Monday, March 02, 2009

Math Problem #2

I'm sure this is not the second math problem I have put up on this blog, but I started writing "Math Prob..." and the only other title entry was Problem #1, so I guess I should start up a series.

We did a fun math problem today in class, and I thought I would share the problem, and my extension of the problem with my internet friends.

Draw a 5x5 square of dots, so five dots across in a row, and five rows down:

. . . . .
. . . . .
. . . . .
. . . . .
. . . . .

The above drawing might not be a perfect square, but ideally the space between dots would make a perfect square for each foursome of dots.

The two questions are:
1) How many different-sized squares can you make?
2) How many total squares can you make?

The two questions are a bit trickier than meets the eye. One hint is to see what area of boxes you can make. Can you make a box with an area of 1 (assuming the distance between each dot is 1)? How about 2?

I've got answers for both, although I'm not sure if my answer to the second part of this question is correct, so I'd like someone to try and see if we get the same answer.

We used Geo-boards in class and had rubber-bands to band around the pegs, if you have an old Geo-board lying around at home.



Blogger DrChako said...

1. You can only make 4 different sized squares. The areas are 1, 4, 9 and 16.

2. For each sized square, you can make the following number of squares:
1 - 16
4 - 9
9 - 4
16 - 1

Pretty cool when you plot it out.


12:09 PM  

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