Reasoning, convincing and proving

There are 514 NRICH Mathematical resources connected to Reasoning, convincing and proving
Sixty-Seven Squared
problem
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Sixty-seven squared

Age
16 to 18
Challenge level
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Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?
Product Sudoku
problem
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Product sudoku

Age
11 to 16
Challenge level
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The clues for this Sudoku are the product of the numbers in adjacent squares.

Shape Times Shape
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Shape times shape

Age
7 to 11
Challenge level
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These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?
Stats statements
problem
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Stats statements

Age
16 to 18
Challenge level
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Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Dangerous driver?
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Dangerous driver?

Age
16 to 18
Challenge level
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Was it possible that this dangerous driving penalty was issued in error?
The car that passes
problem
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The car that passes

Age
7 to 11
Challenge level
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What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?

Polygon Pictures
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Polygon pictures

Age
11 to 14
Challenge level
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Can you work out how these polygon pictures were drawn, and use that to figure out their angles?

Always, Sometimes or Never?
problem
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Always, sometimes or never?

Age
5 to 11
Challenge level
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Are these statements relating to odd and even numbers always true, sometimes true or never true?

Always, Sometimes or Never? KS1
problem
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Always, Sometimes or Never? KS1

Age
5 to 7
Challenge level
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Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?