High School Algebra (Wisconsin Standards)

Seeing Structure in Expressions (A.SSE)

• M.A.SSE.A.1 Interpret expressions that represent a quantity in context.
  • a. Interpret terms, factors and coefficients.
  • b. Interpret complicated expressions by viewing parts as single entities.
• M.A.SSE.A.2 Use the structure of an expression to find ways to rewrite it, e.g. a difference of squares.
• M.A.SSE.B.3 Rewrite an expression in an equivalent form that reveals properties of the quantity.
  • a. Factor a quadratic to find zeros.
  • b. Complete the square to find a maximum or minimum.
  • c. Use exponent properties to rewrite exponential expressions.
• M.A.SSE.B.4 Derive the sum formula for a finite geometric series and apply it, e.g. to loan payments.

Arithmetic with Polynomials and Rational Expressions (A.APR)

• M.A.APR.A.1 Know that polynomials stay polynomials under addition, subtraction and multiplication, and carry out these operations.
• M.A.APR.B.2 Know and use the Remainder Theorem.
• M.A.APR.B.3 Find zeros of factorable polynomials and use them to sketch a rough graph.
• M.A.APR.C.4 Prove polynomial identities and use them to explain number relationships, such as quick squaring.
• M.A.APR.C.5 Know and use the Binomial Theorem to expand (x + y)^n.
• M.A.APR.D.6 Rewrite simple rational expressions as q(x) + r(x)/b(x) using division or technology.
• M.A.APR.D.7 Understand rational expressions form a system like rational numbers; add, subtract, multiply and divide them.

Creating Equations (A.CED)

• M.A.CED.A.1 Create one-variable equations and inequalities, including linear, quadratic, simple rational and exponential, to solve problems.
• M.A.CED.A.2 Create equations in two or more variables for relationships and graph them with labeled, scaled axes.
• M.A.CED.A.3 Represent constraints with equations, inequalities or systems and judge whether solutions are viable.
• M.A.CED.A.4 Rearrange formulas to solve for a chosen quantity.

Reasoning with Equations and Inequalities (A.REI)

• M.A.REI.A.1 Justify each step of solving a simple equation from the equality before it.
• M.A.REI.A.2 Solve simple rational and radical equations and show how extraneous solutions can arise.
• M.A.REI.B.3 Solve one-variable linear equations and inequalities, including ones with letter coefficients.
• M.A.REI.B.4 Solve quadratics by inspection, square roots, completing the square, the formula, factoring or graphing; write complex solutions.
• M.A.REI.C.5 Justify that adding a multiple of one equation to another keeps a system's solutions.
• M.A.REI.C.6 Solve systems of two linear equations exactly and approximately.
• M.A.REI.C.7 Solve a simple linear–quadratic system algebraically and graphically.
• M.A.REI.C.8 Write a system of linear equations as one matrix equation.
• M.A.REI.C.9 Use an inverse matrix, if it exists, to solve linear systems, with technology for 3 × 3 or larger.
• M.A.REI.D.10 Understand the graph of a two-variable equation as the set of all its solutions.
• M.A.REI.D.11 Explain why intersection x-values of y = f(x) and y = g(x) solve f(x) = g(x) and find them approximately.
• M.A.REI.D.12 Graph solutions of linear inequalities in two variables as half-planes and of systems as overlapping regions.