Modelling Scientific Exploration and Discovery - July 2010, Stage 4&5

This month our problems and games model the process of scientific exploration and discovery. When you first begin tackling a problem, you might make some observations which could lead to a tentative, incomplete theory or hypothesis. You might try something rather random to test your hypothesis, which you subsequently modify. Then you will become more systematic in your testing and your hypothesis will be reconstructed based on your new insight. At any time, the theory you have is the one that best fits the evidence you have gathered so far.

Problems

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Charlie's Delightful Machine

Stage: 3 and 4 Challenge Level: Challenge Level:1

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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A Little Light Thinking

Stage: 4 Challenge Level: Challenge Level:1

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

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How Do You React?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

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Guessing the Graph

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

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Spectrometry Detective

Stage: 5 Challenge Level: Challenge Level:1

From the atomic masses recorded in a mass spectrometry analysis can you deduce the possible form of these compounds?

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The Not-so-simple Pendulum 1

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

See how the motion of the simple pendulum is not-so-simple after all.

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Black Box

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This black box reveals random values of some important, but unusual, mathematical functions. Can you deduce the purpose of the black box?

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The Real Hydrogen Atom

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Dip your toe into the world of quantum mechanics by looking at the Schrodinger equation for hydrogen atoms

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The Not-so-simple Pendulum 2

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Things are roughened up and friction is now added to the approximate simple pendulum

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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