1. Is it? Evaluating the risk Eating bacon sandwiches is bad for you!

2. If you eat a bacon sandwich every day, your risk of getting bowel cancer at some point in your life is increased by 20%. Eating bacon sandwiches is bad for you!

3. If you eat a bacon sandwich every day, your risk of getting bowel cancer at some point in your life is increased by 20%. Sounds bad! What do you think? Eating bacon sandwiches is bad for you!

4. If you eat a bacon sandwich every day, your risk of getting bowel cancer at some point in your life is increased by 20%. Sounds bad! What do you think? Eating bacon sandwiches is bad for you! Before we can decide how bad this is, we need to know what this is 20% of.

5. But why does it matter what its 20% of? 20% is 20%, isnt it?

6. Whats 20% of 100 people? What about 20% of 10 people? Or 20% of 150 people? Colour the right number of squares on your worksheet.

7. 20% of 100 people = 20 20% of 10 people = 2 20% of 150 people = 30

8. 20% of 100 people = 20 20% of 10 people = 2 20% of 150 people = 30 2 is a lot fewer people than 20 or 30

9. The missing information … even if they dont eat bacon sandwiches We need to know how many people will get bowel cancer even if they dont eat bacon sandwiches to know whether we should worry about a 20% increase or not. If theres a large risk anyway, then a 20% increase will be a lot more people. If there isnt a large risk anyway, then a 20% increase will be a much smaller number of people.

10. The missing information … even if they dont eat bacon sandwiches We need to know how many people will get bowel cancer even if they dont eat bacon sandwiches to know whether we should worry about a 20% increase or not. If theres a large risk anyway, then a 20% increase will be a lot more people. If there isnt a large risk anyway, then a 20% increase will be a much smaller number of people.

11. The missing information … even if they dont eat bacon sandwiches We need to know how many people will get bowel cancer even if they dont eat bacon sandwiches to know whether we should worry about a 20% increase or not. If theres a large risk anyway, then a 20% increase will be a lot more people. If theres only a small risk anyway, then a 20% increase will be a much smaller number of people.

12. The risk that a person will get bowel cancer at some point in their life is about 1 in 18, which is roughly 5%. This means that even if they never eat a bacon sandwich about 5 people in every 100 will get bowel cancer. 20% of 5 people is 1 person. So an extra person can be expected to get bowel cancer if 100 people eat bacon sandwiches throughout their lives.

13. It is this risk – the absolute risk of getting bowel cancer – which is increased by 20% if someone eats a bacon sandwich every day.

14. The risk that a person will get bowel cancer at some point in their life is about 1 in 18, which is roughly 5%. This means that even if they never eat a bacon sandwich about 5 people in every 100 will get bowel cancer. 20% of 5 people is 1 person. So an extra person can be expected to get bowel cancer if 100 people eat bacon sandwiches throughout their lives.

15. On your worksheet colour a random 5% of smiley faces on each grid to show people who will get bowel cancer regardless of eating bacon sandwiches

16. 5% of 100 is 5 5% of 60 is 3 5% of 140 is 7

17. Using a different colour add the extra cases of bowel cancer which would occur if all these people ate bacon sandwiches every day

18. An extra 20% of 5 is 1, giving a total of 6. An extra 20% of 3 is 0.6, giving a total of 3 or 4. An extra 20% of 7 is 1.4, giving a total of 8 or 9.

19. The missing information … A 20% increase sounds a lot, doesnt it. But because its 20% of a small absolute risk, it actually means that we should expect just one extra person to get bowel cancer in every 100 who eat bacon sandwiches every day. What do you think? Will this stop you eating bacon sandwiches?

20. Motivate Project Millennium Mathematics Project University of Cambridge We are grateful to the Wellcome Trust for funding this project. © University of Cambridge