Transcript Teaching Techniques from my classroom

A farmer has 1600 yards of fence to enclose a rectangular field. What
are the dimensions of the rectangle that encloses the most area?
A  xw
2 x  2 w  1600
w  800  x
A  x (800  x )   x  800 x
2
x
b

800
 400
w  800  400  400
2a
2(  1)
The farmer should make the rectangle 400 yards by 400 yards to
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enclose the most area.
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1st station:
Indicate the length of available fence
Design the rectangular field to be fenced
1. Fence three or four sides and place some
interior fences
2. Should be a different design than your
neighbor’s field
Use L and W for your labels

1.
2.
3.
Move to the next station
 2nd
1.
2.
3.
station:
Check and complete/correct the work
of the previous group
Write the constraint equation
Write the objective equation in
terms of one variable (the length,
or the width)
Move to the next station

1.
2.
3.
4.
3rd station
Check and complete/correct the work of
the previous group
Use algebra to find the length (or
width) of the rectangular field with
largest area
Find the largest area that can be
enclosed
Give the dimensions of the rectangle
of largest area
Move to the next station
 4th
1.
2.
3.
4.
station
Check and complete/correct the
work of the previous group
Without the calculator, sketch
the graph of the area function
Label variables along the axes;
include units
Label relevant points
 What
if there are more than 4
groups in the class?
 Other
groups are seated using
different color paper.
 Instead
of circulating students,
circulate the papers


Optimizing area
What do we need to be given?
◦ Length of fence = _________

What else we need to be given?
◦ Design of field

Show all work related to this type of problem