Understanding / Fluency / Problem-Solving / Reasoning
Measurement and geometry: Equal areas
Summary of task
Students were asked to justify the conditions for when a kite and a trapezium would have the same area.
At this year level understanding includes describing patterns involving indices and recurring decimals, identifying commonalities between operations with algebra and arithmetic, connecting rules for linear relations with their graphs, explaining the purpose of statistical measures and explaining measurements of perimeter and area.
At this year level fluency includes calculating accurately with simple decimals, indices and integers; recognising equivalence of common decimals and fractions including recurring decimals; factorising and simplifying basic algebraic expressions and evaluating perimeters and areas of common shapes and volumes of three-dimensional objects.
At this year level problem-solving includes formulating and modelling practical situations involving ratios, profit and loss, areas and perimeters of common shapes and using two-way tables and Venn diagrams to calculate probabilities.
At this year level reasoning includes justifying the result of a calculation or estimation as reasonable, deriving probability from its complement, using congruence to deduce properties of triangles, finding estimates of means and proportions of populations.
Recalls the area formula for a kite and for a trapezium and expresses the formulas in relation to the given diagrams
Investigates the conditions under which a kite and a trapezium will have the same area by comparing the components of the respective area formulas
Deduces that if a kite and a trapezium are such that the length of one diagonal of the kite is equal to height of the trapezium then, for the areas to be equal, the length of the other diagonal of the kite must be the same as the sum of the lengths of the parallel sides of the trapezium
Chooses appropriate dimensions for a kite and a trapezium to demonstrate the truth of the conclusion reached
Makes a statement that describes and generalises the condition for a kite and a trapezium to have the same area