Cuboid fish tanks

Cuboid fish tanks

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Marking Student Responses
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This task is about working out the volume of different cuboids given the height, length and width.
a)
Find the volumes of the fish tanks marked A, B, and C.
 
 
 
Tank A: ____________ cm3        Tank B: ____________ cm3       Tank C: ____________ cm3
 
b)
How many millilitres of water would each of the three tanks hold?
 
 
 
Tank A: ___________ ml         Tank B: ___________ ml         Tank C: ___________ ml
 
c) i)
Which two tanks could be filled to the top from a bucket holding 29 litres of water without overflowing?
 
Tanks __________ and __________ 
 
  ii)
Providing there were no spills, how much water would be left in the bucket after the two tanks had been filled?
 
_______________
 
d) i) If the volume of water from each tank was tipped into a bigger bucket that weighed 1 kg when empty, what would this bucket weigh with all the water in it?
    (A) Less than 50 kg
    (B) Between 51 kg and 60 kg
    (C) Between 61 kg and 70 kg
    (D) More than 70 kg
 
  ii)
Explain how you worked out your answer. Show your working.
 
 
 
 
Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Keywords: 
volume, capacity, cuboids, conversion of units, weight
Description of task: 
Students calculate the volume of three different cuboid-shaped fish tanks given the height, length and width.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Measurement sense, sets 7-8
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y8 (10/1996)

Y9 (10/1996)
a)   Volume A = 14400 cm3
Volume B = 12000 cm3
Volume C = 18000 cm3		 difficult
difficult
difficult		 moderate
moderate
moderate
b)   Tank A = 14400 ml
Tank B = 12000 ml
Tank C = 18000 ml
[If answers to b) are identical to a) the mark should be given.]		 very difficult
very difficult
very difficult		 difficult
difficult
difficult
c) i)
ii)		 Tanks A and B
2.6 litres of water would be left.
(29 – 14.4 – 12.0) litres		 very difficult
very difficult		 difficult
very difficult
d) i)
ii)		 A
The principle to be applied is that 1 litre of water weighs 1 kg + weight of empty bucket.
volume is:
12 l + 14.4 l + 18 l = 44.4 l
weight is:
12 kg + 14.4 kg + 18 kg + 1 kg bucket = 45.4 kg		 very difficult
very difficult		 very difficult
very difficult
Diagnostic and formative information: 
  Common errors Likely calculation Likely reason
a)
 
d)		 92, b) 70, c) 80
 
B & C, 1 litre remains		 90 = 60 + 20 + 12 Adds dimensions rather than multiplying them, i.e., 92 = 60 + 20 + 12
Fills bucket from tanks rather than tanks from bucket. Incorrect interpretation of question.