How Big?

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

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.

Ratio. smartphone. Calculating with ratio & proportion. Similarity. Visualising. Creating expressions/formulae. Fractions. Area.

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