Work sample
Mathematics – Year 9
Work sample: Solving problems related to volume and capacity – Water supply
Relevant part of the achievement standard
By the end of Year 9, students express numbers in scientific notation and apply the index laws to numbers.
They expand and factorise algebraic expressions .and solve problems involving simple interest. Students
solve linear equations using graphical and algebraic techniques.
Students list outcomes, assign and determine probabilities for events. They construct displays and
investigate the position of the mean and median and describe the shape of the distribution.
Students calculate areas of shapes and volume and surface area of right prisms. They investigate similar
and congruent triangles and problems involving Pythagoras’ theorem. Students recognise the connection
between similarity and the trigonometric ratios and use trigonometry to solve right-angled triangle problems.
Summary of task
Students were required to plan how to make the best use of available rainwater. They were asked to use
mathematical reasoning to:
•
predict how much rainwater could be collected from a roof each month using local rainfall data
•
develop an appropriate rainwater use plan and choose a suitable rainwater tank
Student attainment of the achievement standard is determined at the end of a reporting period after
reviewing relevant assessment evidence.
Work sample – November 2010
Year 9
© ACARA 2010 (except where otherwise indicated).
Page 1 of 10
Work sample
Mathematics – Year 9
Work sample: Solving problems related to volume and capacity – Water supply
Annotations
Calculates the volume of
the cylinder correctly.
Work sample – November 2010
Year 9
© ACARA 2010 (except where otherwise indicated).
Page 2 of 10
Work sample
Mathematics – Year 9
Work sample: Solving problems related to volume and capacity – Water supply
Annotations
This part is not attempted.
Calculates correctly, but
sets out poorly. There are
incorrect equivalencies.
Work sample – November 2010
Year 9
© ACARA 2010 (except where otherwise indicated).
Page 3 of 10
Work sample
Mathematics – Year 9
Work sample: Solving problems related to volume and capacity – Water supply
Annotations
Calculates volume
accurately and uses
correct units.
Work sample – November 2010
Year 9
© ACARA 2010 (except where otherwise indicated).
Page 4 of 10
Work sample
Mathematics – Year 9
Work sample: Solving problems related to volume and capacity – Water supply
Annotations
Calculates the volume
of the triangular prism
correctly.
Draws an accurate
conclusion from the
information.
Work sample – November 2010
Year 9
© ACARA 2010 (except where otherwise indicated).
Page 5 of 10
Work sample
Mathematics – Year 9
Work sample: Solving problems related to volume and capacity – Water supply
Annotations
Recognises the need to
convert units to complete
the calculation.
Calculates the volume of
water in cubic metres and
correctly converts to litres.
Work sample – November 2010
Year 9
© ACARA 2010 (except where otherwise indicated).
Page 6 of 10
Work sample
Mathematics – Year 9
Work sample: Solving problems related to volume and capacity – Water supply
Annotations
Correctly calculates the
expected rainfall.
Work sample – November 2010
Year 9
© ACARA 2010 (except where otherwise indicated).
Page 7 of 10
Work sample
Mathematics – Year 9
Work sample: Solving problems related to volume and capacity – Water supply
Work sample – November 2010
Year 9
© ACARA 2010 (except where otherwise indicated).
Page 8 of 10
Work sample
Mathematics – Year 9
Work sample: Solving problems related to volume and capacity – Water supply
Annotations
This is not a clear
statement as there is not a
direct relationship between
the average monthly
rainfall collected and the
number of litres.
Work sample – November 2010
Year 9
© ACARA 2010 (except where otherwise indicated).
Page 9 of 10
Work sample
Mathematics – Year 9
Work sample: Solving problems related to volume and capacity – Water supply
Annotations
These statements relate
to the sustainability priority
evident in the Australian
curriculum.
Supports conclusions with
accurate calculations and
information.
Annotation summary
This work sample demonstrates a sound knowledge of area, volume and surface area.
Acknowledgement:
ACARA acknowledges the contribution of trial school teachers and students in providing the tasks and work samples. The annotations written by ACARA
are referenced to the Australian curriculum achievement standards.
Work sample – November 2010
Year 9
© ACARA 2010 (except where otherwise indicated).
Page 10 of 10