Going fishing

Going fishing

Pencil and paper
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This task is about solving maths problems with proportions.
illustration: two girls fishing
Chloe and Jess went fishing together.

a)

The first fish Chloe caught weighed 9 kg.   After the head was removed the body weighed only half as much.   

 

What was the weight of the head? __________ kg

 

b) Chloe and Jess each caught a fish, together they weighed 12 kg.   If Chloe's fish weighed twice as much as Jess's, what did each fish weigh?
  
 
i)
 
ii)
Chloe's fish __________ kg
 
Jess's fish __________ kg
   

c)

Chloe caught another fish.   When its head and tail were removed it weighed two-thirds of what it did before.   

If the head and tail weighed 2.5 kg, what did the fish weigh to begin with?

 

__________ kg

  

d)

Jess ended the day by catching an enormous fish, weighing 21 kg.   

The tail weighed half as much as the head, and the head weighed half as much as the body.   

 

What did the body weigh?__________ kg

Task administration: 
This task is completed with pencil and paper.
Levels:
4, 5
Keywords: 
Description of task: 
Students calculate the weight of parts of a fish from given proportions.
Learning Progression Frameworks
This resource can provide evidence of learning associated with within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
   Y10 (09/1998)
a)   4.5 very easy
b) i)
ii)
8
4
very easy
very easy
c)   7.5 moderate
d)   12
[t + 2t + 4t = 21; or b + 12 b + 1b = 21]
moderate
Diagnostic and formative information: 
  Student response Likely calculation Likely reason
b) i)
    ii)
9
3
3c + c = 12 Using three times as much instead of twice.
b) i)
    ii)
24
12
2c + c = 36 Using combined weight for Colin's fish and doubling for Fiona's (correct ratio of weights).
d) 5.25
10.5
15.75
4t = 21 Interpreting the tail as being 14  rather than 17 of the weight.