The US has a highly regional system, but as I understand it pre-algebra is taught starting around sixth grade (~11 year olds), which may line up a little closer to your expectations.
In most advanced countries this would be the beginning of Junior High a.k.a. Middle School. By that time the students have been thoroughly introduced to pre-algebraic reasoning already, and are broadly getting practice in it (and being taught some more advanced notions around, e.g. exponents and powers, which are of course foundational for later teaching) as preparation for actual algebraic expressions to be introduced.
In the really old days algebra was A LOT harder too. Look up an old book like Chrystal.
I do not recall it being particularly difficult and most students were able to do this stuff. I'd say that by the end we had 100% success at this out of the 50 students or so in my class. Is this algebra in the US or is it the group theory stuff we studied later on. The group theory stuff was _much_ later (12th standard - 17+ years) and we didn't go too advanced. Mostly simple stuff like proving something is a group or Abelian, etc.
The syllabus I studied was the Tamil Nadu State Board, which is considered less rigorous than the Central Board, so I can only assume the kids elsewhere were studying more advanced stuff. But overall, that sort of timing hasn't hampered me or most of my classmates from then, so one must assume it's not too bad to study group theory that late.
Your parent comment is talking about solving a single linear equation such as "5x + 2 = 1". That's where "algebra" begins in a US pre-university context.
In a university context, "algebra" does indeed refer to group theory, and the basic concept of manipulating a numeric variable goes by the more elevated name "college algebra".
Just in case you think I might be misleading you somehow, here's a cheat sheet product for a "college algebra" course; again, "college algebra" refers to the material that would normally be covered in or before high school, except that it's being covered in college. So the idea of this product is that current college students will buy it to help them understand what's going on in class, or to review for a test.
https://www.amazon.com/College-Algebra-Quick-Study-Academic/...
> RULE: if a, b, and c are any real numbers and a = b, then a + c = b + c.
[later]
> Some equations require more than one inverse operation to solve.
> EX[AMPLE]: Solve the equation 5x + 3x - 1 = 15
at one large public school district -- 80 elementary schools, middle schools and high schools -- almost half of 8th graders cannot do basic elementary school math problems.. (edit) official estimates are that about 13% of the students do not finish high school at all.. that is the local school district here in a crowded port city in California near San Francisco. also note that more than forty unique non-English languages are spoken at homes existing in this school district.. also a non-zero number of homes where serious drug abuse occurs.. things like that..
* reads, writes, sorts and compares natural numbers 0–10,000;
* presents a number as the sum of units, tens, hundreds and thousands;
* reads and writes ordinal numbers;
* adds and subtracts numbers mentally within 100, and in writing within 10,000;
* knows the multiplication table (multiplies and divides by single-digit numbers mentally within 100);
* knows the names of the members and results of four arithmetic operations;
* finds the numerical value of a letter in equations by trial and error or by analogy;
* determines the correct order of operations in an expression (parentheses, multiplication/division, addition/subtraction).
So you have elements of pre-algebra but actual algebra will be covered only in the 4th/5th grade (10-12 yo).
Generally in the US it is:
* K ~5 yo
* 1st ~6 yo
* 2nd ~7 yo
* 3rd ~8 yo
* 4th ~9 yo
* 5th ~10 yos
Give or take of course since birthdays don't align perfectly.
That seems to roughly align to US standards for the same age but not the same grade.
While not a focus, very basic forms of algebra is introduced as early as 1st grade through problems such as "4 + _ = 9".
Are the standards really that low? AIUI in most developed countries w/ the significant exception of the U.S. (and to a lesser extent, other English speaking countries), 4th and 5th grade math are for teaching the earliest elements of pre-algebra. (Meaning that algebraic expressions are very much not used, but the style of reasoning is clearly intended as preparation for that). They may get a lot of practice with fractions or multiple-digit arithmetic, but the basic procedures are not new to them in 4th grade. It seems to me that the U.S. educational system is underserving these kids quite significantly by not catering to their potential and actual skills for mathematical reasoning, which while not fully developed (and very much tied to "concrete" skillsets, as opposed to a real capacity for abstraction) are still quite substantial.