Step 4 Objective

Develop strategies for solving problems and use these strategies both in working within mathematics and in applying mathematics to practical contexts.


What if pupils find this a barrier?

diagram showing three lines crossing

Line Crossings

  • Draw three straight lines (line segments) so that some cross over each other.
  • How many crossings are there?
  • Try different arrangements of the lines. What is the maximum number of possible crossings?
  • Try using more lines.
  • Is there a rule for the maximum for any number of lines? If so, write it down.

Use the problem Line Crossings.

Look at the different diagrams you have drawn with six (or five or ...) lines

  • Which one has the fewest (or most) crossings?
  • Explain how you may get more (or fewer) crossings.
  • What type of diagram will give you the fewest (most) crossings for any number of lines?
  • What different types of diagram can you draw to get different numbers of crossings?