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
State there are 15 ways of shading 2 squares out of 6 without repeats.
Probing questions
Which ways of organising information have you found most helpful? How does it help?
What have you found out?
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.
You have drawn different patterns, using three (or four) lines. It gets more complicated when you use even more lines.
- Draw different diagrams for five (or six) lines. Start with those where there are only a few crossings (intersections).
- How can you show that your work is organised?
<< Previous Step | Next Step >>