Being curious

  • Make 37 Poster
    problem

    Make 37

    Age
    5 to 11
    Challenge level
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    Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?

  • Pick's Theorem
    problem

    Pick's theorem

    Age
    14 to 16
    Challenge level
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    Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

  • Take Three From Five
    problem

    Take three from five

    Age
    11 to 16
    Challenge level
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    Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

  • Fitted
    problem

    Fitted

    Age
    7 to 11
    Challenge level
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    Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

  • problem

    Ladybirds in the garden

    Age
    5 to 7
    Challenge level
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    In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

  • Halving
    problem

    Halving

    Age
    5 to 7
    Challenge level
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    These pictures show squares split into halves. Can you find other ways?

  • Largest product
    problem

    Largest product

    Age
    11 to 14
    Challenge level
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    Which set of numbers that add to 100 have the largest product?
  • Think of Two Numbers
    problem

    Think of two numbers

    Age
    11 to 14
    Challenge level
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    Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
  • Square Corners
    problem

    Square corners

    Age
    7 to 11
    Challenge level
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    What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

  • In the Money
    problem

    In the money

    Age
    7 to 11
    Challenge level
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    One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?