A lot depends are you talking theoretical or not.
Since I have to work I can't stay home so even if I wanted to I couldn't, but I'd generally prefer to and would do it nights and weekends as augementation.
The schools where I am are somewhat safe, but not terrifically well equipped. They don't have a high school radio station or public access production system, they probably don't have fantstic lab facilities for chemistry and physics.
My personal algebra skills are iffy, my geometry skills are so so and my trig skills are limited.
So it would be a joint learning experience.
Most of my math skills come from my professional computer programming in single user software. So that is a skill I would homeschool strong.
My background is heavily BASIC but I did work in Modula 2, understand Pascal and C and a little C++ and most recently downloaded C# which I intend to unschool on.
Microsoft makes lite versions of the NET system available free along with the documentation and it even integrates with SQL server
Not personal SQL, but SQL Server the full size puppy
Since my mother devised her own homeschool system to teach me keyboarding I'd probably work with her concept which was the think concenpt. You think of the fingers on your hande on the QWERTY keyboard and what row and finger is used for what letter.
That is a good ROTE system for learning touch typing.
I mastered it at age 7 and it got me an A in middle school typing at the age of 13 because I was doing 50 WPM.
My mother also homeschooled me in music notation and theory and emparted a system she learned in a private institute.
To this day when I do studio work with a singer and some song is in the wrong key I can sit behind a guitar or piano and find her range and figure out in a few minutes what changes to make in the charts for the best performance.
In working with bands I was the one who always came up with the chartes from the albums because I could listen to it and figure the progression out in moments and come up with charts and arragements.
I've done this under the most difficult of conditions with a tape that's between keys (in the cracks) and a piano that's out of tune. I remember the girls wanted to do this Pointer sisters song "I'm so excited" and it took me an hour to get what the piano and syth player were doing. After that point I was able to do the song enough for them to sing it.
I had to integrate both the doddling on the piano and the chord patterns on the syth track to make a composite.
All of this came from homeschooling and unschooling, no high school teacher can show you how to effectively do this.
My mother just showed me the basics of how to count steps and make all your chords that way.
My mother used to do this for me on her accordion. She'd get into the 7th, minior 7th and minors 6s, diminished and augmented.
I'd play some song for her I'd want to learn and in 5 minute she'd give me a run down of the chords
I'm still not as fast as she was, but I can hold my own after all these years.
I still have all my camera equipment so I can still teach photography but my darkroom equipment is long gone. I'd proably teach as I learned.
I get the Edmunds Optical Bench for $50 and show them how to make telescopes, microscopes and enlargers.
My first enlarger was a shoe box with a magnifying glass and a toilet paper roll as the lens barrel.
I currently show girl scouts how to pre-film for the Fuji 922 and tell them about the basic chemical proceses and light processes of film.
We also teach them to print on the Frontier machine and do color adjustments and density adjustments.
We generally spend half an evening with girls 9-13 and they each do their own roll of film from start to finish.
They get to work on half a million dollars in professioinal equipment.
I also have video and 16mm equipment, but all my editing stuff is long gone (I used to have rewinds, viewscopes) so I'd have to rent gear or buy it on Ebay to do 16mm A and B roll work for a sound film with insivisble splices.
I also have and older version of Pinnacle Studio and Premier and Vegas Video so I can show them non linear editing.
Since I learned all sorts of lighting tricks I can show them how to do a natural lighted interior with BBA bulbs.
Since I know my electricity to a degree I can show them how to size out a breaker box and determine where the circuits are so they won't overload things.
I still have Quick Time producer and Adobe PDF maker so I can show them how to imbed videos into E-documents and books.
Between Studio and Quick time we can render almost anything, which I used to do for singers for their demo materials and web sites.
I made E-CDs that play in normal walkman and CD players and also show videos and pictures on a computer
I also have light scribe so we can make laser labled disks.
My old software offerings will show them how to make jewel case covers with pictures and logos.
That was once by top seller.
Since I was an amateur astronomer since childhoold I've been meaning to get another telescope and we'd do that with a start chart and I'd invest in a new Observer's Handbook, which was $3 when I was a kid but is more like $50 today.
I first got published in sky and telescope at 16.
I sort of know where the ring neubla still is, and definately know where the great nebula in orion is and where the pleadeds are and can find the major planets just by looking up at the sky.
I know how to do astro photography and hve been trying to teach this guy I know how to do it.
I used to do it with a $5 camera.
The secret was doing your own darkroom work. So I'd have to go to Ritz and start a darkroom again with tanks and reels and tri chem packs and microdol.
I haven't tried putting a web cam to the telescope, but it's theoreticlly possble. It has a wide angle enough lens to work effectively, but the USB cables are short.
We probably have to experiment with splicing longer cables and using op amps to boost the signal.
So we get into electronics that way and I was schooled at the age of 11 in electronics (tubes of course).
My starting disseratation in electronics would be to buy a cheap metromone and open the back and describe to them exactly what is going on, which typically is a battery conntected to a potentiometer (variable resistor that changes the voltage of the 9 volt battery from 9 volts to less than a volt), diodes to keep the electric flow in one direction, an electrolytic capacitor to collect the voltage and release it in one fell swoop to the speaker and LED light.
The capacitor and potentiometer regulates the speed of the clicks. It takes longer at 3 volts to fill that capcitor up than it does at 9 volts. Thus to slow the speed down you cut the voltage.
Very simple, effective device that demonstrats rudimentary DC electricty principals.
Since I did a history of invention for optical and chemical and electronic visuals for a book I'm writing on TV and Motion Pictures, I'd go through the history with them.
Amber and silk cloth for static electricity.
We'd try and make a leyden jar
Use the amber to charge it
Try and make a chemical wet cell battery (I am told household salt can be used, but I never tried it).
Show how electricty from a batter into a wire can pull a magenet from north to the wire (emf) and do the bar magnet and metal fileing experiment over paper.
I've already demontrated to pre teens how electro plating works with Zinc Strips, 9 V batter and copper sulfate dissolved in a glass of water.
It plates half of one zinc strip copper.
That's how CD and DVD masters are made by electroplating the glass master and growing a metal part.
You won't even learn this stuff in college half the time. Not unless you take an Engineering major or a chemistry major.
Yet electroplating is a major occupational field.
It's how plated gold is made.
It's how DVD and CDs are made at the plant
It's a part of audio work since the 1950s when they first started making vinyl records.
This is where homeschooling shines the most. Giving a rounded education on how the world works.
I'm also told you can do the plating experiment with table salt and copper wire or strips, as metalical salt is nickel colored.
Salt is a metal you know.
So electrolysis should bind the sodium metal to the copper wire or strip.
It also details anode and cathode and there is also a gas released at either the anode or cathode during the reaction process.
I've always wondered if one could set up a small oil refinery at home. It would be useful in teaching organic chemistry showing how the refining process renders methane, pentane, butane and how you eventually render motor oil, kerosene, gasoline, machine oil.
Something to cook a beaker worth of crude oil and distill a little of this and a little of that.
Photo cells and light bulbs to demonstrate how a video signal is created on a rudimentary level.
A ball and socket joint with a steel or iron rod can be used to show how magnitism works to move things and even draw things.
You can attach a small LED laser to the steel rod.
You build your own Yoke coil to generate magnetic fields up and down and sideways
This is how CRT TV sets work, except they use a stream of electrons instead of a metal rod.
But the principals are the same.
You build two DC occilator circuits using a modified principal of what you learned with the metronome.
You want a capacitor to release a charge at two different levels. A slow one up and down and a fast one sideways.
A flyback circuit that shuts the LED off and returns it to the left.
This draws scan lines on a white sheet of paper some distance away.
It is a rudimentary TV set and even a rudimentry computer printer because that's sort of how a laser printer works.
These things take time, investment and yu can fail from time to time.
But teaches real world physics.
You can integrate math into this, since all these processes have well defined laws and formuals.
Taking our little light scribe experiment yu can integrate it with algebra, gemometry and trig.
Drawing a circle involves sine, cosine and geometrical x,y coordinates plus a diameter or radius.
The concept is to integrate the math with the electronic circuit to direct a magentic field to do these tricks.
This, then, demonstrates vector graphics.
Your scan lines demonstrates raster graphics.
At least the principal, you probably can't get it fast enough to leave a full image.
Most of what I detailed comes from unschooling and homeschooling and very little comes from brick schooling.
I did pick a lot of people's brains (my cousins are math professors, engineers, our friends worked for Atari, I was trained by engineers at Admiral Television in Chicago) and a lot of reading and playing a lot of what if games.
What if I do this?
What IF I put some Velox printing paper on one side of a shoe box and my negative on the other side with a light behind it and mount a magnifying glass inside the box?
You try it, it either works or it don't.
Getting a lecture out of a brick school teacher or reading a book only takes you so far.
Application of what you learn is a key step in the process.
Computer programming is learning what operators and functions do so you can put them to work doing a task.
You want to write a text processor with justification and work wrap you have to devise a system that measures the line, holds words in a que (variable), dumps those words down on the line if there is enough room or puts them down to the next line and fills the previous lines with extra padding spaces.
That's all an algebraic process.
It's all working with variables and numbers.
You have to hold things in areas.
Keep count of things.
Define what a space is
Keep count of spaces
Keep track of line size
Use math equations to add extra spaces
Re-write lines with extra spaces
When you do the process and watch it work for the first time and realize you just did what programmers at Microsoft do and you didn't copy the work from their coding, you came up with it from your brain, you feel good about what you can do!
When yo write your own paint program and come up with an idea for making an airbrush tool with different size "holes" for a varied stream or a varied look and you play with it and see what it does it's a very strange feeling.
You use the circle tool to create a red ball.
Then you use your air brush tool to make small white area on the top left and it starts to make the ball look 3-D.
You turn it into an elipse and use black to generate a air bush shadown at the base of the ball and now you are really going 3-D.
And you created all the tools to do this.
You actually feel like a kid again.
You're having fun playing with your code to create different shapes, textures.
Learning is about accomplishment. You sit and learn a music instrument but until you can play a song you haven't accomplished anything.