Conjecturing and generalising

  • About Average
    problem
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    About Average

    Age
    11 to 14
    Challenge level
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    Can you find sets of numbers which satisfy each of our mean, median, mode and range conditions?

  • Beach Huts
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    Beach Huts

    Age
    11 to 14
    Challenge level
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    Can you figure out how sequences of beach huts are generated?

  • Growing Surprises
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    Growing Surprises

    Age
    11 to 14
    Challenge level
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    Can you find the connections between linear and quadratic patterns?

  • Polygon Rings
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    Polygon Rings

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

  • Same Answer
    problem
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    Same Answer

    Age
    11 to 14
    Challenge level
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    Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?

  • More Isometric Areas
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    More Isometric Areas

    Age
    11 to 14
    Challenge level
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    Isometric Areas explored areas of parallelograms in triangular units. Here we explore areas of triangles...

  • Counting Factors
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    Counting Factors

    Age
    11 to 14
    Challenge level
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    Is there an efficient way to work out how many factors a large number has?

  • Legs Eleven
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    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?

  • Sum Equals Product
    problem

    Sum Equals Product

    Age
    11 to 14
    Challenge level
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    The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 × 1 [1/3]. What other numbers have the sum equal to the product and can this be so for any whole numbers?

  • Where can we visit?
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    Where Can We Visit?

    Age
    11 to 14
    Challenge level
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    Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?