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Common Core Mapping for High School: Algebra




 
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

Related Topics:
Common Core for Mathematics, Common Core Lesson Plans and Worksheets Algebra I

Seeing Structure in Expressions

Code

Standard

Lessons

Worksheets

Games

HSA-SSE.A.1
HSA-SSE.A.1a
HSA-SSE.A.1b

Interpret expressions that represent a quantity in terms of its context.
A. Interpret parts of an expression, such as terms, factors, and coefficients.
B. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.

Interpret Expressions

Interpret the structure of expressions

Structure in expressions

Algebraic Expression Games

HSA-SSE.A.2

Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2).

Difference of Squares

Perfect Square Trinomials

Factor by Grouping

Factor by Trial & Error

Factor (Area Model)

Algebra Worksheets

Difference of squares 1

Difference of squares 2

Difference of squares 3

Factor by grouping

Factor quadratics 1

Factor quadratics 2

Linear binomials

Factor polynomials with two variables

Radical equations

Factor Expressions Games

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.

See Below


 

HSA-SSE.B.3a

Factor a quadratic expression to reveal the zeros of the function it defines.

Zeros of Quadratic Functions

Solving quadratics by factoring

Solving quadratics by factoring 2

Algebra Games

HSA-SSE.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)

Complete the Square (Min, Max)

Completing the square 1

Completing the square 2

Vertex of a parabola

 

HSA-SSE.B.3c

Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15can be rewritten as (1.151/12)12t ȍ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

Geometric Sequences & Applications

Geometric Sequence

Nth Term of a Geometric Sequence

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.

Geometric Series & Applications

Calculate finite geometric series

Geometric Series Word Problems




Arithmetic with Polynomials and Rational Expressions

Code

Standard

Lessons

Worksheets

Games

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.

Add & Subtract Polynomials

Multiply Polynomials

Add & Subtract Polynomials

Multiply Binomials 1

Multiply Binomials 2

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).

Remainder Theorem

Factor Theorem

Remainder Theorem

Remainder Theorem

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.

Zeros of Polynomials & Graphs

Use zeros to graph polynomials

HSA-APR.C.4

Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 - y2)2 + (2xy)2 can be used to generate Pythagorean triples.

Polynomial Identities

Polynomial Identities

HSA-APR.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.

Binomial Theorem

Binomial Theorem

Binomial Theorem

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.

Inspection

Long Division

Synthetic Division

Computer Algebra System

Comparing Coefficients

Divide polynomials by binomials

Divide polynomials by binomials

Divide polynomials by binomials

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.

Simplify Rational Expressions

Add & Subtract Rational Expressions

Multiply & Divide Rational Expressions

Simplify

Simplify

Simplify

Simplify

Add & subtract

Add & subtract

Add & subtract

Add & subtract

Add & subtract

Multiply & divide

Multiply & divide

Multiply & divide

Multiply & divide

Multiply & divide

 


 

Creating Equations*

Code

Standard

Lessons

Worksheets

Games

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.

Create Equations & Inequalities

Modeling with one-variable equations and inequalities

Create Equations & Inequalities

Words to Algebra Games

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.

Linear Equations

Quadratic Equations

Rational Functions

Exponential Functions

Graph Linear Equations

Solve Quadratic Equations

Modeling with two-variable equations and graphs

Equation of Line Games

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.

Represent Constraints

Modeling constraints with two-variable inequalities

Systems of Equations Word Problems

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.

Rearrange Formulas

Manipulate formulas

Solving equations in terms of a variable

Rearrange Formulas



Reasoning with Equations and Inequalities

Code

Standard

Lessons

Worksheets

Games

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.

1-Step Equations

2-Step Equations

Multi-Step Equations

Understand process for solving linear equations

Understand process for solving quadratic equations

Algebra Worksheets

Equations with variables on both sides

Algebra Games

HSA-REI.A.2

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Rational Equations

Radical Equations

Extraneous solutions to rational equations

Rational equations 1

Rational equations 2

Extraneous solutions to radical equations

Radical Equations

 

HSA-REI.B.3

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

Linear Inequalities

Compound Inequalities

Multi-step linear inequalities

Compound inequalities

 

HSA-REI.B.4

Solve quadratic equations in one variable.

See Below


 

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)2 = q that has the same solutions. Derive the quadratic formula from this form.

Complete the Square and Quadratic Formula

Completing the square 1

Completing the square 2

 

HSA-REI.B.4b

Solve quadratic equations by inspection (e.g., for x2 = 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 Ѧnbsp;bi for real numbers a and b.

Solve Quadratic Equations

Quadratic Formula

Derive Quadratic Formula

Solve quadratics by taking the square root

Solve quadratics by factoring

Solve quadratics by factoring 2

Using the quadratic formula

Quadratic formula with complex solutions

Types of solutions to quadratic equations

 

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.

Understand Systems of Equations

Graphically understand systems of equations

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.

Solve Systems of Equations

Systems of Equations Worksheets

Systems of equations

Graphing systems of equations

Systems of equations word problems

 

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 x2 + y2 = 3.

Systems of Linear and Quadratic Equations

Systems of nonlinear equations

 

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).

Systems of Equations & Matrices

Row Echelon Form & Reduced Row Echelon Form

Writing systems of equations as matrix equations

Solving matrix equations

Matrix Equations

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).

Graphs of Equations

Interpret graphs of linear and nonlinear functions

Graphs of Equations

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.

Intersection of Graphs

Successive Approximation (Newton's Method)

Graphs of Exponential Functions

Intersecting functions

Points of Intersection

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.

Graph Linear Inequalities & System of Linear Inequalities

Graph linear inequalities

Graph & solve linear inequalities

Graph systems of inequalities

Graph & solve systems of inequalities

 


 

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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