Reasoning, convincing and proving

There are 514 NRICH Mathematical resources connected to Reasoning, convincing and proving
Discrete Trends
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Discrete trends

Age
16 to 18
Challenge level
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Find the maximum value of n to the power 1/n and prove that it is a maximum.
Wallpaper
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Wallpaper

Age
5 to 7
Challenge level
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These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?

Magic Vs
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Magic vs

Age
7 to 11
Challenge level
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Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Back fitter
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Back fitter

Age
14 to 18
Challenge level
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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?

What numbers can we make?
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What numbers can we make?

Age
11 to 14
Challenge level
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Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

A City of Towers
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A city of towers

Age
5 to 7
Challenge level
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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?

There's a limit
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There's a limit

Age
14 to 18
Challenge level
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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?
Lens Angle
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Lens angle

Age
14 to 16
Challenge level
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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.
Seven Squares - Group-worthy Task
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Seven squares - group-worthy task

Age
11 to 14
Challenge level
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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?
How do you do it?
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How do you do it?

Age
7 to 11
Challenge level
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This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.