### How Big?

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

### Do Unto Caesar

At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the assets of the players at the beginning of the evening? ### Oh for the Mathematics of Yesteryear A garrison of 600 men has just enough bread ... but, with the news that the enemy was planning an attack... How many ounces of bread a day must each man in the garrison be allowed, to hold out 45 days against the siege of the enemy? # Cereal Mix ##### Stage: 3 Challenge Level: ### Why do this problem: A simple problem to get students starting to think about ratio. ### Possible approach : Ask students to suggest possible combinations and their suggestions could be written up for everyone in the group to see. ### Key questions : • Do all these combinations cost$£5$per kg? How do you find out? • Do any of these combinations give identical mixes? How do you find out? • Are there any relationships between the quantities of the different ingredients? ### Possible extension : Students can be pressed to explore and articulate more explicitly the degree of freedom possible within the constraint that the final mix should cost$£5\$ per kg.

Ask students to include a visualisation of why that result (ratio relationship for Apricots, Nuts & Seeds) might be expected.

### Possible support :

For students who need more support than the text of the problem.
Ask each student to generate a result price for a ratio mix of their own choice.

List these mix costs, with the Apricot / Nut / Seed ratio that produced them as reference for the next task.

Ask students to find ratios of ingredients that will put a mixture cost per kg in between each value listed.