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 can predict the sequence of results for the total number of half-time scores.
They make explicit a rule for calculating the total number of possible half-time scores for a given final score.
They can write the rule algebraically.
The formula for finding the number of half time scores is:
Add 1 to each score and multiply the two resulting numbers together.
Example
If the score was 3-2 (3 + 1) x (2 + 1) = 4 x 3 = 12
If the score was m-n (m + 1)(n + 1)
Probing questions
What did you find out in solving this problem/exploring this task?
Did you notice any links with other work you have done?
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.
Ask the pupil to look back at the earlier solutions and explain how the patterns are developing. Then ask them to extend the problem as was started in Step 9 Line Crossing.