- Starting from given problems or contexts, progressively refine or extend the mathematics used to generate fuller solutions
Examples of what pupils should know and be able to do
Final score investigation
The final score in a football game was 2–1.
- List possible half-time scores.
- How many are there?
- Investigate other final score.
Examples drawn from 'Final score'
Pupils extend the Step 8 example by considering the results for any given full-time score.
- How did you extend your task?
- How did you use the answer to the initial problem to help solve the fuller problem?
- Explain how your final solution can be used to solve your first problem.
What if pupils find this a barrier?
Use 'Line crossings investigation'
- How would you work out the number of crossings if you have an extra line in your diagram (but you are not allowed to draw the lines)?
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.