|
To encourage a systematic way of working.
To compare a range of recording formats.
To develop a generalisation based first on addition and then on multiplication.
|
| Resources |
Vocabulary |
|
A3 paper – two or three sheets per table
Felt tip markers
|
possible, impossible, certain, nil,systematic, relationship, pattern |
| Organisation |
|
Near ability small groups at each table
|
| Whole Class Preparation: (about 10 mins) |
Decide on sport involving two teams: football, netball, or rounders, for example.
The school team plays a match at home. They win 2-1. Why does the 2 come first? Home team.
What are possible half-time scores for this match? 1 – 0, 1 – 1. List suggestions on the board as
they are called out.
What does ‘nil’ mean? What does ‘one-all’ mean?
What score is always a possibility at half-time, whatever the final outcome? 0 – 0. Why?
What would be an impossible half-time score for a 2 – 1 win? 2 – 3. Why?
Ensure that pupils know that the final score is also a possibility at half-time.
|
| Group Work: (about 10 mins) |
What about a final score of..? Give two different scores to each table, for example, 2 – 3, 4 –
2, 3 – 2, 2 – 4, 3 – 3, 4 – 4, depending on ability).
Ask yourselves how you know that you have got all the possible half-time scores. Check whether
you have written down any twice by mistake or if you have missed any out.
Be sure to record your results in a systematic way and be ready to tell others how you did this.
|
| Class Sharing: (about 5-10 mins) |
Look at the scores 2 – 3 and 3 – 2. Children compare and report back on how many possible
half-time scores they found and how they recorded them.
Ask children to demonstrate different methods on the board, particularly those who have missed possible scores out. Why did we miss some out?
How many possibilities are there for the half time score? Record 12.
Take contributions from other groups with different final scores. Emphasise the value of systematic methods.
Find all the possible scores for 3 – 1, using someone else’s systematic method. Allow about 2 minutes. List results on the board.
|
| Small Group Work: (about 15 mins) |
|
Ask the children to look for patterns or relationships in the results of the scores tried so far, some from their groups and some from those on the board.
Test these relationships using a range of scores, including one involving nil.
Jot down what you have noticed
What happens to the total of half-time scores when we increase the final score of one of the teams by 1? Ask children to try 3 – 3, then 3 – 4, then 3 – 5.
|
| Class Sharing: (about 10 mins) |
|
Collect two or three examples of systematic recording on the board. Which of these helps us to predict the number of possible half-time scores easily?
What if we have a big score like 99-5? Can you explain this in words?
Can you see some relationship between the final number of possibilities and the final score of each of the two teams?
Can you now express this using the letters h and a? (h + 1) x (a + 1)
Think about what you have done. Describe your ways of being systematic and how you tried to come up with a rule.
|
