Working out stock rates

Working out stock rates

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about solving maths problems involving rates.
illustration: sheep in a farm paddock
 

Tana has a paddock on each side of his house.
The table shows the area of each paddock, and how many sheep are in each.
 

 

 Paddock Name
East West South North
Area (in hectares) 3.7 18.4 6.4 5.7
Number of sheep 23 128 50 36
  
The stock rate is the number of sheep per hectare.
 
a) What is the stock rate of
 
 
i)
 
ii)
the North paddock? __________ sheep per hectare (to 1 d.p.)
 
the South Paddock? __________ sheep per hectare (to 1 d.p.)
 
b)
What is the overall stock rate over all four paddocks?
 
 
 
 
 

Overall stock rate = __________ sheep per hectare (to 1 d.p.)

 
c)
The maximum recommended stock rate for winter is 7 sheep per hectare.
How many sheep need to be shifted from the South paddock for winter?
 
 
 
 
There will need to be __________ sheep shifted.
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Keywords: 
rates
Description of task: 
Students work out the stock rate (number of sheep per hectare) for a farm and use it to determine the maximum number of sheep for the winter.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Multiplicative thinking, sets 8-9
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
   

Y10 (08/2000)

a)

i)
ii)

6.3
7.8

moderate
moderate

b)

  

6.9 [accept 6.9 to 7.0]

very difficult

c)

  

6 sheep

very difficult
 
Diagnostic and formative information: 
 

Common error

Likely calculations

Likely reason

b)

6.8

Averages the four rates rather than calculating the overall rate.
Next steps: 
Extension
Ask students:
Can Tana redistribute the sheep over the four paddocks so that no paddock is overstocked?
 
Answer:
No – If each paddock can never have more than 7 sheep per hectare.
Yes – If the average stock rate on each field is to be less than 7 (i.e., sometimes a field can be overstocked and sometimes understocked by rotating the sheep) because the average stock rate is less than 7.