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Back in high school I aced math and barely had to work at it. Slept in a lot of those classes but the teachers wouldn't give me a hard time about it since I did so well and almost always had the highest grade, often over 100%. Looking back, I wish they challenged me a lot more or recommended that I take more difficult classes.
I remember classmates asking teachers "what do we need to know this stuff for" with the answer nearly always being something about shopping, usually at the supermarket. The best I could tell my friends at that time was knowing algebra really well helped some in Chemistry class and a lot more in Physics.
When I took Calculus in college is when I started to realize the significance of Algebra. Not an official answer from a professor or anything, this is just the conclusion that I came up with:
Algebra is pretty much the basic building blocks to other forms of mathematics which enable you to solve really interesting and important real-world problems.
Knowing algebra (and trigonometry) enables you to better learn & understand Calculus. With calculus you can solve problems such as determining the strongest geometric shape for a particular structure that needs to handle a specific stress load, determining the weight of an astronaut (or something else) a specific distance from the surface of the Earth or even things like determining the optimal design for a rain gutter so that it has the capacity to handle a specific flow of rainwater runoff from the roof while at the same time minimizing the amount of materials to construct the gutter in order to minimize construction costs. You can't get those answers with algebra alone, afaik, but by learning algebra you can then learn calculus where you are able to solve those types of problems.
If you compare learning math to learning a language...
- Learning letters would be like learning numbers
- Learning to spell words is like learning basic arithmetic
- Learning to write sentences is like learning algebra
- Writing essays might be like solving problems in Calculus
- And then writing books might be like solving larger problems with higher levels of mathematics
Maybe all of that will help with explaining how algebra fits in and what it enables you to build up to in math.
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