Transcript Checkerboard Powerpoint 1

How many squares are in a
checkerboard?
By :Gloria Gonzalez
And Ieni Vargas
How many squares are in a checkerboard?
o Let's see if we can get you started and
then YOU can come up with the answer.
o This question implies "squares of any size."
How about if we make a Table and collect
our data; we might find a pattern going on.
o If you look at the smallest size square on a
checkerboard, we can call that a 1 unit by 1
unit square. There are 64 of that size.
The next size square is a 2 unit by 2 units square.
It's okay to use These more than once in different new squares.
The top left-hand corner Has 4 of the 1x1's which make a 2x2.
See it? Good, then move right One square and find a new 2x2 made
with two of the 1x1's you just used And two 1x1's right next to
them. Likewise you can shift down just one Row and use two that
you've already used. Count all of these 2x2's. You should come up
with 49.Our table would look like this:
Size
1*1
2*2
3*3
4*4
number of squares
64
49
Ect..
You go ahead and complete this table. After you're
done you still have To add up the right hand column to
get the total number of squares on a Checkerboard.
Let's get back to the question of a pattern. Is there
anything you? Notice about the numbers in the right
hand column? Is there a relation To the number of 1x1
squares on a side of the checkerboard? 2x2's? Etc.?
Say you have an 8x8 checkerboard. There are many
other little and Big squares inside of that so counting
them all how many are there? (E.g. counting all the 1x1,
2x2, 3x3, 4x4, 5x5, 6x6, 7x7, 8x8).
Suppose you have a square checkerboard of
some other size - not 8x8 –What is the
easiest way to find how many squares there
are in it?
Make sure that when you are done you will
be able to find the number Of squares in any
size checkerboard within 2 minutes.
I tried counting the squares individually, but
that wouldn't be quick Enough for 12x12.
Could you please give me some tips for how
to Approach this problem?
THANKS FOR YOUR
TIME.