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# Step 9

Represent problems and synthesise information in algebraic, geometric or graphical form; move from one form of presentation to another to gain a different perspective on the problem/task

### Examples of what pupils should know and be able to do

There are six different ways to shade two squares in this shape. Can you find them all?

Try using different rectangles made up of more squares.

Try shading three squares.

#### Examples drawn from 'Shading squares'

Pupils explain why they have chosen a particular presentation. The presentation may be symbolic or diagrammatic, as with the Shading Squares activity.

### Probing questions

• How does this representation link to this other one? What does each tell you?
• What does this form tell you that the other forms cannot?

### What if pupils find this a barrier?

#### Use 'Line crossings investigation'

Look at your table of results.

• Can you explain a rule for finding the number of intersections for any number of lines?
• How would you write this down?

#### Line crossings investigation

• 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.