Being curious

  • Electric Kettle
    problem

    Electric kettle

    Age
    14 to 16
    Challenge level
    filled star empty star empty star

    Explore the relationship between resistance and temperature

  • Beelines
    problem

    Beelines

    Age
    14 to 16
    Challenge level
    filled star empty star empty star

    Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

  • Triangle midpoints
    problem

    Triangle midpoints

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

  • Doesn't add up
    problem

    Doesn't add up

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

  • Expenses
    problem

    Expenses

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    What is the largest number which, when divided into these five numbers in turn, leaves the same remainder each time?

  • Fair Shares?
    problem

    Fair shares?

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    A mother wants to share some money by giving each child in turn a lump sum plus a fraction of the remainder. How can she do this to share the money out equally?

  • What's Possible?
    problem

    What's possible?

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

  • Arclets
    problem

    Arclets

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".
  • Pick's Theorem
    problem

    Pick's theorem

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

  • problem

    Triangles and petals

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?