Visualising and representing

  • Pair Products
    problem

    Pair products

    Age
    14 to 16
    Challenge level
    filled star empty star empty star

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

  • Picturing Square Numbers
    problem

    Picturing square numbers

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

  • Colour Wheels
    problem

    Colour wheels

    Age
    7 to 11
    Challenge level
    filled star empty star empty star

    Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

  • Folded A4
    problem

    Folded A4

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    What shapes can be made by folding an A4 sheet of paper only once?

  • An Unusual Shape
    problem

    An unusual shape

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    Can you maximise the area available to a grazing goat?

  • Rolling Around
    problem

    Rolling around

    Age
    11 to 14
    Challenge level
    filled star filled star empty star
    A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
  • A Square in a Circle
    problem

    A square in a circle

    Age
    7 to 11
    Challenge level
    filled star filled star empty star
    What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?
  • Inside Seven Squares
    problem

    Inside seven squares

    Age
    7 to 11
    Challenge level
    filled star filled star empty star

    What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

  • Special Numbers
    problem

    Special numbers

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?