6.1 
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:


6.1A 
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.
 TxRCFP:
 Using operations with integers and positive rational numbers to solve problems
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 Using expressions and equations to represent relationships in a variety of contexts
 Understanding data representation
 TxCCRS:
 VII.D. Problem Solving and Reasoning – Realworld problem solving
 VII.D.1. Interpret results of the mathematical problem in terms of the original realworld 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, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld 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.

6.1B 
Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
Process Standard

Use
A PROBLEMSOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEMSOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION
Including, but not limited to:
 Problemsolving model
 Analyze given information
 Formulate a plan or strategy
 Determine a solution
 Justify the solution
 Evaluate the problemsolving process and the reasonableness of the solution
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Using operations with integers and positive rational numbers to solve problems
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 Using expressions and equations to represent relationships in a variety of contexts
 Understanding data representation
 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 problemsolving process.
 VII.D. Problem Solving and Reasoning – Realworld problem solving
 VII.D.2. Evaluate the problemsolving process.

6.1C 
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.
 TxRCFP:
 Using operations with integers and positive rational numbers to solve problems
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 Using expressions and equations to represent relationships in a variety of contexts
 Understanding data representation
 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.

6.1D 
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, AND LANGUAGE AS APPROPRIATE
Including, but not limited to:
 Mathematical ideas, reasoning, and their implications
 Multiple representations, as appropriate
 Symbols
 Diagrams
 Language
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Using operations with integers and positive rational numbers to solve problems
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 Using expressions and equations to represent relationships in a variety of contexts
 Understanding data representation
 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, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld situations.

6.1E 
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.
 TxRCFP:
 Using operations with integers and positive rational numbers to solve problems
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 Using expressions and equations to represent relationships in a variety of contexts
 Understanding data representation
 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.

6.1F 
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 nonexamples, patterns, etc.
 Current knowledge to new learning
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Using operations with integers and positive rational numbers to solve problems
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 Using expressions and equations to represent relationships in a variety of contexts
 Understanding data representation
 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.

6.1G 
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.
 TxRCFP:
 Using operations with integers and positive rational numbers to solve problems
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 Using expressions and equations to represent relationships in a variety of contexts
 Understanding data representation
 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.

6.9 
Expressions, equations, and relationships. The student applies mathematical process standards to use equations and inequalities to represent situations. The student is expected to:


6.9A 
Write onevariable, onestep equations and inequalities to represent constraints or conditions within problems.
Supporting Standard

Write
ONEVARIABLE, ONESTEP INEQUALITIES TO REPRESENT CONSTRAINTS OR CONDITIONS WITHIN PROBLEMS
Including, but not limited to:
 Inequality – a mathematical statement composed of algebraic and/or numeric expressions set apart by an inequality symbol
 Variable – a letter or symbol that represents a number
 One variable on one side of the inequality
 Coefficient – a number that is multiplied by a variable(s)
 Integers
 Products of integers limited to an integer multiplied by an integer
 Decimals
 Limited to positive decimal values
 Fractions
 Limited to positive fractional values
 Constant – a fixed value that does not appear with a variable(s)
 Integers
 Decimals
 Limited to positive decimal values
 Fractions
 Limited to positive fractional values
 Onestep inequalities
 A "step" only refers to an action involving both sides of the inequality (combining like terms on a single side of the inequality does not constitute a step).
 Solution set – a set of all values of the variable(s) that satisfy the inequality
 Constraints or conditions
 Distinguishing between equations and inequalities
 Characteristics of equations
 Equates two expressions
 Equality of the variable
 One solution
 Characteristics of inequalities
 Shows the relationship between two expressions in terms of >, ≥, ≤, or ≠
 Inequality of the variable
 One or more solutions
 Equality and inequality words and symbols
 Equal to, =
 Greater than, >
 Greater than or equal to, ≥
 Less than, <
 Less than or equal to, ≤
 Not equal to, ≠
 Relationship of order of operations within an inequality
 Order of operations – the rules of which calculations are performed first when simplifying an expression
 Parentheses/brackets: simplify expressions inside parentheses or brackets in order from left to right
 Exponents: rewrite in standard numerical form and simplify from left to right
 Limited to positive whole number exponents
 Multiplication/division: simplify expressions involving multiplication and/or division in order from left to right
 Addition/subtraction: simplify expressions involving addition and/or subtraction in order from left to right
 Onevariable, onestep inequalities from a problem situation
Note(s):
 Grade Level(s):
 Grade 6 introduces writing onevariable, onestep equations and inequalities to represent constraints or conditions within problems.
 Grade 7 will write onevariable, twostep equations and inequalities to represent constraints or conditions within problems.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to represent relationships in a variety of contexts
 TxCCRS:
 II.D. Algebraic Reasoning – Representing relationships
 II.D.1. Interpret 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.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.

6.9B 
Represent solutions for onevariable, onestep equations and inequalities on number lines.
Supporting Standard

Represent
SOLUTIONS FOR ONEVARIABLE, ONESTEP INEQUALITIES ON NUMBER LINES
Including, but not limited to:
 Inequality – a mathematical statement composed of algebraic and/or numeric expressions set apart by an inequality symbol
 Variable – a letter or symbol that represents a number
 One variable on one side of the inequality
 Coefficient – a number that is multiplied by a variable(s)
 Integers
 Products of integers limited to an integer multiplied by an integer
 Decimals
 Limited to positive decimal values
 Fractions
 Limited to positive fractional values
 Constant – a fixed value that does not appear with a variable(s)
 Integers
 Decimals
 Limited to positive decimal values
 Fractions
 Limited to positive fractional values
 Onestep inequalities
 A "step" only refers to an action involving both sides of the inequality (combining like terms on a single side of the inequality does not constitute a step).
 Solution set – a set of all values of the variable(s) that satisfy the inequality
 Constraints or conditions
 Distinguishing between equations and inequalities
 Characteristics of equations
 Equates two expressions
 Equality of the variable
 One solution
 Characteristics of inequalities
 Shows the relationship between two expressions in terms of >, ≥, ≤, or ≠
 Inequality of the variable
 One or more solutions
 Equality and inequality words and symbols
 Equal to, =
 Greater than, >
 Greater than or equal to, ≥
 Less than, <
 Less than or equal to, ≤
 Not equal to, ≠
 Representations of solutions to onestep inequalities on a number line
 Closed circle
 Greater than or equal to, ≥
 Less than or equal to, ≤
 Open circle
 Greater than, >
 Less than, <
 Not equal to, ≠
 Solutions to realworld situations represented on a number line
 Situations may require determining if a particular value is part of the solution set
 Value is considered part of the solution if the value makes the inequality true.
Note(s):
 Grade Level(s):
 Grade 6 introduces representing solutions for onevariable, onestep equations and inequalities on number lines.
 Grade 7 will represent solutions for onevariable, two step equations and inequalities on number lines.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to represent relationships in a variety of contexts
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 II.C. Algebraic Reasoning – Solving equations, inequalities, and systems of equations and inequalities
 II.C.1. Describe and interpret solution sets of equalities and inequalities.
 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.

6.9C 
Write corresponding realworld problems given onevariable, onestep equations or inequalities.
Supporting Standard

Write
CORRESPONDING REALWORLD PROBLEMS GIVEN ONEVARIABLE, ONESTEP INEQUALITIES
Including, but not limited to:
 Inequality – a mathematical statement composed of algebraic and/or numeric expressions set apart by an inequality symbol
 Variable – a letter or symbol that represents a number
 One variable on one side of the inequality
 Coefficient – a number that is multiplied by a variable(s)
 Integers
 Products of integers limited to an integer multiplied by an integer
 Decimals
 Limited to positive decimal values
 Fractions
 Limited to positive fractional values
 Constant – a fixed value that does not appear with a variable(s)
 Integers
 Decimals
 Limited to positive decimal values
 Fractions
 Limited to positive fractional values
 Onestep inequalities
 A "step" only refers to an action involving both sides of the inequality (combining like terms on a single side of the inequality does not constitute a step).
 Solution set – a set of all values of the variable(s) that satisfy the inequality
 Constraints or conditions
 Distinguishing between equations and inequalities
 Characteristics of equations
 Equates two expressions
 Equality of the variable
 One solution
 Characteristics of inequalities
 Shows the relationship between two expressions in terms of >, ≥, ≤, or ≠
 Inequality of the variable
 One or more solutions
 Equality and inequality words and symbols
 Equal to, =
 Greater than, >
 Greater than or equal to, ≥
 Less than, <
 Less than or equal to, ≤
 Not equal to, ≠
 Relationship of order of operations within an inequality
 Order of operations – the rules of which calculations are performed first when simplifying an expression
 Parentheses/brackets: simplify expressions inside parentheses or brackets in order from left to right
 Exponents: rewrite in standard numerical form and simplify from left to right
 Limited to positive whole number exponents
 Multiplication/division: simplify expressions involving multiplication and/or division in order from left to right
 Addition/subtraction: simplify expressions involving addition and/or subtraction in order from left to right
 Corresponding realworld problem situation from a onevariable, onestep inequality
Note(s):
 Grade Level(s):
 Grade 6 introduces writing corresponding realworld problems given onevariable, onestep equations or inequalities.
 Grade 7 will write a corresponding realworld problem given a onevariable, twostep equation or inequality.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to represent relationships in a variety of contexts
 TxCCRS:
 VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
 VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
 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.
 IX.B. Connections – Connections of mathematics to nature, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld situations.

6.10 
Expressions, equations, and relationships. The student applies mathematical process standards to use equations and inequalities to solve problems. The student is expected to:


6.10A 
Model and solve onevariable, onestep equations and inequalities that represent problems, including geometric concepts.
Readiness Standard

Model, Solve
ONEVARIABLE, ONESTEP INEQUALITIES THAT REPRESENT PROBLEMS, INCLUDING GEOMETRIC CONCEPTS
Including, but not limited to:
 Inequality – a mathematical statement composed of algebraic and/or numeric expressions set apart by an inequality symbol
 Variable – a letter or symbol that represents a number
 One variable on one side of the inequality
 Coefficient – a number that is multiplied by a variable(s)
 Integers
 Products of integers limited to an integer multiplied by an integer
 Decimals
 Limited to positive decimal values
 Fractions
 Limited to positive fractional values
 Constant – a fixed value that does not appear with a variable(s)
 Integers
 Decimals
 Positive or negative decimal values
 Fractions
 Positive or negative fractional values
 Onestep inequalities
 A "step" only refers to an action involving both sides of the inequality (combining like terms on a single side of the inequality does not constitute a step).
 Solution set – a set of all values of the variable(s) that satisfy the inequality
 Constraints or conditions
 Distinguishing between equations and inequalities
 Characteristics of equations
 Equates two expressions
 Equality of the variable
 One solution
 Characteristics of inequalities
 Shows the relationship between two expressions in terms of >, ≥, ≤, or ≠
 Inequality of the variable
 One or more solutions
 Equality and inequality words and symbols
 Equal to, =
 Greater than, >
 Greater than or equal to, ≥
 Less than, <
 Less than or equal to, ≤
 Not equal to, ≠
 Relationship of order of operations within an inequality
 Order of operations – the rules of which calculations are performed first when simplifying an expression
 Parentheses/brackets: simplify expressions inside parentheses or brackets in order from left to right
 Exponents: rewrite in standard numerical form and simplify from left to right
 Limited to positive whole number exponents
 Multiplication/division: simplify expressions involving multiplication and/or division in order from left to right
 Addition/subtraction: simplify expressions involving addition and/or subtraction in order from left to right
 Models and solutions to solve onevariable, onestep inequalities from problem situations (concrete, pictorial, algebraic)
 Solutions to onevariable, onestep inequalities from geometric concepts
Note(s):
 Grade Level(s):
 Grade 4 introduced geometric concepts such as geometric attributes, parallel and perpendicular lines, and angle measures including complementary and supplementary angles.
 Grade 5 represented and solved multistep problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity.
 Grade 7 will model and solve onevariable, twostep equations and inequalities.
 Grade 7 will write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to represent relationships in a variety of contexts
 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.1. Describe and interpret solution sets of equalities and inequalities.
 II.C.3. Recognize and use algebraic properties, concepts, and algorithms to solve equations, inequalities, and systems of linear equations and inequalities.
 III.C. Geometric and Spatial Reasoning – Connections between geometry and other mathematical content strands
 III.C.1. Make connections between geometry and algebraic equations.
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.3. Determine a solution.
 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.B. Communication and Representation – Interpretation of mathematical work
 VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
 IX.A. Connections – Connections among the strands of mathematics
 IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.

6.10B 
Determine if the given value(s) make(s) onevariable, onestep equations or inequalities true.
Supporting Standard

Determine
IF THE GIVEN VALUE(S) MAKE(S) ONEVARIABLE, ONESTEP INEQUALITIES TRUE
Including, but not limited to:
 Inequality – a mathematical statement composed of algebraic and/or numeric expressions set apart by an inequality symbol
 Variable – a letter or symbol that represents a number
 One variable on one side of the inequality
 Coefficient – a number that is multiplied by a variable(s)
 Integers
 Products of integers limited to an integer multiplied by an integer
 Decimals
 Limited to positive decimal values
 Fractions
 Limited to positive fractional values
 Constant – a fixed value that does not appear with a variable(s)
 Integers
 Decimals
 Limited to positive decimal values
 Fractions
 Limited to positive fractional values
 Onestep inequalities
 A "step" only refers to an action involving both sides of the inequality (combining like terms on a single side of the inequality does not constitute a step).
 Solution set – a set of all values of the variable(s) that satisfy the inequality
 Constraints or conditions
 Distinguishing between equations and inequalities
 Characteristics of equations
 Equates two expressions
 Equality of the variable
 One solution
 Characteristics of inequalities
 Shows the relationship between two expressions in terms of >, ≥, ≤, or ≠
 Inequality of the variable
 One or more solutions
 Equality and inequality words and symbols
 Equal to, =
 Greater than, >
 Greater than or equal to, ≥
 Less than, <
 Less than or equal to, ≤
 Not equal to, ≠
 Relationship of order of operations within an inequality
 Order of operations – the rules of which calculations are performed first when simplifying an expression
 Parentheses/brackets: simplify expressions inside parentheses or brackets in order from left to right
 Exponents: rewrite in standard numerical form and simplify from left to right
 Limited to positive whole number exponents
 Multiplication/division: simplify expressions involving multiplication and/or division in order from left to right
 Addition/subtraction: simplify expressions involving addition and/or subtraction in order from left to right
 Evaluation of given value(s) as possible solutions of onevariable, onestep inequalities
 Value is considered part of the solution if the value makes the inequality true.
Note(s):
 Grade Level(s):
 Grade 5 represented and solved multistep problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity.
 Grade 7 will determine if the given value(s) make(s) onevariable, twostep equations and inequalities true.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to represent relationships in a variety of contexts
 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.
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.4. Justify the solution.
