Resource: Building a Fence

Print Background Essay

This video segment dramatizes the following word problem: Harry is asked to build a rectangular fence in his grandmother's backyard. His cousin Harley has already erected one side of the rectangle, and it measures 12 feet in length. Five pieces of fencing remain to construct the other three sides of the rectangle: one 8 ft. piece, one 6 ft. piece, one 4 ft. piece, and two 3 ft. pieces. How should he arrange these pieces?

When faced with a challenging construction or design project, it is often most efficient to break the project into steps. Sometimes the appropriate plan of action is not immediately apparent, and it takes some brainstorming and sketching to figure out how to proceed.

There are many steps you can take to break a problem into parts. The first step is to look at the given information. It may be helpful to record it on paper if there is a lot of information. The next step is to identify the problem. That is, what are you trying to achieve? Then look at the given information and determine if you have all the data necessary to solve the problem. If not, gather any additional information you think may be missing. It is possible that there is some given information that will not be used at all. At this point it may also be possible to use the data to estimate the solution. Later in the process, the actual answer can be compared with this initial estimation as a way to do a quick check for accuracy.

The next step is to determine the strategy for solving the problem. This may include drawing a diagram, writing an equation, performing calculations, or recognizing possible solutions to be tested using a model or the guess-and-check method. Once the strategy has been chosen, it must then be carried out, or tested, until a solution is reached. It is worth noting that in some cases, there will be more than one solution to the problem.

Once a solution has been found, it is worth examining it to make sure it is a reasonable solution. Suppose the problem involved finding the average age of a classroom of students and your solution was 145 years old? That answer should alert you to the fact that you made a mistake in your calculations. Another way to check your result is to compare it to the initial estimate.

To learn more about quadrilaterals, check out Perimeter and Area Together, Skate-Off: Round One, and Skate-Off: Final Round, Inez vs. Rimm.

To learn more about the design process, check out What Is the Design Process? and Design for Function.

Print Questions for Discussion

• The pieces of fence given are 8 ft, 6 ft, 4 ft, 3 ft, and 3 ft long. Using these pieces, how did Harry form the rectangle?
• What tools were helpful in putting up this fence? What if you didn't have one of the tools, can you think of something else you could use instead?
• Harry made a rectangular fence. Could he have made a fence of a different shape using the pieces he was given? If so, list the other shapes and label the length of the sides. 
• Harry forgot to include a gate. How would his design process have been different if he knew that a 3 ft. gate would have to be installed?
• Have you ever built something? What steps did you go through? What tools did you use? Did you use a drawing or a model?