7.1 
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:


7.1A 
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:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:

7.1B 
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:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:
 VIII. Problem Solving and Reasoning

7.1C 
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:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:
 VIII. Problem Solving and Reasoning

7.1D 
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.
 TxRCFP:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:
 IX. Communication and Representation

7.1E 
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:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:
 IX. Communication and Representation

7.1F 
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:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:

7.1G 
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:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:
 IX. Communication and Representation

7.7 
Expressions, equations, and relationships. The student applies mathematical process standards to represent linear relationships using multiple representations. The student is expected to:


7.7A 
Represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b.
Readiness Standard

Represent
LINEAR RELATIONSHIPS USING VERBAL DESCRIPTIONS, TABLES, GRAPHS, AND EQUATIONS THAT SIMPLIFY TO THE FORM y = mx + b
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 as constants and coefficients
 Coefficient – a number that is multiplied by a variable(s)
 Constant – a fixed value that does not appear with a variable(s)
 Integers
 Decimals
 Fractions
 Constant rate of change – a ratio when the dependent, yvalue, changes at a constant rate for each independent, xvalue
 Linear relationship – a relationship with a constant rate of change represented by a graph that forms a straight line
 One quantity is dependent on the other
 Two quantities may be directly proportional to each other
 Can be classified as a positive or negative relationship
 Can be expressed as a pair of values that can be graphed as ordered pairs
 Graph of the ordered pairs matching the relationship will form a line
 Linear proportional relationship
 Linear
 Passes through the origin (0, 0)
 Represented by y = kx
 Constant of proportionality represented as
 When b = 0 in y = mx + b, then k = m
 Linear nonproportional relationship
 Linear
 Does not pass through the origin (0, 0)
 Represented by y = mx + b, where b ≠ 0
 Constant rate of change represented as m = or m =
 Rate of change is either positive, negative, zero, or undefined
 Various representations to describe algebraic relationships
 Verbal descriptions
 Tables
 Graphs
 Equations
 In the form y = mx + b(slope intercept form)
Note(s):
 Grade Level(s):
 Grade 6 identified independent and dependent quantities from tables and graphs.
 Grade 6 wrote an equation that represents the relationship between independent and dependent quantities from a table.
 Grade 6 represented a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b.
 Grade 8 will represent linear nonproportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0.
 Grade 8 will write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations.
 Grade 8 will distinguish between proportional and nonproportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 TxCCRS:
 I. Numeric Reasoning
 II. Algebraic Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation

7.10 
Expressions, equations, and relationships. The student applies mathematical process standards to use onevariable equations and inequalities to represent situations. The student is expected to:


7.10A 
Write onevariable, twostep equations and inequalities to represent constraints or conditions within problems.
Supporting Standard

Write
ONEVARIABLE, TWOSTEP EQUATIONS AND INEQUALITIES 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
 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 equation or inequality
 Coefficient – a number that is multiplied by a variable(s)
 Integers
 Decimals
 Fractions
 Constant – a fixed value that does not appear with a variable(s)
 Integers
 Decimals
 Fractions
 Twostep equations and inequalities
 A “step” only refers to an action involving both sides of the equation or inequality (combining like terms on a single side of the equation or inequality does not constitute a step).
 Solution set – a set of all values of the variable(s) that satisfy the equation or 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 equation or 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 numer 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, twostep equations from a problem
 Onevariable, twostep inequalities from a problem
Note(s):
 Grade Level(s):
 Grade 6 wrote onevariable, onestep equations and inequalities to represent constraints or conditions within problems.
 Grade 7 represents writing onevariable, twostep equations and inequalities to represent constraints or conditions within problems.
 Grade 8 will write onevariable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 TxCCRS:
 II. Algebraic Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections

7.10B 
Represent solutions for onevariable, twostep equations and inequalities on number lines.
Supporting Standard

Represent
SOLUTIONS FOR ONEVARIABLE, TWOSTEP EQUATIONS AND INEQUALITIES ON NUMBER LINES
Including, but not limited to:
 Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
 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 equation or inequality
 Coefficient – a number that is multiplied by a variable(s)
 Integers
 Decimals
 Fractions
 Constant – a fixed value that does not appear with a variable(s)
 Integers
 Decimals
 Fractions
 Twostep equations and inequalities
 A “step” only refers to an action involving both sides of the equation or inequality (combining like terms on a single side of the equation or inequality does not constitute a step).
 Solution set – a set of all values of the variable(s) that satisfy the equation or 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 equations and inequalities on a number line
 Closed circle
 Equal to, =
 Greater than or equal to, ≥
 Less than or equal to, ≤
 Open circle
 Greater than, >
 Less than, <
 Not equal to, ≠
Note(s):
 Grade Level(s):
 Grade 6 represented solutions for onevariable, onestep equations and inequalities on number lines.
 Grade 7 represents solutions for onevariable, twostep 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 describe relationships in a variety of contexts, including geometric problems
 TxCCRS:
 II. Algebraic Reasoning
 IX. Communication and Representation

7.10C 
Write a corresponding realworld problem given a onevariable, twostep equation or inequality.
Supporting Standard

Write
A CORRESPONDING REALWORLD PROBLEM GIVEN A ONEVARIABLE, TWOSTEP EQUATION OR INEQUALITY
Including, but not limited to:
 Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
 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 equation or inequality
 Coefficient – a number that is multiplied by a variable(s)
 Integers
 Decimals
 Fractions
 Constant – a fixed value that does not appear with a variable(s)
 Integers
 Decimals
 Fractions
 Twostep equations and inequalities
 A “step” only refers to an action involving both sides of the equation or inequality (combining like terms on a single side of the equation or inequality does not constitute a step).
 Solution set – a set of all values of the variable(s) that satisfy the equation or 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 equation or 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 numer 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 from a onevariable, twostep equation
 Corresponding realworld problem from a onevariable, twostep inequality
Note(s):
 Grade Level(s):
 Grade 6 wrote corresponding realworld problems given onevariable, onestep equations or inequalities.
 Grade 7 writes corresponding realworld problems given onevariable, twostep equations or inequalities.
 Grade 8 will write a corresponding realworld problem when given a onevariable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 TxCCRS:
 II. Algebraic Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections

7.11 
Expressions, equations, and relationships. The student applies mathematical process standards to solve onevariable equations and inequalities. The student is expected to:


7.11A 
Model and solve onevariable, twostep equations and inequalities.
Readiness Standard

Model, Solve
ONEVARIABLE, TWOSTEP EQUATIONS AND INEQUALITIES
Including, but not limited to:
 Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
 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 equation or inequality
 Coefficient – a number that is multiplied by a variable(s)
 Integers
 Decimals
 Fractions
 Constant – a fixed value that does not appear with a variable(s)
 Integers
 Decimals
 Fractions
 Twostep equations and inequalities
 A “step” only refers to an action involving both sides of the equation or inequality (combining like terms on a single side of the equation or inequality does not constitute a step).
 Solution set – a set of all values of the variable(s) that satisfy the equation or 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 equation or 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 numer 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
 Model and solve onevariable, twostep equations (concrete, pictorial, algebraic)
 Model and solve onevariable, twostep inequalities (concrete, pictorial, algebraic)
 Solutions to onevariable, twostep equations from a problem situation
 Solutions to onevariable, twostep inequalities from a problem situation
Note(s):
 Grade Level(s):
 Grade 6 modeled and solved onevariable, onestep equations and inequalities that represented problems, including geometric concepts.
 Grade 8 will model and solve onevariable equations with variables on both sides of the equal sign that represent mathematical and realworld problems using rational number coefficients and constants.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 TxCCRS:
 I. Numeric Reasoning
 II. Algebraic Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections

7.11B 
Determine if the given value(s) make(s) onevariable, twostep equations and inequalities true.
Supporting Standard

Determine
IF THE GIVEN VALUE(S) MAKE(S) ONEVARIABLE, TWOSTEP EQUATIONS AND INEQUALITIES TRUE
Including, but not limited to:
 Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
 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 equation or inequality
 Coefficient – a number that is multiplied by a variable(s)
 Integers
 Decimals
 Fractions
 Constant – a fixed value that does not appear with a variable(s)
 Integers
 Decimals
 Fractions
 Twostep equations and inequalities
 A “step” only refers to an action involving both sides of the equation or inequality (combining like terms on a single side of the equation or inequality does not constitute a step).
 Solution set – a set of all values of the variable(s) that satisfy the equation or 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 equation or 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 numer 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 a given value(s) as a possible solution to onevariable, twostep equations
 Evaluation of a given value(s) as a possible solution to onevariable, twostep inequalities
Note(s):
 Grade Level(s):
 Grade 6 determined if the given value(s) make(s) onevariable, onestep equations or inequalities true.
 Grade 8 will identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 TxCCRS:
 I. Numeric Reasoning
 II. Algebraic Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
