You told my partner and I to change the color of things that are different in our papers.
Problem Statement: You have a pool table with pockets only in the four corners. If a ball is always shot from the bottom left corner at 45°, and it always bounces at 45° , how many times will it bounce before it lands in a pocket? I worked with a partner, but I spent more time on bigger dimensions and a table of our data, while my partner spent more time on smaller dimensions Pool Table Dimensions Number of
Rebounds
Corner it lands in(A, B,
C, or D)
1x1
0
C
10x10
0
C
2x1
1
B
2x4
1
D
3x6
1
D
2x6
2
C
2x7
2
B
2x8
3
D
8x12
3
B
2x3
3
B
10x6
6
C
30x18
6
C
2x4
8
D
3x8
9
D
4x7
9
B
4x10
9
B
5x7
10
C
7x10
15
D
19x10
25
C
19x20
The process we used was to draw rectangles,
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I spent more time working on a table of our data and larger dimensions, but lost my place, while my partner spent most of her time working on smaller dimensions and finding patterns and relationships between those. We found that this equation that can be used to find the number of rebounds and worked for some rectangles: (length+width) - 2 = rebounds (EX. 7+10= 17, 17 - 2= 15) We tried this with our rectangles that we had drawn, but it didn’t work for all of them. For instance, it didn’t work for squares, and it didn’t work for rectangles with one side length of one. So we found a few extra rules to go through before you use the first rule that we found. If the height is two and the other side length is an even number then use this equation: (x/2)-1 = rebounds (EX. 2 by 6, do (6/2)-1= 2 rebounds) If that doesn’t apply, and one side length is half the length of the other, then the number of rebounds is 1.(EX. 4 by 2) If that doesn’t apply, and one side length is 1, then subtract 1 from the other side lengths and that is the number of rebounds.(EX. 10 - 1= 9) If that doesn’t work, and one side is a multiple of ten, reduce, and then use this equation: [(x+10) - 4] / 2 = rebounds (EX. [(6+10) - 4] / 2]