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Mathline

Activity II: Pricing a Deck (Grades 5-8)

How Many Shingles? | Pricing a Deck | Fencing the Yard | Career Connections | More Math Concepts

Objectives:

  • Reason from reading and examining a drawing
  • 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.

    adobe acrobat Student Activity (PDF File)
    Answers (PDF File)

    Sundeck 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 in. x 5 in.)

    Activity 2 Image

    Figure 1. The Handy's deck, with dimensions.
    Activity 2 Image

    Figure 2. Horizontal pattern deck.

    Activity 2 Image

    Figure 3. X-pattern deck.

    Activity 2 Image

    Figure 4. Inverted V-pattern deck.