Get from arithmetic to quadratics without the gap in the middle — number sense first, then letters standing in for numbers, then the equations that need both.
Most algebra mistakes are really arithmetic mistakes. Negatives, operation order, factors and powers get settled here so they stop biting later.
The jump from calculating a number to describing a relationship — and the balancing move that solves for the unknown.
Writing, simplifying, and substituting into algebraic expressions.
Solving one-step and two-step equations by balancing both sides.
Slope, y-intercept, graphing straight lines, and systems of equations.
Inequality symbols, solving, and graphing on a number line.
Rules for manipulating powers, spotting the rule behind a sequence, and handling expressions with several terms.
All six index laws, negative indices, and fractional indices.
Arithmetic and geometric sequences, nth term, and pattern rules.
Polynomial expressions, degree, adding, subtracting, and multiplying polynomials.
Simplifying, multiplying, dividing, adding, and subtracting fractions that contain algebraic expressions.
Where school algebra is heading: solving a pair of equations at once, the quadratic, and the idea of a function tying it all together.