Step 9 Objective

Starting from given problems or contexts, progressively refine or extend the mathematics used to generate fuller solutions.


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.

  • How would you work out the number of crossings if you have an extra line in your diagram (but you are not allowed to draw the lines)?