I. Clybiau mini
Introduction |
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An activity based on a game with some of the features of golf. Children multiply ‘weights’ and ‘strengths’ to give ‘distances’ and then add those distances. The focus then switches to systematic generation of numbers, leading to the construction and analysis of tables that list all the combinations of two given sets of numbers. |
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 : Imagining a game stripped to its mathematical essentials |
Children recall their existing knowledge of golf. They imagine a number game where the clubs are denoted as a set of weights (2, 4, 6, 8, 10), while a 'stroke' is a set of strengths (1/2,1,3,5,7). Explain that we are going to find the distance the ball travels, and that each distance is a product of a weight and a hit strength: so a club of weight '4', hit with a strength '3' produces a distance of 12. Children use their own strategies involving multiplication and either addition or subtraction to cover some pre set distances using club weights and hit strengths. Children then share their strategies. Bracketing, if used, is made explicit. They recognise that some numbers can be arrived at with one stroke, and that different methods of arriving at the same number are efficient to varying degrees. |
Episode 2: Exploring systematic enumeration |
Children list all the distances it is possible to reach with one stroke and prove that some distances in the range of numbers 1-100 cannot be covered this way. They work on systematic listing by strengths or by weights and recognise that combining ordered lists produces a two-way table that is similar to the multiplication table. This needs to be analysed for repeats and for impossible distances. Higher attainers can be asked to combine two strokes in addition and subtraction. They can explore the patterns of generating numbers in the tables, symmetry and contours, and the possibility of redundant or less useful clubs or stroke strengths. |
Reflection |
Children recognise that they have progressed from dealing with single examples to an overall system. They compare the two-way table with the one created in the Sports League lesson. |
BEFORE YOU TEACH |
The focus is on generating numbers using multiplication and addition, rather than practising number skills. Later this is shifted to strategies for calculation of all possibilities. Children can use a calculator. |