Over the last few weeks in project maths we have done the billiard ball activity.
In this activity you are on a pool table and there is no middle pockets. The ball will always start from the bottom left corner. The first thing that we had to do was guess how many times the ball would bounce before going in, but with a twist each bounce has to be on a 45 degree angle. Sometimes this could be quite challenging because if you did not quite get it straight then your whole grid would be stuffed up and you will most likely not get the correct answer.
This was very hard to just guess the exact pocket that it would go into so we started to look for patterns and strategy’s. I found a lot of different patterns but they were only to predict one number such as a 1 by 1 grid or a 5 by 8 grid size. Some of my patterns were…..
3 by …..= The answer is one more then the second number except for 3 by 3 because for every 1st and 2nd number that is the same it will always equal 0. And much more
After having a think about different patterns we then started to think about one formula that will work to predict every single pocket! This was very challenging. I started to do this by guessing and checking. I then checked with the teacher and he said that I got the two part correct. I just did not know what to do with the 2, I just knew to use one in the end formula.
This helped me a lot because then I started to think about everything I could do with a 2.
After re grouping with the class I worked out what the formula was…..
You need to simplify both numbers or half them as much as you can but both the same amount. You can also not go into minus numbers or decimals. Once you have done that the most that you can you add the width and the length together and -2. For example……
10 by 8= simplify down to 5 by 4 is the most you can do now 5+4=9-2=7 which is your answer.
I think this was challenging to find the formula because you needed to test so many different things and then you would finally get it. Below is some of my working out.