Reasoning, convincing and proving

There are 514 NRICH Mathematical resources connected to Reasoning, convincing and proving
Times Tables Shifts
problem
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Times tables shifts

Age
7 to 11
Challenge level
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In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

missing multipliers
problem
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Missing multipliers

Age
7 to 14
Challenge level
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What is the smallest number of answers you need to reveal in order to work out the missing headers?
Let's Investigate Triangles
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Let's investigate triangles

Age
5 to 7
Challenge level
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Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

Picture Story
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Picture story

Age
14 to 16
Challenge level
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Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
How old am I?
problem
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How old am i?

Age
14 to 16
Challenge level
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In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
Angle Trisection
problem
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Angle trisection

Age
14 to 16
Challenge level
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It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.
Halving
problem
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Halving

Age
5 to 7
Challenge level
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These pictures show squares split into halves. Can you find other ways?

Break it up!
problem
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Break it up!

Age
5 to 11
Challenge level
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In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

Arithmagons
problem
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Arithmagons

Age
11 to 16
Challenge level
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Can you find the values at the vertices when you know the values on the edges?

Sizing them Up
problem
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Sizing them up

Age
5 to 7
Challenge level
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Can you put these shapes in order of size? Start with the smallest.