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:
 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.

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:
 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.

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:
 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.

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, 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:
 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:
 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.

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:
 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.

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:
 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.

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:
 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.

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:
 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.

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.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.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.

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:
 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.
 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.
 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.

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.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.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.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.

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.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.

7.11C 
Write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships.
Supporting Standard

Write, Solve
EQUATIONS USING GEOMETRY CONCEPTS, INCLUDING THE SUM OF THE ANGLES IN A TRIANGLE, AND ANGLE RELATIONSHIPS
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
 Decimals
 Fractions
 Constant – a fixed value that does not appear with a variable(s)
 Integers
 Decimals
 Fractions
 Solution set – a set of all values of the variable(s) that satisfy the equation
 Equations from geometry concepts
 Angle measures as numeric and/or algebraic expressions
 Sum of the angles in a triangle
 Other angle relationships
 Adjacent angles – two nonoverlapping angles that share a common vertex and exactly one ray
 Complementary angles – two angles whose degree measures have a sum of 90°
 Supplementary angles – two angles whose degree measures have a sum of 180°
 Straight angle – an angle with rays extending in opposite directions and whose degree measure is 180°
 Congruent angles – angles whose angle measurements are equal
 Arc(s) on angles are usually used to indicate congruency (one set of congruent angles would have 1 arc, another set of congruent angles would have 2 arcs, etc.).
 Arcs and tick marks on angles can be used to indicate congruency (one set of congruent angles would have 1 arc with 1 tick mark, another set of congruent angles would have 1 arc with 2 tick marks, etc.)
 Vertical angles – a pair of nonadjacent, nonoverlapping angles formed by two intersecting lines creating angles that are opposite and congruent to each other
 Reallife situation involving angle measures
Note(s):
 Grade Level(s):
 Grade 4 determined the measure of an unknown angle formed by two nonoverlapping adjacent angles given one or both angle measures.
 Grade 6 extended previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle.
 Grade 6 modeled and solved onevariable, onestep equations and inequalities that represent problems, including geometric concepts.
 Grade 8 will use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angleangle criterion for similarity of triangles.
 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.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 III.C. Geometric and Spatial Reasoning – Connections between geometry and other mathematical content strands
 III.C.1. Make connections between geometry and algebraic equations.
 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.

7.13 
Personal financial literacy. The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in one's life as a knowledgeable consumer and investor. The student is expected to:


7.13D 
Use a family budget estimator to determine the minimum household budget and average hourly wage needed for a family to meet its basic needs in the student's city or another large city nearby.
Supporting Standard

Use
A FAMILY BUDGET ESTIMATOR
Including, but not limited to:
 Budget – a monthly or yearly spending and savings plan for an individual, family, business, or organization
 Family budget estimator – determines the monthly or annual base income that is needed for a family
 Components of a family budget estimator
 Location of family
 Number of parents/guardians in the household
 Number of children in the household
 Basic needs
 Housing
 Food
 Medical Insurance
 Medial outofpocket expenses
 Transportation
 Child care
 Other family needs
 Savings (e.g., emergencies, retirement, college, etc.)
 Federal taxes
 Payroll tax
 Income tax
 Earned income credit
 Child tax credit
 Budget components are usually rounded to the nearest whole dollar amount.
 Values of budget components vary depending on location within a country, state, city, or county.
 Data from multiple sources is used to create a family budget estimator.
To Determine
THE MINIMUM HOUSEHOLD BUDGET AND AVERAGE HOURLY WAGE NEEDED FOR A FAMILY TO MEET ITS BASIC NEEDS IN THE STUDENT'S CITY OR ANOTHER LARGE CITY NEARBY
Including, but not limited to:
 Wage – the amount usually earned per hour or over a given period of time
 Basic needs – minimum necessities
 Minimum household budget is usually a monthly budget and is determined by finding the difference between the sum of the cost of basic needs, savings, and taxes and the total household income
 Average hourly wage is calculated by dividing the minimum household budget by the number of hours worked each month by each working adult in the household
 A typical workweek is considered 40 hours or 8 hours per day.
 The number of hours worked per month varies depending on the number of working days in the month but can usually be considered as 20 working days per month.
 Average hourly wage needed in the student’s city
 Average hourly wage needed in nearby larger city
 Career opportunities to meet family budget needs
Note(s):
 Grade Level(s):
 Grade 5 balanced a simple budget.
 Grade 7 introduces using a family budget estimator to determine the minimum household budget and average hourly wage needed for a family to meet its basic needs in the student's city or another large city nearby.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 IX.A. Connections – Connections among the strands of mathematics
 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.

7.13E 
Calculate and compare simple interest and compound interest earnings.
Supporting Standard

Calculate, Compare
SIMPLE INTEREST AND COMPOUND INTEREST EARNINGS
Including, but not limited to:
 Positive rational numbers – the set of numbers that can be expressed as a fraction , where a and b are counting (natural) numbers
 Various forms of positive rational numbers
 Counting (natural) numbers
 Decimals
 Percents converted to equivalent decimals or fractions for multiplying or dividing
 Principal of an investment – the original amount invested
 Simple interest for an investment – interest paid on the original principal in an account, disregarding any previously earned interest
 Compound interest for an investment – interest that is calculated on the latest balance, including all compounded interest that has been added to the original principal investment
 Formulas for interest from STAAR Grade 7 Mathematics Reference Materials
 Simple interest
 I = Prt, where I represents the interest, P represents the principal amount deposited, r represents the interest rate in decimal form, and t represents the number of years the amount is deposited
 Compound interest
 A = P(1+r)^{t}, where A represents the total accumulated amount, including the principal and earned compounded interested, P represents the principal amount, r represents the interest rate in decimal form, and t represents the number of years the principal amount is deposited
 Comparing simple and compound interest earnings
Note(s):
 Grade Level(s):
 Grade 4 compared the advantages and disadvantages of various savings options.
 Grade 8 will calculate and compare simple interest and compound interest earnings.
 Algebra I will refer to 1 + r in the compound interest formula, A = P(1 + r)^{t}, as the factor and will be given the variable b.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 IX.A. Connections – Connections among the strands of mathematics
 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.

7.13F 
Analyze and compare monetary incentives, including sales, rebates, and coupons.
Supporting Standard

Analyze, Compare
MONETARY INCENTIVES, INCLUDING SALES, REBATES, AND COUPONS
Including, but not limited to:
 Monetary incentives
 Sale – a reduced amount or price of an item
 May be offered by a store or manufacturer depending on the location of the purchase
 Rebate – an amount returned or refunded for purchasing an item or items
 May be offered by the store or manufacturer
 May be instant or require a rebate form with proof of purchase to be mailed in
 Coupon – an amount deducted from the total cost of an item
 May be offered by manufacturers or by retailers
 Some retailers may allow coupons to be stacked by accepting both a store coupon and a manufacturer’s coupon.
Note(s):
 Grade Level(s):
 Grade 3 identified the costs and benefits of planned and unplanned spending decisions.
 Grade 8 will explain how small amounts of money invested regularly, including money saved for college and retirement, grow over time.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
