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Interactive

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Source: WISCONLINE

This media asset was adapted from "My Uncle's House" by WISCONLINE.

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In this interactive activity adapted from the Wisconsin Online Resource Center, use mathematics and measuring skills to solve a construction problem. Play a game using tools (including a tape measure, notepad, and calculator) to determine how many shingles are needed to reroof a house. Learn about the importance of proper planning and how miscalculating the amount of materials needed can add to the cost and time spent on a project.

Background Essay

What do landscaping, hotel construction, and space exploration have in common? Math! From designing a garden, to building a hotel, to investigating Mars, mathematical skills are the key to a successful project. Proper planning and accurate measurements and calculations are the foundation for most professions. Basic math skills (such as numeric operations, algebra, geometry, measuring, and modeling) are critical and may very well mean the difference between a project's success and its failure.

When a family hires the owner of a small landscaping business to design their backyard, the landscaper must make a plan based on their wants or needs. To begin, he must make measurements of the area and develop an idea of how he would like to transform the yard. He may then construct a scale drawing to help with the design process. He then needs to calculate the surface area of the plant beds and the volume of soil needed to fill them in, make a list of the types and quantities of plants to be used, and then estimate the costs of all the materials needed. In addition, he needs to estimate the amount of time required to complete the project in order to calculate labor costs.

As the owner of a small business, the landscaper cannot afford to waste time returning to the garden store to pick up more supplies, or to pay restocking fees for unused materials, so it is important that he estimate the materials needed as accurately as possible. He also needs to be able to complete the project in a timely manner and within budget in order to both satisfy the customer and make a profit.

Errors in planning and calculations can cause major problems. In the landscaping example, mistakes may result in loss of profits and the ultimate failure of the company. However, errors can also have far more dire consequences. For example the deadly collapse of the Kansas City Hyatt Regency Hotel walkways in 1981 could have been prevented if the proper calculations had been completed to determine whether the walkways were structurally sound. NASA's Mars Climate Orbiter is another famous example of a relatively simple mathematical error leading to spectacular failure: Because the engineering team used English units while NASA used metric units, the spacecraft failed to enter orbit around Mars and instead became a \$125 million disaster.

Discussion Questions

• Explain how to find the area of a trapezoidal roof pitch.
• List the steps used to calculate the number of bundles required to cover a roof with shingles.
• Why should 5 percent be added to all estimates?
• Why do you think shingles are sold in "squares" and "bundles" instead of packages of, say, 100 shingles?

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