Conjecturing and generalising

problem
The great tiling count

Age

7 to 11

Challenge level

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
problem
Doplication

Age

7 to 11

Challenge level

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
problem
I'm eight

Age

5 to 11

Challenge level

Find a great variety of ways of asking questions which make 8.
problem
Pebbles

Age

7 to 11

Challenge level

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
problem
Chocolate

Age

7 to 14

Challenge level

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?
problem
Consecutive numbers

Age

7 to 14

Challenge level

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
problem
Cuisenaire squares

Age

7 to 11

Challenge level

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
problem
Counting counters

Age

7 to 11

Challenge level

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
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Problem solving, using and applying and functional mathematics

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
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Making maths: be a mathemagician

Surprise your friends with this magic square trick.