Creating and manipulating expressions and formulae

  • Interactive Number Patterns
    problem
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    Interactive Number Patterns

    Age
    14 to 16
    Challenge level
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    How good are you at finding the formula for a number pattern ?

  • Partly Painted Cube
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    Partly Painted Cube

    Age
    14 to 16
    Challenge level
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    Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

  • problem
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    Simplifying Doughnut

    Age
    14 to 16
    Challenge level
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    Can you match up these equivalent algebraic expressions?

  • Training schedule
    problem
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    Training Schedule

    Age
    14 to 16
    Challenge level
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    The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

  • Attractive Tablecloths
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    Attractive Tablecloths

    Age
    14 to 16
    Challenge level
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    Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

  • Difference of Two Squares
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    Difference of Two Squares

    Age
    14 to 16
    Challenge level
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    What is special about the difference between squares of numbers adjacent to multiples of three?

  • Pythagoras Perimeters
    problem
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    Pythagoras Perimeters

    Age
    14 to 16
    Challenge level
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    If you know the perimeter of a right angled triangle, what can you say about the area?

  • Puzzling Place Value
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    Puzzling Place Value

    Age
    14 to 16
    Challenge level
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    Can you explain what is going on in these puzzling number tricks?

  • The square top of a red gift box with a bow.
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    Square Number Surprises

    Age
    14 to 16
    Challenge level
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    There are unexpected discoveries to be made about square numbers...

  • Two blank square picture frames on a wooden floor.
    problem
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    2-Digit Square

    Age
    14 to 16
    Challenge level
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    A 2-digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?