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.
Example drawn from Shading Squares
Try shading these squares.
Draw at least three different ways of shading two squares out of four.
And then can draw all six ways of shading two squares out of four.
Probing questions
What have you noticed?
Tell me what the diagram(s)/results are showing.
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 three lines so they do not cross.
- Draw three lines so they do cross.
- Show me where they cross.
- You have drawn some diagrams. Tell me how many lines there are and how many crossings (intersections) there are [you could put a large dot at each crossing]