Examples of what pupils should know and be able to do
Shading Squares
There are six different ways to shade two squares in this shape.
Can you find them all?
What about this shape?
How many ways are there?
Try using different rectangles made up of more squares.
Try shading three squares.
Examples drawn from Shading Squares
Show evidence of using a systematic approach in finding several pairs when shading two squares out of 6.
Probing questions
Why did you...?
How did your diagrams/table/graph help?
What other diagrams did you think of using?
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.
- For each diagram explain how many lines and how many crossings there are. Write this down next to each diagram.
- What is the best way of writing this information down?
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