Electricians and industrial machinery mechanics keep buildings powered and factories running. These careers are in demand, and most people enter them through paid apprenticeships or a two-year degree instead of a four-year degree.

This beginner course prepares you for that route in three modules. Hands-On STEM covers systems thinking and troubleshooting, why safety comes first on every job, and what a day in each trade really looks like. Earn While You Learn maps apprenticeships, journeyman and master licences, associate degrees and certifications, and helps you start an hours and skills log and prepare for the aptitude test and interview. Trade Math practises fractions and tape measures, Ohm's law and area formulas, and conduit offsets with basic trigonometry, using small fill-in-the-blank calculators.

The platform teaches the knowledge, not the licence. Electricians need a registered apprenticeship (about 4 to 5 years of supervised hours plus classroom instruction), a journeyman exam and a state or local licence. Industrial mechanics need an apprenticeship or associate degree with supervised hours and site safety training. Safety content here is awareness level only. It builds on the STEM Foundations course.

Hands-on technical careers you can enter through apprenticeship: troubleshooting, safety awareness, the routes in, and the trade math you will use every day.

Foundations for Skilled Technical STEM Careers

## Why it matters

Electricians and industrial machinery mechanics spend a large part of their day on one question: *why is this not working?* A conveyor stops, a breaker keeps tripping, a pump is noisy, a light flickers. Customers and plant managers do not pay for guesses. They pay for someone who can find the real cause quickly, fix it once, and leave the system safe. That skill is called **troubleshooting**, and it rests on **systems thinking**.

## Core idea: everything is a system

A system is a set of parts that work together to do a job. Almost every system you will meet in the trades has the same four pieces:

- **Input or source**: where the energy or signal comes from (the utility supply, a battery, compressed air, a motor shaft).
- **Path**: how it gets where it is going (wires, pipes, belts, gears, hydraulic lines).
- **Control**: what decides when and how much (switches, relays, sensors, valves, a PLC).
- **Load or output**: the thing that does the useful work (a motor, a light, a heater, a press).

When the output is wrong, the fault is somewhere in the source, the path, the control or the load itself. Thinking this way turns a confusing machine into a short list of places to look. It also reminds you that parts affect each other: a worn bearing makes a motor draw more current, which heats the wiring, which trips the overload. The trip is the symptom; the bearing is the cause.

## A repeatable troubleshooting method

Good technicians do not all use the same words, but they follow roughly the same steps:

1. **Gather information.** What exactly is wrong? When did it start? What changed? Ask the operator, read the work order, check the maintenance history.
2. **Observe the system.** Look, listen and (where it is safe) feel for heat or vibration. Read indicator lights and error codes. Compare with a machine that works.
3. **List likely causes.** Use the source, path, control, load model. Start with causes that are common and easy to check.
4. **Test, do not guess.** Check one thing at a time with the right instrument and the right procedure. On a long path, test in the middle first (the **half-split** method): if the signal is good at the midpoint, the fault is downstream; if not, it is upstream. Each test halves the search area.
5. **Fix the root cause.** Replacing a blown fuse without asking why it blew means you will be back tomorrow.
6. **Verify and document.** Run the system, confirm the original symptom is gone, and write down what you found and did.

## Worked example: the garage light that will not turn on

Here is a household example you can reason through without touching any wiring.

- **Symptom:** a ceiling light in a garage does not come on at the switch.
- **Information:** it worked yesterday; the garage door opener on the same wall still works.
- **System:** source (the breaker panel), path (cable to the switch and on to the light), control (the wall switch), load (the bulb or fixture).
- **Likely causes, easiest first:** a burned-out bulb, a tripped breaker or GFCI, a failed switch, a loose connection.
- **Checks a homeowner can safely make:** swap in a bulb that works in another lamp. Look at the panel to see if a breaker is tripped. Press the reset on any GFCI outlet in the garage.

If none of that fixes it, the remaining causes are inside the switch box or fixture. That is where a qualified electrician takes over, because opening boxes and testing conductors means working near energized parts. Notice that systems thinking still did most of the work: four quick checks eliminated the most common causes without any tools.

## Worked example: a machine that runs slow

A mechanic is told a packaging machine runs slower than normal.

- **Source:** is the motor getting the right supply and speed reference?
- **Path:** belts can slip, chains can stretch, a gearbox can lose oil and drag.
- **Control:** a speed setting may have been changed on the drive or the operator panel.
- **Load:** a jammed product guide may be adding friction.

The mechanic checks the drive settings first (easy, common), then belt tension with the machine locked out, then the gearbox oil level. The belt is glazed and slipping. They replace it, then ask *why it wore early*: the pulleys are misaligned. Aligning them is the root-cause fix.

## Common mistakes

- **Shotgunning:** replacing parts until the problem goes away. It is expensive and hides the real cause.
- **Changing two things at once.** If the problem disappears, you will not know which change fixed it.
- **Skipping the conversation.** Operators often know exactly when a noise started.
- **Ignoring safety to save time.** Troubleshooting is when many injuries happen, because the machine is often half-working. Lockout and testing procedures still apply. You will learn those with your employer, not on your own.
- **Not writing it down.** The next technician (often future you) needs the history.

## Electronics in the trades

Modern equipment mixes mechanical parts with electronics: sensors, variable frequency drives, programmable logic controllers (PLCs) and smart meters. You do not need to be an electronics engineer, but you do need to read a basic diagram, understand that a sensor sends a signal to a controller, and know that a "dead" machine may have a perfectly good motor and a failed sensor. Later courses in this path, Electrical Circuits and Industrial Controls, cover these in depth.

## Quick recap

- A system has a source, a path, a control and a load. Faults live in one of them.
- Troubleshoot in order: gather information, observe, list causes, test one thing at a time, fix the root cause, verify and document.
- Half-splitting a long path finds faults fast.
- Real diagnostic work on live equipment needs employer training and supervision.


Use systems thinking and a step-by-step method to find the real cause of a fault.

Electronics, systems, and troubleshooting

Industrial Electrical Troubleshooting Made Simple

Systems Thinking Explained: How to See the Bigger Picture

## Why it matters

Electricity, rotating machinery, stored pressure and heavy loads do not give second chances. In the United States, electrocution and being caught in or struck by equipment are among the leading causes of death on construction and industrial job sites, according to OSHA. The good news is that almost all of these injuries are preventable with procedures that every trade already knows. A professional is someone who follows them every time, even when a job is small, late or "only for a second".

This lesson is **awareness level only**. It explains why safety comes first and what the main systems are. Before you do any of this work for real, you need training from your employer, apprenticeship or school, and supervision by a qualified person.

## Core idea: safety is part of the job, not extra paperwork

A strong **safety culture** means everyone on a crew expects safe work and has the right to stop a job that looks unsafe. You will hear phrases like "stop work authority" and "if in doubt, ask". New apprentices are often nervous to speak up. Good supervisors want you to, because the newest person is often the one who notices that a guard is missing.

Three ideas show up on every job:

- **Hazard recognition.** Before starting, ask: what energy is here (electrical, mechanical, hydraulic, pneumatic, thermal, gravity)? What could go wrong? Many crews write this down in a short job hazard analysis or pre-task plan.
- **Hierarchy of controls.** The best fix removes the hazard (de-energize the circuit). Next come engineering controls (guards, barriers), then administrative controls (procedures, signs, training), and last **personal protective equipment** (PPE). PPE is the last line of defence, not the first.
- **Energy control.** Before servicing equipment, workers isolate and lock out every energy source and verify it is dead. This is called **lockout/tagout (LOTO)**. OSHA has a specific standard for it. You will learn your site's procedure step by step during training; never improvise it.

## Electrical safety in plain words

- Treat every conductor as live until it has been tested by a qualified person with a proper procedure.
- Current through the body, not voltage alone, causes harm. Even ordinary household voltage can kill.
- **Arc flash** is a sudden release of energy when current jumps through air. It can cause severe burns at a distance. NFPA 70E is the US standard that covers electrical safety in the workplace, including arc flash protection.
- Water, damaged cords and missing covers all raise the risk. GFCI protection exists for this reason.

## Tools: right tool, right condition, right use

Tools are the trade's daily companions, and misuse of simple hand tools causes many cuts, strains and eye injuries.

- **Inspect before use.** Cracked handles, mushroomed chisel heads, frayed cords and missing guards mean the tool is tagged out and replaced.
- **Use the tool for its job.** A screwdriver is not a pry bar; pliers are not a wrench.
- **Insulated tools** rated for electrical work are marked (for example with a 1000 V symbol). They are a backup, not permission to work live.
- **Meters** must be rated for the circuits they test (look for the CAT rating) and checked on a known source before and after use. You will learn the proper test sequence in training.
- **Power tools:** keep guards on, unplug before changing bits or blades, and secure the workpiece.
- **PPE basics:** safety glasses on every job, hearing protection around loud equipment, gloves suited to the task (but never gloves near rotating parts that can catch them), hard hat and safety boots on construction sites.

## Worked example: a "quick" job

A mechanic is asked to clear a jam on a conveyor. The jam is small and the line is behind schedule. The operator says, "Just reach in, it takes ten seconds."

A professional response:

1. Recognize the hazards: the motor, the moving belt, and gravity (product above the jam).
2. Follow the site's lockout procedure: notify the operator, shut down, isolate, lock and tag, and verify that the conveyor cannot start.
3. Clear the jam with a tool, not a hand, if the procedure says so.
4. Remove locks only when everyone is clear, following the procedure.
5. Ask why the jam happened and report it, so it does not keep happening.

The extra five minutes is the job. Many serious amputations happen in exactly this "ten seconds" situation.

## Systems thinking and safety

The systems thinking from the last lesson applies to safety too. Energy enters a machine in more than one way: a press may have electrical power, compressed air and a raised ram held by hydraulics. Locking out only the electrical disconnect leaves two energy sources live. Thinking in systems helps you ask "what else could move?"

## Common mistakes

- Assuming someone else turned it off.
- Using damaged tools because the replacement is in the truck.
- Wearing PPE that does not fit the hazard (cotton gloves near a lathe, sunglasses instead of safety glasses).
- Staying quiet when something looks wrong.
- Learning LOTO or live testing from videos instead of from a qualified trainer on your site.

## Where to learn more

- OSHA, including the Electrical and Lockout/Tagout topic pages: https://www.osha.gov/ (Checked on 2026-10-23.)
- NFPA 70E, Standard for Electrical Safety in the Workplace: https://www.nfpa.org/ (Checked on 2026-10-23.)

## Quick recap

- Safety culture means everyone expects safe work and can stop unsafe work.
- Identify every energy source, use the hierarchy of controls, and lock out before servicing.
- Inspect tools, use them for their purpose, and match PPE to the hazard.
- This is awareness only: real procedures come from employer training and supervision.


Why safety comes first on every job: hazards, the hierarchy of controls, lockout and tool care (awareness level).

Safety, tools, and systems thinking

Electrical Safety Basic Training for Non-Electricians | Schneider Electric

Hand and Power Tool Safety Training from SafetyVideos.com

## Why it matters

"Skilled trades" covers many jobs. Two careers in this path, **electrician** and **industrial machinery mechanic** (often called a millwright or maintenance mechanic), share a lot: both are hands-on, both reward careful troubleshooting, and both are usually entered through an apprenticeship. But a typical day looks quite different. Knowing what the work is really like helps you choose the right path and answer the classic interview question, "Why this trade?"

## The electrician

Electricians install, maintain and repair electrical power, lighting, communications and control systems. The US Bureau of Labor Statistics groups them under occupation 47-2111. Common specialties include:

- **Residential:** wiring new homes, adding circuits, replacing panels, troubleshooting outlets and lighting.
- **Commercial:** offices, schools and stores, often with conduit, larger panels and fire alarm or data systems.
- **Industrial:** factories and plants, with motors, drives and control panels.
- **Maintenance:** an in-house electrician who keeps a hospital, campus or plant running.

**A sample day for a commercial apprentice:**

- 6:30 a.m. Arrive, sign in, and join the crew's toolbox talk on today's hazards (for example, working near an open floor edge).
- 7:00 a.m. Pull materials from the gang box and follow the journeyman to the third floor.
- Morning: measure, cut and bend conduit for a run of lighting circuits; mount boxes; keep the work neat and to the drawings.
- Lunch.
- Afternoon: pull wire through the conduit, label circuits, and clean up the area.
- 3:00 p.m. The foreman reviews progress. You note your hours and tasks in your log.

Apprentices also attend classroom instruction, often in the evenings or in block weeks, covering electrical theory, code and safety.

**What the work demands:** reading blueprints and the electrical code (in the US, the National Electrical Code, NFPA 70, as adopted by your state or city), trade math, colour vision for wire identification, comfort with ladders and tight spaces, and steady attention to safety.

## The industrial machinery mechanic (millwright)

Industrial machinery mechanics and millwrights install, maintain and repair factory equipment: conveyors, pumps, compressors, packaging lines, robots and production machines. BLS groups them under occupation 49-9041 (with millwrights at 49-9044). Their work is a blend of mechanical, hydraulic, pneumatic and some electrical skills.

**A sample day on a plant maintenance crew:**

- 7:00 a.m. Shift handover: the night crew reports that line 3's filler is leaking and a conveyor motor is running hot.
- Morning: **preventive maintenance (PM)** rounds. Check oil levels, grease bearings, inspect belts and chains, record vibration readings.
- Late morning: a **breakdown call**. Line 3 stops. You lock out the filler with your supervisor, find a failed seal, replace it, and test the machine with the operator.
- Afternoon: help **align a new pump** and motor with a dial indicator or laser tool, then update the work order in the computerized maintenance management system (CMMS).
- End of shift: hand over to the next crew.

**What the work demands:** mechanical aptitude, precision measurement (thousandths of an inch), reading manuals and schematics, welding or fabrication in some shops, and the ability to stay calm when an expensive line is down.

## Side by side

| | Electrician | Industrial machinery mechanic |
|---|---|---|
| Main focus | Electrical systems in buildings and equipment | Mechanical systems in production equipment |
| Typical workplaces | Construction sites, homes, commercial buildings, plants | Factories, warehouses, utilities, food and drink plants |
| Common entry | Registered apprenticeship (about 4–5 years) | Apprenticeship or associate degree in industrial maintenance |
| Licence | State or local licence usually required | Usually no state licence; employer qualifications and certifications |
| Schedule | Often early starts; travel between sites | Often shift work, nights or weekends to keep lines running |
| Typical tools | Benders, meters, wire strippers, fish tape | Wrenches, dial indicators, alignment tools, rigging |

## Worked example: matching interests to a trade

Jordan likes building things from scratch, does not mind moving between job sites, and enjoys seeing a finished building. Sam likes figuring out why things break, enjoys taking engines apart, and prefers working in one place with a regular crew.

- Jordan is a strong match for **construction electrician** work.
- Sam is a strong match for **industrial maintenance**.

Both would benefit from the same foundations: math, safety, reading drawings and troubleshooting. Many people move between the two later, for example an electrician who becomes a plant maintenance electrician, or a mechanic who adds electrical and PLC skills.

## Common misconceptions

- **"Trades are only for people who struggled in school."** Both trades use algebra, geometry and technical reading every day, and apprenticeships test for them.
- **"It is all heavy lifting."** There is physical work, but judgment and accuracy matter more than strength.
- **"There is no career ladder."** Paths lead to journeyman, foreman, master electrician, estimator, maintenance planner, reliability engineer or business owner.

## Find real data

Pay and job outlook vary by region and change each year. Look them up rather than trusting a number in a video:

- BLS Occupational Outlook Handbook: https://www.bls.gov/ooh/ (Checked on 2026-10-23.)
- CareerOneStop (US Department of Labor): https://www.careeronestop.org/ (Checked on 2026-10-23.)

## Quick recap

- Electricians focus on electrical systems in buildings and equipment, usually with a state or local licence.
- Industrial machinery mechanics keep production equipment running, often on shifts.
- Both use math, safety, drawings and troubleshooting, and both are usually entered through supervised apprenticeship.


Compare a day in the life of an electrician and an industrial machinery mechanic.

A day in the trade

Electricians Career Video

Millwrights, Industrial Machinery Mechanics and Maintenance Workers Career Video

Systems thinking and troubleshooting, why safety comes first on every job, and a day in the life of an electrician and an industrial mechanic.

Hands-On STEM

## Why it matters

The biggest advantage of skilled technical careers is that you can often **earn while you learn**. Instead of paying for four years of school before your first paycheck, an apprentice is hired, paid, and trained on the job. But the routes in have their own vocabulary (apprentice, journeyman, master, JATC, registered, licensed) and their own gates. This lesson maps them so you know what to aim for.

An important honest point first: **this platform cannot replace supervised field hours.** It can teach you the math, safety awareness, drawing reading and theory. The licence itself comes from documented work under qualified supervision and from exams set by your state or local authority.

## Core idea: three routes, often combined

### 1. Registered apprenticeship

A **registered apprenticeship** is a program approved by the US Department of Labor or a state apprenticeship agency. It combines:

- **On-the-job training (OJT):** paid work under a journeyman or other qualified mentor.
- **Related technical instruction (RTI):** classroom or online lessons, often evenings or block weeks.
- **Progressive wages:** pay rises as you complete hours and pass levels.
- **A nationally recognised credential** when you finish.

For electricians, a typical program lasts about **4–5 years**, with around **8,000 hours** of supervised on-the-job work plus several hundred hours of classroom instruction. Exact numbers depend on the program and state.

Programs are run by different sponsors:

- **Union programs**, run jointly by the IBEW (the electricians' union) and NECA (contractors) through local joint apprenticeship and training committees (JATCs), using curriculum from the Electrical Training Alliance.
- **Merit-shop (non-union) programs**, for example through IEC or ABC chapters.
- **Employer programs**, where a single company or plant registers its own apprenticeship. This is common for industrial maintenance.

### 2. Associate degrees and technical certificates

Community and technical colleges offer two-year **associate degrees** and shorter certificates in electrical technology, industrial maintenance, mechatronics and similar fields. These teach the theory and lab skills in a structured way. Some count toward apprenticeship classroom hours, and many plants hire maintenance technicians straight from these programs. For **industrial machinery mechanics**, an associate degree plus employer training is a very common route.

### 3. Industry certifications

Certifications prove a specific skill. They do not replace a licence, but they help you get hired and promoted. Examples:

- **OSHA 10-hour or 30-hour** outreach cards (safety awareness; see next lesson).
- **NIMS** credentials for machining and industrial maintenance skills.
- **SMRP CMRT** (Certified Maintenance and Reliability Technician) for experienced maintenance techs.
- Manufacturer training on specific drives, PLCs or equipment.

## The electrician licence ladder

Most US states (and some cities) license electricians. The names vary, but the ladder usually looks like this:

1. **Apprentice:** registered with the state or program, works only under supervision. Logs hours.
2. **Journeyman (journey-level) electrician:** has completed the required hours and passed a licensing exam, usually based on the National Electrical Code (NFPA 70) and theory. Can work without direct supervision on most tasks.
3. **Master electrician or electrical contractor:** more years of experience and another exam. Can pull permits, supervise others and, with business licensing and insurance, run a company.

Some states also have residential-only or specialty licences. The edition of the electrical code that applies, the hours required and the exam details all **vary by state and change over time**, so always check your state licensing board.

## The industrial mechanic route

Industrial machinery mechanics usually do **not** need a state licence. Instead, employers set the requirements:

- An apprenticeship (often 3–4 years) or an associate degree in industrial maintenance.
- Site-specific qualifications, such as lockout/tagout, confined space, forklift or crane operation, and being designated a "qualified person" for certain tasks.
- Optional certifications such as NIMS or SMRP CMRT as you gain experience.

## Worked example: two people, two maps

**Ana, 19, wants to be a licensed electrician in her state.**

1. Finish high school with algebra (done).
2. Find registered electrical apprenticeships near her on apprenticeship.gov and the local JATC and IEC/ABC chapter sites.
3. Apply, take the aptitude test, interview.
4. Work about 4–5 years as an apprentice, logging hours and completing classroom levels.
5. Apply to the state board, pass the journeyman exam.
6. Optionally, after more years, sit for the master licence.

**Marcus, 24, works in a warehouse and wants to move into plant maintenance.**

1. Ask his employer whether they sponsor a maintenance apprenticeship.
2. If not, enrol part-time in an industrial maintenance certificate or associate degree at a community college.
3. Earn an OSHA 10 card and any employer forklift and LOTO training.
4. Apply for maintenance helper or technician roles, then build toward NIMS or CMRT.

## Common mistakes

- **Assuming a short online course makes you an electrician.** Licences require documented supervised hours.
- **Not registering hours properly.** If your hours are not with a registered program or verified by a licensed supervisor, the state may not count them.
- **Copying requirements from another state or a video.** Rules differ and change.
- **Ignoring paid routes.** Many people pay for a private trade school when a paid apprenticeship was available locally. Compare both.

## Official sources

- Apprenticeship.gov (US Department of Labor), including the Apprenticeship Finder: https://www.apprenticeship.gov/ (Checked on 2026-10-23.)
- Electrical Training Alliance (IBEW-NECA): https://www.electricaltrainingalliance.org/ (Checked on 2026-10-23.)
- IEC: https://www.ieci.org/ and ABC: https://www.abc.org/ (Checked on 2026-10-23.)
- Your state electrical licensing board (search "<your state> electrical licensing board").
- NIMS: https://www.nims-skills.org/ and SMRP: https://smrp.org/ (Checked on 2026-10-23.)

## Quick recap

- Registered apprenticeships combine paid supervised work with classroom training.
- Electricians climb apprentice -> journeyman -> master, with state or local licences and exams.
- Industrial mechanics usually follow employer requirements plus optional certifications.
- Always check current rules with the official body and your state.


Map the routes in: registered apprenticeships, the journeyman and master licence ladder, degrees and certifications.

Apprenticeships, associate degrees, and certifications

Registered Apprenticeship 101

How to Become an Electrician | Step-By-Step Guide

Create an hours log with these columns: date, site or job, task, hours, category, supervisor or verifier, notes.

Create a skills checklist with columns: skill, level (observed / with help / independent), verified by, date.

Pick a safe hands-on task you have done recently (assembling furniture, adjusting bike brakes, replacing a battery in a smoke alarm, a shop-class project) and write a full entry: problem, what you checked, what you did, tools used, how you verified it worked, time taken.

Add at least five skills to your checklist that you can honestly rate today (for example: read a tape measure to 1/16 inch, use a level, follow written instructions, use a hex key set).

List the safety training you plan to earn, such as an OSHA 10-hour card from an OSHA-authorised trainer and first aid/CPR, with where you could take each one.

Make a backup: photograph or scan your log and store it somewhere safe.

Set a reminder to add an entry the same day each time you complete a hands-on task.

## Why it matters

In skilled technical work, **evidence is proof that you can do the job safely**. A software developer shows a portfolio of code. A tradesperson shows hours, cards and demonstrated skills. When you apply to an apprenticeship, sit for a licence, or ask for a raise, someone will ask: *What have you done, how many hours, and who can confirm it?* The habit of keeping good records starts now, before your first day on a site.

## The three kinds of evidence

### 1. Work logs (hours and tasks)

Apprentices record their on-the-job hours, usually by category. An electrical program might track categories such as residential wiring, commercial wiring, industrial work, motor controls, and low-voltage systems. A supervisor signs or approves the log. Many programs now use online systems or apps, but the information is the same:

| Date | Site / job | Task | Hours | Category | Supervisor | Notes |
|---|---|---|---|---|---|---|
| 2026-03-02 | Elm St. school | Installed EMT conduit for classroom lighting | 7.5 | Commercial | J. Rivera | First 30 degree offsets |
| 2026-03-03 | Elm St. school | Pulled and labelled branch circuits | 8.0 | Commercial | J. Rivera | Learned colour code for 277/480 V |

Your **licence application** may depend on these hours, so they need to be accurate, legible and backed up. Write them daily; recreating a month of logs from memory is unreliable.

### 2. Safety cards and certificates

These show you have been trained for specific hazards:

- **OSHA Outreach cards (10-hour or 30-hour).** Taught by OSHA-authorised trainers. The 10-hour course is entry-level safety awareness. It is a training card, not a licence or "OSHA certification", and it does not by itself qualify you for any hazardous task. Some employers and states require it.
- **First aid / CPR.**
- **Site or employer qualifications:** lockout/tagout, fall protection, confined space, aerial lift, forklift, arc flash (NFPA 70E) training. These are specific to the employer and must be renewed.

Keep copies (photo or scan) and note expiry dates.

### 3. Tool and skill proficiency

A skills checklist shows what you can do, at what level, and who saw you do it. For example:

| Skill | Level | Verified by | Date |
|---|---|---|---|
| Read a tape measure to 1/16 inch | Independent | Self, shop class | 2026-01-10 |
| Bend a 90 degree stub-up in 1/2 inch EMT | With help | J. Rivera | 2026-03-05 |
| Use a torque wrench to spec | Independent | Instructor | 2026-02-14 |

Levels like "observed", "with help" and "independent" are honest and useful. Never claim a skill you have not actually demonstrated.

## Worked example: a log entry from home

Before you are an apprentice, you can still practise the habit with safe, non-electrical tasks. Suppose you replaced the brake pads on a bicycle.

> **Date:** 2026-10-20. **Job:** Bicycle rear brake. **Problem:** brake squealed and needed hard pressure. **Checked:** pad wear (worn to the line), rim surface (glazed), cable tension. **Did:** replaced pads, cleaned rim, adjusted cable. **Tools:** 5 mm hex key, cable cutter, cleaning cloth. **Verified:** brake stops the wheel firmly on a test ride; no squeal. **Time:** 0.75 h. **Learned:** toe-in reduces squeal.

This is the same structure a maintenance technician writes in a work order: problem, checks, action, verification. Hiring panels notice applicants who already think this way.

## Building a simple portfolio

A trade portfolio can be a folder or binder (and a backed-up digital copy) with:

1. A one-page summary: your goal trade, education, and key cards.
2. Your hours log (or, before an apprenticeship, a practice log).
3. Your skills checklist.
4. Copies of cards and certificates.
5. Photos of your own work (projects you built, shop class pieces). Only photograph job sites with the employer's permission.
6. References: teachers, supervisors or mentors who agreed to vouch for you.

## Common mistakes

- **Waiting until the end of the week to fill in hours.** Numbers drift.
- **Vague entries.** "Worked on site" says nothing; "installed 12 duplex receptacles in a commercial office" shows skill.
- **Losing cards.** Scan them the day you get them.
- **Overstating skills.** Safety depends on people knowing what you can actually do.
- **Doing unsafe tasks at home to "build evidence".** Never practise on mains wiring, live circuits or pressurised systems. Real electrical and machinery skills are built under supervision.

## Try it

Open the **Do** tab. You will set up your own hours and skills log, write your first entry from a safe home task, and list the safety training you plan to earn.

## Quick recap

- Evidence = hours logs, safety cards and verified skills.
- Log daily, by category, with a supervisor's sign-off when you are an apprentice.
- An OSHA 10 card is safety awareness training, not a licence.
- Start the habit now with safe practice logs and a simple portfolio.


Start the hours log, safety-card record and skills checklist that prove you can do the work safely.

Evidence: work logs, safety cards, and tool proficiency

Is an OSHA 10 Card the Same as Being OSHA Certified? | Trade Training Explained

Use the Apprenticeship Finder on apprenticeship.gov (and your local IBEW-NECA JATC, IEC or ABC chapter, or local employers for industrial maintenance) to find at least two programs near you.

Build a tracker table: program, application window and deadline, minimum age, education requirement, documents needed, test used, status.

Gather the documents now: high school transcript or equivalent, ID, and anything else your programs list.

Find out which aptitude test each program uses and look for its official sample or practice material.

Do a 30-minute timed practice set covering fractions, simple equations, proportions and number sequences. Note the topics you missed and review them.

Read one page of a technical manual or safety sheet and summarise it in one sentence, to practise reading comprehension.

Write two STAR answers: 'Why this trade?' and 'Tell us about a time you solved a hands-on problem.'

Write your answer to: 'What would you do if a supervisor asked you to do something you believed was unsafe?'

Do a mock interview with a friend, teacher or mentor and ask for one thing to improve.

## Why it matters

Good apprenticeships are competitive. Many programs receive far more applicants than they have places, so they use a structured process to choose: an application with documents, an **aptitude test**, and an **interview**. The good news is that each step is predictable, and you can prepare for every one.

Details vary by program and change over time, so treat this lesson as a map and check the current rules with the program you are applying to.

## Step 1: Find programs and read the requirements

Search the **Apprenticeship Finder** on apprenticeship.gov, your local IBEW-NECA JATC, IEC or ABC chapter for electrical work, and large local employers or community colleges for industrial maintenance. For each program, note:

- **Minimum age** (often 18 by the start date).
- **Education:** usually a high school diploma or equivalent, often with a passing grade in algebra.
- **Documents:** transcripts, ID, sometimes a driver's licence and reliable transport (job sites move).
- **Application windows:** some programs accept applications only at certain times of year.
- **Physical requirements** and drug testing policies.

Make a simple table with the program, deadline, documents and status so nothing slips.

## Step 2: Prepare for the aptitude test

Many electrical programs use an aptitude assessment with two main parts: **math** (algebra and functions) and **reading comprehension**. Some programs have moved to other standard assessments, and industrial employers may use mechanical reasoning tests. Ask the program which test they use, and use their **official sample questions** if they provide them.

Math topics that come up again and again:

- Fractions, decimals and percentages.
- Order of operations and simple equations: solve 3x + 7 = 25.
- Ratios and proportions.
- Number sequences: what comes next in 2, 6, 18, 54?
- Simple formulas: substitute values and solve.

Worked examples:

- **Equation:** 3x + 7 = 25. Subtract 7: 3x = 18. Divide by 3: x = 6.
- **Sequence:** 2, 6, 18, 54. Each term is multiplied by 3, so the next is 162.
- **Proportion:** if 4 rolls of wire cost $180, 7 rolls cost 180 / 4 x 7 = $315.

Reading comprehension passages are often technical. Practise by reading a paragraph from a manual or a safety sheet and summarising it in one sentence.

**Test-taking tips:**

- Most of these tests are **timed**. Practise with a timer.
- Do not get stuck: mark hard questions and come back.
- Sleep, eat, and arrive early with the required ID.
- Find out the rules on calculators before test day.

## Step 3: Prepare for the interview

The interview panel (often a mix of contractors and union or company representatives) wants to know: *Will this person show up, work safely, learn, and stay for the whole program?*

Common questions:

- Why do you want to be an electrician (or mechanic)?
- Tell us about a time you solved a problem with your hands.
- What do you know about this trade and this program?
- How would you handle a supervisor asking you to do something you think is unsafe?
- Can you get to job sites reliably by 6:30 a.m.?

Answer with the **STAR** method: Situation, Task, Action, Result.

> **Question:** Tell us about a time you solved a mechanical problem.
> **Situation:** My family's lawn mower would not start before a weekend job. **Task:** I needed to get it running without paying for a repair. **Action:** I checked the simple things first: fuel, the spark plug and the air filter. The filter was clogged, so I cleaned it, and I replaced the old fuel. **Result:** It started on the second pull. I keep a short log of maintenance now so it does not happen again.

That answer shows troubleshooting, initiative and record keeping, the exact skills from this course.

For the safety question, the strong answer is clear: you would stop, explain your concern, ask for guidance, and follow the procedure. Panels are listening for respect *and* safety.

## Step 4: Present your evidence

Bring a tidy folder: résumé, transcripts, cards (OSHA 10 if you have it), your practice log and skills checklist from the last lesson, and references. Dress neatly and practically. Turn off your phone.

## Step 5: Follow up and keep going

Send a short thank-you message. If you are placed on a ranked list, ask how long lists usually last and whether you can improve your rank (more math courses, related work experience). If you are not accepted, ask what to improve and reapply. Many successful electricians applied more than once.

## Common mistakes

- Missing the application window or a required document.
- Not practising timed math.
- Saying "I just like working with my hands" with no example.
- Badmouthing a past employer.
- Overstating experience. Panels can tell, and safety depends on honesty.

## Try it

Open the **Do** tab to build your application tracker, practise timed math, and draft two STAR answers.

## Quick recap

- Read each program's requirements and deadlines carefully.
- Practise algebra, fractions and reading comprehension with a timer, using official samples where available.
- Use STAR stories that show troubleshooting, safety and reliability.
- Follow up, and reapply if needed.


Prepare your documents, the aptitude test and the interview for a competitive apprenticeship.

Applying to an apprenticeship

The IBEW Aptitude Test Has Changed - Here's What You Need To Know

Trade Apprenticeship Interview: Top 5 Things to Say and Not to Say in 2026

Apprenticeships, licences, associate degrees and certifications; keeping an hours and skills log; applying to an apprenticeship.

Earn While You Learn

## Why it matters

In the US trades, most measurements are still in **inches and fractions of an inch**. Electricians measure box heights and conduit runs; mechanics measure shaft lengths, shims and bolt sizes; everyone reads a tape measure many times a day. A mistake of 1/8 inch can mean a bracket that does not line up or a part that does not fit. Fraction fluency is also a big part of apprenticeship aptitude tests.

## Core idea: reading a tape measure

On a standard imperial tape, each inch is divided into 16 equal parts. The marks get shorter as the fractions get smaller:

- The **longest** mark in the middle of each inch is **1/2**.
- The next longest marks are **1/4** and **3/4**.
- Then **1/8, 3/8, 5/8, 7/8**.
- The shortest marks are the **sixteenths**: 1/16, 3/16, 5/16 and so on.

Count the small marks from the last whole inch. If the measurement is 9 inches and 11 small marks, it is **9 11/16 in**. If the count is even, simplify: 10/16 = 5/8, so 9 and 10 marks is **9 5/8 in**.

Most tapes also mark every 16 inches (a common stud spacing) and show feet: 7' 4 1/2" means 7 feet 4 and a half inches, or 7 x 12 + 4.5 = **88.5 inches**.

## Adding and subtracting fractions

To add fractions, they need a **common denominator** (the same bottom number). Tape fractions make this easy because 2, 4, 8 and 16 all divide into 16.

**Example 1: 3/8 + 5/16**

- Convert 3/8 to sixteenths: multiply top and bottom by 2, giving 6/16.
- Add: 6/16 + 5/16 = **11/16**.

**Example 2: two pieces, 5 3/8 in and 2 7/16 in, laid end to end**

- Add the whole inches: 5 + 2 = 7.
- Add the fractions: 3/8 = 6/16, and 6/16 + 7/16 = 13/16.
- Total: **7 13/16 in**.

**Example 3: 7/8 + 3/4**

- 7/8 stays 7/8; 3/4 = 6/8.
- 7/8 + 6/8 = 13/8, which is more than one whole inch.
- 13/8 = 1 5/8 (because 8/8 = 1, with 5/8 left over).

**The general rule** (works for any fractions): a/b + c/d = (a x d + c x b) / (b x d), then simplify by dividing top and bottom by their greatest common divisor. For 1/2 + 1/4: (1 x 4 + 1 x 2) / (2 x 4) = 6/8 = **3/4**.

**Subtraction** works the same way. A 96 in stick minus a 35 5/8 in cut: 96 = 95 8/8, and 95 8/8 - 35 5/8 = **60 3/8 in** (ignoring the width of the saw cut, the "kerf", which you should allow for in real work).

## Converting decimals and metric

Calculators and digital calipers give decimals. To turn a decimal inch into the nearest sixteenth, multiply by 16 and round:

- 0.30 in x 16 = 4.8, which rounds to 5, so **5/16 in**.
- 2.69 in: the fraction part 0.69 x 16 = 11.04, so **2 11/16 in**.

Common equivalents worth memorising: 1/8 = 0.125, 1/4 = 0.25, 3/8 = 0.375, 1/2 = 0.5, 5/8 = 0.625, 3/4 = 0.75, 7/8 = 0.875.

Metric: **1 inch = 25.4 mm** exactly. Machinery from many manufacturers uses metric bolts, so mechanics switch often: 3/4 in = 0.75 x 25.4 = 19.05 mm, which is why a 19 mm wrench nearly fits a 3/4 in bolt (but use the correct one: "nearly" strips heads).

## Worked example: centring a box

An electrician needs to centre a light box on a wall that is 11' 5 1/4" wide.

1. Convert to inches: 11 x 12 + 5 1/4 = 137 1/4 in.
2. Halve it: 137 1/4 / 2. Half of 137 is 68 1/2; half of 1/4 is 1/8. Total: 68 1/2 + 1/8 = 68 4/8 + 1/8 = **68 5/8 in**.
3. Mark 68 5/8 in from either end, and check from the other end.

## Common mistakes

- **Miscounting marks.** Count from the last whole inch, and double-check by reading the next larger mark (for example, 10/16 should sit on the 5/8 mark).
- **Adding denominators.** 1/2 + 1/4 is not 2/6. Convert to a common denominator first.
- **Forgetting to simplify.** 12/16 should be written 3/4.
- **Mixing feet and inches.** Convert everything to inches before adding.
- **Hooking errors.** The tape's end hook slides slightly to account for its own thickness on push and pull measurements. Do not "fix" it; keep the hook clean and undamaged.

## Try it

Open the **Do** tab. A small JavaScript fraction calculator is already written except for one line: the numerator when two fractions are added. Fill it in, then use the calculator to check the examples from this lesson.

## Quick recap

- A standard tape divides each inch into 16ths; simplify even counts.
- To add fractions, use a common denominator: a/b + c/d = (ad + cb) / bd, then simplify.
- Decimal to nearest sixteenth: multiply by 16 and round.
- 1 in = 25.4 mm exactly.


Read a tape measure and add, subtract and convert fractional measurements.

Fractions and measurements

Learn how to Read a Tape Measure - Fraction - Measuring and Marking Lesson Series -

Adding Fractions with Unlike Denominators | Math with Mr. J

## Why it matters

Trade work runs on a handful of formulas. Electricians use **Ohm's law** and the **power formula** to size circuits, choose breakers and troubleshoot. Mechanics use **area** to work out the force from a hydraulic cylinder or how much material covers a surface. You do not need to love algebra, but you do need to substitute numbers correctly, keep units straight, and rearrange a formula to find the value you are missing.

## Core idea 1: Ohm's law

Ohm's law links three quantities in a circuit:

- **Voltage (V)**, measured in volts: the electrical "push".
- **Current (I)**, measured in amperes (amps, A): how much charge flows per second.
- **Resistance (R)**, measured in ohms: how much the circuit opposes the flow.

The formula is **V = I x R**. Rearranged:

- **I = V / R** (current = voltage divided by resistance)
- **R = V / I** (resistance = voltage divided by current)

A memory aid is the triangle with V on top and I and R on the bottom: cover the one you want, and the other two show you whether to multiply or divide.

**Example:** a 120 V heater element has a resistance of 10 ohms. I = 120 / 10 = **12 A**.

**Example:** a 12 V battery is connected to a 4 ohm lamp. I = 12 / 4 = **3 A**.

## Core idea 2: the power formula

Power (P) is the rate at which energy is used, in **watts (W)**: **P = V x I**. Rearranged: **I = P / V**.

**Example:** a 1,440 W space heater on a 120 V circuit draws I = 1440 / 120 = **12 A**. On a 15 A circuit that is a big share of the capacity. For loads that run for hours (called continuous loads), the electrical code generally limits them to about 80% of the circuit rating, which for 15 A is 12 A. You will learn the exact code rules, and how your state adopts them, in your apprenticeship classes.

Combining the two formulas gives handy variations such as **P = I^2 x R** and **P = V^2 / R**. For the heater: P = 120^2 / 10 = 14,400 / 10 = 1,440 W, the same answer.

These numbers describe what an electrician calculates *on paper*. Measuring voltage or current on real circuits requires the right meter, training and supervision.

## Core idea 3: area formulas

- **Rectangle:** A = length x width. A room 12 ft x 14 ft has A = **168 sq ft**.
- **Triangle:** A = 1/2 x base x height.
- **Circle:** A = pi x r^2, or, using the diameter, A = pi x d^2 / 4. A circle 2 in across has A = 3.1416 x 1^2 = **3.14 sq in**.

**Units matter.** 1 sq ft = 12 x 12 = **144 sq in**, not 12. A 3 ft x 2 ft panel is 6 sq ft or 864 sq in.

## Worked example: hydraulic cylinder force (mechanic)

The force a hydraulic cylinder pushes with is **Force = Pressure x Area**.

- A cylinder has a 2 in bore (inside diameter). Area = pi x 2^2 / 4 = **3.14 sq in**.
- The system pressure is 1,000 psi (pounds per square inch).
- Force = 1,000 x 3.14 = about **3,142 lb**.

If the bore were 4 in, the area would be pi x 16 / 4 = 12.57 sq in, and the force about 12,566 lb: doubling the diameter **quadruples** the force. This is why a small hydraulic cylinder can lift so much, and why stored hydraulic pressure must be released and locked out before maintenance.

## Worked example: lighting a room (electrician)

A workshop is 20 ft x 30 ft. The lighting design calls for about 1 watt of LED lighting per square foot.

1. Area = 20 x 30 = 600 sq ft.
2. Lighting load = 600 x 1 = 600 W.
3. Current at 120 V = 600 / 120 = **5 A**.

The real design follows the drawings and code, but this quick check tells you the plan is reasonable.

## A method for any formula

1. **Write the formula** before touching numbers.
2. **List what you know**, with units.
3. **Rearrange** to isolate the unknown.
4. **Substitute** and calculate.
5. **Sanity-check**: is the answer in the right units and a believable size? A household appliance drawing 1,200 A is a mistake.

## Common mistakes

- **Multiplying when you should divide.** Use the triangle or rearrange on paper.
- **Mixing units:** kilowatts with watts, inches with feet, diameter with radius.
- **Using the diameter in pi x r^2.** Halve it first, or use pi x d^2 / 4.
- **Rounding too early.** Keep full precision until the final answer.
- **Treating a calculation as permission.** Knowing the current a circuit should draw does not make it safe to test it live.

## Try it

Open the **Do** tab. The trade calculator has the power and area formulas written for you. Your job is one line: Ohm's law for current.

## Quick recap

- Ohm's law: V = I x R, so I = V / R and R = V / I.
- Power: P = V x I, so I = P / V.
- Area: rectangle L x W; circle pi r^2 or pi d^2 / 4; 1 sq ft = 144 sq in.
- Force from a cylinder = pressure x area.


Apply Ohm's law, the power formula and area formulas to everyday trade calculations.

Formulas on the job

Ohms Law Explained - The basics circuit theory

Electrical Formulas - Basic Electricity For Beginners

## Why it matters

Conduit, pipe and tubing rarely run in perfectly straight lines. When a run of electrical conduit needs to step around a beam, a pipe or a box, the electrician bends an **offset**: two equal bends that shift the conduit sideways and then continue in the original direction. Getting the marks right first time saves material and time, and it is one of the most visible signs of skill on a job site. The math behind it is basic right-triangle trigonometry, and the same ideas help mechanics with angles, slopes and shims.

## Core idea: the offset is a right triangle

Picture the conduit stepping over an obstacle. The two bends at angle **theta** form a right triangle:

- The **offset depth** (how far the conduit must move sideways) is the side **opposite** the angle.
- The **distance between bends** (along the conduit, from one bend mark to the other) is the **hypotenuse**.

From trigonometry, **sin(theta) = opposite / hypotenuse**. Rearranged:

> **distance between bends = offset depth / sin(theta)**

The number 1 / sin(theta) is called the **multiplier** (or cosecant). Trade tables list it so you can just multiply.

| Bend angle | Multiplier (1 / sin) | Shrink per inch of offset (trade table) |
|---|---|---|
| 10 degrees | 5.76 (often rounded to 6) | 1/16 in |
| 22.5 degrees | 2.61 | 3/16 in |
| 30 degrees | 2.00 | 1/4 in |
| 45 degrees | 1.41 | 3/8 in |
| 60 degrees | 1.15 | 1/2 in |

## Worked example 1: a 6 inch offset with 30 degree bends

- Offset depth = 6 in.
- sin(30 degrees) = 0.5, so the multiplier is 2.
- Distance between bends = 6 / 0.5 = **12 in**.

So the two bend marks go 12 inches apart.

## Worked example 2: a 10 inch offset with 45 degree bends

- sin(45 degrees) = 0.7071.
- Distance between bends = 10 / 0.7071 = 14.14 in.
- To the nearest sixteenth: 0.14 x 16 = 2.3, which rounds to 2, so 2/16 = **14 1/8 in**.

## Shrink

Because the conduit now travels diagonally for part of its length, an offset "uses up" a little extra conduit compared with a straight run. This lost length is called **shrink**. The exact geometry gives:

> **shrink = offset depth x tan(theta / 2)**

For the 6 in offset at 30 degrees: 6 x tan(15 degrees) = 6 x 0.268 = 1.61 in. The trade-table shortcut of 1/4 in per inch of offset gives 6 x 1/4 = **1 1/2 in**, close enough for most work with a hand bender. Your instructor will show how your bender and your crew apply shrink when marking a stick, because the marking conventions depend on the bender and the direction you bend.

## Choosing the angle

- **Smaller angles** (10 or 22.5 degrees) make gentler bends that are easier to pull wire through, but they need more distance between bends.
- **Larger angles** (45 or 60 degrees) fit tight spaces but add more resistance to the wire pull.

The code also limits the **total degrees of bends** between pull points (in the US, 360 degrees between pull points for most conduit types). An offset with two 30 degree bends uses 60 of those degrees.

## Converting angles for JavaScript

Calculators and programming languages compute sine with angles in **radians**, not degrees. To convert: **radians = degrees x pi / 180**. In JavaScript:

```javascript
const radians = 30 * Math.PI / 180;      // 0.5236
console.log(Math.sin(radians));          // 0.5 (very close to it)
```

Forgetting this conversion is the most common bug in trade calculators: `Math.sin(30)` treats 30 as radians and returns -0.988.

## Worked example 3: checking a field measurement

An apprentice wants a 4 in offset with 22.5 degree bends and wonders whether 10 1/2 in between bends is right.

- sin(22.5 degrees) = 0.3827. Distance = 4 / 0.3827 = 10.45 in.
- To the nearest sixteenth: 0.45 x 16 = 7.2, rounds to 7, so **10 7/16 in**.

10 1/2 in (10 8/16) is 1/16 in long: a small but real difference on a tight offset.

## Common mistakes

- **Using cosine or tangent instead of sine** for the distance between bends. Remember: depth is opposite, distance is the hypotenuse.
- **Degrees versus radians** in calculators and code.
- **Unequal bends.** Both bends of an offset must be the same angle, or the conduit will not come back parallel.
- **Dog legs.** If the two bends are not in the same plane, the conduit twists. Sight down the conduit after bending.
- **Practising on the wrong things.** Bending practice belongs in a shop or apprenticeship lab with proper benders and supervision. At home, practise the math on paper.

## Try it

Open the **Do** tab. The offset calculator already converts degrees to radians, computes shrink, and rounds to the nearest sixteenth. You write the one line that computes the distance between bends.

## Quick recap

- An offset is a right triangle: depth is opposite, distance between bends is the hypotenuse.
- Distance between bends = depth / sin(angle); the multiplier is 1 / sin(angle).
- Shrink = depth x tan(angle / 2); trade tables round it per inch of offset.
- Convert degrees to radians before using `Math.sin`.


Compute the distance between bends and the shrink of a conduit offset with right-triangle trigonometry.

Offsets, angles, and bends

Pipe Trig

How To Make 30° Offset Bends Using Multipliers and Shrink

Fractions and tape measures, Ohm's law and area formulas, and conduit offsets with right-triangle trigonometry.

Foundations for Skilled Technical STEM Careers

About this course

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Hands-On STEM

Earn While You Learn

Trade Math

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