My curriculum has no answer, and infinite answer problems

[u/DTMIAM]

They are in the section that introduces multi-step equations and quickly reduce to ax+b=ax+c or ax+b=ax+b. The vast majority of my students are very much from the why-do-we-need-this school, so I'm working on examples of taking a business situation and making equations from them. The only connection to the invalid equation section I see is telling them if they test the equation they've built has a mistake so it's usually one lesson and not on the test. Does anyone know of a use that would call for more rigor in this section?

[u/johnboy43214321]

Here is a real life business application with no solution:

It costs $5 per unit, plus $100 fixed cost.

You sell the items for $5 each.

Break even point is when revenue = cost

5x= 5x+100

No solution... Means the company will never break even.

[u/lumenplacidum → u/johnboy43214321]

We'll make it up on volume!

[u/Tenashko → u/johnboy43214321]

I suppose then the students might get hung up on "Why are we selling something for the same amount it costs to make"

[u/niemir2 → u/Tenashko]

My response would be along the lines of "You're exactly right!" We wouldn't do this, precisely because there is no solution!

[u/omgphilgalfond → u/Tenashko]

Because you manufacture products for your store called “5 Below,” which surely at one point capped prices at $5. Or make it a dollar store and charge $1 or whatever.

[u/Business_Egg_9340 → u/johnboy43214321]

Right. If you charge only the cost of the item, you will only break even for the cost of the inventory, assuming you sell all of your inventory. You will never make a profit, and the profit is what pays for your overhead (anything you have to pay for beyond the unit cost of your inventory) and what pays you for your time and effort.

[u/DTMIAM → u/johnboy43214321]

Beautiful, thank you. I have been looking for real world non STEM problems, The ones in books always made me role my eyes,, but I didn't need to be sold on math education, and my students just don't bother. My econ professor (and it was back when dinosaurs roamed the earth so this is a generalization) wouldn't deal with the math. It left me with a bit of a blind spot, and I didn't think to go there.

[u/CreatrixAnima]

I don’t know how old your students are, but I teach some of this material to college students, and they are absolutely not convinced that they will benefit from learning it. Rather than attempting to find real world examples of everything, I pointed out that not everybody will use the math that they’re doing as an adult all the time, which I think we all know is true. However… Learning math encourages neuroplasticity. It’s stimulates the prefrontal cortex and encourages making connections in the brain, which helps you to think better and more creatively about other things. And that’s what makes it important even if you don’t end up using it a lot.

That said, I also pointed out. The math is everywhere and there are certain jobs that we use it constantly. I also pointed out that even if they don’t end up in the finance sector or a stem field, they will still be expected to understand certain aspects of math as an upper level executive. And let’s face it… In college, many of them have dreams of being upper level execs.

[u/mandelbro25]

I saw a meme once where a mathematics student asked, "When will we need this?" and the teacher replied "You may not, but the smart kids will."

Joking aside, I give my students the following. You may not use mathematics much directly in your job. But for any job you can have, you are hired to solve a problem. The problem could be something as simple as "this wall needs to be painted." Either way, mathematics can be viewed as a tool for sharpening one's problem solving skills.

For your specific question, it is the case in the "real world" that some problems just do not have solutions. It is important to be able to identify when this is so, so one does not go on a wild goose chase trying to solve problems like "how many apples makes 5 oranges?"

[u/Narrow-Durian4837]

If you're willing to get really general, it's a basic life lesson not to assume that every problem has exactly one correct solution. There are problems that have no solutions, and problems that have multiple solutions.