Conjecturing and generalising

problem
Starting to explore four consecutive numbers

Age

11 to 16

Challenge level
game

Celebrate 25 years of NRICH

Age

5 to 14

To celebrate NRICH's 25th birthday, why not play this special version of our classic game, Got It? Can you devise a strategy so that you will always win?
problem
Counting stick conjectures

Age

5 to 11

Challenge level

How many rectangles can you see? Are they all the same size? Can you predict how many rectangles there will be in counting sticks of different lengths?
problem
Diagonally square

Age

7 to 11

Challenge level

Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?
article
Why dialogue matters in primary proof

In this article for Primary teachers, Ems explores three essential features of proof, all of which can be developed in the context of primary mathematics through talk.
problem
Difference of odd squares

Age

14 to 18

Challenge level

$40$ can be written as $7^2 - 3^2.$ Which other numbers can be written as the difference of squares of odd numbers?
problem
What does it all add up to?

Age

11 to 18

Challenge level

If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?
problem
Three neighbours

Age

7 to 14

Challenge level

Take three consecutive numbers and add them together. What do you notice?
game
Favourite

Dicey array

Age

5 to 11

Challenge level

Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?
problem
Guess what?

Age

7 to 11

Challenge level

Can you find out which 3D shape your partner has chosen before they work out your shape?