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Archimedes and Numerical Roots

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

Ladder and Cube

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

More or Less?

Are these estimates of physical quantities accurate?

Biology Measurement Challenge

Age 14 to 16 Challenge Level:

Why do this problem ?

These interesting questions will allow students to practise using different units of measurement whilst developing awareness of orders of magnitude in scientific contexts. Some also require students to find additional information.  As with any problems involving approximation, they offer opportunity for classroom discussion and justification.

Possible approach

There are several parts to this question, some easier, some more challenging. The individual images could be used as starters or filler activities for students who finish classwork early. Enthusiastic students might work through them in their own time. If students disagree with each other, or with the answers provided, this could lead to productive discussion.

Key questions

Do you have all the information you need to decide where a particular image should fit in the list? If not, where can you find out what you need?
What formulae will you need to use?
How accurate do you think the answer is?
What 'order of magnitude' checks could you make to test that your answer is sensible?

Possible extension

Challenge students to come up with their own images and questions about order of magnitude.

Possible support

Start with questions which seem most accessible and encourage whole class discussion of the values given.  The article Getting Started with Solving Rich Tasks might be helpful.