The Common Core math standards for K-8 grades are much more rigorous than our current math requirements here in Cape Elizabeth. Here are some examples:
2nd Grade students (CCSS.Math.Content.2.OA.C.4) should be able to "use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; and write an equation to express the total as a sum of equal addends."
There is a great lessen/explanation of this Common Core standard on the LearnZillon web site at https://learnzillion.com/lessonsets/761-write-equations-that-use-addition-to-find-the-total-number-of-objects-in-an-array
I know the "educationeese" language is a bit off-putting but just imagine a class of 2nd graders playing with 9 checkers on a table. Arrange them in a 3x3 square. Now ask them to think of ways to count the 9 checkers. Some will count 1-2-3-4-5-6-7-8-9. Others may count 1-2-3, 1-2-3, 1-2-3. The teacher will have them talk about the different ways they are counting the blocks and lead them in the direction of counting the 9 checkers by the method 3 + 3 + 3 = 9
This exposes the 2nd graders to several different math concepts; multiplication, an equation (algebra), arrays (which they will see in high school algebra II as matrix algebra) The teacher never need mention the words "multiply" or "algebra" or (heaven forbid) "matrix"; but merely encourage the 2nd graders to exchange ideas on different ways of counting the 9 checkers.
3rd Grade students (CCSS.Math.Content.3.OA.D.8) should be able to "solve two-step word problems using the four operations and represent these problems using equations with a letter standing for the unknown quantity."
This Learn Zillion video gives a feel for what sort of math lesson might be taught to meet this standard. If our Cape 3rd graders can meet this standard, then Algebra in 7th or 8th grade will be easy for them to understand.
8th Grade students (CCSS.Math.Content.8.EE.C.8) should be able to "analyze and solve pairs of simultaneous linear equations".
These types of problems begin with 2 separate algebra equations such as:
3X - 2Y = 9
5X + 6Y = 43
Neither equation can be solved by itself because each contains 2 unknown variables. The student must solve one equation for one of the variables in terms of the other; then substitute the resultant expression into the second equation. Today 99% of our 8th graders are NOT able to solve these types of problems because the technique isn't taught until Algebra II which many students don't take until their junior year in high school
Here's the type of thing that concerns me about our math program at Cape.
I tutor 9th grade Honors Physics students 3 or 4 days a week. Last week, I was working with one of the 9th graders and the problem we were working on (a block sliding down a ramp) eventually got to the point where we had a simple equation that required the student to solve for the force "F".
The student hesitated. He was unsure how to solve this because the unknown "F" was in the denominator of the right side of the equation. His first inclination was to divide both sides of the equation by "F". We worked on it for a minute or two and, with some prompting by me, he finally realized/remembered that he had to first multiply both sides of the equation by "F"; then divide both sides of the equation by "0.355" in order to isolate "F" on one side of the equation.
Now this student had taken Algebra in the 7th grade and Geometry in the 8th grade and was taking Algebra II currently. The solution to this simple equation should have been as automatic as tying his shoelaces. And his situation is not unique. Typically about a third of the 9th grade Honors Physics need help/reminders in order to solve this type of an equation - and almost 100% of them have already completed a year of Algebra in middle school.