Arranging Blocks in GroupsDate: 06/13/98 at 17:31:26 From: Kathy Watson Subject: Rectangular arrangement of squares Elise wants to make a rectangular arrangement out of 24 squares. If one side must be 8 squares, what will be the dimensions of the rectangle? I tried to draw a picture but I don't understand this. Date: 06/13/98 at 19:47:10 From: Doctor Sorelle Subject: Re: Rectangular arrangement of squares Hi Kathy, Drawing a picture was a very good way to start. Let's do this with a different problem so that you'll get a chance to work with this one on your own. What if we want to make a rectangle out of 6 squares? If one side must be 3 squares, what are the dimensions of the rectangle? So first let's draw the 6 squares: [ ] [ ] [ ] [ ] [ ] [ ] Okay, now we just have to rearrange them. But the question gave us specific instructions for how to rearrange them. First, they have to be in a rectangle. Second, one of the sides of the rectangle has to be 3 squares long. Let's put those 3 squares into place together just so we can see what that would look like: [ ] [ ] [ ] But now there are still 3 squares left over. How can we include them in the arrangement? Remember we have to follow the rules. We have three columns and the remaining 3 squares have to fit into them. I think they can fit in like this: [ ] [ ] [ ] [ ] [ ] [ ] So now we have a 3 by 2 rectangle. Do you see why? We have 3 columns (up and down, like columns in a building) and 2 rows (left and right, like rows in a theater). This problem could also have been done with division and multiplication. We could have said that we knew we had 6 squares total and that those 6 squares had to be divided into 3 groups (the columns). [ ] [ ] [ ] [ ] [ ] [ ] Then we would have wanted to find the number of squares in each group (the rows). To do that we would have divided the 6 squares into 3 groups or 6/3 and gotten 2. To get back to the total number of squares in the rectangle (6) we would have multiplied the dimensions (3 by 2). Do you think you can do your problem now? If you need more help please write back. -Doctor Sorelle, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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