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.'

Proficiencies

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.

1 Fluency
Connects the concepts of percentage, fraction and decimal by accurately representing 60% as a fraction and a decimal and explains why the representations are equal 2 Problem-Solving
Chooses the side length of the square to be 5 metres, with the explanation that ‘it is easy to figure out 60% of 20’ following calculation of the perimeter of the square (20 metres) 3 Reasoning
Justifies the choice of a square as an appropriate shape for the area to be fenced 4 Understanding
Accurately calculates 60% of the perimeter of the fence (painted part) to be 12 (metres) and accurately represents the length of the painted part on a diagram representing the fence 5 Understanding
Recalls that the square and the regular pentagon are shapes that have all of their sides of equal length 6 Reasoning
Justifies the choice of a regular pentagon as an alternative shape for the area to be fenced and correctly identifies the number of sides of the fence (3 of 5) that would be painted

  • Annotations

  • 1
    Fluency
    Connects the concepts of percentage, fraction and decimal by accurately representing 60% as a fraction and a decimal and explains why the representations are equal
  • 2
    Problem-Solving
    Chooses the side length of the square to be 5 metres, with the explanation that ‘it is easy to figure out 60% of 20’ following calculation of the perimeter of the square (20 metres)
  • 3
    Reasoning
    Justifies the choice of a square as an appropriate shape for the area to be fenced
  • 4
    Understanding
    Accurately calculates 60% of the perimeter of the fence (painted part) to be 12 (metres) and accurately represents the length of the painted part on a diagram representing the fence
  • 5
    Understanding
    Recalls that the square and the regular pentagon are shapes that have all of their sides of equal length
  • 6
    Reasoning
    Justifies the choice of a regular pentagon as an alternative shape for the area to be fenced and correctly identifies the number of sides of the fence (3 of 5) that would be painted