Step 5 Objective

Solve problems and investigate in a range of contexts, explaining and justifying methods and conclusions; begin to generalise and to understand the significance of a counter-example.


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.

Pupils draw different numbers of lines and crossings.

What can you say about the number of crossings when there are a few lines?

Explain what happens to the number of crossings when you get more lines?