Teaching Techniques from 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? 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  1 st station: 1. Indicate the length of available fence 2. 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

 2 nd station: 1. Check and complete/correct the work of the previous group 2. Write the constraint equation 3. Write the objective equation in terms of one variable (the length, or the width) Move to the next station

 3 rd 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

 4 th 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