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 Instructional Focus DocumentAlgebra I
 TITLE : Unit 01: Linear Expressions, Equations, and Inequalities (one variable) SUGGESTED DURATION : 15 days

#### Unit Overview

Introduction
This unit bundles student expectations that address polynomial expressions of degree one, operations with polynomial expressions of degree one, and solving linear equations and inequalities in one variable. Solving formulas and literal equations for a specified variable are also addressed. Concepts are incorporated into both mathematical and real-world problem situations. According to the Texas Education Agency, mathematical process standards including application, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace.

Prior to this Unit
In Grade 5, students used equations with a variable to represent an unknown quantity. In Grade 6, students wrote and solved one variable, one-step equations and inequalities, representing solutions on a number line. In Grade 7, students wrote and solved one variable, two-step equations and inequalities, representing solutions on a number line. In Grade 8, students wrote, modeled, and solved one variable equations with variables on both sides using rational number coefficients and constants.

During this Unit
Students define polynomial expressions and perform operations (addition, subtraction, scalar multiplication) with polynomials of degree one, including rewriting a polynomial to an equivalent form when distributing by a rational scale factor. Students determine the quotient of a polynomial of degree one divided by a polynomial of degree one. Students make connections between expressions and equations, and solve linear equations in one variable, including variables on both sides and the application of the distributive property. Students model both mathematical and real-world problem situations using equations. Students solve linear inequalities in one variable, including variables on both sides and the application of the distributive property. Students model both mathematical and real-world problem situations using inequalities. Students solve mathematical formulas (including solving for y), scientific formulas, and other literal equations for a specified variable.

Other considerations: Reference the Mathematics COVID-19 Gap Implementation Tool HS Algebra I

After this Unit
In Unit 03 and Unit 04, students will apply their understanding of degree one polynomial operations, linear equations, linear inequalities, and literal equations when studying linear functions and applications of linear functions. The concepts in this unit will also be applied in later units in Algebra I and subsequent mathematics courses.

In Algebra I, solving linear equations in one variable is identified as STAAR Readiness Standard A.5A and part of STAAR Reporting Category 3: Writing and Solving Linear Functions, Equations, and Inequalities. Solving linear inequalities in one variable is STAAR Supporting Standard A.5B. Simplifying polynomial expressions of degree one using all four operations is identified as STAAR Supporting Standards A.10A, A.10C, and A.10D. Solving formulas and literal equations for a specified variable is STAAR Supporting Standard A.12E. All STAAR Supporting Standards are subsumed under STAAR Reporting Category 1: Number and Algebraic Methods. This unit is supporting the development of Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning B1; II. Algebraic Reasoning A1, B1, C2, C3, D1, D2; V. Statistical Reasoning A1, C2; VII. Problem Solving and Reasoning A1, A2, A3, A4, A5, B1, C1, D1, D2; VIII. Communication and Representation A1, A2, A3, B1, B2, C1, C2, C3; IX. Connections A1, A2, B1, B2, B3.

Research
According to the National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics (2000), students should develop an understanding of the algebraic properties that govern manipulation of symbols in expressions, equations, and inequalities. According to Navigating through Algebra in Grades 9 – 12:

“High school students continue to develop fluency with mathematical symbols and become proficient in operating on algebraic expressions in solving problems. Their facility with representation expands to include equations, inequalities, systems of equations, graphs, matrices, and functions, and they recognize and describe the advantages and disadvantages of various representations for a particular situation. Such facility with symbols and alternative representations enables them to analyze a mathematical situation, choose an appropriate model, select an appropriate solution method, and evaluate the plausibility of their solutions.” (NCTM, 2002, p. 3)

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics, Inc.
National Council of Teachers of Mathematics. (2002). Navigating through algebra in grades 9 – 12. Reston, VA: National Council of Teachers of Mathematics, Inc.
Texas Education Agency & Texas Higher Education Coordinating Board. (2009). Texas college and career readiness standards. Retrieved from http://www.thecb.state.tx.us/index.cfm?objectid=E21AB9B0-2633-11E8-BC500050560100A9

 Numeracy requires the ability to work flexibly with quantities in order to recognize, reason, and solve situations of varying contexts in everyday life, society, and the work place. How is numeracy like literacy? What are some examples of numeracy in everyday life, society, and the work place? How does context influence understanding of a quantity? Why is the ability to work flexibly with quantities essential to developing the foundations of numeracy? Understanding and generalizing operational relationships leads to more sophisticated representations and solution strategies in order to investigate or solve problem situations in everyday life. What relationships exist within and between mathematical operations? How does generalizing operational relationships lead to developing more flexible, efficient representations and/or solution strategies? Why is understanding the problem solving process an essential part of learning and working mathematically?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• The ability to represent quantities in various forms develops the understanding of equivalence and allows for working flexibly with algebraic expressions in order to communicate and reason about quantities.
• How can expressions be used to represent situations?
• What mathematical conventions are used when representing expressions? Why?
• How can it be determined if two expressions are equivalent?
• How are properties and operational understandings used to generate equivalent expressions?
• Why can it be useful to simplify expressions?
• Number and Algebraic Methods
• Expressions
• Linear
• Patterns, Operations, and Properties
• Associated Mathematical Processes
• Application
• Problem Solving Model
• Tools and Techniques
• Communication
• Representations
• Relationships
• Justification
 Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

 Quantitative relationships model problem situations efficiently and can be used to make generalizations, predictions, and critical judgments in everyday life. What patterns exist within different types of quantitative relationships and where are they found in everyday life? Why is the ability to model quantitative relationships in a variety of ways essential to solving problems in everyday life?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• Equations and inequalities can be written, transformed, and solved using various methods to make critical judgments, with different methods being more efficient or informative depending on the structure of the equation or inequality.
• How does knowing more than one solution strategy build mathematical flexibility?
• How can equations and inequalities be used to represent relationships between quantities?
• How do solutions to inequalities differ from solutions to equations?
• Why must solutions be justified in terms of problem situations?
• What methods can be used to write linear equations and linear inequalities?
• What methods can be used to solve linear equations and linear inequalities?
• How does the structure of the equation influence the selection of an efficient method for solving linear equations?
• How are properties and operational understandings used to transform linear equations and linear inequalities?
• Functions, Equations, and Inequalities
• Equations and Inequalities
• Linear
• Patterns, Operations, and Properties
• Associated Mathematical Processes
• Application
• Problem Solving Model
• Tools and Techniques
• Communication
• Representations
• Relationships
• Justification
 Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

 Quantitative relationships model problem situations efficiently and can be used to make generalizations, predictions, and critical judgments in everyday life. What patterns exist within different types of quantitative relationships and where are they found in everyday life? Why is the ability to model quantitative relationships in a variety of ways essential to solving problems in everyday life?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• Equations can be written, transformed, and solved using various methods to make critical judgments, with different methods being more efficient or informative depending on the structure of the equation.
• How can equations be used to represent relationships between quantities?
• How are properties and operational understandings used to transform literal equations?
• How does the context of the problem situation affect which variable to solve for in a literal equation?
• What is the purpose for solving for a specific variable in a literal equation?
• Number and Algebraic Methods
• Relations and Functions
• Formulas
• Literal equations
• Patterns, Operations, and Properties
• Associated Mathematical Processes
• Application
• Problem Solving Model
• Tools and Techniques
• Communication
• Representations
• Relationships
• Justification
 Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

#### MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS

Misconceptions:

• Some students may think that a constant term can be combined with a variable term (e.g., 2x + 5 = 7x) rather than constant terms only combining with other constant terms and like-variable terms combining with like-variable terms.
• Some students may think that in the graph or table method of solving the equation, the y-value is the answer rather than the x-value.
• Some students may think that the negative in front of the parentheses is distributed only to the first term of the expression in parentheses rather than to all terms of the expression in parentheses.
• Some students may think that answers to both equations and inequalities are exact answers rather than correctly identifying the solutions to equations as exact answers and the solutions to inequalities as range of answers.
• Some students may think that whenever a negative is involved, the order of the inequality switches rather than only switching the order of inequality when multiplying or dividing by a negative.

#### Unit Vocabulary

• Algebraic expression – a generalization that is a combination of variables, numbers (constants and coefficients), and operators
• Binomial – two term expression; e.g., 4 – 2y, 3a + 1
• Degree of a polynomial – same as the degree of the term in the polynomial with the highest degree
• Degree of term – sum of the powers on the variables in the term
• First degree polynomial – polynomial whose highest degree term contains one variable with power of one
• Linear equation in one variable – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
• Linear inequality in one variable – a mathematical statement composed of algebraic and/or numeric expressions set apart by an inequality symbol
• Literal equations – equations in which all or part of the terms are expressed in variables
• Monomial – one term expression; e.g., –2.5x,
• Polynomial expression – monomial or sum of monomials not including variables in the denominator or under a radical
• Trinomial – three term expression

Related Vocabulary:

 Associative property Commutative property Distributive property Equation Equivalent Evaluate Expression Graphic solution Inequality Inverse operation Numeric solution Proportions Rates Reciprocal Ratios Simplify Solve Terms
Unit Assessment Items System Resources Other Resources

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Unit Assessment Items that have been published by your district may be accessed through Search All Components in the District Resources tab. Assessment items may also be found using the Assessment Center if your district has granted access to that tool.

System Resources may be accessed through Search All Components in the District Resources Tab.

Texas Higher Education Coordinating Board – Texas College and Career Readiness Standards

Texas Education Agency – Mathematics Curriculum

Texas Education Agency – STAAR Mathematics Resources

Texas Education Agency Texas Gateway – Revised Mathematics TEKS: Vertical Alignment Charts

Texas Education Agency Texas Gateway – Mathematics TEKS: Supporting Information

Texas Education Agency Texas Gateway – Interactive Mathematics Glossary

Texas Education Agency Texas Gateway –Resources Aligned to Algebra I Mathematics TEKS

Texas Instruments – Graphing Calculator Tutorials

TAUGHT DIRECTLY TEKS

TEKS intended to be explicitly taught in this unit.

TEKS/SE Legend:

• Knowledge and Skills Statements (TEKS) identified by TEA are in italicized, bolded, black text.
• Student Expectations (TEKS) identified by TEA are in bolded, black text.
• Student Expectations (TEKS) are labeled Readiness as identified by TEA of the assessed curriculum.
• Student Expectations (TEKS) are labeled Supporting as identified by TEA of the assessed curriculum.
• Student Expectations (TEKS) are labeled Process standards as identified by TEA of the assessed curriculum.
• Portions of the Student Expectations (TEKS) that are not included in this unit but are taught in previous or future units are indicated by a strike-through.

Specificity Legend:

• Supporting information / clarifications (specificity) written by TEKS Resource System are in blue text.
• Unit-specific clarifications are in italicized, blue text.
• Information from Texas Education Agency (TEA), Texas College and Career Readiness Standards (TxCCRS), Texas Response to Curriculum Focal Points (TxRCFP) is labeled.
• A Partial Specificity label indicates that a portion of the specificity not aligned to this unit has been removed.
TEKS# SE# TEKS SPECIFICITY
A.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
A.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
Process Standard

Apply

MATHEMATICS TO PROBLEMS ARISING IN EVERYDAY LIFE, SOCIETY, AND THE WORKPLACE
Including, but not limited to:

• Mathematical problem situations within and between disciplines
• Everyday life
• Society
• Workplace

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxCCRS:
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.1. Interpret results of the mathematical problem in terms of the original real-world situation.
• IX.A. Connections – Connections among the strands of mathematics
• IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
• IX.A.2. Connect mathematics to the study of other disciplines.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
• IX.B.2. Understand and use appropriate mathematical models in the natural, physical, and social sciences.
• IX.B.3. Know and understand the use of mathematics in a variety of careers and professions.
A.1B Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.
Process Standard

Use

A PROBLEM-SOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEM-SOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION
Including, but not limited to:

• Problem-solving model
• Analyze given information
• Formulate a plan or strategy
• Determine a solution
• Justify the solution
• Evaluate the problem-solving process and the reasonableness of the solution

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxCCRS:
• I.B. Numeric Reasoning – Number sense and number concepts
• I.B.1. Use estimation to check for errors and reasonableness of solutions.
• V.A. Statistical Reasoning – Design a study
• V.A.1. Formulate a statistical question, plan an investigation, and collect data.
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.1. Analyze given information.
• VII.A.2. Formulate a plan or strategy.
• VII.A.3. Determine a solution.
• VII.A.4. Justify the solution.
• VII.A.5. Evaluate the problem-solving process.
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.2. Evaluate the problem-solving process.
A.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.
Process Standard

Select

TOOLS, INCLUDING REAL OBJECTS, MANIPULATIVES, PAPER AND PENCIL, AND TECHNOLOGY AS APPROPRIATE, AND TECHNIQUES, INCLUDING MENTAL MATH, ESTIMATION, AND NUMBER SENSE AS APPROPRIATE, TO SOLVE PROBLEMS
Including, but not limited to:

• Appropriate selection of tool(s) and techniques to apply in order to solve problems
• Tools
• Real objects
• Manipulatives
• Paper and pencil
• Technology
• Techniques
• Mental math
• Estimation
• Number sense

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxCCRS:
• I.B. Numeric Reasoning – Number sense and number concepts
• I.B.1. Use estimation to check for errors and reasonableness of solutions.
• V.C. Statistical Reasoning – Analyze, interpret, and draw conclusions from data
• V.C.2. Analyze relationships between paired data using spreadsheets, graphing calculators, or statistical software.
A.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Process Standard

Communicate

MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, GRAPHS, AND LANGUAGE AS APPROPRIATE
Including, but not limited to:

• Mathematical ideas, reasoning, and their implications
• Multiple representations, as appropriate
• Symbols
• Diagrams
• Graphs
• Language

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxCCRS:
• II.D. Algebraic Reasoning – Representing relationships
• II.D.1. Interpret multiple representations of equations, inequalities, and relationships.
• II.D.2. Convert among multiple representations of equations, inequalities, and relationships.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
• VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
A.1E Create and use representations to organize, record, and communicate mathematical ideas.
Process Standard

Create, Use

REPRESENTATIONS TO ORGANIZE, RECORD, AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:

• Representations of mathematical ideas
• Organize
• Record
• Communicate
• Evaluation of the effectiveness of representations to ensure clarity of mathematical ideas being communicated
• Appropriate mathematical vocabulary and phrasing when communicating mathematical ideas

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxCCRS:
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
A.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
Process Standard

Analyze

MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:

• Mathematical relationships
• Connect and communicate mathematical ideas
• Conjectures and generalizations from sets of examples and non-examples, patterns, etc.
• Current knowledge to new learning

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxCCRS:
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.1. Analyze given information.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
• VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
•  VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
• IX.A. Connections – Connections among the strands of mathematics
• IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
• IX.A.2. Connect mathematics to the study of other disciplines.
A.1G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Process Standard

Display, Explain, Justify

MATHEMATICAL IDEAS AND ARGUMENTS USING PRECISE MATHEMATICAL LANGUAGE IN WRITTEN OR ORAL COMMUNICATION

Including, but not limited to:

• Mathematical ideas and arguments
• Validation of conclusions
• Displays to make work visible to others
• Diagrams, visual aids, written work, etc.
• Explanations and justifications
• Precise mathematical language in written or oral communication

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxCCRS:
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.4. Justify the solution.
• VII.B. Problem Solving and Reasoning – Proportional reasoning
• VII.B.1. Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
• VII.C. Problem Solving and Reasoning – Logical reasoning
• VII.C.1. Develop and evaluate convincing arguments.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
A.5 Linear functions, equations, and inequalities. The student applies the mathematical process standards to solve, with and without technology, linear equations and evaluate the reasonableness of their solutions. The student is expected to:
A.5A Solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides.

Solve

LINEAR EQUATIONS IN ONE VARIABLE, INCLUDING THOSE FOR WHICH THE APPLICATION OF THE DISTRIBUTIVE PROPERTY IS NECESSARY AND FOR WHICH VARIABLES ARE INCLUDED ON BOTH SIDES

Including, but not limited to:

• Linear equation in one variable – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
• Linear equations in one variable including parentheses and variables on both sides of the equation
• Mathematical problem situations
• Real-world problem situations
• Multiple representations of mathematical and real-world problem situations
• Algebraic generalizations
• Missing coordinate of a solution point to a function
• Verbal
• Methods for solving equations
• Concrete and pictorial models (e.g., algebra tiles, etc.)
• Tables and graphs with and without technology
• Transformation of equations using properties of equality
• Distributive property
• Operational properties
• Possible solutions, including special cases
• No solution, empty set, ∅
• Infinite solutions, all real numbers, ℜ
• Relationships and connections between the methods of solution
• Justification of solutions to equations
• Justification of reasonableness of solutions in terms of mathematical and real-world problem situations

Note(s):

• Grade 5 used equations with variables to represent missing numbers.
• Grade 6 solved one-variable, one-step equations.
• Grade 7 solved one-variable, two-step equations.
• Grade 8 solved one-variable equations with variables on both sides.
• Algebra I introduces solving one-variable equations that include those for which the application of the distributive property is necessary and for which variables are included on both sides.
• Algebra II will introduce solving absolute value linear equations.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxCCRS:
• II.A. Algebraic Reasoning – Identifying expressions and equations
• II.A.1. Explain the difference between expressions and equations.
• II.B. Algebraic Reasoning – Manipulating expressions
• II.B.1. Recognize and use algebraic properties, concepts, and algorithms to combine, transform, and evaluate expressions (e.g., polynomials, radicals, rational expressions).
• II.C. Algebraic Reasoning – Solving equations, inequalities, and systems of equations and inequalities
• II.C.2. Explain the difference between the solution set of an equation and the solution set of an inequality.
• II.C.3. Recognize and use algebraic properties, concepts, and algorithms to solve equations, inequalities, and systems of linear equations and inequalities.
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.3. Determine a solution.
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.1. Interpret results of the mathematical problem in terms of the original real-world situation.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.2. Understand and use appropriate mathematical models in the natural, physical, and social sciences.
A.5B Solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides.
Supporting Standard

Solve

LINEAR INEQUALITIES IN ONE VARIABLE, INCLUDING THOSE FOR WHICH THE APPLICATION OF THE DISTRIBUTIVE PROPERTY IS NECESSARY AND FOR WHICH VARIABLES ARE INCLUDED ON BOTH SIDES

Including, but not limited to:

• Linear inequality in one variable – a mathematical statement composed of algebraic and/or numeric expressions set apart by an inequality symbol
• Inequality symbols
• > (is greater than)
• < (is less than)
• ≥ (is greater than or equal to)
• ≤ (is less than or equal to)
• ≠ (is not equal to)
• Linear inequalities including parentheses and variables on both sides of the equation
• Mathematical problem situations
• Real-world problem situations
• Multiple representations of mathematical and real-world problem situations
• Algebraic generalizations
• Verbal
• Solutions to include numeric, graphic, and verbal representations
• Methods for solving inequalities
• Concrete and pictorial models (e.g., algebra tiles, etc.)
• Graphs and tables with and without technology
• Transformation of inequalities using properties of inequalities
• Distributive property
• Operational properties
• Special cases for empty set, Ø, and all real numbers, ℜ
• Relationships and connections between the methods of solution
• Justification of solutions to inequalities
• Differentiation between solutions of equations and inequalities
• Justification of reasonableness of solutions in terms of mathematical and real-world problem situations

Note(s):

• Grade 6 solved one-variable, one-step inequalities.
• Grade 7 solved one-variable, two-step inequalities.
• Grade 8 wrote one-variable inequalities with variables on both sides.
• Algebra I introduces solving one-variable inequalities, including those for which the application of the distributive property is necessary and for which variables are included on both sides.
• Algebra II will introduce solving absolute value linear inequalities.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxCCRS:
• II.A. Algebraic Reasoning – Identifying expressions and equations
• II.A.1. Explain the difference between expressions and equations.
• II.C. Algebraic Reasoning – Solving equations, inequalities, and systems of equations and inequalities
• II.C.2. Explain the difference between the solution set of an equation and the solution set of an inequality.
• II.C.3. Recognize and use algebraic properties, concepts, and algorithms to solve equations, inequalities, and systems of linear equations and inequalities.
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.3. Determine a solution.
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.1. Interpret results of the mathematical problem in terms of the original real-world situation.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.2. Understand and use appropriate mathematical models in the natural, physical, and social sciences.
A.10 Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions. The student is expected to:
A.10A

Add and subtract polynomials of degree one and degree two.

Supporting Standard

POLYNOMIALS OF DEGREE ONE

Including, but not limited to:

• Algebraic expression – a generalization that is a combination of variables, numbers (constants and coefficients), and operators
• Polynomial expression – monomial or sum of monomials not including variables in the denominator or under a radical
• Monomial – one term expression; e.g., –2.5x,
• Binomial – two term expression; e.g., 4 – 2y, 3a + 1
• Trinomial – three term expression
• Degree
• Degree of term – sum of the powers on the variables in the term
• Degree of a polynomial – same as the degree of the term in the polynomial with the highest degree
• First degree polynomial – polynomial whose highest degree term contains one variable with power of one
• Ex: 3x + 8; The highest degree term is 3x, and the power on x is one.
• Ex: –2x – 5y; Both terms are degree one with the power on x and y both equal to one.
• Simplifying polynomials by addition/subtraction using concrete models
• Algebra tiles
• Simplifying polynomials by addition/subtraction algebraically
• Clear grouping symbols using the distributive property.
• Combine like terms.
• Place terms in order
• Alphabetical order
• Decreasing degree order
• Applications of addition/subtraction of polynomials in mathematical problem situations

Note(s):

• Previous grade levels calculated the perimeter of triangles and rectangles.
• Grade 6 generated and compared equivalent expressions using concrete models, pictorial models, and algebraic properties of operations.
• Algebra I introduces operations with polynomials of degree two.
• Algebra II will extend operations with polynomials of degree three and degree four, including division of polynomials.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxCCRS:
• II.A. Algebraic Reasoning – Identifying expressions and equations
• II.A.1. Explain the difference between expressions and equations.
• II.B. Algebraic Reasoning – Manipulating expressions
• II.B.1. Recognize and use algebraic properties, concepts, and algorithms to combine, transform, and evaluate expressions (e.g., polynomials, radicals, rational expressions).
A.10C

Determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend.

Supporting Standard

Determine

THE QUOTIENT OF A POLYNOMIAL OF DEGREE ONE WHEN DIVIDED BY A POLYNOMIAL OF DEGREE ONE

Including, but not limited to:

• Degree one polynomial divided by another degree one polynomial
• Division of polynomials
• Division by factoring
• Cancellation of common factors in the numerator and denominator
• Array method
• Long division
• Long division format with divisor outside division box, dividend inside the division box, and quotient on top of division box
• Missing terms in series represented by adding a zero term
• Applications of division of polynomials in mathematical problem situations

Note(s):

• Previous grade levels calculated the area of triangles and rectangles.
• Algebra I introduces operations with polynomials of degree one and degree two.
• Algebra II will extend operations with polynomials of degree three and degree four.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxCCRS:
• II.A. Algebraic Reasoning – Identifying expressions and equations
• II.A.1. Explain the difference between expressions and equations.
• II.B. Algebraic Reasoning – Manipulating expressions
• II.B.1. Recognize and use algebraic properties, concepts, and algorithms to combine, transform, and evaluate expressions (e.g., polynomials, radicals, rational expressions).
A.10D

Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property.

Supporting Standard

Rewrite

POLYNOMIAL EXPRESSIONS OF DEGREE ONE IN EQUIVALENT FORMS USING THE DISTRIBUTIVE PROPERTY

Including, but not limited to:

• Polynomial expression – monomial or sum of monomials not including variables in the denominator or under a radical
• First degree polynomial – polynomial whose highest degree term contains one variable with power of one
• Factorization of the greatest common factor (GCF)
• Operations on polynomials
• Multiplication

Note(s):

• Algebra I introduces operations with polynomials of degree one and degree two.
• Algebra II will extend operations with polynomials of degree three and degree four.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxCCRS:
• II.A. Algebraic Reasoning – Identifying expressions and equations
• II.A.1. Explain the difference between expressions and equations.
• II.B. Algebraic Reasoning – Manipulating expressions
• II.B.1. Recognize and use algebraic properties, concepts, and algorithms to combine, transform, and evaluate expressions (e.g., polynomials, radicals, rational expressions).
A.12 Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions. The student is expected to:
A.12E Solve mathematic and scientific formulas, and other literal equations, for a specified variable.
Supporting Standard

Solve

MATHEMATIC AND SCIENTIFIC FORMULAS, AND OTHER LITERAL EQUATIONS, FOR A SPECIFIED VARIABLE

Including, but not limited to:

• Literal equations – equations in which all or part of the terms are expressed in variables
• Two variable linear equations
• Mathematical formulas
• Scientific formulas
• Transforming literal equations is subsumed within solving
• Solving for one of the variables in two variable linear equations.
• Solving formulas for a specified variable
• Mathematical formulas
• Scientific formulas

Note(s):