Teaching Techniquesfrom Maria Aronne’s 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?

2 2 1600x w A xw

800w x 2(800 ) 800A x x x x

800400

2 2( 1)

bx

a

800 400 400w

The farmer should make the rectangle 400 yards by 400 yards to enclose the most area. Copyright © 2013 Pearson

Education, Inc. All rights reserved

Gallery Walk

1st station: 1. Indicate the length of available fence2. 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

3. Use L and W for your labels

Move to the next station

2nd station:

1. Check and complete/correct the work of the previous group

2. Write the constraint equation3. Write the objective equation in

terms of one variable (the length, or the width)

Move to the next station

3rd station

1. Check and complete/correct the work of the previous group

2. Use algebra to find the length (or width) of the rectangular field with largest area

3. Find the largest area that can be enclosed

4. Give the dimensions of the rectangle of largest area

Move to the next station

4th station

1. Check and complete/correct the work of the previous group

2. Without the calculator, sketch the graph of the area function

3. Label variables along the axes; include units

4. 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

Quiz without instructions