Ball Bearings

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

Overarch 2

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?

Cushion Ball

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

Population Dynamics - Part 5

Why do this problem ?

Practice with the use of numbers is a crucial biological skill. These interesting questions will allow you to practise these skills whilst developing awareness of orders of magnitude in scientific contexts.

Possible approach

There are several parts to this question. The individual pieces could be used as starters or filler activities for students who finish classwork early. Enthusiastic students might work through them in their own time. Since there is no absolutely 'correct' answer to many of these questions, they might productively be used for discussion: students create their own answers and then explain them to the rest of the class. Does the class agree? Disagree? Is there an obvious best 'collective' answer?

Key questions

• What assumptions will you need to make in this question?
• How accurate do you think you answer is?
• What order of magnitude checks could you make to test that your answer is sensible?

Possible extension

Can students make up similar questions? Can they put any upper or lower bounds on the numbers?

Possible support

Students might struggle with the 'open' nature of the questions. To begin, they might like to read the Student Guide to Getting Started with rich tasks