Conjecturing and generalising

problem
Cuboid challenge

Age

11 to 16

Challenge level

What's the largest volume of box you can make from a square of paper?
problem
Wipeout

Age

11 to 16

Challenge level

Can you do a little mathematical detective work to figure out which number has been wiped out?
problem
Rhombus it

Age

11 to 16

Challenge level

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.
game

One, three, five, seven

Age

11 to 16

Challenge level

A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.
problem
More magic potting sheds

Age

11 to 16

Challenge level

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
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
How old am I?

Age

14 to 16

Challenge level

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
problem
Pair products

Age

14 to 16

Challenge level

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
problem
The better choice

Age

14 to 16

Challenge level

Here are two games you can play. Which offers the better chance of winning?
problem
Counting fish

Age

14 to 16

Challenge level

I need a figure for the fish population in a lake. How does it help to catch and mark 40 fish?