Mathematics proficiencies

Understanding / Fluency / Problem-Solving / Reasoning

Year 6

Number and algebra: Fractions and decimals and percentages

Summary of task

Students were given the following problem to solve:

‘A school is enclosed by a fence that has sides of equal length. 60% of the whole fence has been painted black. How many different ways can you draw what the fence might look like? Look at each of your drawings and represent the painted section as a fraction. Represent it as a decimal.'


At this year level understanding includes describing properties of different sets of numbers, using fractions and decimals to describe probabilities, representing fractions and decimals in various ways and describing connections between them, and making reasonable estimations.

At this year level fluency includes representing integers on a number line, calculating simple percentages, using brackets appropriately, converting between fractions and decimals, using operations with fractions, decimals and percentages, measuring using metric units and interpreting timetables.

At this year level problem-solving includes formulating and solving authentic problems using fractions, decimals, percentages and measurements, interpreting secondary data displays and finding the size of unknown angles.

At this year level reasoning includes explaining mental strategies for performing calculations, describing results for continuing number sequences, explaining the transformation of one shape into another and explaining why the actual results of chance experiments may differ from expected results.