When Students Interview a Skilled Tradesperson As Part of Module 2, They Will Brainstorm

Math for the Workplace 12

Carpentry Information Sheet

Number Sense

Carpenters work with fractions, decimals, percentages, ratios and proportions daily. They must be able to translate among percentages, decimals, and fractions. Carpenters must often express comparable quantities as a ratio and use proportion to solve for an unknown quantity. This process is used in converting linear measurements to appropriate units in both the imperial and the metric systems.

Carpenters must also be proficient in evaluating numbers involving powers of 10. These evaluations are then applied to calculations involving technical formulae and scientific notation. In addition, they must be able to convert between standard notation and scientific notation.

Operation Sense

Calculations performed by carpenters include addition, subtraction, multiplication, and division of whole numbers, decimals and fractions. All calculations that result from operations with fractions must be reduced to lowest terms. Carpenters must be able to solve multiple-operation equations following rules for order of operations. They must also be able to calculate a percentage of a number and be able to round decimals accurately to the appropriate place value.

Carpenters must be capable of manipulating an equation and/or formula to isolate a variable which leads to solving for the unknown quantity. Often, the equation is the result of expressing a word problem in equation form.

Very often, carpenters deal with triangles, circles, and rectangles. Therefore, they must be able to calculate squares, roots, and powers of numbers in order to apply these concepts to calculations involving the Pythagorean Theorem and the formulae used for determining the area of circles and the area of rectangles.They also must apply formulae for volume.

In addition, they must be able to calculate profit as a percentage of job costs as well as calculate all taxes for job estimates.

Measurement

Measurement plays a major role in the daily tasks performed by carpenters. They must be precise and accurate in taking measurements and proficient in expressing linear measures in appropriate units. They must also be capable of converting and comparing imperial measurements to equivalent imperial units. These same skills must be applied to metric measurements and equivalent metric units.

Carpenters must be able to convert metric linear measurement to imperial measurement and vice versa, given baseequivalencies. This is a skill thatis applied daily.

They must be able to identify the hypotenuse of a right-angled triangle and be able to apply Pythagorean Theorem to calculate length of sides of a right-angled triangle. They must also use angle sum rule for triangles to calculate the measure of an unknown angle.

Calculation of squares, roots, and powers of numbers is required in order to apply these concepts to determine the area of circles, triangles, and rectangles.

Carpenters must be able to read and to interpret blueprint drawings with precision and accuracy.

Geometry

Carpenters must understand the properties of supplementary and complementary angles and apply this understanding to calculate the measure of an unknown angle. They must understand symmetry and other geometric properties. Well developed spatial sense is critical to a carpenter.

Statistics

Being able to select information from a line graph is also a skill that must be perfected.They must also be capable of reading and interpreting code books and/or technical manuals.

Possible Project Ideas

1. Drafting - A student considering construction as a trade should be able to draw up and read a relatively detailed house plan. Drawing a plan and describing the math used, e.g. scales, measurement, could be a project. The plan could be for a kitchenor for a dog house if it needs to be scaled down.

2. Cost of Building - Building stores offer house plans, as does the internet. Using a house plan, a student should be able to calculate how much material is necessary to build a house.

Notes to Teachers:

It takes hours of work to do this project.

By using a material list given to one of the local contractors, the student could ensure that they include all the same materials on their job. Quantities would be different, of course, as their structure would differ.

Basic information is needed, for example:

Wall studs and floor joists are spaced at 16".
Roof trusses are spaced at 24"
Material for roofing is determined by Pythagorean Theorem, multiplied by two.
Interior wall areas, l x w, multiplied by two for interior walls, when calculating for gyproc and paint.
Trim for doors and windows.
Square area is used for flooring.

There are many details in this project and it is quite difficult. It can make a big difference in whether a contractor makes money or loses money.

To make this an achievable assignment, some thought would have to be given to all the information the students would need, what information they would have to gather, and what sort of written work they would have to pass in as finished product.

This project can be downsized to designing and building a deck or a mini-barn for the back yard.

3. Roofing -

[A] Design the Truss - A building 28 feet wide and 38 feet long needs roof trusses with a 6/12 pitch and one foot overhang for the eaves all the way around.

Information:

Some of the following information could be given (scaffolding) or student could research the information independently.

For every 12 inches of length you must rise 6 inches. How long will the top chord be?Use this length to determine how many bundles of shingles are needed. Three bundles cover approx. 100 square feet. Don't forget the cap.

There are 15 shingles in a bundle. One shingle makes three caps. Each cap covers 5 5/8" inches. The cap runs the length of the roof, don't forget the overhang.

[B] A Collar Tie - To keep the roof from sagging, a collar tie must be added. It is a two by four that joins the two opposing top chords at 8 feet as requested by the client. It will support the gyproc ceiling. How long are these collar ties from long point to long point?

[C] Finally, the client wants a three foot high knee wall built down both sides of the attic to finish the room and help support the trusses. If the slope is 6/12, how far out from the end wall will this wall be built? How much floor space does this leave the customer? How long is the sloped part of his ceiling? The top of the knee wall must be cut on an angle. At what degree should you set your saw?

Math For The Workplace 12: Carpentry Information Sheet August 2008