Mathematics for the Trades N.Potter 2MAR2016

“Strong skills, especially in math, will prepare students for success in apprenticeship and a career in the trades.” http://www.careersintrades.ca/uploads/documents/PDFs/Educator_Workshop.pdf

“If you like to work with your hands and are creative, the skilled trades are a good choice. These careers require people with strong skills in reading and writing, math and science.”

Mathematics topics common to all trades at STC:

Fractions

Decimals

Percent

Ratio and Proportion

Formulas/Algebra

Measurement/Conversion between Units

Basic Geometry

Perimeter, Area and Volume Additional math topics for some trades:

Advanced Geometry; Circle Geometry

Trigonometry

Vectors Key Math Indicators for Success in Level 1 Skilled Trades:

Proficiency in Adding, Subtracting, Multiplying (including cross cancelling) and Dividing Fractions

Good “Number Sense”

Ability to perform basic calculations without a calculator

Good analytical and problem solving skills

Knowledge of both the Metric and Imperial systems of measurement

Ability to manipulate formulas; Cross multiply

All Trades Require Math

science-all.com

Additionally:

Positive attitude o Overcoming the “I’m not good in math” label

o Think of math background as a brick wall

godumplingsgo.com

o Why do I need math?

o Unrealistic expectations

o Overcoming “linear thinking”

Genuine desire to be in the trades

Willingness to work hard to improve math skills

Advantages of Learning Math At the Skills Training Centre:

You directly apply the math you learn. What you do in math class, you practice in the shop. By learning the principles and practicing them in repeated applications, they become second nature to you.

You work on improving your basic math skills by hand and with a calculator. This helps you develop your number sense or estimating skills, to recognize if your solution makes sense.

You are challenged to look at math in different ways, and to try different techniques for solving problems. (eg. Lattice multiplication)

Students are encouraged to ask questions and see how math can provide creative solutions.

You have math support available if you need it. Students come from a wide variety of math backgrounds. Post-secondary math courses have a 1-hour tutorial scheduled. Free drop in math tutoring is available for anyone needing help.

Math upgrading is available for students who want to improve their math skills before starting a post-secondary trade program.

In any right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

Offset: the distance between the centrelines of 2 parallel pipes

Diagonal: The c-c length of the connecting pipe Rise: The vertical distance between fittings for

vertical parallel pipes Run: The horizontal distance between fittings

for horizontal parallel pipes

In any 45˚, 45˚, 90˚ Triangle:

The legs are the same length

The Hypotenuse is about 1.414 times as big as the legs

The legs are about 0.707 times as big as the hypotenuse

For pipes with 45˚ fittings: Offset = Run (or Rise) Diagonal = 1.414 x Offset (or Rise or Run) Offset (or Rise or Run) = 0.707 x Diagonal

MATHEMATICS FOR THE SKILLED TRADES A LOOK AT HOW DIFFERENT TRADES USE THE PYTHAGOREAN THEOREM

Use the PYTHAGOREAN THEOREM to find the 3rd side of a right triangle when we know the other 2 sides.

To find the hypotenuse: 𝒄𝟐 = 𝒂𝟐 + 𝒃𝟐 (hypotenuse)2 = (one leg)

2 + (the other leg )

2

Or: 𝒄 = √𝒂𝟐 + 𝒃𝟐

To find a leg: 𝒂𝟐 = 𝒄𝟐 − 𝒃𝟐 (one leg)2 = (hypotenuse)

2 – (the other leg)

2

Or: 𝒂 = √𝒄𝟐 − 𝒃𝟐

PLUMBING TRADE CALCULATIONS: Solving Right Triangles: Offset Calculations Plumbers install and repair plumbing fixtures and water, waste disposal, drainage and gas systems in residential,

commercial and industrial buildings. (www.careersintrades.ca)

They perform a number of tasks, from simple installation of pipes and fittings to complex calculations and planning in specialized environments such as hospitals. (www.careersintrades.ca)

A plumber’s skills are also applicable in maintenance, service work, hydronic heating, and medical gas cross connection controls and inspections. (www.careersintrades.ca)

“An interest in construction, and good math skills are assets for plumbers. They must be able to understand and follow detailed plans, and be good problem solvers and able to apply their analytical abilities in a wide assortment of situations”. (www.careersintrades.ca)

The 45˚, 45˚, 90˚ Triangle:

Or:

Mathematics for Plumbers and Pipe Fitters, 7th Ed., Lee Smith

Calculating a Plumbing Offset Determine the combined length (c-c) of pipes J, K and L in the following diagram, with 45˚ fittings. Express the answer in the combined units of feet and inches to the nearest inch.

UNIQUE TO PLUMBING MATH:

Benchmarks and Percent Grades

Rolling Offsets

Fitting Allowances

1 foot = 12 inches or 1’ = 12”

ELECTRICAL TRADE CALCULATIONS: Solving Right Triangles: Impedance, Reactance, Resistance Triangles

Electricians design, build and install electrical systems. Their calculations will often involve Ohm’s Law that relates current, resistance and voltage.

An industrial electrician’s work day is never the same. They may start out troubleshooting and solving different problems found in various electrical equipment, and then move on to installing or testing electrical control systems, generators, regulators or transformers. (www.careersintrades.ca)

Mechanical aptitude, manual dexterity, and excellent problem-solving skills are a few of the key qualities that industrial electricians possess. They need strong analytical, mathematical and organizational skills to plan out the sequences of work for different jobs according to schematics, drawings and specifications.(www.careersintrades.ca)

When a resistor, an inductor, and a capacitor are connected in series with an AC source, the impedance, Z, is used to measure how much the flow of current in the AC circuit is restricted by all circuit elements. Impedance triangles, below, can be solved using the Pythagorean Theorem or trigonometry.

UNIQUE TO ELECTRICAL MATH:

Cosine Law Vectors and phasors:

PPM Electricians, 9th Edition, Stephen L. Herman

Bending Metal Plate

After the bend, the inside length is smaller than the outside length.

WELDING TRADE CALCULATIONS Solving Right Triangles: Determining the amount of material needed for a weldment

Welding involves the joining of metals using manual, semiautomatic and automatic arc welding equipment. Welders generally plan their work from drawings and blueprints and may use hand tools and machines to fabricate, assemble and weld products. There are many different types of welding depending on the material, equipment and techniques used, the nature of the final product and the degree of expertise required. (www.careersintrades.ca)

Welders must also be able to read and understand blueprints or drawings and to follow simple instructions precisely. Knowledge of computerized tools and machinery, analytical ability and communication skills are all important for success in this field. Good math skills are an asset. (www.careersintrades.ca)

UNIQUE TO WELDERS:

BENDING METAL How Dimensions Change When Metal is Bent:

It is often necessary to bend flat metal plate to form angles,

corners or circles.

Because metal can be compressed and stretched, bending metal will change its dimensions.

This must be taken into consideration when determining how much flat stock is required to form a piece

Inside corner is compressed

Outside corner is

stretched

TOOL & DIE/ MACHINIST TRADE CALCULATIONS Solving Right Triangles: Positioning tools to machine plates

Tool and die makers and machinists start with raw pieces of metal and, using machines like lathes, drill presses, milling machines and grinders, produce parts that are needed in manufactured pieces. They work to very specific and precise dimensions.

They are among the most highly skilled workers in the economy. They produce tools, dies, and special moulds for the machines that make many of the products and equipment we use every day — like clothes, airplanes, furniture, and even candy. Tool and die makers work in mould shops, shipyards, rail yards, refineries, pulp and paper mills, mines, smelters and overhaul shops. They work from drawings, computer-aided designs, and must have a good grasp of the properties of metal, plastic, rubber and composite materials. (www.careersintrades.ca)

Tool and die makers must be excellent problem-solvers. They must also be good with computers and quickly adapt to technological advances in robotics and lasers. Most tool and die makers have a background in mathematics and physics. (www.careersintrades.ca)

A machinist is to metal what a carpenter is to wood. They set up and run machines that cut or grind metal and other materials into products with very precise dimensions. Their work is forever evolving due to the rapid pace of technological changes. You’ll often find machinists in industries that manufacture machinery equipment, motor vehicle parts or aerospace parts. (www.careersintrades.ca)

UNIQUE TO TOOLING TRADES:

Bevels, V-slots and dovetails,

Complex Machine Applications

Mathematics for Machine Technology, Smith & Peterson, 6th Edition