Rule of Three

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

Square Pegs

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

How Big?

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

Cereal Mix

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.