I teach 2nd graders and I also tutor at a nationwide company. I have been assigned tutoring students who are studying secondary level algebra, and I can only help them so much. No problem with the lessons on the company’s program, but their homework sometimes leaves me scratching my head, because I have no confidence in skills I haven’t used in 30 years. The basics of algebra, such as finding an unknown number, no problem. The quadratic equation? Never since I aced college algebra. Geometry? shapes, perimeters and area, of course. Proofs? Only the logic and and not the Z pattern. Trigonometry? Thank God, never, because I could not fathom the whole thing as a student.
Discussing math with a student, it occurred to me that “You’re going to need this when you grow up” may have been an exaggeration. Other than working in STEM fields, how much of high school math do you use in your everyday life?
I work in construction, so I use my phone’s calculator quite a lot. 
I am in IT. I add, subtract, multiply, divide. I also count. Anything beyond simple 42+35 type calculations I use Excel.
I’ve never used standard deviation or cosine (I may have co-signed).
I’m a store cashier. When someone wants to split a payment, I can tell them how much is due without a calculator. When someone pays in cash, I can figure out the change without looking at the machine.
Well, as a photographer there are a couple of places where math is handing, especially multiplying and dividing by two, to help understand how aperture, shutter speed, and ISO are related. There is also something called the inverse-square law that states the intensity of the light decreases by the square of the distance to the subject. So, if I have a perfect exposure with a light 2 feet away from the subject, if I place the light 4 feet away (so twice the distance), my subject will be illuminated with 1/4 of the light (1/2^2). If I place the light 6 feet away (three times the distance), my subject will only have 1/9 of the light. At 8 feet (4 times the distance) it will be 1/16 of the light. I would have to compensate by adjusting my aperture and/or ISO and/or shutter speed (if using ambient light), and or flash power (if using electronic flash) appropriately.
Do you need to know this? No, but understanding it does help in troubleshooting and figuring out hot to set up lights or your subject a bit more quickly. I suppose you don’t need to know the exact mathematical relationship, but just understand that lighting does not fall off linearly with distance to subject.
One of my favorites from last year was that my parents live directly over a flight path. We were wondering about how high the planes flew over my parents house. I said, hey, would could figure this out. They live a few miles or so directly southwest of the airport. We used the Pythagorean theorem to figure out their diagonal distance to the airport (Chicago is a grid city, so it’s pretty easy.) We then looked up that the approach angle for airports is generally 3 degrees. So now we had distance-to-airport as the base of another right triangle, a 3 degree angle between the base and hypoteneuse, and our other unknown side of the triangle representing altitude. So, tangent is opposite over adjacent, so our equation became tan(3 degrees) = x/distance to airport. Ergo, tan(3 degrees) times our distance to airport should give us our altitude estimate. They live about 4.75 miles from the airport as the crow flies, so that plane was somewhere around 1300 feet.
OK, that’s not exactly a practical day-to-day use of math, but rather just one to satisfy our curiosity, but my memories of trig and geometry came in handy. I also feel like I’m using the pythagorean theorem reasonably often to compute diagonal distances, but I’m failing to come up with another example.
I’m an engineer who works with satellites, so I use it in my job a lot, but I actually use it more in every day life.
I use it to divide recipes when I want to feed 2 vs the 8 the recipe calls for. I use geometry to make sure boards I use in my woodshop are square (actual mechanical squares are only so big). I use rudimentary calculus to estimate areas when I’m trying to divide uneven things into equal parts (I obviously don’t use equations, but understanding the principles of calculus (which I hated in school BTW) helps me to do a better job of dividing. Obviously use it in my checkbook and when buying things. Comparison shopping–thing W costs X and is financed at a Y interest rate for Z years, thing A costs B with a C interest rate for D years, which is the better deal, etc.
I think that a lot of people say they never use math, but its so ingrained in what we do, we don’t think of it as math, just life. The crux of math’s usefulness in life is it allows you to predict and plan ahead. I think many of those who are unsuccessful in life didn’t “do the math”.
I know enough math to keep track of my checkbook balance. I can convert my weight from kilos to pounds. I go to dialysis and get weighed before and after in kilos, but I’m still used to thinking in pounds and ounces. I don’t need to do much advanced math. I can multiply and divide using pencil and paper.
I realise this isn’t what you asked, but by excluding “STEM fields” it seems like you are asking how to teach your students to use mathematics, paradoxically leaving out all the fields that actually use intermediate to advanced mathematics (including pure mathematics itself!) thus making it artificially useless.
My suggestion is not to be afraid to pick applied “STEM” problems from engineering, economics, medicine, chemistry, architecture, etc., that can be resolved using secondary-level mathematics, and you will be able to find ones that require calculus, algebra, geometry, trigonometry, solving equations both numerically and analytically, whatever you need. For motivated or advanced students, you could introduce a few problems like from the secondary-school mathematical olympiads, which do not require any advanced theory, merely clever thinking.
A very good friend of mine hated math, barely finished high school and received her diploma. Her first job was working in a Singer store, back when they sold patterns, fabric, and notions.
Boy, did she learn and use fractions in a hurry! A customer would hand her a pattern and she would calculate all the yardage needed for each project, and then hand-write (back in the covered wagon days, of course) the sales ticket.
Later on, one of her passionate hobbies was cooking, so that meant doubling or even halving recipes, and calculating the nutritional values, too!
I ended up in the engineering field. I started at the bottom of the totem pole with drafting, and that was before computers were invented, because we hand-chiseled those maps out of stone.
I had the usual adding and subtracting, and highways have curves, which are always fun! Calculations using coordinates meant trigonometry. The old-timers talked about the volumes of tables books they used, and reams of scratch paper to do those calculations. We had ancient WANG computers to run traverses.
With GPS, many calculations are now three-dimensional, and the computer models are awesome!
My granddaughter was recently diagnosed with Type One Diabetes. We’ve got numbers and math all over the place! And taking the Nutritional Information from food labels triggers a whole cascade of calculations as you try to find a “reasonable” serving amount.
Math? Our lives are covered with it!
~VOW
As a trial lawyer, I have to be able to calculate 1/3 of any recovery for my fee.
Driving. Calculate miles per gallon, estimate ranges, time of arrival, average speeds. Good stuff, that ‘Maths’.
I teach math, so I’m not the kind of person you’re looking for. But I want to take this opportunity to advance an idea:
Many people think of Mathematics as a collection of isolated skills and techniques, many of which you have to learn in school but most people never have any use for—solving a quadratic equation, calculating the area of a trapezoid, finding the derivative of a particular kind of function, etc. etc. etc.
In one sense, I suppose this is true; but in another sense, I think it makes sense to think of Mathematics as all one big thing, and the more you learn about it and practice it and work with it, the better you get at that big thing. That thing involves figuring things out; working with numbers and shapes and patterns and quantities and relationships; reasoning logically and seeing what does or does not follow from what; generalizing and abstracting and, conversely, taking general principles and seeing how they apply to specific situations. The more of Mathematics you learn—if you really do come to understand it, and you’re not just going through the motions—the better you get at that; and that way of thinking has all sorts of uses.
Using calculus you can figure out the surface area of a slice of a cone. That was useful when I was putting lights on a Christmas tree and needed to figure out how many lights to put on each row of branches. A Christmas tree is basically a cone, so you can figure out what percentage of the outside total each row of branches you have, so you put the same percentage of the number of lights you have on that row.
I view advanced math (anything beyond alebra) and any other advanced (i.e. beyond the minimum standards for that grade) studies as suitable for those who have a genuine interest and/or proclivity for the that subject. I’ve never aspired to be an engineer or anything that would require higher math and have ended up in accounting, where my basic knowledge of algebra is all I need.
When I was in middle school, I was in all the same top level classes as my friends from elementary except for math, which is one of the numerous reasons I dropped out (and back in at the start of the new school year). I justified it then and appreciate it now that while my friends were doing calculus, I had spent my time reading up on things that piqued my interest. “No, I can’t do trig, but I do know more about the Vietnam War than what I see and read in the daily news.”
As an artist, I use math all the time. Usually geometry, sometimes trig.
In commodities trading, many products are traded in fractions. Grains and treasuries off the top of my head.
Simple math I use all the time to figure out which of misleading deals at the grocery is best without finding the unit price on the tag. Much faster.
I’m writing a hard sf book, and I’ve calculated orbits and such to ensure that the action is realistic.
A long time ago I was in a car dealer and the manager was trying to sell me a lease option versus financing. I was able to compute the full cost in my head and told him that it was a bad deal. I blew his mind. 
Ratio and proportion, quite often, even if only for comparing grocery prices. As a woodworker, I work with angles quite often. As an electrician, I used algebra and trigonometry very often. On occasion I need to find the area or volume of something, so having memorized those formulas many decades ago comes in handy.
Most of the math I use in daily life is stuff I learned in grade school: mostly simple arithmetic, areas, volumes, decimals, fractions, percentages, and averages. I use that sort of thing all the time to calculate sales tax, discounts, cost per unit, for halving or doubling ingredients in a recipe, calculating the right size pan to put my halved or doubled recipe into, figuring out how much fertilizer to spread on the garden, fuel economy, whether it pays to buy a more efficient appliance, and so on.
One thing I learned in high school that I use a fair amount is interpolation and extrapolation. Just the other day I used interpolation to calculate the proper ratios of heavy cream and 1% milk to mix together to make something approximating whole milk. If memory serves, it was 6% of heavy cream and 94% of 1% milk.
Another high-school trick I use sometimes is converting betting odds on political races and sporting events into the probabilities of this or that contestant winning. Correcting for vigorish is something they never taught me in high school; I had to figure that out for myself.
Something I learned in college was the easy way to calculate exponential growth and compound interest. A few years ago, I used it, just to satisfy my idle curiosity, to estimate when New Hampshire’s population would surpass Maine’s. I could have done the calculation with grade-school math, but it would have been inconvenient.
It’s nothing I learned in high school or college, but I have used the website Packomania to figure out how to best arrange yeast buns in a pan so that each bun gets about the same amount of space to rise. If you have a round pan and between 3 and 6 buns, they should all be evenly spaced around the outside. If you have between 7 and 9, have one in the center and the rest around the edge. With ten buns, two go side-by-side in the middle with the rest around the edge. With 11 or 12, arrange three in a triangle pattern in the middle with the rest around the edge. And so on.
I do woodworking as a hobby, and fractions and geometry come into that constantly. Likewise when I DIY re-tiled my bath, and tiled the floor.
Any time you need to do measurements, if you’re using inches, you need to know your fractions in order to be precise. Likewise if you need to find the middle of something, or center one thing precisely on another.
Right after college, I worked at a copy shop. We had a self-service copy discount during certain hours. But, we had volume discounts on full-service copies, which used a somewhat complicated pricing structure. We were asked regularly which one was cheaper. No one had figured out the exact number of copies where full service became cheaper. I used calculus to figure out the break-even point.
When I took calculus in high school, I thought it was boring. It was presented in theory form, and even the word problems were ridiculous – if a ladder is sliding down a wall, no one is going to be calculating anything before it stops doing that, nor will it be useful. But we did some real world problems, like finding the optimal dimensions of a soda can if you wanted to minimize the amount of aluminum used, and I loved those projects. When I took calculus in college, the problems seemed more grounded in real world applications, like economics – finding the intersection of supply and demand curves, e.g. Some kids might like the abstract presentation, but it never held my interest as much as applications I could see in the real world.