the third vase from the remaining two. There are two ways to pick a vase (because there are two to choose from). Now we have: total combinations of four items = number of choices for first picked vase (4) x number of choices for second picked vase (3) x number of choices for third picked vase (2) x combinations of remaining one vase Now we are down to the last vase in the box. There is one one way to pick that vase. total combinations of four items = number of choices for first picked vase (4) x number of choices for second picked vase (3) x number of choices for third picked vase (2) x number of choices for fourth picked vase (1) total combinations of four items = 4 x 3 x 2 x 1 Now, I am not suggesting that you show them equations. Instead, actually put four vases in a box. And ask them how many choices there are for picking a vase in order to arrange it. I think they will get the right answer. Then write that down and take that vase out of box. And ask again. The only complicated part is telling them that you MULTIPLY the answers for how many ways there are to choose. Another fun way to do this is to let the kids discover the idea. Start with 2 kids and ask them how many ways they can get in line. They will quickly figure out that there are 2 ways--AB or BA. Then put a third kid with them and ask the same question. They will have great fun rearranging themselves and find there are six ways--ABC, ACB, BAC, BCA, CAB, and CBA. Then you can try four kids. Ask them to record their results and look for patterns. Having this be a discovery activity will make it much more fun and meaningful for them than just telling them to multiply the number from each step. - Doctor Jeremiah, The Math Forum http://mathforum.org/dr.math/ Date: 05/08/2006 at 10:08:52 From: Amy Subject: Thank you (word problem about arrangement) Thank you Thank you Thank you!! What a great and thorough response! I love this math doctor. |
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