Conjecturing and generalising

There are 405 NRICH Mathematical resources connected to Conjecturing and generalising
Keep it simple
problem
Favourite

Keep it simple

Age
11 to 14
Challenge level
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Can all unit fractions be written as the sum of two unit fractions?
Shapely Lines
problem
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Shapely lines

Age
5 to 7
Challenge level
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This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

Journeys in Numberland
problem
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Journeys in numberland

Age
7 to 11
Challenge level
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Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Cubes within Cubes
problem
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Cubes within cubes

Age
7 to 14
Challenge level
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We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

How Many Miles To Go?
problem
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How many miles to go?

Age
11 to 14
Challenge level
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How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
Areas of parallelograms
problem
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Areas of parallelograms

Age
14 to 16
Challenge level
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Can you find the area of a parallelogram defined by two vectors?
Growing Garlic
problem
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Growing garlic

Age
5 to 11
Challenge level
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Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

Crossed Ends
problem
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Crossed ends

Age
11 to 14
Challenge level
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Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Strike it out
problem
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Strike it out

Age
5 to 11
Challenge level
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Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Count The Digits
problem
Favourite

Count the digits

Age
5 to 11
Challenge level
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In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?