Ratio and proportion

  • Tin Tight
    problem

    Tin Tight

    Age
    14 to 16
    Challenge level
    2 out of 3

    What's the most efficient proportion for a 1 litre tin of paint?

  • Small pepper seedlings in turquoise pots.
    problem

    Square Ratio

    Age
    14 to 16
    Challenge level
    2 out of 3

    A square is divided into four rectangles and a square. Can you work out the ratio of the side lengths of the rectangles?

  • Pythagoras’ Comma
    problem

    Pythagoras' Comma

    Age
    14 to 16
    Challenge level
    2 out of 3

    Using an understanding that 1:2 and 2:3 were good ratios, start with a length and keep reducing it to 2/3 of itself. Each time that took the length under 1/2 they doubled it to get back within range.

  • Eight Ratios
    problem

    Eight Ratios

    Age
    14 to 16
    Challenge level
    2 out of 3

    Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.

  • Small tomato seedlings in pink pots.
    problem

    Shepherd's Flock

    Age
    14 to 16
    Challenge level
    2 out of 3

    Does Joseph have too many sheep in his flock...

  • The Fastest Cyclist
    problem

    The Fastest Cyclist

    Age
    14 to 16
    Challenge level
    2 out of 3

    Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?

  • From all corners
    problem

    From All Corners

    Age
    14 to 16
    Challenge level
    3 out of 3

    Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.

  • Same Height
    problem

    Same Height

    Age
    14 to 16
    Challenge level
    3 out of 3

    A trapezium is divided into four triangles by its diagonals. Can you work out the area of the trapezium?

  • Televisual Technology
    problem

    Televisual Technology

    Age
    14 to 16
    Challenge level
    3 out of 3

    If a new and an old television have screens of the same area, what is the ratio of their widths?

  • Orbiting Billiard Balls
    problem

    Orbiting Billiard Balls

    Age
    14 to 16
    Challenge level
    3 out of 3

    What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?