Exploring and noticing

  • Numerically Equal
    problem
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    Numerically equal

    Age
    7 to 11
    Challenge level
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    Can you draw a square in which the perimeter is numerically equal to the area?

  • Twenty Divided into Six
    problem
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    Twenty divided into six

    Age
    7 to 11
    Challenge level
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    Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

  • Mystery Matrix
    problem
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    Mystery matrix

    Age
    7 to 11
    Challenge level
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    Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

  • 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?

  • Fractions in a Box
    problem
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    Fractions in a box

    Age
    7 to 11
    Challenge level
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    The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

  • problem
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    One wasn't square

    Age
    7 to 11
    Challenge level
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    Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

  • All the Digits
    problem
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    All the digits

    Age
    7 to 11
    Challenge level
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    This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

  • problem
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    Reach 100

    Age
    7 to 11
    Challenge level
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    Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

  • problem
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    Two primes make one square

    Age
    7 to 11
    Challenge level
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    Can you make square numbers by adding two prime numbers together?

  • problem
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    Cycling squares

    Age
    7 to 11
    Challenge level
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    Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?