Modelling Scientific Exploration and Discovery - July 2010, Stage 1&2

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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Our Numbers

Stage: 1 Challenge Level: Challenge Level:1

These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?

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I Like ...

Stage: 1 Challenge Level: Challenge Level:1

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

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Fit These Shapes

Stage: 1 and 2 Challenge Level: Challenge Level:1

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

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Light the Lights Again

Stage: 2 Challenge Level: Challenge Level:1

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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Which Numbers? (1)

Stage: 2 Challenge Level: Challenge Level:1

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

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Light the Lights

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

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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Which Numbers? (2)

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

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?