Conjecturing and generalising

  • Dice Stairs
    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?

  • Roll over the dice
    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?

  • Counting Counters
    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?

  • Cuisenaire Squares
    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?

  • Pebbles
    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?

  • A silver magic wand and confetti on a blue background.
    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?

  • Magic Circles
    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?
  • Rope Mat
    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?

  • Crossings
    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?

  • Move a Match
    problem

    Move a Match

    Age
    7 to 11
    Challenge level
    2 out of 3

    How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?