Reasoning, convincing and proving
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Find the maximum value of n to the power 1/n and prove that it is a
maximum.
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Wallpaper
These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?
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Magic vs
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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Back fitter
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
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What numbers can we make?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
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A city of towers
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
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There's a limit
Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you
notice when successive terms are taken? What happens to the terms
if the fraction goes on indefinitely?
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Lens angle
Find the missing angle between the two secants to the circle when
the two angles at the centre subtended by the arcs created by the
intersections of the secants and the circle are 50 and 120 degrees.
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Seven squares - group-worthy task
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
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How do you do it?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.