
Legend:  Knowledge and Skills Statements (TEKS) identified by TEA are in italicized, bolded, black text.
 Student Expectations (TEKS) identified by TEA are in bolded, black text.
 Student Expectations (TEKS) are labeled Readiness as identified by TEA of the assessed curriculum.
 Student Expectations (TEKS) are labeled Supporting as identified by TEA of the assessed curriculum.
 Student Expectations (TEKS) are labeled Process standards as identified by TEA of the assessed curriculum.
 Portions of the Student Expectations (TEKS) that are not included in this unit but are taught in previous or future units are indicated by a
strikethrough.

Legend:  Supporting information / clarifications (specificity) written by TEKS Resource System are in blue text.
 Unitspecific clarifications are in italicized, blue text.
 Information from Texas Education Agency (TEA), Texas College and Career Readiness Standards (TxCCRS), Texas Response to Curriculum Focal Points (TxRCFP) is labeled.
 A Partial Specificity label indicates that a portion of the specificity not aligned to this unit has been removed.

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 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:
 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

7.4 
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:
 I. Numeric Reasoning
 II. Algebraic Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections

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. Numeric Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections

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. Numeric Reasoning
 II. Algebraic Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections

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. Numeric Reasoning
 II. Algebraic Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections

7.4E 
Convert between measurement systems, including the use of proportions and the use of unit rates.
Supporting Standard

Convert
BETWEEN MEASUREMENT SYSTEMS, INCLUDING THE USE OF PROPORTIONS AND THE USE OF UNIT RATES
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
 Convert units between measurement systems.
 Customary to metric
 Metric to customary
 Multiple solution strategies
 Dimensional analysis using unit rates
 Unit rates
 Scale factor between ratios
 Proportion method
 Conversion graph
Note(s):
 Grade Level(s):
 Grade 4 converted measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table.
 Grade 5 solved problems by calculating conversions within a measurement system, customary or metric.
 Grade 6 converted units within a measurement system, including the use of proportions and unit rates.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Representing and applying proportional relationships
 TxCCRS:
 I. Numeric Reasoning
 IV. Measurement Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation

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:


7.13B 
Identify the components of a personal budget, including income; planned savings for college, retirement, and emergencies; taxes; and fixed and variable expenses, and calculate what percentage each category comprises of the total budget.
Supporting Standard

Identify
THE COMPONENTS OF A PERSONAL BUDGET, INCLUDING INCOME; PLANNED SAVINGS FOR COLLEGE, RETIREMENT, AND EMERGENCIES; TAXES; AND FIXED AND VARIABLE EXPENSES
Including, but not limited to:
 Budget – a monthly or yearly spending and savings plan for an individual, family, business, or organization
 Budgets based on financial records help people plan and make choices about how to spend and save their money
 Components of a personal budget
 Income – money earned or received
 Savings for college – money saved for continuing education beyond high school
 Savings for retirement – money saved over the period of time an individual is employed to be spent once the individual retires from their occupation
 Savings for emergencies – money saved for unexpected expenses (e.g., car repairs, emergency healthcare, etc.)
 Taxes – money paid to local, state, and federal governments to pay for things the government provides to its citizens
 Various types of taxes
 Income tax – a percentage of money paid on the earned wages of an individual or business for the federal and/or state governments as required by law
 Payroll tax – a percentage of money that a company withholds from its employees for the federal government as required by law
 Sales tax – a percentage of money collected by a store (retailer), in addition to a good or service that was purchased, for the local government as required by law
 Property tax – a percentage of money collected on the value of a property for the local government as required by law
 Expense – payment for goods and services
 Fixed expenses – expenses that are consistent from month to month
 Variable expenses – expenses that vary in cost from month to month
Calculate
WHAT PERCENTAGE EACH CATEGORY OF A PERSONAL BUDGET COMPRISES OF THE TOTAL BUDGET
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
 Proportional reasoning to determine percentages within a budget
 Proportional reasoning to determine amounts within a budget
Note(s):
 Grade Level(s):
 Grade 5 balanced a simple budget.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 TxCCRS:
 I. Numeric Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections
