Step 3 Objective

Begin to refine ways of recording and use appropriate mathematical symbols correctly.


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.

  • Draw other diagrams using only four (or five) lines; how many different numbers of intersections (crossings) can you get?
  • How many more diagrams with a different number of intersections can you draw using four (or five) lines?
  • How might you record the maximum number of crossings for three, four, five lines?
  • Are there other ways?