Conjecturing and generalising

Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Can you make square numbers by adding two prime numbers together?

This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you work out the rule for each light?

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

This challenge combines addition, multiplication, perseverance and even proof.

Try out this number trick. What happens with different starting numbers? What do you notice?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?