Creating and manipulating expressions and formulae

  • Crossed Ends
    problem

    Crossed ends

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

  • How much can we spend?
    problem

    How much can we spend?

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    A country has decided to have just two different coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

  • Your number was...
    problem

    Your number was...

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

  • Perimeter Expressions
    problem

    Perimeter expressions

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?

  • Shape Products
    problem

    Shape products

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

  • Number Pyramids
    problem

    Number pyramids

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    Try entering different sets of numbers in the number pyramids. How does the total at the top change?

  • Can they be equal?
    problem

    Can they be equal?

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    Can you find rectangles where the value of the area is the same as the value of the perimeter?

  • Summing Consecutive Numbers
    problem

    Summing consecutive numbers

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

  • Beach Huts
    problem

    Beach huts

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    Can you figure out how sequences of beach huts are generated?

  • The Simple Life
    problem

    The simple life

    Age
    11 to 14
    Challenge level
    filled star filled star empty star
    The answer is $5x+8y$... What was the question?