Intermath | Workshop Support

A pen for the pony 

Problem Statement

To make a pen for her new pony, Pam will use an existing fence as one side of the pen. If she has ninety-six meters of fencing, what are the dimensions of the largest rectangular pen she can make?


GPS Alignment

M6M. Measurement

Students will understand the systems of units for measuring perimeter, area, and volume. They will also understand how to measure the volume and surface area of solid figures. Students will understand the systems of units of measuring (customary and metric) and measure quantities efficiently.


M6M1. Students will convert from one unit to another within one system of measurement (customary or metric) by using proportional relationships.


M6M2. Students will use appropriate units of measure for finding the perimeter, area, and volume and express the answer using the appropriate unit.


Problem setup

We drew the one side of the fence that we start with. Then, we drew the sides of the rest of the fence. We put numbers in Excel to see what numbers made the largest fence.


Plans to Solve/Investigate the Problem

Then we realized that one of the students had come up with the right answer at the beginning. She divided 96 in half and it is 48. This is the length of the side of the fence opposite the piece of existing fence, so it is the value of both of these sides. Then she divided the remaining 48 in half to be the length of the other two sides. The number for these sides is 24. 


Investigation/Exploration of the Problem

The formula for Area is A=length x width. So, the area is 48 x 24 which equals 1152m squared. According to the information we gathered on Excel, this is the largest rectangular pen she can make.


Extensions of the Problem

Pam actually has another 3/4 of a foot for fencing. How does this change the dimensions of the pen?

First we must convert 3/4 foot to meters. She just adds this to the total amount of fencing she has. Then she can approach the problem in the same fashion.

Author & Contact
Pam Joseph

Link(s) to resources, references, lesson plans, and/or other materials
Link 1
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