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Common Core High School Algebra Teaching and Learning Resources

Domain: REI: Reasoning with Equations and Inequalities

Common Core Math

Select the cluster for resources on this page:

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REI-A: Understand solving equations as a process of reasoning and explain the reasoning

Standards:

 

Technology-enhanced investigations:

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

absolute value rules linear inequality polynomial rational function
Cramer's rule linear system of equations quadratic equation solve
exponential function logarithm rules quadratic formula solve graphically
extraneous solution matrix radical rules system of equations
linear equation matrix inverse rational equation system of inequalities

 

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.

Purple Math:

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.

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.

Constructed-response:

Khan Academy: Practice questions with videos.

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:

 

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REI-B: Solve equations and inequalities in one variable

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).

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.

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.

LearnZillion:

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: Virtual Manipulatives (requires Java):

Thinking Mathematics:

Wisc-Online, Learning Objects:

Purple Math:

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

YouTube video lessons:

Multiple Choice:

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

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

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:

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.

MATHguide.com:

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:

Mathematics Vision Project, Secondary 1 Student Edition:

 

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REI-C: Solve systems of equations

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:

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:

YouTube.com video lessons:

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

Multiple Choice:

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.

Wisc-­Online, Learning Objects: 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: Precalculus: Matrices is a comprehensive unit with practice questions and videos.  Use 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:

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.

 

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REI-D: Represent and solve equations and inequalities graphically

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.

Purple Math: Graphing Linear Inequalities

Shodor Interactivate:

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

YouTube video lessons:

Multiple Choice:

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:

Khan Academy: Algebra 1: Functions and Algebra 2: Advanced Equations and Functions are comprehensive units with practice questions and videos.  Use 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:

Mathematics Vision Project, Secondary 1 Student Edition:

Mathematics Vision Project, Secondary 3 Student Edition:

 

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REI Unit: Reasoning with Equations and Inequalities Performance Task

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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