Most lately? I’ve been working on a project (purely for my own fun) to 3d print parts to a musical instrument. As part of that, I need to figure out how to make smooth tunnels through the insides of the solid pieces. One end of the tunnel has to be here, coming out perpendicular to this wall, and the other end has to be there, perpendicular to that one, and they have to meet smoothly in the middle. Each piece is an arc of a circle (or more precisely, of a torus), but what angle of arc? With what radius? And how much does it need to be twisted? Lots of geometry and trigonometry in figuring that out, and that’s somewhat mathy, but even more mathy, I needed to figure out how to even set up the calculations. Writing down the equations (which nowadays can be solved by taking a picture of them with the appropriate app) isn’t the start of the problem; it’s very nearly the end of it.
The “sliding ladder problem” is one of those classics that appears in just about every Calculus textbook. Yes, it’s artificial and contrived and not useful. The reason it, and problems like it, are so popular is that it can stated quickly and simply and doesn’t require any specialized background knowledge to understand what’s going on. That’s not the case with many realistic real-world applications.
Google can do math, just type the equation in the URL area if you have Chrome.
I use math to calculate tips for servers, I take 10% and double it unless the server is really bad.
Outside of my job (IT field, so a decent amount of math and logic), the school concepts I tend to use reasonably often:
- Basic arithmetic
- Fractions/Decimal/Percentages of quantities
- Exponentiation and logarithms (compounding value-type calculations)
Of course I’m using a calculator or Excel, I’m not breaking out pencil-and-paper.
Can’t say I use geometry/trig much in my day-to-day life.
I use my knowledge of basic probability a lot to figure out where the statistics in newspaper articles are bullshit, obfuscation, or gilding the lily (so, quite frequently)
Buying construction materials. Estimating time and fuel for trips. Money, in many ways. Where to drill the holes in the little support plates I want to go make next.
And, STEM. Kids might be more interested in science if they knew that a major function of scientists is to play, which is really a process for figuring things out. Generally I play, or do pretend play games in my head, to come up with a way I think something works. Then I start trying stuff in a more measured and planned way. One of my last steps will be to sort through what I’ve already done, or add to it, so that something plausibly counts as part of the Scientific Method, so I can write something up. It’s pretty similar to what little kids like to do, only with a multibillion dollar company to pay for it, and a little more discipline. Just a little.
Here’s some math near and dear to the heart of every student: Calculating your grade point average. It involves finding the dot product of two vectors among other steps. It is simply an application of a weighted average.
In airplanes, the exact location of the center of gravity is critical. All pilots are supposed to know how to compute it. But I wonder how many pilots have ever noticed:
The procedure for finding the center of gravity of an airplane is exactly identical, step-by-step-by-step, to the procedure for computing a grade point average!
With some familiarity with math, you can notice things like that.
Also, a bit of trig helps with understanding g-factors. Did you know that an airplane banked at n degrees experiences a G force of sec(n degrees)?
Finally someone mentions statistics!
The famous quote is “There are three kinds of lies: lies, damned lies, and statistics”. Anyone that doesn’t have a working knowledge of statistics is innumerate, and will be taken advantage of throughout their life (what is worse is that they aren’t fit to weigh in on subjects like the economy, but they do, usually vociferously)
As someone who works in a school but doesn’t have an education background, I can’t tell you how many times I’ve thought “not statistically significant” or “inadequate sample size”. I was horrible at high school algebra, but I took a stats class called Research Methods in grad school that taught me to catch BS much more effectively.
My big trick is to be able to convert an order written in micrograms per kilogram per minute for a product packaged as milligrams per cc into a rate of milliliters per hour. Quickly and under a fair amount of pressure.
As a baker professionally I use math to change the amounts in recipes. There’s a standard amount, and I can enlarge it or make less. Also there’s conversion from measured amounts to weighed amounts, or back and forth from metric to American measures.
Can you ask the students to come up with “real world examples” from their world experience? I have no idea what that might be: calculating interest on cell phone bills? Divvying up snacks that you bring to class? Calculating the volume of farts?
I’m sure the textbooks have improved but the examples I remember were so esoteric as to be completely confusing. “A farmer wants to divide their acreage between their children equally” just started me thinking, “what is an acreage? Is an acre bigger than our house? Does equal mean equal in size? What if one section is filled with rocks…is that equal? Why can’t the farmer just pace off sections? And why can’t they just agree to work together anyway? Whattya mean, time’s up?”
Putting them in small groups to devise questions might help, especially with the quiet students who are not inclined to jump up and shout out answers, and you can have them try to work out the solutions and then supply formulas to expand the principle.
I think, and IANANumberPerson, that one problem with classroom teaching can be some people just “get” the solutions without knowing how they got there and the temptation is to simply seek and reward the right answer. I distinctly remember an 8th grade math class on probability where the answer to the question just jumped out at me and I got it. When the teacher said, “Good! Now use that same reasoning to get the answer to this question,” I had no idea and so went from class superstar to idiot in seconds.
My wife can easily divide a pie into more or less equal pieces of any number (well, I tell her there’s no point in anything more than eighths, unless the pie is the size of a kitchen table) just by eyeballing it; I am completely mystified by this. If pressed, I deal with the situation of divvying up pie for seven by cutting it into halves, then quarters, then eighths, and eating the extra piece before serving to guests.
But I suspect your students could come up with questions they would like to solve and that might be exciting for you and them.
At home? Cooking*, personal finance, travel planning, home improvement, crafting/hobbies. But mostly just math I learned before high school.
*I had to do some highschool chemistry in the kitchen the other day. I thought I was out of sodium citrate, but I had citric acid and baking soda. Turns out I’d ordered and received more citrate but realized that after cooking.
At work? Statistics mostly. Some occasional algebra. Often talking about calculus but rarely actually doing it
The one area I’ve personally used much beyond the basics is 3D graphics like video games and simulations. These days there are engines/libraries for most of it but you still need to understand the concepts.
Almost three dozen posts, and no references yet about converting grams to quarter ounces?
I’m not sure if I’m proud or ashamed.
Anything a car dealer is pushing is a bad deal(for the customer). No maths needed.
If you’re writing grant applications, you’ll often need to calculate a cost/benefit ratio. In fact for some street-related grants, you must meet a specific cost/benefit ratio or you don’t qualify. Some air quality grants rate applications on cost/pounds of pollutants removed.
You’ll also need to provide an estimate of the costs of your proposed project. That will require applying percentages. You multiply and sum your construction items, then add a % for contingency, a % for environmental paperwork, a % for design, a % for inspection, a % for project management, etc.
Figuring out what my retirement benefit would be required a spreadsheet. It’s based on years of seniority X a percentage based on your age at retirement (maximum 2.5% at 63) X your salary (averaged for your last three years). Then you get paid for unused vacation time but your unused sick leave is added to your seniority - or the other way around.
Figuring the return from the 457 (like a 401k) requires aspirational mathematics.
Most engineering math becomes tables or templates for anything that’s done often. It’s a waste of time to recalculate from principles every time. Your kids might like playing with one of the online asphalt calculators. Here’s one. There are more than a few. Some also calculate other matherials. You type in how long the street you’re fixing is (in feet), how wide it is (in feet), and how deep the asphalt is (in inches - hint: you need at least 8 inches for a public street) and it tells you how many tons of asphalt you need to order.
If you’re a construction company bidding on a job, you’ll be told either the size of the street to be installed (square feet & depth) or the estimated tons of asphalt needed. Your bid will include the cost/ton of the asphalt + transportation + application (equipment and worker salary) + whatever else is needed, including overhead. If the item was per ton, you save all the delivery tags. (You’d probably better save them anyway, but if you’re paid by ton, you want proof that it went over the estimate.)
What is the essence of math? Not numbers: The Pythagorean Theorem was proven without numbers multiple times over. Not geometry, as multiple kinds of math have no connection to geometry. Not notation, which is probably more recent than you imagine.
The essence is logical thinking, taking problems and breaking them down and solving them, with one step leading logically to the next. That kind of logical thinking is the true essence of mathematics, and I use it all the time to develop, test, and debug software. Most programmers don’t have much use for the specific kinds of math that is taught as math in high school and college, and arithmetic is best done by machine anyway, but logical problem-solving is the foundation of the field.
I’m aware this doesn’t justify your course very well, but the fact is your course is pretty hard to justify except as a means to get into a good college, which opens the door to a more interesting job than they’d have otherwise. The best way to justify the current math course progression from algebra to trigonometry to calculus is as a pipeline to produce physicists and civil and mechanical engineers, but I’m not even sure how accurate that is as history and in any event the justification is irrelevant now. It’s simply lists of things you must know to get to the good stuff, like the Classics were merely lists of things you had to master to get a job in the Civil Service during the British and Chinese Empires.
I just used trig and geometry to lay out a new driveway for my house based on the minimum turning radius for F-250 that would be the worst turning radius vehicle that I might own in the next 20 years.
I don’t do a lot of quadratic formula stuff but that is because I rarely model non linear things outside of work. Its fairly common for me to take two data point, create a trend line and extrapolate to a third data point.
I convert vessel volume to surface area and footprint as a regular part of my job. I do a lot of fluid flow and thermodynamic calculations but I have a fairly STEM heavy job.
Probably the most advanced math that I use in my private life is trig based. I build structures with non standard angles, and use sin/cosine/etc to figure out lengths and angles. That way I am not constrained to the normal range of building construction. An example would be unusual roof rafter angles. Another would be lengths and angles on non standard wall angles with other walls.