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# Step 1

Try different approaches to solve a problem

### 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 list some possible half-time scores if the final score is 1-1.

### Probing questions

• How did you decide what to do?
• How did you go about exploring/solving this problem?
• Could you solve this problem in a different way? How?

### What if pupils find this a barrier?

#### Use 'Line crossings investigation'

• What happens if you used four (or five) lines instead of the three?
• How did you count the line crossings?

#### 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.