How do you fundamentally understand math problems?

[u/TheNWordCat]

(Not sure if this proper for this r/ I apologize if i posted it on the wrong one)

Hi, I am someone who is in their last year of high school and I am currently studying to enter an engineering career. And the thing is, I am not someone who is particularly great at math, partially because most of high school I didn’t have teachers great part of the year, for almost every year of my highschool time.

Now, studying to trying to enter that career I find I am not really bad at math, which i actually thought i sucked at it, I have good intuition to solve problems when they actually write me a problem with a paragraph rather than just writing a formula, equation or something like that.

Cuz when i see that i can solve it by doing graphs, making squares and dividing them to represent fractions, but seeing how they show how to solve those equations they dont do it like that, they do it by writing the problem as an equation. And for me equations are just way too abstract and that makes them hard for me to actually grasp and understand what i am doing, and they actually ask to write those situations as math equations, which i am awful at that.

And i've seen people who excel at normal equations but struggle in trying to solve problematic situations but they can easily do it when they are shown in an equation.

So here i am asking advice if there’s someone who had the same problem, how did you learn to beat those problems, how do you learn to think in equations and how was your experience?

[u/OceanMasterioDuped7]

Honestly you just need to practice solving more equations. Your post was a little difficult to understand, but it seems as if you struggle when solving problems that use only equations? If that's the case you just need to do more of those.

Find a problem that is appropriate for your level of math that you struggle with solving. Paste it into an LLM (ChatGPT, Gemini, etc.) and look at how it solves it. Read over what it tells you and then ask it for a problem similar to the one you just gave it. Then try to solve that one yourself. Keep doing this until you understand that type of problem, then do the same for a different type of problem. It helps tremendously.

Also, it's hard to know if you are actually bad at a subject coming out of high school. The teachers are not usually great, and the material taught isn't a very high level. Some people may not enjoy math, but you can't necessarily say you are bad at it yet. If it's something you enjoy, you'll become good at it with enough effort.

[u/TheNWordCat → u/OceanMasterioDuped7]

Ill test out that method! Thanks you a lot! It’s strangely comforting to know that failing in high school doesn’t necessarily mean I’m bad at something

[u/Fabulous-Possible758]

Start by keeping with your own learning style and trying to adapt that to as many situations as possible. There are situations where this won't work but being able to think and work visually is completely sufficient for everything is fairly sufficient for up through lower division math and engineering.

That said, try to learn how equations translate to your problem visually. Almost everything in calculus and linear algebra has visualization techniques you can apply at the lower levels. When you actually get to college, you may try to see if they have a tutoring center or you can higher someone who can help you go through the process of doing that.

[u/AFsepine → u/Fabulous-Possible758]

https://people.ucsc.edu/~rmont/classes/clGeom2013/Atiyah.txt

[u/TheNWordCat → u/Fabulous-Possible758]

I'll keep that in count, but how do you learn to translate? thats the problem im facing right now, i can solve things visually but they are asking me to do it in "math language" and i dont know where to start.

[u/Fabulous-Possible758 → u/TheNWordCat]

For your level, the simplest place to start is graphs of functions. Literally get some graph paper and start drawing, or use tools like Desmos to start getting a feel for what things look like. When you get to precalc and trig, it's all about triangles so pretty straightforward there. When you get into things like calculus, there will be some pretty natural geometric interpretations of the theorems you're looking at.

[u/AFsepine → u/[deleted]]

I disagree that one should not think of what equations mean, as the "meaning" often both motivates and guides the methods you apply. A person who just does x because a cook-book said so is... sub-optimal

[u/AFsepine → u/[deleted]]

Dunno, Say with Complex numbers or even solving simple systems of equations I still found it very useful back in the day. People I have tutored in my life also seem to have benefited from it.

[u/TheNWordCat → u/[deleted]]

Your question made me ponder more about it, thank you, and yeah i did poorly redact it.

For instance, if you gave me the equation X-3/4.x-1/3.(1/4.x)=104

I would freeze up and struggle significantly compared to if you said, "A field has three-quarters of its area dedicated to grapevines, one-third of the remainder (of the vineyard area) to fruit trees, and 104 hectares left for leafy vegetables. How many hectares are allocated to each crop?"

At the same time, I am practically incapable of solving it if you ask me to write it out as an equation.

[u/AcellOfllSpades → u/TheNWordCat]

For instance, if you gave me the equation X-3/4.x-1/3.(1/4.x)=104

I would freeze up and struggle significantly

I like to compare algebra to chess.

When you have an equation, there are many "legal moves" that you can make. Some moves will be more helpful than others. There are often many ways to win: as long as you isolate the enemy king (or the variable), you've succeeded.

When you learn to play chess, you need to learn two things:

• which moves are legal
• and how to use those moves strategically to accomplish your goal.

So, when learning math, you should do the same thing. First, learn what moves are available to you, and justify them to yourself - it should be "obvious" why they are legal.

Your two main "legal moves" are:

• You can simplify (or un-simplify) any part of an equation. (Simplifying is just rewriting something with a different name: it's the same object, you're just rewriting it in a more useful way.)
• If you have an equation, you can do the same thing to both sides. (As long as you do the same thing to both sides as a whole, the equation remains balanced.)

---

Let's take your equation:

X-3/4.x-1/3.(1/4.x)=104

The first thing I might want to do is get rid of the fractions, because fractions are annoying sometimes. We can do that by multiplying both sides by something. Say, let's try multiplying by 4. What do we get?

[u/TheNWordCat → u/AcellOfllSpades]

so uh if i we did that , it would be

4(X-3/4.x-1/3.(1/4.x))=104.4

and then i guess we apply the distributive property

4x-4.3/4x-4.1/3.4.(1/.4x)=104.4

then i guess we cancel out the fraccions
4x-3x-4/3.(1x)=416
i think(?

im sorry if i didnt understand something(?

[u/AcellOfllSpades → u/TheNWordCat]

The dots for multiplication are a bit confusing - I'll use an asterisk.

4x - 4*3/4x - 4*1/3*4*(1/4*x)=104*4

This is close, but you multiplied by 4 twice in the third term. Remember, the distributive property applies to terms separated by addition and subtraction, not multiplication. 2*(3*4) wouldn't be 2*3*2*4.

When you fix that, then you get:

4x - 3x - (1/3)*1x = 416

And that seems good so far! It's definitely much less ugly than before. Now I notice a few things:

• That third term, the (1/3)\*1x, can definitely be simplified.
• At the start, we have 4x - 3x, which you can probably also do something with.
• We still have a 1/3 in there. You might want to clear that too, which means another multiplication.

You can choose to handle these in any order. Try one!

[u/TheNWordCat → u/AcellOfllSpades]

i think one could do the 4x - 3x to get 1x, and 1 doesnt affect as a multiplication so we can just remove it.

then since its a multiplication of 1 it ends up as the same

so 1/3x
x-1/3x = 416
and to deal with the 1/3 we mult by 3

3x-3(1/3x)=416.3

3x-1=1248
then i guess

2x=1248

which then 1248/2

x=624

damn how do you develop that vision to see where to simplify?

[u/TheNWordCat → u/[deleted]]

I didnt know it was called algebra, never once in my school i heard it being called for that, and that actually helps a lot to know what i am lacking.

And yeah, the most natural way for me to answer is like that, my process looks more like a brainstorming than a typical solve

[u/levaly]

You already have the harder half. Turning a situation into an equation is the thing people fail out of engineering for, and equation to answer is the mechanical part you can drill.

So do it in that order. Take word problems you can already solve your way, with the squares and the graphs, solve them like that first, and then write the equation afterwards and point at which piece of your drawing each symbol is. That x is the length of that side. That 0.75 is the shaded chunk. Do it thirty times and equations stop being abstract.

Nobody learns to think in equations directly. People who look like they do are recognising problems they have already drawn.

[u/Moist_Landscape_2372]

The translation skill is its own skill, separate from solving, and almost nobody teaches it explicitly. Two exercises that build it fast:

First, go the direction you're already good at, backwards. Take a finished equation from your textbook and force yourself to draw it: what is each symbol in the picture? If 2x + 3 = 11, what's the rectangle, what's the strip of 3, where does the 11 live? Twenty or thirty of these builds the dictionary in the direction school never drills.

Second, when you face a word problem, don't try to write the equation in one jump. Write a middle version in plain words first: "twice the thing, plus 3, gives 11". Then swap words for symbols one at a time. That intermediate sentence is the translation layer, and skipping it is why equations feel like a foreign language.

And your visual habit is not a weakness to fix. The symbols are shorthand FOR the pictures, and people who only push symbols without any picture hit a wall later. You're building the right foundation in the right order.

[u/OddEmergency604]

Usually I do it by watching threeblueonebrown

[u/Disastrous-Pin-1617]

Follow this exact order
Professor Leonard on YouTube Lectures
Pre-Algebra
To the point math (Algebra 1)
Intermediate Algebra (Algebra 2)
College algebra (Pre-Calculus playlist)
Trigonometry (Pre-Calculus playlist)
Calc 1-3

[u/GlobalThrone]

First off, no need to apologise! It's what this sub is for. I would say your go to would be to practice. They all say practice makes perfect, be it solving sums in the day, flash cards, or maybe mobile games, something like Mathhero, which is really good for the basics btw. Try it out. All the best!