Exploring and noticing

  • problem

    Abundant numbers

    Age
    7 to 11
    Challenge level
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    48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

  • Zios and Zepts
    problem

    Zios and Zepts

    Age
    7 to 11
    Challenge level
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    On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

  • problem

    Wonky watches

    Age
    7 to 11
    Challenge level
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    Mandeep's watch loses two minutes every hour. Adam's watch gains one minute every hour. Can you work out what time they arrived at the airport?

  • Pizza Cut
    problem

    Pizza cut

    Age
    7 to 11
    Challenge level
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    Using only six straight cuts, find a way to make as many pieces of pizza as possible. (The pieces can be different sizes and shapes).
  • Egyptian Rope
    problem

    Egyptian rope

    Age
    7 to 11
    Challenge level
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    The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

  • problem

    Watch the clock

    Age
    7 to 11
    Challenge level
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    During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

  • What's in a Name?
    problem

    What's in a name?

    Age
    5 to 7
    Challenge level
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    What do you notice about these squares of numbers? What is the same? What is different?

  • Arranging the Tables
    problem

    Arranging the tables

    Age
    7 to 11
    Challenge level
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    There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
  • Thinking Mathematically - Short Problems
    problem

    What two ...?

    Age
    7 to 11
    Challenge level
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    56 406 is the product of two consecutive numbers. What are these two numbers?

  • Special 24
    problem

    Special 24

    Age
    7 to 11
    Challenge level
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    Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.