Apply the Pythagorean theorem
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 boards required for each pattern of decking.
Pricing a Deck
What will that deck cost?
Mr. and Mrs. Handy are building a sun deck adjacent to their home. The diagram in Figure 1 shows the framing and dimensions of the deck. Mrs. Handy has designed three patterns for the decking, which are shown in Figures 2-4. Mr. Handy will be laying the decking to keep the cost to a minimum.
On sale, pre-stained 2 in. x 6 in. brown treated lumber is advertised at the following prices
|
Length
(ft.) |
4 |
6 |
8 |
10 |
12 |
14 |
16 |
|
Price
(dollars) |
4.29 |
4.99 |
5.79 |
6.99 |
8.49 |
9.99 |
12.29 |
Since these prices are lower than the current prices for special brown treated or green treated deck boards, the Handys decided to use the 2 in. x 6 in. brown treated lumber as deck boards.
Problem: Using the prices for brown treated lumber and any variety of the lengths of lumber, determine the minimum cost of each of the three deck designs. (The actual measure of 2 in. x 6 in. stock is 1 ½ in. x 5 ½ in.)
Figure 1. The Handy's deck, with dimensions.
Figure 2. Horizontal pattern deck.
Figure 3. X-pattern deck.
Figure 4. Inverted V-pattern deck.
