Examples of what pupils should know and be able to do
Hollow Squares
Here is a hollow square.
- How many pegs form the square on the outside?
- How many pegs are there in the hollow?
- Draw some more hollow squares.
- Investigate.
Examples drawn from Hollow Squares.
As in Step 6 but with mathematical explanations about the patterns in the results.
Probing questions
How would you convince a friend... a penpal?
How would you convince me?
Does this work for any value? How do you know?
What special cases should you check?
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.
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