M. Sgoriau Hanner Amser
| Introduction |
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| This activity starts with systematic listing, grouping and ordering of pairs of scores in a match. The focus then switches to the total number of results possible for each match, and the multiplicative relationship involved. This allows some pupils to approach advanced generalisations in everyday language or, if appropriate, with algebraic notation. |
| This activity has two episodes. Each episode consists of an introduction, paired or group work and whole class sharing. The session must finish with a whole class reflection phase, regardless of how far the class has got. |
| Episode 1: Possible half-time scores for one final score |
| Children are given a final score in a game and asked for possible half-time scores. They work out all the possibilities, including the nil scores, and the final score itself. This involves realising that the possibilities are mathematical and are unrelated to whether they seem likely or not in a specific game between the two known teams. Children use a systematic approach to ensure that no half-time score is missing or repeated. Small groups of children work on generating half-time scores for two different final scores, ensuring they are systematic in some way. Some children are asked to work with larger scores. Children are encouraged to think about several ways to list the scores. The sharing phase focuses on recording, in this case, keeping the first number the same while changing the second, or vice versa, or starting with 0 – 0, 1 – 1, followed by the rest, and the advantages of each. |
| Episode 2: Relating the total number of possibilities to the final score |
| The attention now shifts to the total number of possibilities for any given final score. Children look for patterns in the results they have generated so far, both in their groups and as a class. The question ‘What happens to the total of possible half-time scores when we increase one of the final scores by 1?’ is posed. And the suggestion is made that they start with 3 – 3 and then work out the possibilities for 3 – 4 and 3 – 5. Children talk about the mathematical features they are working with and any relationship they find between them. They see the additive relationship and begin to see the multiplicative relations involved for individual scores. Some children may recognise a rule that applies to any number. They will be asked to put this into words and explain why it works. |
| Reflection |
| Children describe how they have been systematic and how they attempted to reach some general means for calculating the total number of scores possible. |
| BEFORE YOU TEACH |
| Work with the class on a single example of a final score first, then discuss ways to list possible half- time scores systematically. Do not progress to the total number of possibilities until you are confident that the children can work systematically. |