SOME SUMIMATIVE PROBLEMS TO TRY
THIS PROBLEM CAN BE USED TO EVALUATE YOUR LEARNING IN CRITERION D: APPLYING MATHEMATICS IN REAL-LIFE CONTEXTS
A farmer wishes to build a pen (enclosure) to protect his chickens from predatory flowers. He wants the chickens to have as much freedom and room to move as possible. The fencing panels come in 1 metre panels (i.e. no decimal values possible, integers only) and he can only afford 100 panels.

The farmer can vary the lengths of the sides of the pen, which will affect the area. Planning restrictions say that the pen must be rectangular and must be in the form provided below because all 4 sides must add to 100m.
Plan for the pen
1. Identify relevant elements of authentic real-life situations.
Explain why as the length of the pen increases, the width decreases.
Explain why the sides of the pen have been labelled as x and (50-x)
Show why the area (y) is represented by the function
y=-x^2+50 x
ii. Select appropriate mathematical strategies when solving authentic real-life situations.
The farmer wants to know what areas he would be able to find for different lengths. By choosing different lengths (values for $x$ ), find the corresponding areas. You may use a table to show your results
iii. Apply the selected mathematical strategies successfully to reach a solution.
Represent the quadratic function on a graph to show how area changes with length
Find the optimum dimensions (both length and width) of the pen for the farmer
iv. Justify the degree of accuracy of a solution How realistic is this problem? Would your answer help the farmer? How dose to the 'real' value can you get with a function?
v. Justify whether a solution makes sense in the context of the authentic real-life situation.
How does this problem relate to other situations where the resources are limited?
In what other similar situations could you use this strategy?