Conjecturing and generalising

  • Cuisenaire Squares
    problem

    Cuisenaire Squares

    Age
    7 to 11
    Challenge level
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    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
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    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
    Favourite

    Round and Round the Circle

    Age
    7 to 11
    Challenge level
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    What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

  • Magic Constants
    problem

    Magic Constants

    Age
    7 to 11
    Challenge level
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    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?
  • Making Boxes
    problem
    Favourite

    Making Boxes

    Age
    7 to 11
    Challenge level
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    Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

  • Magic Circles
    problem

    Magic Circles

    Age
    7 to 11
    Challenge level
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    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
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    How many centimetres of rope will I need to make another mat just like the one I have here?
  • Amy's Dominoes
    problem
    Favourite

    Amy's Dominoes

    Age
    7 to 11
    Challenge level
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    Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?

  • problem
    Favourite

    Reach 100

    Age
    7 to 11
    Challenge level
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    Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

  • problem
    Favourite

    Two Primes Make One Square

    Age
    7 to 11
    Challenge level
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    Can you make square numbers by adding two prime numbers together?