Conjecturing and generalising

There are 405 NRICH Mathematical resources connected to Conjecturing and generalising
Which is cheaper?
problem
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Which is cheaper?

Age
14 to 16
Challenge level
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When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?
Factors and Multiples Game
game
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Factors and multiples game

A game in which players take it in turns to choose a number. Can you block your opponent?

Sticky Triangles
problem
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Sticky triangles

Age
7 to 11
Challenge level
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Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Enclosing Squares
problem
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Enclosing squares

Age
11 to 14
Challenge level
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Can you find sets of sloping lines that enclose a square?
Egyptian Fractions
problem
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Egyptian fractions

Age
11 to 14
Challenge level
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The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

Shear Magic
problem
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Shear magic

Age
11 to 14
Challenge level
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Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?
Carrying Cards
problem
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Carrying cards

Age
7 to 11
Challenge level
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These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
Parallel lines
problem
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Parallel lines

Age
11 to 14
Challenge level
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How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?
Magic Vs
problem
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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?

Nice or Nasty
problem
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Nice or nasty

Age
7 to 14
Challenge level
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There are nasty versions of this dice game but we'll start with the nice ones...