Conjecturing and generalising

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

Magic Constants

Age

7 to 11

Challenge level

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
problem

Magic Circles

Age

7 to 11

Challenge level

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
problem

Rope Mat

Age

7 to 11

Challenge level

How many centimetres of rope will I need to make another mat just like the one I have here?
problem

Crossings

Age

7 to 11

Challenge level

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?
problem

Button-Up Some More

Age

7 to 11

Challenge level

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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

Bundles of Cubes

Age

7 to 11

Challenge level

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
problem

Truth or Lie

Age

7 to 11

Challenge level

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?
problem

Lost Books

Age

7 to 11

Challenge level

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?