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.

6.7 
Expressions, equations, and relationships. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to:


6.7A 
Generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization.
Readiness Standard

Generate
EQUIVALENT NUMERICAL EXPRESSIONS USING ORDER OF OPERATIONS, INCLUDING WHOLE NUMBER EXPONENTS AND PRIME FACTORIZATION
Including, but not limited to:
 Rational numbers – the set of numbers that can be expressed as a fraction , where a and b are integers and b ≠ 0. The set of rational numbers is denoted by the symbol Q.
 Various forms of positive and negative rational numbers, including absolute values
 Integers
 Products of integers limited to an integer multiplied by an integer
 Quotients of integers limited to an integer divided by an integer
 Decimals
 Products of decimals limited to a positive decimal value multiplied by a positive decimal value
 Quotients of decimals limited to a positive decimal value divided by a positive decimal value
 Fractions
 Products of fractions limited to a positive fractional value multiplied by a positive fractional value
 Quotients of fractions limited to a positive fractional value divided by a positive fractional value
 Expression – a mathematical phrase, with no equal sign or inequality symbol, that may contain a number(s), a variable(s), and/or an operator(s)
 Exponent – in the expression x^{y}, x is called the base and y is called the exponent. The exponent determines the number of times the base is multiplied by itself.
 Equivalent numerical expressions
 Each step in the simplification process generates an equivalent expression
 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 whole number positive 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
 Prime factorization – the process of decomposing a composite number as a unique product of prime factors
Note(s):
 Grade Level(s):
 Grade 5 described the meaning of parentheses and brackets in a numeric expression.
 Grade 5 simplified numerical expressions that do not involve exponents, including up to two levels of grouping.
 Algebra I will add and subtract polynomials of degree one and degree two.
 Algebra I will multiply polynomials of degree one and degree two.
 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.
 I.B. Numeric Reasoning – Number sense and number concepts
 I.B.2. Interpret the relationships between the different representations of numbers.
 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).
 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.

6.7B 
Distinguish between expressions and equations verbally, numerically, and algebraically.
Supporting Standard

Distinguish
BETWEEN EXPRESSIONS AND EQUATIONS VERBALLY, NUMERICALLY, AND ALGEBRAICALLY
Including, but not limited to:
 Expression – a mathematical phrase, with no equal sign or inequality symbol, that may contain a number(s), a variable(s), and/or an operator(s)
 Expressions that contain a variable may represent different numbers depending on the value assigned to the variable.
 Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
 Equations that contain a variable may be proven true or false by replacing the variable with a number.
 Various representations of expressions and equations
 Verbally
 Numerically
 Algebraically
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.
 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.
 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.

6.7C 
Determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations.
Supporting Standard

Determine
IF TWO EXPRESSIONS ARE EQUIVALENT USING CONCRETE MODELS, PICTORIAL MODELS, AND ALGEBRAIC REPRESENTATIONS
Including, but not limited to:
 Rational numbers – the set of numbers that can be expressed as a fraction , where a and b are integers and b ≠ 0. The set of rational numbers is denoted by the symbol Q.
 Various forms of positive and negative rational numbers
 Integers
 Products of integers limited to an integer multiplied by an integer
 Quotients of integers limited to an integer divided by an integer
 Decimals
 Products of decimals limited to a positive decimal value multiplied by a positive decimal value
 Quotients of decimals limited to a positive decimal value divided by a positive decimal value
 Fractions
 Products of fractions limited to a positive fractional value multiplied by a positive fractional value
 Quotients of fractions limited to a positive fractional value divided by a positive fractional value
 Expression – a mathematical phrase, with no equal sign or inequality symbol, that may contain a number(s), a variable(s), and/or an operator(s)
 Expressions with and without a variable
 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 whole number positive 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
 Equivalence of various representations of numerical expressions (concrete, pictorial, algebraic)
 Equivalence of various representations of algebraic expressions (concrete, pictorial, algebraic)
Note(s):
 Grade Level(s):
 Grade 6 introduces determining if two expressions are equivalent using concrete models, pictorial models, and algebraic representations.
 Algebra I will rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property.
 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.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).
 VIII.B. Communication and Representation – Interpretation of mathematical work
 VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.

6.7D 
Generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties.
Readiness Standard

Generate
EQUIVALENT EXPRESSIONS USING THE PROPERTIES OF OPERATIONS: INVERSE, IDENTITY, COMMUTATIVE, ASSOCIATIVE, AND DISTRIBUTIVE PROPERTIES
Including, but not limited to:
 Rational numbers – the set of numbers that can be expressed as a fraction , where a and b are integers and b ≠ 0. The set of rational numbers is denoted by the symbol Q.
 Various forms of positive and negative rational numbers
 Integers
 Products of integers limited to an integer multiplied by an integer
 Quotients of integers limited to an integer divided by an integer
 Decimals
 Products of decimals limited to a positive decimal value multiplied by a positive decimal value
 Quotients of decimals limited to a positive decimal value divided by a positive decimal value
 Fractions
 Products of fractions limited to a positive fractional value multiplied by a positive fractional value
 Quotients of fractions limited to a positive fractional value divided by a positive fractional value
 Expression – a mathematical phrase, with no equal sign or inequality symbol, that may contain a number(s), a variable(s), and/or an operator(s)
 Expressions with and without a variable
 Properties of operations
 Identity (Additive)
 Identity (Multiplicative)
 Commutative (Addition)
 Commutative (Multiplication)
 Associative (Addition)
 Rule (a + b) + c = a + (b + c)
 Associative (Multiplication)
 Rule (a • b) • c = a • (b • c)
 Distributive
 Inverse (Additive)
 Inverse (Multiplicative)
 Rule a • = 1
 Equivalent expressions using the properties of operations, including the combining of like terms
Note(s):
 Grade Level(s):
 Grade 6 introduces generating equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties.
 Algebra I will rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property.
 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.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).
 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.

6.9 
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 EQUATIONS TO REPRESENT CONSTRAINTS OR CONDITIONS WITHIN PROBLEMS
Including, but not limited to:
 Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
 Variable – a letter or symbol that represents a number
 One variable on one side of the equation
 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 equations
 A "step" only refers to an action involving both sides of the equation (combining like terms on a single side of the equation does not constitute a step).
 Solution set – a set of all values of the variable(s) that satisfy the equation
 Constraints or conditions
 Equality words and symbols
 Relationship of order of operations within an equation
 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 equations 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 EQUATIONS ON NUMBER LINES
Including, but not limited to:
 Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
 Variable – a letter or symbol that represents a number
 One variable on one side of the equation
 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 equations
 A "step" only refers to an action involving both sides of the equation (combining like terms on a single side of the equation does not constitute a step).
 Solution set – a set of all values of the variable(s) that satisfy the equation
 Constraints or conditions
 Equality words and symbols
 Representations of solutions to onestep equations on a number line
 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 equation 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 EQUATIONS
Including, but not limited to:
 Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
 Variable – a letter or symbol that represents a number
 One variable on one side of the equation
 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 equations
 A "step" only refers to an action involving both sides of the equation (combining like terms on a single side of the equation does not constitute a step).
 Solution set – a set of all values of the variable(s) that satisfy the equation
 Constraints or conditions
 Equality words and symbols
 Relationship of order of operations within an equation
 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 equation
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 EQUATIONS THAT REPRESENT PROBLEMS, INCLUDING GEOMETRIC CONCEPTS
Including, but not limited to:
 Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
 Variable – a letter or symbol that represents a number
 One variable on one side of the equation
 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 equations
 A "step" only refers to an action involving both sides of the equation (combining like terms on a single side of the equation does not constitute a step)
 Solution set – a set of all values of the variable(s) that satisfy the equation
 Constraints or conditions
 Equality words and symbols
 Relationship of order of operations within an equation
 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 onevariable, onestep equations from problem situations (concrete, pictorial, algebraic)
 Solutions to onevariable, onestep equations from geometric concepts
 Sum of the angles in a triangle, complementary angles, supplementary angles, sum of angles in a quadrilateral, etc.
 Supplementary angles – two angles whose degree measures have a sum of 180°
 Complementary angles – two angles whose degree measures have a sum of 90°
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 EQUATIONS TRUE
Including, but not limited to:
 Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
 Variable – a letter or symbol that represents a number
 One variable on one side of the equation
 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 equations
 A "step" only refers to an action involving both sides of the equation (combining like terms on a single side of the equation does not constitute a step)
 Solution set – a set of all values of the variable(s) that satisfy the equation
 Constraints or conditions
 Equality words and symbols
 Relationship of order of operations within an equation
 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 equations
 Value is considered part of the solution if the value makes the equation 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.
