Explaining, convincing and proving

  • Perimeter Challenge
    problem

    Perimeter challenge

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

    Can you deduce the perimeters of the shapes from the information given?

  • Colourful Cube
    problem

    Colourful cube

    Age
    11 to 14
    Challenge level
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    A colourful cube is made from little red and yellow cubes. But can you work out how many of each?

  • Gabriel's Problem
    problem

    Gabriel's problem

    Age
    11 to 14
    Challenge level
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    Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

  • Polygon Rings
    problem

    Polygon rings

    Age
    11 to 14
    Challenge level
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    Join pentagons together edge to edge. Will they form a ring?

  • Star Polygons
    problem

    Star polygons

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

    Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?

  • Legs Eleven
    problem

    Legs eleven

    Age
    11 to 14
    Challenge level
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    Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

  • Think of Two Numbers
    problem

    Think of two numbers

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

    Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

  • Children at Large
    problem

    Children at large

    Age
    11 to 14
    Challenge level
    filled star filled star empty star
    There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
  • An Unusual Shape
    problem

    An unusual shape

    Age
    11 to 14
    Challenge level
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    Can you maximise the area available to a grazing goat?

  • More Number Pyramids
    problem

    More number pyramids

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

    When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...