Embedded Files
Introduction
Introduction
On the right is a very strange snooker table. It has only has four pockets and the ball always travels at an angle of 45° to the sides of the table.
Given the width and height of a table can you predict which pocket the ball will end up in and how many times will it bounce off one of the sides?
To get a better idea of how it works click here and here. Investigate this problem on your own, if you need some help, take a look at the following prompts:
Let's start small, what width and height should you begin with?
For your chosen width and height, which pocket will the ball end up in and how many times will it bounce off one of the sides?
Thinking systematically, what should you change next? What should you keep the same?
How may you organise your results in a table? How many columns do you need? What should you have as headings of the columns?
What if you organise width, height and bounces in a 2 way table?
What conjectures can you make? Here are more prompts should you need them:
When the table is a square - how many times will it bounce off one of the sides? Which pocket will the ball end up in?
What do you notice when the height is a multiple of the width or vice versa?
What do you notice when the height is one more than the width or vice versa?
What do you notice when the height and the width are co-prime (when two numbers have no common factors other than 1)? Can you come up with a rule for the number of bounces?
What do you notice about which pocket the ball ends up in? What is the relationship between, A, B, C and D?
What other interesting rules have you noticed?
Apply your rules to find answers to the following questions.
Further Practice
Further Practice
Some of the essential skills introduced in this lesson are "multiples", "HCF" and "LCM". Practise these relevant skills on DrFrostMaths, CorbettMaths, MyiMaths and Eedi.
For some word problems take a look at these worksheets on k5learning or these on cuemaths
Transum
Transum
Try these self-marked exercises on transum to check your understanding: factor trees and HCF and LCM.
Looking for something fun to play with your friend? Try this "Flabbergasted" game. The winner is the last person standing.
For more goodies on factors, multiples and prime look at these activities on transum.
Extension
Extension
More excellent tasks on apply what "HCF" and "LCM" can be found on nrich. Below are a few:
Charlie's Delightful Machine - Can you work out how to switch the lights on? Can you develop a strategy to work out the rules controlling each light?
Once you are confident that you can work out the rules, have a go at A Little Light Thinking
If you want something more challenging, try Four Coloured Lights
Page updated
Report abuse