Letters and symbols represent numbers and objects in mathematics. However, many of us are probably not aware that we use them in different ways. Below are the different uses of letters and symbols in algebra.

1.) **Generalized Arithmetic** – symbols/letters stand as “pattern generalizers”

Example 1 : 3 + 5 = 5 + 3 is generalized as *a *+ *b* = *b* + *a*

Example 2 : – 2 · 3 = -6, – 1 · 5 = – 5 is generalized as – *x* · *y* = -6

Example 3: *y* = *m*x + *b*

2.) **Unknowns **– symbols/letters are used as place holders of a specific value

Example 1 : 2*x* + 3 = 15* *

Example 2 : 3x = 4

3.) **Variables** – symbols/letters represent a varying quantity

Example 1 : y = 5*x* + 3

Example 2 : *y = 2 ^{x} *

4.) **Constants** – symbols/letters with a constant value

Example 1 : ≈ 3.1416

Example 2 : *e* ≈ 2.71828

* *

I am looking for a way students can keep track of things like x, meaning a variable, or multiplication, or an axis. Yet when we are seeking a trigonometric number it is called theta? If only math was more visual I think artists could keep it in their heads instead of learning and losing it.

I do not know of any strategy to solve this problem except conceptual understanding. I agree with you. Sometimes, there are many symbols in mathematics that are supposedly introduced prematurely. Not that they are unimportant, but needs a little bit of mathematical maturity. 🙂

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