Step 9 Objective

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.
picture of a line art football

Examples drawn from Final Score

Pupils extend the Step 8 example by considering the results for any given full-time score.


Probing questions

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?

diagram showing three lines crossing

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.

  • 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)