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
Produce some (but not necessarily all) possible half-time scores for a
final score of 2-1 and at least one other final score.
Final score 2-1
There are 6 possible half-time scores
1-0, 0-0, 2-0, 1-1, 2-1, 0-1.
Final score 5-3
There are 24 possible half-time scores
4-2, 1-0, 2-2, 1-1, 0-0, 3-3,
4-1, 4-3, 5-1, 5-2, 5-3, 2-3,
1-2, 1-3, 0-1, 0-2, 0-3.
Final score 3-3
There are 16 possible half-time scores
0-0, 0-1, 0-2, 0-3, 1-1, 1-2, 1-3,
2-1, 2-2, 2-3, 3-1, 3-2, 3-3.
Probing questions
Why did you decide to approach the problem in this way? Tell me how you broke down the problem or calculation into simpler steps. What information did you need to carry out the tasks?
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.
Look at the different diagrams you have drawn with six (or five or ...) lines
- Which one has the fewest (or most) crossings?
- Explain how you may get more (or fewer) crossings.
- What type of diagram will give you the fewest (most) crossings for any number of lines?
- What different types of diagram can you draw to get different numbers of crossings?
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