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Common Core for Mathematics

Common Core Lesson Plans and Worksheets Algebra I

Algebra Overview

**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 functions

**Creating Equations**

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

**Seeing Structure in Expressions**

HSA-SSE.A.1 Interpret expressions that represent a quantity in terms of its context. |

HSA-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. For example, see x |

HSA-SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. HSA-SSE.B.3a Factor a quadratic expression to reveal the zeros of the function it defines. |

HSA-SSE.B.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. |

HSA-SSE.B.3c Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15 |

HSA-SSE.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. |

**Arithmetic with Polynomials and Rational Expressions**

HSA-APR.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. |

HSA-APR.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). |

HSA-APR.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. |

HSA-APR.C.4 Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x |

HSA-APR.C.5 (+) Know and apply the Binomial Theorem for the expansion of (x + y) |

HSA-APR.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. |

HSA-APR.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. |

**Creating Equations**

HSA-CED.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. |

HSA-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. |

HSA-CED.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. |

HSA-CED.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. |

HSA-REI.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. |

HSA-REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. |

HSA-REI.A.2 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. |

HSA-REI.B.4 Solve quadratic equations in one variable. HSA-REI.B.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x -p) |

HSA-REI.B.4b Solve quadratic equations by inspection (e.g., for x |

HSA-REI.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. |

HSA-REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. |

HSA-REI.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 |

HSA-REI.C.8 HSA-REI.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). |

HSA-REI.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). |

HSA-REI.D.11 Explain why the x-coordinates 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. |

HSA-REI.D.12 Graph the solutions to a linear inequality in two variables as a half-plane (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 half-planes. |

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