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More or Less?
Age 14 to 16
Challenge Level 
Why do this problem ?
This problem gives practice with the use of estimating numbers and making choices about the information to use in a question. These are crucial mathematical skills in the sciences. These interesting questions will allow students to practise these skills whilst developing awareness of orders of magnitude in scientific contexts. As with any problems involving approximation, they offer opportunity for classroom discussion and justification.Possible approach
There are several parts to this question, arranged in approximate order of difficulty. 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?
The questions are arranged for printing out into cards in this Word 2003 document .
Key questions
- What assumptions will you need to make in this question?
- 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
Can students make up similar questions? Can they put any upper or lower bounds on the actual numbers that would arise from a detailed calculation?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.You may also like
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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?
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?
