Conjecturing and generalising

  • Growing Surprises
    problem
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    Growing Surprises

    Age
    11 to 14
    Challenge level
    1 out of 3

    Can you find the connections between linear and quadratic patterns?

  • Polygon Rings
    problem
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    Polygon Rings

    Age
    11 to 14
    Challenge level
    1 out of 3

    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
    2 out of 3

    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
    2 out of 3

    Isometric Areas explored areas of parallelograms in triangular units. Here we explore areas of triangles...

  • Counting Factors
    problem
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    Counting Factors

    Age
    11 to 14
    Challenge level
    2 out of 3

    Is there an efficient way to work out how many factors a large number has?

  • Legs Eleven
    problem
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    Legs Eleven

    Age
    11 to 14
    Challenge level
    2 out of 3

    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?

  • Where can we visit?
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    Where Can We Visit?

    Age
    11 to 14
    Challenge level
    2 out of 3

    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: ×2 and -5. What do you think?

  • 1 Step 2 Step
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    1 Step 2 Step

    Age
    11 to 14
    Challenge level
    2 out of 3

    Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

  • Egyptian Fractions
    problem
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    Egyptian Fractions

    Age
    11 to 14
    Challenge level
    2 out of 3

    The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

  • Farey Sequences
    problem
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    Farey Sequences

    Age
    11 to 14
    Challenge level
    2 out of 3

    There are lots of ideas to explore in these sequences of ordered fractions.