Measurement and geometry: The combined area of spaces
Summary of task
Students were asked to solve the following problem:
‘The school has been donated 36 square metres of artificial grass that need to be laid in the upper playground to create two quiet areas. Draw at least two possible solutions on grid paper displaying the shapes of the two grass areas. One grass area cannot be a rectangle. Out of your two solutions, which layout would be more appropriate for the users and why?’
Proficiencies
At this year level problem-solving includes formulating, modelling and recording authentic situations involving operations, comparing large numbers with each other, comparing time durations and using properties of numbers to continue patterns.
At this year level reasoning includes using generalising from number properties and results of calculations, deriving strategies for unfamiliar multiplication and division tasks, comparing angles, communicating information using graphical displays and evaluating the appropriateness of different displays.
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Annotations
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Understanding
Applies knowledge of geometrical shapes and of area in analysing and investigating the problem -
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Problem-Solving
Designs two sets of areas each totalling 36 square metres (as required) as potential solutions to the problem -
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Reasoning
Evaluates the two solutions and provides a justification for choosing the second set of areas as the better solution