Step 7 Objective
Use logical argument to establish the truth of a statement; begin to give mathematical justifications and test by checking particular cases.
- 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.
- Put all of your results (for greatest number of crossings) into a table.
- What patterns can you see? How would you explain them?
- Look at your table/pattern, how might you know if some of your results are wrong?
With 5 lines I can draw a lot of patterns with different number of crossings.
When lines are parallel there are no crossings.
You have to be careful because if you make some lines longer they will cross other lines.
The more jumbled the picture the more crossings there are.
