Mathematics Assessment Map – Sample at Level 5
Soccer tournament
Context
Students were asked to explain a procedure for working out the number of matches to be played in a soccer tournament (i.e. a ‘round robin’ tournament) where each of ten teams is to play every other team once only.
The element of the Working mathematically standard addressed by the task is:
Students develop simple mathematical models for real situations.
Stimulus
Dr Maths: Soccer tournament
Help Dr Maths answer this perplexing question:
Dear Doc
I’ve been put in charge of organising a soccer tournament, involving ten teams. How many games will be played in the tournament, if each team plays each other team once? This information will be a great help with my scheduling. Please show me how to work it out so that I can answer similar questions for myself in future.
Your friend,
Soccer Sam
Sample
The following samples illustrate the kinds of responses that students typically produce when they have achieved the elements of the standard addressed by this task.
Sample A
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Sample B
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Annotation
Working mathematically – Level 5
Sample A
- The student identifies that the solution is equivalent to the sum of the first n – 1 whole numbers, where n = 10, without listing each combination explicitly.
Sample B
- The student uses a geometric model to assist in explaining the multiplication principles applied, including the division by 2 to eliminate repetition.
Element of Working mathematically
Students develop simple mathematical models for real situations.
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