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
As in Step 6, the pupils can work systematically and then refine the written explanation so that it is clear what the diagrams are showing.
Probing questions
Why did you decide to use this diagram/graph? Did you discount other forms of diagram/graph? Why is this form better?
How has your use of notation and symbols helped you to record your findings?
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.
- What does the table of results show?
- Can you write this down?
- How does it help us to see whether there are incorrect results?
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