Conjecturing and generalising

problem
Multiply multiples 1

Age

7 to 11

Challenge level

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
problem
Two spinners

Age

5 to 7

Challenge level

What two-digit numbers can you make with these two dice? What can't you make?
problem
Play to 37

Age

7 to 11

Challenge level

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
problem
Super computer

Age

14 to 16

Challenge level

What is the units digit of the given expression?
problem
Little difference

Age

14 to 16

Challenge level

What is the value of $2015 \times 2017 - 2016 \times 2016$?
problem
Journeying in Numberland

Age

7 to 11

Challenge level

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
problem
Strange bank account

Age

11 to 14

Challenge level

Imagine a very strange bank account where you are only allowed to do two things...
problem
Snake coils

Age

7 to 11

Challenge level

This challenge asks you to imagine a snake coiling on itself.
problem
Walking the squares

Age

7 to 11

Challenge level

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
problem
Perimeter possibilities

Age

11 to 14

Challenge level

I'm thinking of a rectangle with an area of 24. What could its perimeter be?