# [A] Algebra

Students’ prior knowledge includes:

• Students understand the connections between proportional relationships, line, and linear equations (grade 8)
• Students analyze and solve linear equations and pairs of simultaneous linear equations (grade 8)
• Students analyze proportional relationships and use them to solve real-world and mathematical problems (grade 7)
• Students use properties of operations to generate equivalent expressions (grade 7)
• Students solve real-life and mathematical problems using numerical and algebraic expressions and equations (grade 7)
• Students reason about and solve one-variable equations and inequalities (grade 6)
##### Seeing Structure in Expressions
• Interpret the structure of expressions.
• Write expressions in equivalent forms to solve problems.
##### Arithmetic with Polynomials and Rational Functions
• Perform arithmetic operations on polynomials.
• Understand the relationship between zeros and factors of polynomials.
• Use polynomial identities to solve problems.
• Rewrite rational expressions.
##### Creating Equations and inequalities
• Create equations that describe numbers or relationships.
##### Reasoning with Equations and Inequalities
• Understand solving equations as a process of reasoning and explain the reasoning.
• Solve equations and inequalities in one variable.  Solve systems of equations.
• Represent and solve equations and inequalities graphically

## MAT-HS.A Overview: [A] Algebra

### MAT-HS.A-SSE Domain: [A-SSE] Seeing Structure in Expressions

• MAT-HS.A-SSE.01 Interpret expressions that represent a quantity in context
• SSE.01.a Interpret parts expressions, such as terms, factors, and coefficients
• SSE.01.b Interpret expressions by viewing one or more of their parts as a single entity
• MAT-HS.A-SSE.02 Use the structure of an expression to Identify ways to rewrite it
• MAT-HS.A-SSE.03 Choose and produce an equivalent form of an expression
• MAT-HS.A-SSE.03.a factor a quadratic expression to reveal the zeros of the function it define
• SSE.03.b Complete the square in a quadratic expression to reveal the maximum or mini
• SSE.03.c Use the properties of exponents to transform expressions for exponential fu
• MAT-HS.A-SSE.04 Derive the formula for the sum of a finite geometric series

### MAT-HS.A-APR Domain: [A-APR] Arithmetic with Polynomials and Rational Expressions

• MAT-HS.A-APR.01 Understand that polynomials form a system analogous to the integers
• MAT-HS.A-APR.02 Know and apply the Remainder Theorem
• MAT-HS.A-APR.03 Identify zeros of polynomials when suitable factorizations are available
• MAT-HS.A-APR.04 Prove polynomial identities and use them to describe numerical relationships
• MAT-HS.A-APR.05 Know and apply the Binomial Theorem for the expansion of (x + y)^n
• MAT-HS.A-APR.06 Rewrite simple rational expressions in different forms
• MAT-HS.A-APR.07 Understand rational expressions form a system analogous to rational numbers

### MAT-HS.A-REI Domain: [A-REI] Reasoning with Equations and Inequalities

• MAT-HS.A-REI.01 Explain each step in solving a simple equation
• MAT-HS.A-REI.02 Solve simple rational and radical equations in one variable
• A-REI.03.a Solve linear equations in one variable
• REI.03.b Solve linear inequalities in one variable
• MAT-HS.A-REI.03 Solve linear equations and inequalities in one variable
• MAT-HS.A-REI.04 Solve quadratic equations in one variable
• MAT-HS.A-REI.04.a Use the method of completing the square to transform any quadratic equation
• A-REI.04.b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square
• MAT-HS.A-REI.05 Prove a solution set for 2 variable equation A + N times 2 var equation B
• MAT-HS.A-REI.06 Solve systems of linear equations in two variables exactly and with graphs
• MAT-HS.A-REI.07 Solve and graph a system of a linear and a quadratic equation in 2 variables
• MAT-HS.A-REI.08 Represent a system of linear equations as a single matrix equation
• MAT-HS.A-REI.09 Find inverse of a matrix and use it to solve systems of linear equations
• MAT-HS.A-REI.10 Understand a graph is the set of an equation's solutions
• MAT-HS.A-REI.11 Explain why the xcoord. of where y=f(x) and y=g(x) intersect Solve f(x) = g(x)
• MAT-HS.A-REI.12 graph the solutions to a linear inequality in two variables as a half plane

### A Sample of HS Math Concept ALGEBRA to Become Ready for College and Career

#### Seeing Structure in Expressions

• Interpret the structure of expressions.
• Write expressions in equivalent forms to solve problems.

#### Creating Equations and inequalities

• Create equations that describe numbers or relationships.

#### Arithmetic with Polynomials and Rational Functions

• Perform arithmetic operations on polynomials.
• Understand the relationship between zeros and factors of polynomials.
• Use polynomial identities to solve problems.
• Rewrite rational expressions

#### Reasoning with Equations and Inequalities

• Understand solving equations as a process of reasoning and explain the reasoning.
• Solve equations and inequalities in one variable.
• Solve systems of equations.
• Represent and solve equations and inequalities graphically.