Explaining, convincing and proving
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problemBig and small numbers in physics - group task
Work in groups to try to create the best approximations to these physical quantities. - 
problemNegative powers
What does this number mean? Which order of 1, 2, 3 and 4 makes the highest value? Which makes the lowest?
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problemConsecutive negative numbers
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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problem9 weights
You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance? - 
problemOverlaps
What does the overlap of these two shapes look like? Try picturing it in your head and then use some cut-out shapes to test your prediction.
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problemThe great weights puzzle
You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest? - 
problemGutter
Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?