Common Core High School Algebra Teaching and Learning Resources
Domain: REI: Reasoning with Equations and Inequalities
Select the cluster for resources on this page:
REIA: Understand solving equations
as a process of reasoning and explain the reasoning
REIB: Solve equations and
inequalities in one variable
REIC: Solve systems of equations
REID: Represent and solve equations
and inequalities graphically
REI Unit: Reasoning with Equations and Inequalities
Performance Task identified by New York City School System.
REIA: Understand solving equations
as a process of reasoning and explain the reasoning
Standards:
 REIA.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.
 REIA.2. Solve simple rational and radical
equations in one variable, and give examples showing how extraneous
solutions may arise.
Technologyenhanced investigations:
Mathwords.com: Math Dictionary:
Key vocabulary for this domain. Use with REIA, REIB, REIC
and REID:
LearnZillion:
 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 REIA.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 REIA.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 REIA.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 SSEB.3.c and REIA.1; Function
standards IFC.8.b, BFB.4.a, and LEA1.(a, c); and Statistics
and Probability standards IDB.6.a, ICA.1, ICB.4, CPA.2, and
MDA.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 24. 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 HSAREI.A.1:
5 manipulatives: Solving quadratic equations with integer
coefficients, solution of quadratic equations, twostep equations,
solving multiplication equations, solving simple equations.
Multiple Choice:
Khan Academy: Practice questions with videos.
Constructedresponse:
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 REIA.1, REIA.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 REIA.1.
Mathematics Vision Project,
Secondary
3 Student Edition:

Module 4: Rational Functions: This module contains 7 classroom tasks.
Multiple standards are addressed. Standards REIA.2, REID.11
are among those found in task 7.
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REIB: Solve equations and
inequalities in one variable
Standards:
 REIB.3. Solve linear equations and
inequalities in one variable, including equations with coefficients
represented by letters.
 REIB.4. Solve quadratic equations in one
variable.
 REIB.4.a. 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.
 REIB.4.b. Solve quadratic equations by
inspection (e.g., for x^{2} = 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 ± bi for real numbers a and
b.
Technologyenhanced investigations:
Art of Problem Solving:
Introduction to Algebra Videos: These are the videos that go with
each of the sections within the 13chapter textbook, Introduction to
Algebra. View Ch. 3 OneVariable Linear Equations, Ch. 4,
section 5: Introduction to MultiVariable Equations, Ch. 9
Introduction to Inequalities, Ch. 10 Quadratic EquationsPart 1
(includes factoring); and Ch. 13 Quadratic EquationsPart 2 ( includes
completing the square, proving the quadratic formula, using the
quadratic formula, the discriminant, and quadratic problem solving).
Course Hero: CollegeAlgebra:
Solving Linear Equations and Inequalities contains an overview of
methods with vocabulary, worked examples. Aligns with REIB.
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 REIB.
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 corequisite is some working
experience with algebra, like factoring x^{2} 2x into
x(x2). 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 SSEB.3.a, CEDA.2,
and REIB.4.b and Function standards IFB.4, IFC.7.a, IFC.8.a,
BFB.3.
LearnZillion:
 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 REIB.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 REIB.4.b.
Omnicalculator.com: Quadratic formula returns the roots of a
quadratic equation, including complex roots. Users can enter a
quadratic in standard form, symmetryvertex form, or factored form.
Explanation of theory is included. Aligns with REIB.4.
WisWeb: Virtual Manipulatives (requires Java):

Solving Equations with Balance Strategy: game. Learners solve
linear equations of increasing difficulty with this game, showing
their steps indicating operations to be performed on each side of
the given equation, or you can enter your own equation. Use this
applet with standard REIB.3.

Linear Equations, Test: Learners solve linear equations, showing
their step by step solutions with this Java virtual manipulative.
There are five levels of difficulty for problems in this test. Use
this applet with standard REIB.3.
Thinking Mathematics:
WiscOnline, Learning Objects:
Purple Math:
Wolfram Demonstrations Project:
Download the free Wolfram CDF player
to interact with the following manipulatives:
 US Common Core State Standard Math HSAREI.B.3:
5 manipulatives: Graphs of inequalities, twostep 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 HSAREI.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).
Multiple Choice:
CK12: Algebra: Video examples, practice problems
online, and real world
applications. The following align with REIB.3:
Khan Academy: Practice questions with videos. Use with REIB.4:
Constructedresponse:
Achieve the Core:
Quadratic Equations MiniAssessment (pdf or Word docx)
can be used to evaluate students' understanding of algebra standards REIB.4 and CEDA.1 in order to prepare to teach this material or to check for
student ability to demonstrate understanding and apply these concepts.
CK12: Algebra: Video examples, shortanswer practice problems
online, and real world
applications. The following align with REIB.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 paperpencil and then by using their mouse to
roll over a box, they see the solution to problems presented. Use
with standards REIB.3 and REIB.4.
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:
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REIC: Solve systems of equations
Standards:
 REIC.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.
 REIC.6. Solve systems of linear equations
exactly and approximately (e.g., with graphs), focusing on pairs of
linear equations in two variables.
 REIC.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^{2} + y^{2} = 3.
 REIC.8. (+) Represent a system of linear
equations as a single matrix equation in a vector variable.
 REIC.9. (+) 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 × 3 or greater).
Technologyenhanced investigations:
Art of Problem Solving:
Introduction to Algebra Videos: These are the videos that go
with each of the sections within the 13chapter textbook, Introduction to Algebra. View Ch. 5 MultiVariable 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 CEDA.2 and REIC.6.

Systems of Equations: Word Problems 1:
Students explore two reallife 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
CEDA.2 and REIC.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 CEDA.2 and REIC.6.
LearnZillion:
Math Planet,
Algebra 1:
Following align with REIC.6. Each includes an example and
video instruction.
Math Planet,
Algebra 2: Following align with REIC.8 and REIC.9.
Each includes an example and video instruction.
Wolfram Demonstrations Project:
Download the free Wolfram CDF player
to interact with the following manipulatives:
 US Common Core State Standard Math HSAREI.C.6:
11 manipulatives: Lines2 points, When two runners meet,
Twobytwo linear systems, Intersecting lines using
slopeintercept form, Finding a pattern (linear equations), Two
points determine a line, Lines: pointslope, Lines:
slopeintercept, a linear programming scenario, the Fundamental
Theorem of linear programming, and algebra quiz.
 US Common Core State Standard Math HSAREI.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 socalled 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 CEDA.3 and REIC.6.
Purple Math:
YouTube.com video lessons:
Following YouTube video lessons align with REIC.8 and
REIC.9:
Multiple Choice:
Constructedresponse:
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 paperpencil and then by using their mouse to
roll over a box, they see the solution to problems presented. Use
with standards REIC.5 and REIC.6 and REIC.8.
WiscOnline, 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 REIC.8 and REIC.9.
Performance tasks:
Georgia Standards of Excellence Framework:
 PreCalculus 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 VMC.6,
VMC.7, VMC.8, VMC.9, VMC.10, VMC.12 and algebra standards REIC.8,
REIC.9.
 PreCalculus 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 GPEA.1, GPEA.2, and GPEA.3, and algebra standard
REIC.7.
Illustrative Mathematics:
Algebra:
Inside Mathematics: MARS Tasks:

Coffee: Students use a chart to solve simultaneous equations.
This task aligns with function standard BFA.1 and algebra standard
REIC.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 REIC.6, REID.10, and REID.11.
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 REIC.5, REIC.6, REID.12, and CEDA.2, CEDA.3,
and CEDA.4.
 Task 7: Shopping for Cats and Dogs; and
Task 8: Can You Get to the Point, Too? align to both standards REIC.5
and REIC.6.
 Task 6: Get to the Point; and Task 10: Taken Out of
Context align to standard REIC.6.
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 BFA.1b,
algebra standards CEDA.2, REIC.6, and mathematical practice standards 1, 4, 5, and 7.
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REID: Represent and solve equations
and inequalities graphically
Standards:
 REID.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).
 REID.11. Explain why the xcoordinates
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.
 REID.12. Graph the solutions to a linear
inequality in two variables as a halfplane (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 halfplanes.
Technologyenhanced investigations:
Art of Problem Solving:
Introduction to Algebra Videos: These are the videos that go with
each of the sections within the 13chapter 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
yintercept, or to identify the slope and yintercept from a linear
equation written in slopeintercept form. Aligns with standard CEDA.2,
and REID.10.

Linear Equations: Points, Intercepts, and Slopes, Oh My!:
Students learn to graph lines using the x and yintercepts of
equations, as well as how to graph a line when given an equation
in pointslope form. Aligns with standard CEDA.2, and
REID.10.

Linear Equations: Word Problems:
Learn to apply linear equations and their graphs to realworld
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 CEDA.2 and REID.10.
LearnZillion:
 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
REID.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
REID.11.
 Lesson set:
Graph the solutions to a linear inequality as a halfplane, and
the solutions to a system of linear inequalities as an
intersection of halfplanes. Six video lessons using
graphing: Graph a linear inequality with a < or ≤ symbol, graph
a linear inequality with a > or ≥ symbol, check the halfplane
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 REID.12.
Southeast Comprehensive Center of SEDL: Video:
Represent and solve equations and inequalities graphically:
This video aligns with standard REID.11. View online or download.
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:
Videos at YouTube.com:
Multiple Choice:
Constructedresponse:
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 paperpencil and then by using their mouse to
roll over a box, they see the solution to problems presented. Use
the following with REID.10 and REID.11:
Khan Academy:
Algebra 1: Functions and
Algebra 2:
Advanced Equations and Functions are comprehensive units with practice
questions and videos. Use with REID.12.
Performance tasks:
Illustrative Mathematics:
Algebra:

Taxi!:
Aligns with REID.10 and function standard LEB.5.

Two
Squares are Equal: Solve the quadratic using as many methods as
possible. This aligns with standards REIB.4 and REID.11.
 Population
and Food Supply: This involves linear and exponential functions.
Aligns with REID.11 and function standards LEA.2 and LEA.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 REID.12.

Fishing
Adventures 3: Students are given a real world problem
in which they write equations and graph inequalities to solve it.
Aligns with REID.12 and CEDA.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 REIC.6, REID.10, and REID.11.
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 REIC.5, REIC.6, REID.10, REID.12, and
CEDA.2, CEDA.3, and CEDA.4. Task 6 aligns with REID.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 REID.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 REID.11.
Mathematics Vision Project,
Secondary
3 Student Edition:

Module 4: Rational Functions: This module contains 7 classroom tasks.
Multiple standards are addressed. Standards REIA.2, REID.11
are among those found in task 7.
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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 curriculumembedded CCLS
aligned task and instructional supports. The task is embedded in a 45
week unit on reasoning with Equations and Inequalities.” Algebra
standards addressed include REIA.1, REIB.3, REIC.6, and CEDA.2,
CEDA.3. Mathematical Practices standards include MP.1, MP.3,
MP.4, and MP.7.
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Common Core Math:
Intro  HS Algebra Domain:
SSE  APR  CED  REI 