Exploring and noticing

  • Sizing them Up
    problem

    Sizing them up

    Age
    5 to 7
    Challenge level
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    Can you put these shapes in order of size? Start with the smallest.

  • Trapezium Four
    problem

    Trapezium four

    Age
    14 to 16
    Challenge level
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    The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

  • Substitution Cipher
    problem

    Substitution cipher

    Age
    11 to 14
    Challenge level
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    Find the frequency distribution for ordinary English, and use it to help you crack the code.

  • Domino Sorting
    problem

    Domino sorting

    Age
    5 to 7
    Challenge level
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    Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

  • Real Statistics
    problem

    Real statistics

    Age
    7 to 11
    Challenge level
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    Have a look at this table of how children travel to school. How does it compare with children in your class?

  • Magic potting sheds
    problem

    Magic potting sheds

    Age
    11 to 16
    Challenge level
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    Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
  • Brush Loads
    problem

    Brush loads

    Age
    7 to 11
    Challenge level
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    How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

  • Tables Without Tens
    problem

    Tables without tens

    Age
    7 to 11
    Challenge level
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    Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.
  • Areas of parallelograms
    problem

    Areas of parallelograms

    Age
    14 to 16
    Challenge level
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    Can you find the area of a parallelogram defined by two vectors?

  • Warmsnug Double Glazing
    problem

    Warmsnug double glazing

    Age
    14 to 16
    Challenge level
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    How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?