Step 10 Objective
Examine critically, improve and justify the choice of mathematical presentation, explaining features selected.
- 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.
(Pupils have rule (n/2)(n − 1) or the rule in words.)
- That is a good rule; explain to me what it means.
- Why is this rule more useful than drawing diagrams and counting intersections?
(Pupils have explained that for every extra line, the number of extra crossings is one less than the new total number of lines.)
- Can you explain why this (algebraic) rule is more helpful in finding the number of crossings than just adding the number of extra crossings each time? Can you write that down?