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 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
 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, 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:
 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.

7.3 
Number and operations. The student applies mathematical process standards to add, subtract, multiply, and divide while solving problems and justifying solutions. The student is expected to:


7.3B 
Apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers.
Readiness Standard

Apply, Extend
PREVIOUS UNDERSTANDINGS OF OPERATIONS TO SOLVE PROBLEMS USING ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION OF RATIONAL NUMBERS
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
 Decimals
 Fractions
 Percents converted to equivalent decimals or fractions for multiplying or dividing
 Equivalent representations of a negative number
 Generalizations of integer operations
 Addition and subtraction
 If a pair of addends has the same sign, then the sum will have the sign of both addends.
 If a pair of addends has opposite signs, then the sum will have the sign of the addend with the greatest absolute value.
 A subtraction problem may be rewritten as an addition problem by adding the opposite of the integer following the subtraction symbol, and then applying the rules for addition.
 Multiplication and division
 If two rational numbers have the same sign, then the product or quotient is positive.
 If two rational numbers have opposite signs, then the product or quotient is negative.
 When multiplying or dividing two or more rational numbers, the product or quotient is positive if there are no negative signs or an even number of negative signs.
 When multiplying or dividing two or more rational numbers, the product or quotient is negative if there is one negative sign or an odd number of negative signs.
 Connections between generalizations for integer operations to rational number operations for addition and subtraction
 Recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values.
 Connections between generalizations for integer operations to rational number operations for multiplication and division
 Mathematical and realworld problem situations
 Multistep problems
 Multiple operations
Note(s):
 Grade Level(s):
 Grade 6 multiplied and divided positive rational numbers fluently.
 Grade 6 determined, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.

7.4 
Proportionality. The student applies mathematical process standards to represent and solve problems involving proportional relationships. The student is expected to:


7.4A 
Represent constant rates of change in mathematical and realworld problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt.
Readiness Standard

Represent
CONSTANT RATES OF CHANGE IN MATHEMATICAL AND REALWORLD PROBLEMS GIVEN PICTORIAL, TABULAR, VERBAL, NUMERIC, GRAPHICAL, AND ALGEBRAIC REPRESENTATIONS, INCLUDING d = rt
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
 Decimals
 Fractions
 Constant rate of change – a ratio when the dependent, yvalue, changes at a constant rate for each independent, xvalue
 Proportional mathematical and realworld problems
 Unit conversions within and between systems
 d = rt
 In d = rt, the d represents distance, the r represents rate, and the t represents time.
 Connections between constant rate of change r, in d = rt, to the constant of proportionality, k, in y = kx
 Various representations of constant rates of change in mathematical and realworld situations
 Pictorial
 Tabular (vertical/horizontal)
 Verbal
 Numeric
 Graphical
 Algebraic
Note(s):
 Grade Level(s):
 Grade 6 compared two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multiplicative relationships.
 Grade 6 gave examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients.
 Grade 6 represented mathematical and realworld problems involving ratios and rates using scale factors, tables, graphs, and proportions.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Representing and applying proportional relationships
 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.
 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.
 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.

7.4B 
Calculate unit rates from rates in mathematical and realworld problems.
Supporting Standard

Calculate
UNIT RATES FROM RATES IN MATHEMATICAL AND REALWORLD PROBLEMS
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
 Decimals
 Fractions
 Percents converted to equivalent decimals or fractions for multiplying or dividing fluently
 Unit rate – a ratio between two different units where one of the terms is 1
 Rate – a multiplicative comparison of two different quantities where the measuring unit is different for each quantity
 Various representations of rates
 Verbal (e.g., for every, per, for each, to, etc.)
 Symbolic (e.g., , 2 to 7, etc.)
 Multiplication/division to determine unit rate from mathematical and realworld problems
 Speed
 Density ()
 Price
 Measurement in recipes
 Student–teacher ratios
 Unit conversions within and between systems
Note(s):
 Grade Level(s):
 Grade 7 introduces calculating unit rates from rates in mathematical and realworld problems.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Representing and applying proportional relationships
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 II.D. Algebraic Reasoning – Representing relationships
 II.D.1. Interpret multiple representations of equations, inequalities, and relationships.
 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.
 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.

7.4C 
Determine the constant of proportionality (k = y/x) within mathematical and realworld problems.
Supporting Standard

Determine
THE CONSTANT OF PROPORTIONALITY () WITHIN MATHEMATICAL AND REALWORLD PROBLEMS
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
 Decimals
 Fractions
 Percents converted to equivalent decimals or fractions for multiplying or dividing fluently
 Constant rate of change – a ratio when the dependent, yvalue, changes at a constant rate for each independent, xvalue
 Constant of proportionality – a constant ratio between two proportional quantities denoted by the symbol k
 Characteristics of the constant of proportionality
 A graphed proportional relationship where x represents the independent variable and y represents the dependent variable.
 Independent variables describe the input values in a relationship, normally represented by the x coordinate in the ordered pairs (x, y)
 Dependent variables describe the output values in a relationship, normally represented by the y coordinate in the ordered pairs (x, y).
 The constant of proportionality can never be zero.
 Unit rate – a ratio between two different units where one of the terms is 1
 Proportional mathematical and realworld problems
 Unit conversions within and between same system
 d = rt
 In d = rt, the d represents distance, the r represents rate, and the t represents time
 Connections between constant rate of change r, in d = rt, to the constant of proportionality, k, in y = kx
 Various representations of the constant of proportionality
 Tabular (vertical/horizontal)
 Verbal
 Numeric
 Graphical
 Algebraic
Note(s):
 Grade Level(s):
 Grade 6 compared two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multiplicative relationships.
 Grade 8 will solve problems involving direct variation.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Representing and applying proportional relationships
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 II.D. Algebraic Reasoning – Representing relationships
 II.D.1. Interpret multiple representations of equations, inequalities, and relationships.
 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.
 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.

7.4D 
Solve problems involving ratios, rates, and percents, including multistep problems involving percent increase and percent decrease, and financial literacy problems.
Readiness Standard

Solve
PROBLEMS INVOLVING RATIOS, RATES, AND PERCENTS INCLUDING MULTISTEP PROBLEMS INVOLVING PERCENT INCREASE AND PERCENT DECREASE, AND FINANCIAL LITERACY PROBLEMS
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
 Fractions
 Percents converted to equivalent decimals or fractions for multiplying or dividing
 Ratio – a multiplicative comparison of two quantities
 Symbolic representations of ratios
 a to b, a:b, or
 Verbal representations of ratios
 12 to 3, 12 per 3, 12 parts to 3 parts, 12 for every 3, 12 out of every 3
 Units may or may not be included (e.g., 12 boys to 3 girls, 12 to 3, etc.)
 Rate – a multiplicative comparison of two different quantities where the measuring unit is different for each quantity
 Relationship between ratios and rates
 All ratios have associated rates.
 Percent – a part of a whole expressed in hundredths
 Numeric forms
 Algebraic notation as a decimal
 Multistep problems
 Multiple methods for solving problems involving ratios, rates, and percents
 Models (e.g., percent bars, hundredths grid, strip diagram, number line, etc.)
 Decimal method (algebraic)
 Dimensional analysis
 Proportion method
 Scale factors between ratios
 Equivalent representations of ratios, rates and percents
 Various representations of ratios, rates, percents
 Pictorial
 Tabular (vertical/horizontal)
 Verbal
 Numeric
 Graphical
 Algebraic
 Situations involving ratios, rates, or percents
 Ratios
 Rates
 Percent increase – a change in percentage where the value increases
 Percent decrease – a change in percentage where the value decreases
 Financial literacy problems
 Principal – the original amount invested or borrowed
 Simple interest – interest paid or earned on the original principal amount, disregarding any previously paid or earned interest
 Formula for simple interest from STAAR Grade 7 Mathematics Reference Materials
 I = Prt, where I represents the interest, P represents the principal amount, r represents the interest rate in decimal form, and t represents the number of years the amount is deposited or borrowed
 Tax – a financial charge, usually a percentage applied to goods, property, sales, etc.
 Tip – an amount of money rendered for a service, gratuity
 Commission – pay based on a percentage of the sales or profit made by an employee or agent
 Markup – the difference between the purchase price of an item and its sales price
 Markdown – the difference between the original price of an item and its current price
 Appreciation – the increase in value over time
 Depreciation – the decrease in value over time
Note(s):
 Grade Level(s):
 Grade 6 represented ratios and percents with concrete models, fractions, and decimals.
 Grade 6 represented benchmark fractions and percents such as 1%, 10%, 25%, 33% and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers.
 Grade 6 generated equivalent forms of fractions, decimals, and percents using realworld problems, including problems that involve money.
 Grade 6 solved realworld problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole, including the use of concrete and pictorial models.
 Grade 6 used equivalent fractions, decimals, and percents to show equal parts of the same whole.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Representing and applying proportional relationships
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 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.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.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.

7.5 
Proportionality. The student applies mathematical process standards to use geometry to describe or solve problems involving proportional relationships. The student is expected to:


7.5C 
Solve mathematical and realworld problems involving similar shape and scale drawings.
Readiness Standard

Solve
MATHEMATICAL AND REALWORLD PROBLEMS INVOLVING SIMILAR SHAPE AND SCALE DRAWINGS
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
 Fractions
 Percents converted to equivalent decimals or fractions for multiplying or dividing
 Mathematical and realworld problems
 Similar shapes – shapes whose angles are congruent and side lengths are proportional (equal scale factor)
 Similar shapes are proportional when a scale factor is applied to the linear measures, creating a dilated (enlarged or reduced) shape.
 Scale drawings
 Scale drawings are proportional when a scale factor is applied to the linear measures, creating a dilated (enlarged or reduced) scale drawing.
Note(s):
 Grade Level(s):
 Grade 6 represented mathematical and realworld problems involving ratios and rates using scale factors, tables, graphs, and proportions.
 Grade 7 introduces solving mathematical and realworld problems involving similar shape and scale drawings.
 Grade 8 will generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation.
 Grade 8 will compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane.
 Grade 8 will use an algebraic representation to explain the effect of a given positive rational scale factor applied to twodimensional figures on a coordinate plane with the origin as the center of dilation.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Representing and applying proportional relationships
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 III.D. Geometric and Spatial Reasoning – Measurements involving geometry and algebra
 III.D.3. Determine indirect measurements of geometric figures using a variety of methods.
 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.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.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.

7.7 
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:
 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.
 VI.B. Functions – Analysis of functions
 VI.B.1. Understand and analyze features of functions.
 VI.C. Functions – Model realworld situations with functions
 VI.C.2. Develop a function to model a situation.
 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.
