If you don't have long division down by end-fifth and fractions and percentages by end-sixth, then someone is doing something wrong.

The Danish curriculum looked something like this when I went to school:

Primary:
1st: Addition
2nd: Subtraction
3rd: Multiplication
4th: Simple division and ratios
5th: Long division, percentages, classical trig.
6th: Algebra, more classical trig.
7th: Moar algebra
8th: Functions of one variable and general catchup for those who didn't get the 1st-7th curriculum the first time around.
9th: Moar catchup.

Secondary:
10th-12th (in no standardized order): Calculus in univariate functions, vectors, analytical geometry.

In my opinion, everything above 5th on this progression should be optional

Everything from 5th down needs to be mandatory, because it requires the sort of drilling you can really only do to a captive audience: Nobody in the history of ever has voluntarily done four to five thousand simple arithmetic problems over a span of four to five years. But that's roughly what it takes for a person of average aptitude to become functionally numerate from a cold start.

Additionally, in my dream world, 6th and 7th would displace 8th and 9th, and the 6th and 7th years should be used for (mandatory) basic statistical literacy, with a focus on how to (spot people who) lie with numbers - mean vs. median in skewed distributions; fun with time series; build-your-own histogram; units, axes, scaling. With modern computer assistance you don't really need algebra to understand statistics at a "citizen level." People who go into Serious Math will, of course, need to take formal statistics, but not everyone will do that.

- Jake

Friends come and go. Enemies accumulate.