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.
Pupils notice that the number of pegs on the outside is always even.
Probing questions
Have you found a pattern? What did you do that helped?
Have you found a solution? How did you do it?
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.
- Draw some diagrams with intersections.
- What do you notice about the number of lines and the number of intersections?
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