Select the cluster for resources on this page:
REI-A: Understand solving equations as a process of reasoning and explain the reasoning
REI-B: Solve equations and inequalities in one variable
REI-C: Solve systems of equations
REI-D: Represent and solve equations and inequalities graphically
REI Unit: Reasoning with Equations and Inequalities Performance Task identified by New York City School System.
Standards:
Technology-enhanced investigations:
Mathwords.com: Math Dictionary: Key vocabulary for this domain. Use with REI-A, REI-B, REI-C and REI-D:
LearnZillion:
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.
PurpleMath:
Just Math Tutorials, videos by Patrick JMT: Solving an Equation with a Single Radical: After viewing the first example, view the related math videos with examples 2 and 3.
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.
McDougal Littell ClassZone, Algebra 2, 2011: Select resources in Ch. 6 Rational Exponents and Radical Functions and Ch. 8 Rational Functions for interactive practice: Animations (Virtual manipulatives), Games/Vocabulary Flashcards, and PowerPoint lesson examples, and interactive problems within the eWorkbook. See multiple choice below for related sections to use within the eWorkbook. Use with REI-A.
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.
Multiple Choice:
Khan Academy: Practice questions with videos.
Glencoe Online Learning Center, Algebra 2 (2010) self-check quizzes:
McDougal Littell ClassZone, Algebra 2, 2011:
OpenEd:
Constructed-response:
Khan Academy: Practice questions with videos.
OpenEd:
Performance tasks:
Illustrative Mathematics: Algebra:
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:
Mathematics Vision Project, Secondary 3 Student Edition:
Standards:
Technology-enhanced investigations:
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).
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.
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 = x^{2} - 2x + (0 or 1 or 2). The prerequisite or co-requisite is some working experience with algebra, like factoring x^{2} -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.
LearnZillion:
WisWeb: Virtual Manipulatives:
Thinking Mathematics:
Wisc-Online, Learning Objects:
Purple Math:
Algebrahelp.com: Calculator Index: Lists the online calculators provided at the site for solving and working with algebra equations, simplifying expressions, graphing functions, prime factoring numbers, operations with fractions, solving proportions, and so on.
McDougal Littell ClassZone, Algebra 2, 2011: Select resources in Ch. 1 Equations and Inequalities and Ch. 4 Quadratic Functions and Factoring for interactive practice: Animations (Virtual manipulatives), Games/Vocabulary Flashcards, and PowerPoint lesson examples, and interactive problems within the eWorkbook. See multiple choice below for related sections to use within the eWorkbook. Use with REI-B.
Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives:
Multiple Choice:
CK-12: Algebra: Video examples, practice problems online, and real world applications. The following align with REI-B.3:
Glencoe Online Learning Center, Algebra 2 (2010) self-check quizzes:
Khan Academy: See Algebra I: Quadratic Equations and Algebra 2: Polynomial Expressions, Equations and Functions: Practice questions with videos. Use with REI-B.4:
McDougal Littell ClassZone, Algebra 2, 2011:
OpenEd:
Constructed-response:
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:
Khan Academy: See Algebra I: One-variable Linear Equations; Algebra 1: One-variable Linear Inequalities; Algebra I: Quadratic Equations; Algebra 2: Rational Equations and Functions; Algebra 2: Polynomial Expressions, Equations and Functions: Practice questions with videos. Use with REI-B.3 and REI-B.4. For example:
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.
OpenEd:
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.
Performance tasks:
Illustrative Mathematics: Algebra:
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: http://map.mathshell.org/stds.php?standardid=1190
Mathematics Vision Project, Secondary 1 Student Edition:
Standards:
Technology-enhanced investigations:
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.
LearnZillion:
Math Planet, Algebra 1: Following align with REI-C.6. Each includes an example and video instruction.
Math Planet, Algebra 2: Following align with REI-C.8 and REI-C.9. Each includes an example and video instruction.
Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives:
McDougal Littell ClassZone, Algebra 2, 2011: Select resources in Ch. 3 Linear Systems and Matrices for interactive practice: Animations (Virtual manipulatives), Games/Vocabulary Flashcards, and PowerPoint lesson examples, and interactive problems within the eWorkbook. Use with REI-C.
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.
NCTM Illuminations:
National Security Agency: Making Connections: Matrices, Graphs, and Linear Systems: Students use graphing calculators to solve systems of linear equations in two ways. They first solve the systems by graphing the equations and finding the point of intersection. Next, they will solve systems of equations by writing related matrices and finding the solution by using inverse matrices.
PBS Mathline: Meadows or Malls?: Students explore the use of matrices and graphing calculators to solve a complex linear programming problem with six variables.
Purple Math:
YouTube.com video lessons:
Following YouTube video lessons align with REI-C.8 and REI-C.9:
Multiple Choice:
Glencoe Online Learning Center, Algebra 1 (2010) self-check quiz:
Glencoe Online Learning Center, Algebra 2 (2010) self-check quizzes:
McDougal Littell ClassZone, Algebra 2, 2011:
OpenEd:
Constructed-response:
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.
OpenEd:
WiscOnline, Learning Objects: Solving Systems of Linear Equations Using the Addition and Subtraction Method and Solving Systems of Linear Equations using the Substitution Method: Students review each method for solving simultaneous equations and complete a series of practice problems using each 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: see Precalculus: Matrices: Practice questions with videos. Use the following with REI-C.8 and REI-C.9:
Performance tasks:
Georgia Standards of Excellence Framework:
Illustrative Mathematics: Algebra:
Inside Mathematics: MARS Tasks:
Mathematics Assessment Project: Standards: High School: Algebra: http://map.mathshell.org/stds.php?standardid=1190
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.
NCTM's Reasoning and Sense Making Task Library: Over the Hill includes the task overview, teacher notes for its use in the classroom, 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.
Standards:
Technology-enhanced investigations:
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.
LearnZillion:
Southeast Comprehensive Center of SEDL: Video: Represent and solve equations and inequalities graphically: This video aligns with standard REI-D.11. View online or download.
McDougal Littell ClassZone, Algebra 2, 2011: Select resources in Ch. 2 Linear Equations and Functions, Ch. 3 Linear Systems and Matrices and Ch. 4 Quadratic Functions and Factoring for interactive practice: Animations (Virtual manipulatives), Games/Vocabulary Flashcards, and PowerPoint lesson examples, and interactive problems within the eWorkbook. Use with REI-D.
NCTM Illuminations: Supply and Demand: This activity focuses on having students create and solve a system of linear equations in a real-world setting. By solving a system of two equations in two unknowns, students will find the equilibrium point for supply and demand.
Purple Math: Graphing Linear Inequalities
Shodor Interactivate:
Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives:
Multiple Choice:
Glencoe Online Learning Center, Algebra 1 (2010) self-check quiz: Ch. 6, Lesson 8: Systems of Inequalities
Glencoe Online Learning Center, Algebra 2 (2010) self-check quiz: Ch. 3, Lesson 3: Solving Systems of Inequalities by Graphing
McDougal Littell ClassZone, Algebra 2, 2011:
Constructed-response:
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:
OpenEd:
Khan Academy: see Algebra 1: Functions and Algebra 2: Advanced Equations and Functions: Practice questions with videos. Use the following with REI-D.12:
Performance tasks:
Illustrative Mathematics: Algebra:
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: http://map.mathshell.org/stds.php?standardid=1190
Mathematics Vision Project, Secondary 1 Student Edition:
Mathematics Vision Project, Secondary 3 Student Edition:
Performance task:
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.
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