Step 9 Objective
Show some insight into mathematical structure by using pattern and symmetry to justify generalisations, arguments or solutions.
- Examples of what pupils should
know and be able to do - Probing questions
- What if pupils find
this a barrier?
What if pupils find this a barrier?
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 pattern as you add another line; how many extra crossings does it make?
- Why can’t there be any more crossings? Can you explain why?
- If you had 12 lines and you added one more line, what would be the greatest number of possible crossings? Why?