Step 10 Objective
Appreciate the difference between mathematical explanation and experimental evidence.
- 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.
The maximum number of crossings is (n/2)(n − 1), or explained fully without using algebra.
- When you add another line how many extra lines are there? Can you use algebra to explain this?
- Can you explain how you work out how many crossings there are altogether? (If pupils explain 1+2+3+4+5+6, etc., ask if they can explain how they can add this quickly; there are three pairs of 7 [1+6, 2+5, 3+4]).