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
Produce all the ways of shading in two squares out of four, six and eight squares - may develop to three squares out of six, etc.
Probing questions
How would you explain to someone else what your results mean?
Is all the information you have gathered here useful?
Why did you decide to use these graphs/diagrams/tables in this way? How have they helped to further your work? How has your use of notation, diagrams, tables and/or graphs helped you to communicate your results?
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.
Look at your table of results:
- Explain to me what it shows and what it means. How would you write this down?
- How would these results help you to explain what happens when you add another line?
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