Common Core High School Algebra Teaching and Learning Resources

Mathwords.com: Math Dictionary: Key vocabulary for this domain.  Use with REI-A, REI-B, REI-C and REI-D:

Imagine Learning Classroom (formerly LearnZillion) subscription needed:

• Lesson set: Solve and explain simple algebraic equations: This is a series of five video lessons that also include guided practice on this topic.  Videos demonstrate how to recognize properties of unknown values by using real number examples, and addition and subtraction with real number examples; using additive and multiplicative inverses to solve algebraic equations; and using multiple operations to solve linear equations. Aligns with REI-A.1.
• Lesson set: Justify solutions to equations in terms of equation properties: Six lessons delve into solving equations using a balance scale, distributive property, using properties, and working backwards.  Aligns with REI-A.1.
• Lesson set: Solve simple rational and radical equations in one variable: This is a series of four video lessons that also include guided practice on this topic.  Videos demonstrate how to solve rational expressions by using additive and multiplicative inverses, identify extraneous solutions in rational equations by checking solutions, solve radical expressions by using rules of exponents, and determine if a radical equation has an extraneous solution by solving.  Align with REI-A.2.

MIT BLOSSOMS: Video lesson with additional teacher and learner resources.  Description is from the video summary.  Flu Math Games: "This video lesson shows students that math can play a role in understanding how an infectious disease spreads and how it can be controlled."  Additional simulations are included.  Aligns with Algebra standards SSE-B.3.c and REI-A.1; Function standards IF-C.8.b, BF-B.4.a, and LE-A-1.(a, c); and Statistics and Probability standards ID-B.6.a, IC-A.1, IC-B.4, CP-A.2, and MD-A.1.

PatrickJMT videos on YouTube:

• Solving an Equation with a Single Radical (Square Root)-Example 1
• Solving an Equation with a Single Radical (Square Root)-Example 2
• Solving an Equation with a Single Radical (Square Root)-Example 3

Purple Math:

• Solving Radical Equations: Introduction and Examples
• Solving Rational Equations

Shodor Interactivate: Solving Equations: Discussions and activities are designed to help students understand the concepts behind and methods of solving equations. This lesson is best implemented with students working in groups of 2-4.  Also see Equation Solver, which includes the virtual manipulative.

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives: US Common Core State Standard Math HSA-REI.A.1: 5 manipulatives: Solving quadratic equations with integer coefficients, solution of quadratic equations, two-step equations, solving multiplication equations, solving simple equations.

Khan Academy: Practice questions with videos.

• Understand the process for solving quadratic equations by taking square roots. Aligns with REI-A.1.

Khan Academy: HSA-A-REI includes HSA-REI.A.1 and HSA-REI.A.2 Common Core aligned problems.

Also see the following practice questions with videos:

• Equations with variables on both sides: Aligns with REI-A.1.
• Solve square root equations (basic): Aligns with REI-A.2
• Solve square root equations (advanced): Aligns with REI-A.2.
• Analyze extraneous solutions of radical equations: Aligns with REI-A.2.
• Solve equations with 1 rational expression: Numerator and denominator are linear expressions.  Aligns with REI-A.2.
• Solve equations with 1 rational expression (advanced): Numerator and denominator are polynomial expressions.  Aligns with REI-A.2.
• Solve equations with 2 rational expressions.  Aligns with REI-A.2.

Illustrative Mathematics: Algebra:

• Same Solutions? Aligns with standard REI-A.
• Radical Equations: Aligns with standard REI-A.2.

Inside Mathematics: MARS Task: Magic Squares: Students find cell values in magic squares and simple algebraic notation.  This task aligns with standards REI-A.1, REI-A.2.

Mathematics Vision Project, Secondary 1 Student Edition:

• Getting Ready Module:  This module contains 10 classroom tasks.  Task 5: Cafeteria Actions and Reactions; Task 7: Solving Equations, Literally; Task 8: Cafeteria Conundrums; Task 9: Greater Than; and Task 10: Taking Sides align to algebra standard REI-A.1.

Mathematics Vision Project, Secondary 3 Student Edition:

• Module 4: Rational Functions: This module contains 7 classroom tasks.  Multiple standards are addressed. Standards REI-A.2, REI-D.11 are among those found in task 7.

Art of Problem Solving: Introduction to Algebra Videos: These are the videos that go with each of the sections within the 13-chapter textbook, Introduction to Algebra.  View Ch. 3 One-Variable Linear Equations, Ch. 4, section 5: Introduction to Multi-Variable Equations, Ch. 9 Introduction to Inequalities, Ch. 10 Quadratic Equations-Part 1 (includes factoring); and Ch. 13 Quadratic Equations-Part 2 ( includes completing the square, proving the quadratic formula, using the quadratic formula, the discriminant, and quadratic problem solving).

Course Hero: College-Algebra: Solving Linear Equations and Inequalities contains an overview of methods with vocabulary, worked examples.  Aligns with REI-B.

NCTM Illuminations: Algebra Tiles. "Use tiles to represent variables and constants, learn how to represent and solve algebra problem. Solve equations, substitute in variable expressions, and expand and factor. Flip tiles, remove zero pairs, copy and arrange, and make your way toward a better understanding of algebra."  Aligns with REI-B.

Study.com: Algebra: Each of the following algebra chapters includes video lessons with sample problems and a short quiz with each video.  There is a multiple choice chapter test following the last video in each chapter.

• Foundations and Linear Equations: Nine video lessons. View: What makes an equation linear?  Use with REI-B.3.
• Inequalities: Six video lessons on inequalities.  Learn what an inequality is, how to graph 1- and 2-variable inequalities; set notation, compound inequalities, and systems of inequalities; and how to solve and graph absolute value inequalities.  Practice problems are included.  Use with REI-B.3.
• Factoring with FOIL, Graphing Parabolas and Solving Quadratics: 11 video lessons.  Lessons on quadratics include how to solve via completing the square, factoring, and using the quadratic formula.  Use with REI-B.4.

MIT BLOSSOMS: Video lesson with additional teacher and learner resources.  Description is from the video summary.  The Quadratic Equation: It’s Hip to Be Squared: "The lesson begins with three quadratics and their graphs (three parabolas):  y = x² - 2x + (0 or 1 or 2). The prerequisite or co-requisite is some working experience with algebra, like factoring x² -2x into x(x-2). The objective is to connect four things: the formula for y, the graph of y (a parabola), the roots of y and the minimum or maximum of y."  Aligns with Algebra standards SSE-B.3.a, CED-A.2, and REI-B.4.b and Function standards IF-B.4, IF-C.7.a, IF-C.8.a, BF-B.3.

Imagine Learning Classroom (formerly LearnZillion) subscription needed:

• Lesson set: Solve linear equations and inequalities in one variable: This is a series of eight video lessons that also include guided practice on this topic.  Videos demonstrate how to solve equations and word problems involving one variable, including when variables are on both sides in a equation or when some coefficients are letters; how to solve inequalities and inequality word problems using additive and multiplicative inverses; and how to solve compound inequalities.  Aligns with REI-B.3.
• Lesson set: Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula, and factoring: This is a series of ten video lessons that also include guided practice on this topic.  Lessons address each method to solve a quadratic and also include how to determine when the quadratic has no real solutions and how to choose the best method to solve a quadratic. Aligns with REI-B.4.b.

Omnicalculator.com: Quadratic formula returns the roots of a quadratic equation, including complex roots.  Users can enter a quadratic in standard form, symmetry-vertex form, or factored form.  Explanation of theory is included.  Aligns with REI-B.4.

WisWeb: HTML5 Applets:

• Click on the title: Liniar Equations on the list of applets to access the Equations Balance Strategy. Learners solve linear equations of increasing difficulty, showing their steps indicating operations to be performed on each side of the given equation.  Use this HTML5 applet with standard REI-B.3.

Thinking Mathematics:

• Completing the Square: A YouTube video in two parts on solving the quadratic equation using the geometry of a square.
• Deriving the Quadratic Formula: A YouTube video.

Wisc-Online, Learning Objects:

• Factoring the Difference of Two Perfect Squares: In this interactive learning object, learners work problems involving the difference of two perfect squares.

Purple Math:

• Quadratic Formula Explained
• Completing the Square: Quadratic Examples and Deriving the Quadratic Formula
• Solving Quadratic Equations: This is a series of lessons with practice exercises on methods for solving quadratic equations, including factoring, taking roots, completing the square, graphing, using the quadratic formula.  This unit would align with standard REI-B.4.

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives:

• US Common Core State Standard Math HSA-REI.B.3: 5 manipulatives: Graphs of inequalities, two-step equations, solving multiplication equations, solving simple equations, algebra quiz (Choose the type of problem for your quiz. You can also select the number of problems and different forms).
• US Common Core State Standard Math HSA-REI.B.4: 6 manipulatives: Complex zeroes of quadratic functions, solving quadratic equations with integer coefficients, identifying trinomials that are perfect squares, solution of quadratic equations, polynomial roots in the complex plane, algebra quiz (Choose the type of problem for your quiz. You can also select the number of problems and different forms).

YouTube video lessons:

• Solve a simple Quadratic Equation with no linear term (solve by square root method)
• Factoring Quadratics with a Common Factor
• Solve Quadratics by Factoring (includes reminder to set equation =0 as a first step)
• Solve Quadratic Equations using Quadratic Formula
• Solving Quadratic Equations by Graphing includes three examples.
• Completing the Square - Solving Quadratic Equations

CK-12: Algebra: Video examples, practice problems online, and real world applications.  The following align with REI-B.3:

• Applications of Two-Step Equations

Khan Academy: Practice questions with videos.  Use with REI-B.4:

• Algebra I: Quadratic Equations
• Algebra 2: Solve Quadratic Equations with Complex Solutions

Achieve the Core: Quadratic Equations Mini-Assessment (pdf or Word docx) can be used to evaluate students' understanding of algebra standards REI-B.4 and CED-A.1 in order to prepare to teach this material or to check for student ability to demonstrate understanding and apply these concepts.

CK-12: Algebra: Video examples, short-answer practice problems online, and real world applications.  The following align with REI-B.3:

• Applications of Linear Equations (also includes downloadable quiz in multiple choice format)
• Applications of Multi-Step Equations

Khan Academy: HSA-A-REI includes HSA-REI.B.3 and HSA-REI.B.4 Common Core aligned problems.

Also see the following:

• Algebra I: One-variable Linear Equations
• Algebra 1: One-variable Linear Inequalities
• Algebra I: Quadratic Equations
• Algebra 2: Radical Equations and Functions
• Algebra 2: Polynomials: Quadratic Equations with Complex Numbers

L. Spector: The Math Page: Skill in Algebra.  Students see worked examples of concepts and following the presentation within each section, students are presented problems in constructed response form.  They would solve using paper-pencil and then by using their mouse to roll over a box, they see the solution to problems presented.  Use with standards REI-B.3 and REI-B.4.

• Lesson 9: Solving Linear Equations: This includes solving equations with coefficients that are letters, and variables on one or both sides of the equation and equations with fractions.
• Lesson 10: Word Problems: Using linear equations.
• Lesson 11: Inequalities
• Lesson 24: Equations with Fractions: Includes clearing fractions
• Lesson 25: Word Problems that lead to equations with fractions
• Lesson 37: Quadratic Equations: There are three parts, including solutions by factoring, completing the square, using the quadratic formula, the discriminant, and graphing.

MATHguide.com:

• Solving quadratic equations with the formula.  Formula is presented.  Quizmaster presents the quadratic equation.  Fill in answers rounded to nearest tenth and check answers.

• Practice factoring quadratic trinomials with integer coefficients.  Fill in and check answers.

Shodor Interactivate: Algebra Quiz: Learners solve algebraic linear and quadratic equations of one variable. Choose difficulty level, question types, and time limit.

S.O.S. Math: Solving Equations: Linear and Quadratic: Detailed solutions are provided as feedback to equations presented.

Illustrative Mathematics: Algebra:

• Two Squares are Equal: Solve the quadratic using as many methods as possible.  This aligns with standards REI-B.4 and REI-D.11.
• Braking Distance: Aligns with REI-B.4.b.
• Springboard Dive: Aligns with REI-B.4.b and function standard IF-C.8.a.

Inside Mathematics: MARS Task: Quadratic 2009: Students work with a quadratic function in various forms.  This task aligns with function standards IF-B.4, IF-C.7, IF-C.8 and algebra standard REI-B.4.

Mathematics Assessment Project: Standards: High School: Algebra:

• Task 218: Sorting Equations and Identities
• Task 432: Solving Quadratic Equations: Cutting Corners

Mathematics Vision Project, Secondary 1 Student Edition:

• Getting Ready Module: This module contains 10 classroom tasks.  Task 6: Elvira’s Equations; Task 7: Solving Equations, Literally; Task 8: Cafeteria Conundrums; Task 9: Greater Than; and Task 10: Taking Sides align to algebra standard REI-B.3.
• Module 3: Arithmetic and Geometric Sequences: This module contains 10 classroom tasks.  Task 8: What Does It Mean?; and Task 9: Geometric Meanies align to standard REI-B.3.
• Module 4: Linear and Exponential Functions: This module contains 10 classroom tasks.  Task 10: X Marks the Spot aligns to standard REI-B.3.

Art of Problem Solving: Introduction to Algebra Videos: These are the videos that go with each of the sections within the 13-chapter textbook, Introduction to Algebra.  View Ch. 5 Multi-Variable Linear Equations (solving systems, including word problems.)

Concord Consortium STEM resources: Mathematics:  Each of the following includes an applet, student activity, teacher lesson plan, and student assessment.

• Solving Systems of Equations: Two linear equations, with two variables, are presented and students use graphs to solve the system of equations. Students graph the lines and solve the problem using the graphs.  Aligns with CED-A.2 and REI-C.6.
• Systems of Equations: Word Problems 1: Students explore two real-life scenarios that involve solving systems of equations. The first situation involves mixing chemicals to create a new solution while the second situation involves cost and revenue for a bake sale.  Aligns with CED-A.2 and REI-C.6.
• Systems of Equations: Word Problems 2: Students explore two new scenarios that involve solving systems of equations. The first situation involves the travel time for a round trip on an airplane, while the second situation involves calculating the numbers of students and adults attending a high school musical.  Aligns with CED-A.2 and REI-C.6.

Imagine Learning Classroom (formerly LearnZillion) subscription needed:

• Lesson set: Understanding systems of equations in two variables: This is a series of four video lessons that also include guided practice on this topic.  Aligns with REI-C.5.
• Lesson set: Solve systems of linear equations exactly and approximately: This is a series of four video lessons that also include guided practice on this topic.  Videos demonstrate how to solve systems with graphs, substitution, elimination, and include a lesson for solving word problems using systems of equations.  Aligns with REI-C.6.
• Lesson set: Solve simple systems of equations with linear and quadratic equations: This is a series of six video lessons that also include guided practice on this topic.  Videos demonstrate how to solve linear and quadratic systems graphically and algebraically when there are 0, 1, or 2 solutions to the systems.  Aligns with REI-C.7.

Math Planet, Algebra 1: Following align with REI-C.6.  Each includes an example and video instruction.

• The substitution method for solving linear systems
• The elimination method for solving linear systems
• The graphing method for solving linear systems

Math Planet, Algebra 2: Following align with REI-C.8 and REI-C.9.  Each includes an example and video instruction.

• Basic information about matrices
• How to operate with matrices
• Determinants
• Using matrices when solving system of equations

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives:

• US Common Core State Standard Math HSA-REI.C.6: 11 manipulatives: Lines-2 points, When two runners meet, Two-by-two linear systems, Intersecting lines using slope-intercept form, Finding a pattern (linear equations), Two points determine a line, Lines: point-slope, Lines: slope-intercept, a linear programming scenario, the Fundamental Theorem of linear programming, and algebra quiz.
• US Common Core State Standard Math HSA-REI.C.7: 4 manipulatives: the Wire Problem, Maximizing the area of some geometric figures of fixed perimeter, the Intersection of a line and a circle, and Finding a tangent line to a parabola.

MIT BLOSSOMS: Video lesson with additional teacher and learner resources.  Description is from the video summary.  Selfish Drivers: The Braess Paradox and Traffic Planning: "The idea of this lesson is to introduce, in a simplified manner, the so-called Braess Paradox by providing simple examples to clarify that the addition of some new roads to a network does not always lead to an improvement in the liquidity of the traffic; in some cases it might even increase the time required to get from one point to another if all drivers are selfish. The educational objectives for this lesson can be summarized as follows: providing a practical application of mathematics; indicating the importance of scientific research; training the students on methods of counting and surveying all the possibilities in a given problem; and introducing Nash Equilibrium and Braess Paradox in a simplified manner by visual examples."  Aligns with CED-A.3 and REI-C.6.

Purple Math:

• Systems of Linear Equations
• Matrix Inversion: Finding the inverse of a matrix
• Minors and Cofactors: technique for finding determinants of square matrices 4 x 4 or larger.
• Cramer's Rule
• Determinants

YouTube.com video lessons:

• Solve Systems of Linear Equations by Substitution
• Solve Systems of Linear Equations by Elimination (Part 1: you can add or subtract at step 1)
• Solve Systems of Linear Equations by Elimination  (Part 2: first find a common multiple for one variable in both equations, then add or subtract)
• Solve Systems of Linear Equations by Graphing

Following YouTube video lessons align with  REI-C.8 and REI-C.9:

• Introduction to Augmented Matrices to solve systems of equations
• Augmented Matrices: Row Echelon Form to solve a system of equations
• Ex 1: Solve a System of Two Equations with Using an Augmented Matrix (Row Echelon Form)
• Ex 2: Solve a System of Two Equations with Using an Augmented Matrix (Row Echelon Form)
• Ex 3: Solve a System of Two Equations with Using an Augmented Matrix (Row Echelon Form)
• Augmented Matrices: Reduced Row Echelon Form to solve a system of equations, including systems of three or more equations.
  
• Using a Matrix Equation to Solve a System of Equations
• Ex 1: Solve a System of Two Equations Using a Matrix Equation
• Ex 2: Solve a System of Two Equations Using a Matrix Equation
• Ex: Solve a System of Three Equations Using a Matrix Equation
• Solving Systems of Equations using Matrices on the Calculator: use your ti-83+/84+; Example uses 3 equations with 3 unknowns
• Matrix Operations on the TI-83+ TI-84+

L. Spector: The Math Page: Skill in Algebra.  Students see worked examples of concepts and following the presentation within each section, students are presented problems in constructed response form.  They would solve using paper-pencil and then by using their mouse to roll over a box, they see the solution to problems presented.  Use with standards REI-C.5 and REI-C.6 and REI-C.8.

• Lesson 35: Simultaneous Linear Equations: solution methods involving addition, substitution, multiplication, and determinants.
• Lesson 36: Word Problems that lead to simultaneous equations 

Wisc-­Online, Learning Objects: Students review each method for solving simultaneous equations and complete a series of practice problems using each method:

• Solving Systems of Linear Equations Using the Addition and Subtraction Method
• Solving Systems of Linear Equations using the Substitution Method

Algebra Lab: Solving Systems of Linear Equations: Students are provided explanation for review and then complete problems.  Steps in solutions are provided as feedback.

MATHguide.com: Solve systems of linear equations: See examples for solving systems of linear equations with addition, multiplication/addition, and substitution.  Follow each lesson with a quizmaster.  Fill in and check answers.

Khan Academy: HSA-A-REI includes HSA-REI.C.5 thru REI.C.9 Common Core aligned problems.

Also see the following:

• Precalculus: Matrices is a comprehensive unit with practice questions and videos.  Use with REI-C.8 and REI-C.9.

Georgia Standards of Excellence Framework:

• Pre-Calculus Unit 5: Matrices.  This unit contains five tasks: Central High Booster Club, Walk Like a Mathematician, Candy? What Candy?, An Okefenoke Food Web, and a Culminating Task: Vacationing in Georgia.  Tasks align with VM-C.6, VM-C.7, VM-C.8, VM-C.9, VM-C.10, VM-C.12 and algebra standards REI-C.8, REI-C.9.
• Pre-Calculus Unit 6: Conics.  This unit contains eight tasks: Our Only Focus: Circles and Parabolas Review, The Focus is the Foci: Ellipses and Hyperbolas, Deriving the General Equation of a Parabola, Parabolas in Other Directions, Writing the Equations of Parabolas, The Intersection of a Line and a Quadratic, A Conic Application, and Culminating Task: Dr. Cone's New House.  Tasks align with GPE-A.1, GPE-A.2, and GPE-A.3, and algebra standard REI-C.7.

Illustrative Mathematics: Algebra:

• Cash Box: Aligns with algebra standards CED-A and REI.C.6.
• The Circle and the Line: Aligns with standard REI-C.7.

Inside Mathematics: MARS Tasks:

• Coffee: Students use a chart to solve simultaneous equations.  This task aligns with function standard BF-A.1 and algebra standard REI-C.6.
• Graphs (2006): Students use knowledge of graphs and their features to identify the linear equations of graphs shown and write equations of lines.  This task aligns with algebra standards REI-C.6, REI-D.10, and REI-D.11.

Mathematics Assessment Project: Standards: High School: Algebra:

• Task 207: Optimization Problems: Boomerangs
• Task 209: Solving Linear Equations in Two Variables

Mathematics Vision Project, Secondary 1 Student Edition: Module 2: Systems of Equations and Inequalities: This module contains 10 classroom tasks.  Standards addressed in Module 1 include REI-C.5, REI-C.6, REI-D.12, and CED-A.2, CED-A.3, and CED-A.4.

• Task 7: Shopping for Cats and Dogs; and Task 8: Can You Get to the Point, Too? align to both standards REI-C.5 and REI-C.6.
• Task 6: Get to the Point; and Task 10: Taken Out of Context align to standard REI-C.6.

NCTM's Reasoning and Sense Making Task Library: Over the Hill includes the task overview, teacher notes for its use, and student activity sheet.  Aligns with function standard BF-A.1b, algebra standards CED-A.2, REI-C.6, and mathematical practice standards 1, 4, 5, and 7.

Art of Problem Solving: Introduction to Algebra Videos: These are the videos that go with each of the sections within the 13-chapter textbook, Introduction to Algebra.  View Ch. 8 Graphing Lines, including systems of linear equations; and Ch. 9, section 4 Graphing Linear Inequalities.

Concord Consortium STEM resources: Mathematics:  Each of the following includes an applet, student activity, teacher lesson plan, and student assessment.

• y= mx + b: Learn to graph a line using its slope and y-intercept, or to identify the slope and y-intercept from a linear equation written in slope-intercept form.  Aligns with standard CED-A.2, and REI-D.10.
• Linear Equations: Points, Intercepts, and Slopes, Oh My!: Students learn to graph lines using the x- and y-intercepts of equations, as well as how to graph a line when given an equation in point-slope form.  Aligns with standard CED-A.2, and REI-D.10.
• Linear Equations: Word Problems:  Learn to apply linear equations and their graphs to real-world problems. Write an equation based on a word problem, and graph the line described by your equation. Relate the equation and the line to the situation described in words.  Aligns with CED-A.2 and REI-D.10.

Imagine Learning Classroom (formerly LearnZillion) subscription needed:

• Lesson set: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane: This is a series of three video lessons that also include guided practice on this topic.  Videos demonstrate how to create a table of values from an equation, graph an equation using a table of values, and determine if a coordinate pair is a solution to an equation by using its graph.  Aligns with REI-D.10.
• Lesson set: Identify the points of intersection between y = f(x) and y = g(x) as the solutions to f(x) = g(x).  Four video lessons using graphing: Solution of two equations by finding their intersection, solutions to a system with two solutions, systems with no solutions, find two solutions for two equations (one linear and one quadratic).  Aligns with REI-D.11.
• Lesson set: Graph the solutions to a linear inequality as a half-plane, and the solutions to a system of linear inequalities as an intersection of half-planes.  Six video lessons using graphing: Graph a linear inequality with a < or ≤ symbol, graph a linear inequality with a > or ≥ symbol, check the half-plane for correct shading, graph systems of linear inequalities by shading their intersection, check graphing of a system of inequalities, find solutions to linear inequalities from context.  Aligns with REI-D.12.

Purple Math: Graphing Linear Inequalities

Shodor Interactivate:

• Graphit: Graph linear equations and inequalities.
• Linear inequalities: Graph up to four linear inequalities in two variables on the same set of axes to model examples of intersections of inequalities.  Activity worksheets and discussion are also provided.

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives:

• US Common Core State Standard Math HSA-REI.D.10: 2 manipulatives: Bounce time for a bouncing ball, and Graph of Inequalities
• US Common Core State Standard Math HSA-REI.D.11: 1 manipulative: Intersection of a line and a circle
• US Common Core State Standard Math HSA-REI.D.12: 1 manipulative: Graph of Inequalities

YouTube video lessons:

• Paired Data and the Rectangular Coordinate: graph linear equations using x- and y- intercepts; ordered pairs satisfying the equation.
• Solve and graph the linear inequality in one variable: Reviews rule for division by a negative integer when solving
• Graph inequalities in two variables

L. Spector: The Math Page: Students see worked examples of concepts and following the presentation within each section, students are presented problems in constructed response form.  They would solve using paper-pencil and then by using their mouse to roll over a box, they see the solution to problems presented.  Use the following with REI-D.10 and REI-D.11:

• Skill in Algebra: Lesson 33: The Equation and Graph of a Straight Line
• Skill in Algebra: Lesson 37: Quadratic Equations: The graph of a quadratic (parabola)
• Topics in Precalculus: Topic 5: Basic Graphs: introduces the learner to the constant function, identity function, parabola, absolute value, square root, and cubic function.

Khan Academy: HSA-A-REI includes HSA-REI.D.10 thru REI.D.12 Common Core aligned problems.

Also see the following:

• Algebra 1: Functions and Algebra 2: Advanced Equations and Functions are comprehensive units with practice questions and videos.  Use with REI-D.12.

Illustrative Mathematics: Algebra:

• Taxi!: Aligns with REI-D.10 and function standard LE-B.5.
• Two Squares are Equal: Solve the quadratic using as many methods as possible.  This aligns with standards REI-B.4 and REI-D.11.
• Population and Food Supply: This involves linear and exponential functions.  Aligns with REI-D.11 and function standards LE-A.2 and LE-A.3.
• Solution Sets: This task involves determining linear inequalities and begins with a given set of equations and shaded regions on a graph. Aligns with REI-D.12.
• Fishing Adventures 3: Students are given a real world problem in which they write equations and graph inequalities to solve it.  Aligns with REI-D.12 and CED-A.3.

Inside Mathematics: MARS Task: Graphs (2006): Students use knowledge of graphs and their features to identify the linear equations of graphs shown and write equations of lines.  This task aligns with algebra standards REI-C.6, REI-D.10, and REI-D.11.

Mathematics Assessment Project: Standards: High School: Algebra:

• Task 207: Optimization Problems: Boomerangs
• Task 219: Defining Regions Using Inequalities

Mathematics Vision Project, Secondary 1 Student Edition:

• Module 2: Systems of Equations and Inequalities: This module contains 10 classroom tasks.  Standards addressed in Module 1 include REI-C.5, REI-C.6, REI-D.10, REI-D.12, and CED-A.2, CED-A.3, and CED-A.4.  Task 6 aligns with REI-D.10; Task 2: Too Big or Not Too Big, That is the Question; Task 3: Some of One, None of the Other; Task 4: Pampering and Feeding; and Task 5: All for One, One for All, parts 1 & 2, align with REI-D.12.
• Module 5: Features of Functions: This module contains nine classroom tasks.  Task 4: Water Park; Task 5: Pooling it Together; Task 6: Interpreting Functions; and Task 9: Match That Function align with REI-D.11.

Mathematics Vision Project, Secondary 3 Student Edition:

• Module 4: Rational Functions: This module contains 7 classroom tasks.  Multiple standards are addressed. Standards REI-A.2, REI-D.11 are among those found in task 7.

New York City School System: High School Algebra: The Cycle Shop: Unit Overview: “This packet contains a curriculum-embedded CCLS aligned task and instructional supports. The task is embedded in a 4-5 week unit on reasoning with Equations and Inequalities.” Algebra standards addressed include REI-A.1, REI-B.3, REI-C.6, and CED-A.2, CED-A.3.  Mathematical Practices standards include MP.1, MP.3, MP.4, and MP.7.