Seeing Structure in Expressions
Standard 
Lessons 
Worksheets/Games 
HSASSE.A.1 Interpret expressions that represent a quantity in terms
of its context. 
Interpret the structure of expressions 

HSASSE.A.2 Use the structure of an expression to identify ways to rewrite it. For example, see x^{4}  y^{4} as (x^{2})^{2}  (y^{2})^{2}, thus recognizing it as a difference of squares that can be factored as (x^{2}  y^{2})(x^{2} + y^{2}). 
Difference
of Squares 
Algebra Worksheets 
HSASSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. 
See Below 

HSASSE.B.3a Factor a quadratic expression to reveal the zeros of the function it defines. 
Solving quadratics by factoring 

HSASSE.B.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 
Complete
the Square (Solve Quadratics) 
Completing the square 1 
HSASSE.B.3c Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15^{t }can be rewritten as (1.15^{1/12})^{12t }≈ 1.012^{12t }to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. 

HSASSE.B.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments. 
Calculate finite geometric series 
Arithmetic with Polynomials and Rational Expressions
Standard 
Lessons 
Worksheets/Games 
HSAAPR.A.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 
Add & Subtract Polynomials 

HSAAPR.B.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x  a is p(a), so p(a) = 0 if and only if (x  a) is a factor of p(x). 

HSAAPR.B.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. 
Use zeros to graph polynomials 

HSAAPR.C.4 Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^{2} + y^{2})^{2} = (x^{2}  y^{2})^{2} + (2xy)^{2} can be used to generate Pythagorean triples. 
Polynomial Identities 

HSAAPR.C.5 (+) Know and apply the Binomial Theorem for the expansion of (x + y)^{n} in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle. 

HSAAPR.D.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. 
Inspection 
Divide polynomials by binomials 
HSAAPR.D.7 (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. 
Simplify
Rational Expressions 
Simplify 
Creating Equations*
Standard 
Lessons 
Worksheets/Games 
HSACED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 
Modeling with onevariable equations and inequalities 

HSACED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 
Linear
Equations 
Graph
Linear Equations 
HSACED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 
Modeling constraints with twovariable inequalities 

HSACED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R. 
Manipulate formulas 
Reasoning with Equations and Inequalities
Standard 
Lessons 
Worksheets/Games 
HSAREI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 
1Step
Equations 
Understand process for solving linear equations 
HSAREI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. 
Extraneous solutions to rational
equations 

HSAREI.A.2 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

HSAREI.B.4 Solve quadratic equations in one variable. 
See Below 

HSAREI.B.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p)^{2} = q that has the same solutions. Derive the quadratic formula from this form. 

HSAREI.B.4b Solve quadratic equations by inspection (e.g., for x^{2} = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b. 
Solve
Quadratic Equations 
Solve quadratics by taking the square
root 
HSAREI.C.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 
Graphically understand systems of equations 

HSAREI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 
Systems of Equations Worksheets Systems of equations 

HSAREI.C.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = 3x and the circle x^{2} + y^{2} = 3. 

HSAREI.C.8 HSAREI.C.9 (+) Represent a system of linear equations as a single matrix equation in a vector variable. (+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 נ3 or greater). 
Writing systems of equations as matrix equations 

HSAREI.D.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). 
Interpret graphs of linear and nonlinear functions 

HSAREI.D.11 Explain why the xcoordinates of the points where the graphs of the equations y =f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. 
Intersection
of Graphs 

HSAREI.D.12 Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding halfplanes. 
Graph linear inequalities 
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