In this Cyberchase video segment, Harley convinces Harry to help put up a fence in their grandmother's backyard. With no instructions other than to put up the fence in the shape of a rectangle, Harry must figure out how to do this with different lengths of fencing. He breaks the problem down by adding up different combinations of pieces and then drawing a diagram to figure out where to place the pieces.
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.
HARRY: Oh, hello Harley. What's up?
HARLEY: I'm building a fence for Grandma and I need your help.
HARRY: Gee, I'm on my way to Coney Island to go on some rides before it closes.
HARLEY: The deer keep eating her vegetables.
HARRY: I already made plans with Jenna.
HARLEY: It's not for me, it's for Grandma.
HARRY: Ok. I'll be right over.
HARLEY: Well, it's about time you showed up. I've done all the hard work already.
HARRY: It's only been about ten minutes since you called.
HARLEY: I'll be back in a little while -- I'm gonna buy some paint. While I’m gone, just put up the fence. All you have to do is put up the other three sides and make a rectangle.
HARRY: Which pieces go where??? What did Harley say??
HARLEY: All you have to do is put up the other three sides and make a rectangle.
HARRY: Let’s see, twelve feet. If it’s a rectangle, that means the two opposite sides have to be the same length. Harley already did one side.
If this side is twelve feet, then that side has to be twelve feet as well. But what about the other two sides?
There are five pieces of fence left -- one eight-foot section, one six-foot section, one four-foot section and two three-foot sections. I have to make the other twelve-foot side and the two ends of the rectangle from the pieces that are left.
I know that one side is 12 feet. If I combine an eight-foot section with a six-foot section, that equals fourteen, and that's too long. 6+4=10 – that’s too short. 4+3+3 = 10 – that’s also too short. But if I take an eight-foot section with a four-foot section, that equals twelve and can make the other twelve-foot side. And for the ends I have one six-foot piece for one side and two three-foot sections for the other. Perfect.
The string is a guide to show where the fence goes. This tool makes sure the corners are square.
CATE: Nice fence.
CATE: Where's the gate?
CATE: Grandma’s gonna be really mad. She paid Harley $500 and there's no gate. Grandmaaaa!
Academic standards correlations on Teachers' Domain use the Achievement Standards Network (ASN) database of state and national standards, provided to NSDL projects courtesy of JES & Co.
We assign reference terms to each statement within a standards document and to each media resource, and correlations are based upon matches of these terms for a given grade band. If a particular standards document of interest to you is not displayed yet, it most likely has not yet been processed by ASN or by Teachers' Domain. We will be adding social studies and arts correlations over the coming year, and also will be increasing the specificity of alignment.