Work sample
Mathematics – Year 4
Work sample: Problem solving – Hermit crabs
Relevant part of the achievement standard
By the end of Year 4 students recall multiplication facts up to 10 x 10 and the related division facts. They are
familiar with collections up to 100 000. Students recognise and locate familiar fractions on a number line and
make connections between fraction and decimal notations. They solve problems by using relevant number
sentences involving the four operations.
Students describe the probabilities of everyday events. They investigate different methods for data collection,
construct data displays and evaluate their effectiveness.
Students convert between units of time and solve problems involving time duration. They compare areas
of regular and irregular shapes and classify angles. They create symmetrical patterns and interpret the
information contained in maps.
Summary of task
Students were required to use mathematics to set up a hermit crab project. The investigation required
students to:
•
calculate the total cost of items on a shopping list
•
organise a fundraising stall to cover the costs of items purchased
•
organise helpers for a stall by creating a roster
•
make decisions of how to spend excess funds, using all of the funds available
•
explain their mathematical problem solving strategies
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 4
© ACARA 2010 (except where otherwise indicated).
Page 1 of 5
Work sample
Mathematics – Year 4
Work sample: Problem solving – Hermit crabs
Annotations
Constructs number sentences and calculates
correctly.
Work sample – November 2010
Year 4
© ACARA 2010 (except where otherwise indicated).
Page 2 of 5
Work sample
Mathematics – Year 4
Work sample: Problem solving – Hermit crabs
Annotations
Correctly calculates the number of sausages
(however, use of $ sign is inappropriate).
Incorrectly calculates the number of packs of
sausages.
Uses incorrect logic in calculating the number of
loaves. The number sentence does not reflect the
information provided.
Correctly calculates the amount of money raised.
Work sample – November 2010
Year 4
© ACARA 2010 (except where otherwise indicated).
Page 3 of 5
Work sample
Mathematics – Year 4
Work sample: Problem solving – Hermit crabs
Annotations
Calculates time duration correctly (three of the four
time duration calculations are correct).
Makes errors in the placement of crosses.
Work sample – November 2010
Year 4
© ACARA 2010 (except where otherwise indicated).
Page 4 of 5
Work sample
Mathematics – Year 4
Work sample: Problem solving – Hermit crabs
Annotations
Correctly calculates and recognises that all of the
$10.00 needs to be spent.
Demonstrates understanding of spending exactly
$10.00 but fails to use mathematical explanation.
For example, there is no discussion of the need
not to include one of the 2.00 pens which would
result in $0.50 below $10.00 and hence the
inclusion of a $2.50 pen.
Annotation summary
This work sample demonstrates an understanding of problem solving strategies, but several calculations are
incorrect.
Acknowledgement:
ACARA acknowledges the contribution of the Queensland Studies Authority in providing this task, work samples and annotations. The annotations were
modified by ACARA to reflect the Australian curriculum achievement standards.
Work sample – November 2010
Year 4
© ACARA 2010 (except where otherwise indicated).
Page 5 of 5