Conjecturing and generalising

problem

Centred Squares

Age

7 to 11

Challenge level

2 out of 3

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
problem

Dice Stairs

Age

7 to 11

Challenge level

2 out of 3

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
problem

Roll Over the Dice

Age

7 to 11

Challenge level

2 out of 3

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
problem

Counting Counters

Age

7 to 11

Challenge level

2 out of 3

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
problem

Cuisenaire Squares

Age

7 to 11

Challenge level

2 out of 3

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
problem

Pebbles

Age

7 to 11

Challenge level

2 out of 3

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

2 out of 3

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

2 out of 3

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

2 out of 3

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

2 out of 3

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?