Reason from reading and examining a drawing
NCTM Standards:
 Standard 1 Numbers and Operations
 Standard 6 Problem Solving
 Standard 7 Reasoning and Proof
 Standard 8 Communication
 Standard 9 Connections
 Standard 10 Representation
Note to teachers:
This activity can be modified for elementary students by providing the number of sections and posts required for each pattern of fencing.
Fencing the Yard
A couple is planning to erect a fence on three sides of their property. Figure 1 shows the shape of their property and provides the dimensions of the three sides they want to fence.
Figure 1. The couple's property, with the dimensions of the sides to be fenced.
The couple can purchase the fencing they have chosen in standard eightfoot lengths that are six feet high. They can also use a catalog to customorder shorter lengths of this fencing. The manufacturer of the fencing materials recommends using 4 in. x 4 in. treated lumber 10 ft. long for the fence posts and 6 in. x 6 in. treated lumber 10 ft. long for the corner posts.
In their design, the couple plans to use as many eightfoot standard pieces as possible to keep costs to a minimum, but they want to maintain symmetry so that the fencing looks good.
Figure 2. Example of the symmetry the couple wants.
To determine the number of standard 8ft. sections they need, the couple divided the length of each side of the lot by 8. When they divided the 100foot side by 8, they found they would need 12 eightfoot sections and 1 fourfoot section. To be symmetrical, the fence has to be constructed with equal amounts on each end of the fencing along the 100foot length. Because 2foot sections are not available in the catalogue and to maintain symmetry on the 100foot side, the couple decides to use 11 8foot sections and 2 6foot sections.
If they have a budget of $5500 for the fencing, which of the designs can the couple buy? Use the information in the tables to help you make your determination.
Description 
Standard 
Price 
Custom 
Price 
Solid 1 x 4 Red Cedar 
6 ft. x 8 ft.. 
$76.50 
6 ft. x 6 ft. 
$60.00 
PeekABoo 1 x 4 Red Cedar 
6 ft. x 8 ft.. 
$62.25 
6 ft. x 6 ft. 
$48.75 
Board by Board 1 x 4 Red Cedar 
6 ft. x 8 ft.. 
$85.00 
6 ft. x 6 ft. 
$65.50 
Basket Weave 1 x 4 Red Cedar 
6 ft. x 8 ft.. 
$70.00 
6 ft. x 6 ft. 
$55.50 
Basket Weave with Topper 
6 ft. x 8 ft.. 
$88.00 
6 ft. x 6 ft. 
$69.50 
4 in. x 4 in. treated lumber 
10 ft. 
$10.89 


6 in. x 6 in. treated lumber 
10 ft. 
$23.60 


Description 
Custom 
Price 
Custom 
Price 
Solid 1 x 4 Red Cedar 
6 ft. x 5 ft. 
$49.50 
6 ft. x 4 ft. 
$40.00 
PeekABoo 1 x 4 Red Cedar 
6 ft. x 5 ft. 
$40.00 
6 ft. x 4 ft. 
$33.50 
Board by Board 1 x 4 Red Cedar 
6 ft. x 5 ft. 
$55.50 
6 ft. x 4 ft. 
$45.50 
Basket Weave 1 x 4 Red Cedar 
6 ft. x 5 ft. 
$46.50 
6 ft. x 4 ft. 
$38.00 
Basket Weave with Topper 
6 ft. x 5 ft. 
$60.00 
6 ft. x 4 ft. 
$48.00 