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
In the diagram for Step 4, the pupils can explain their system to ensure that they do not have repeats.
Probing questions
What have you found out?
Why do you think this is?
How is your use of mathematical notation and symbols improving? Show me some examples.
How is your use of diagrams improving?
Show me some examples?
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 really good diagrams.
- What can you say (see) from the diagrams with four (five) lines?
- What do you call the lines that don't cross each other?
- How would you explain what happens when there are a lot of crossings?
<< Previous Step | Next Step >>