
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.

6.1 
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:


6.1A 
Apply mathematics to problems arising in everyday life, society, and the workplace.
Process Standard

Apply
MATHEMATICS TO PROBLEMS ARISING IN EVERYDAY LIFE, SOCIETY, AND THE WORKPLACE
Including, but not limited to:
 Mathematical problem situations within and between disciplines
 Everyday life
 Society
 Workplace
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Using operations with integers and positive rational numbers to solve problems
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 Using expressions and equations to represent relationships in a variety of contexts
 Understanding data representation
 TxCCRS:

6.1B 
Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
Process Standard

Use
A PROBLEMSOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEMSOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION
Including, but not limited to:
 Problemsolving model
 Analyze given information
 Formulate a plan or strategy
 Determine a solution
 Justify the solution
 Evaluate the problemsolving process and the reasonableness of the solution
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Using operations with integers and positive rational numbers to solve problems
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 Using expressions and equations to represent relationships in a variety of contexts
 Understanding data representation
 TxCCRS:
 VIII. Problem Solving and Reasoning

6.1C 
Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.
Process Standard

Select
TOOLS, INCLUDING REAL OBJECTS, MANIPULATIVES, PAPER AND PENCIL, AND TECHNOLOGY AS APPROPRIATE, AND TECHNIQUES, INCLUDING MENTAL MATH, ESTIMATION, AND NUMBER SENSE AS APPROPRIATE, TO SOLVE PROBLEMS
Including, but not limited to:
 Appropriate selection of tool(s) and techniques to apply in order to solve problems
 Tools
 Real objects
 Manipulatives
 Paper and pencil
 Technology
 Techniques
 Mental math
 Estimation
 Number sense
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Using operations with integers and positive rational numbers to solve problems
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 Using expressions and equations to represent relationships in a variety of contexts
 Understanding data representation
 TxCCRS:
 VIII. Problem Solving and Reasoning

6.1D 
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Process Standard

Communicate
MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, 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:
 Using operations with integers and positive rational numbers to solve problems
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 Using expressions and equations to represent relationships in a variety of contexts
 Understanding data representation
 TxCCRS:
 IX. Communication and Representation

6.1E 
Create and use representations to organize, record, and communicate mathematical ideas.
Process Standard

Create, Use
REPRESENTATIONS TO ORGANIZE, RECORD, AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:
 Representations of mathematical ideas
 Organize
 Record
 Communicate
 Evaluation of the effectiveness of representations to ensure clarity of mathematical ideas being communicated
 Appropriate mathematical vocabulary and phrasing when communicating mathematical ideas
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Using operations with integers and positive rational numbers to solve problems
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 Using expressions and equations to represent relationships in a variety of contexts
 Understanding data representation
 TxCCRS:
 IX. Communication and Representation

6.1F 
Analyze mathematical relationships to connect and communicate mathematical ideas.
Process Standard

Analyze
MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:
 Mathematical relationships
 Connect and communicate mathematical ideas
 Conjectures and generalizations from sets of examples and nonexamples, patterns, etc.
 Current knowledge to new learning
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Using operations with integers and positive rational numbers to solve problems
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 Using expressions and equations to represent relationships in a variety of contexts
 Understanding data representation
 TxCCRS:

6.1G 
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Process Standard

Display, Explain, Justify
MATHEMATICAL IDEAS AND ARGUMENTS USING PRECISE MATHEMATICAL LANGUAGE IN WRITTEN OR ORAL COMMUNICATION
Including, but not limited to:
 Mathematical ideas and arguments
 Validation of conclusions
 Displays to make work visible to others
 Diagrams, visual aids, written work, etc.
 Explanations and justifications
 Precise mathematical language in written or oral communication
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Using operations with integers and positive rational numbers to solve problems
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 Using expressions and equations to represent relationships in a variety of contexts
 Understanding data representation
 TxCCRS:
 IX. Communication and Representation

6.4 
Proportionality. The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations. The student is expected to:


6.4B 
Apply qualitative and quantitative reasoning to solve prediction and comparison of realworld problems involving ratios and rates.
Readiness Standard

Apply
QUALITATIVE AND QUANTITATIVE REASONING TO SOLVE PREDICTION AND COMPARISON OF REALWORLD PROBLEMS INVOLVING RATIOS AND 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
 Percents converted to equivalent decimals or fractions for multiplying or dividing fluently
 Qualitative – a broad subjective description (e.g., The speed of car A is slower than the speed of car B.)
 Qualitative reasoning to compare and predict
 Ratio – a multiplicative comparison of two quantities
 Comparing ratios (e.g., color is brighter, taste is sweeter, pace is slower, etc.)
 Predictions from ratios
 Qualitative reasoning to compare and predict in realworld problem situations involving rates
 Rate – a multiplicative comparison of two different quantities where the measuring unit is different for each quantity
 Comparing rates (e.g., decreases faster, more per pound, etc.)
 Predictions from rates
 Quantitative – a narrowed objective description associated with a quantity (e.g., The ratio of blue cars to red cars is 6:3; therefore, there are twice as many blue cars as red cars.)
 Quantitative reasoning to compare and predict in realworld problem situations involving ratios
 Comparing ratios (e.g., twice as much, half as sweet)
 Predictions from ratios
 Comparing rates (e.g., decreases half as fast, three times more per pound, etc.)
 Predictions from rates
Note(s):
 Grade Level(s):
 Grade 6 introduces applying qualitative and quantitative reasoning to solve prediction and comparison of realworld problems involving ratios and rates.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 TxCCRS:
 I. Numeric Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections

6.4C 
Give examples of ratios as multiplicative comparisons of two quantities describing the same attribute.
Supporting Standard

Give
EXAMPLES OF RATIOS AS MULTIPLICATIVE COMPARISONS OF TWO QUANTITIES DESCRIBING THE SAME ATTRIBUTE
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 fluently
 Multiplicative comparison of two quantities – a proportional comparison in which one quantity can be described as a multiple of the other
 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.).
 Quantities describing the same attribute
 Proportional representations of multiplicative comparisons
 Strip diagram – a linear model used to illustrate number relationships
 Ratio table
 Double number lines
Note(s):
 Grade Level(s):
 Grade 6 introduces giving examples of ratios as multiplicative comparisons of two quantities describing the same attribute.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 TxCCRS:
 I. Numeric Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation

6.4D 
Give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients.
Supporting Standard

Give
EXAMPLES OF RATES AS THE COMPARISON BY DIVISION OF TWO QUANTITIES HAVING DIFFERENT ATTRIBUTES, INCLUDING RATES AS QUOTIENTS
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 fluently
 Comparison by division of two quantities – a proportional comparison in which one quantity can be described as a ratio of the other
 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
 Quantities describing different attributes
 Proportional representations of comparisons by division
 Ratio table
 Double number lines
 Rates as quotients
Note(s):
 Grade Level(s):
 Grade 6 introduces giving examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients.
 Grade 7 will represent constant rates of change in mathematical and realworld problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt.
 Grade 7 will calculate unit rates from rates in mathematical and realworld problems.
 Grade 7 will determine the constant of proportionality () within mathematical and realworld problems.
 Grade 7 will solve problems involving ratios, rates, and percents, including multistep problems involving percent increase and percent decrease, and financial literacy problems.
 Grade 7 will convert between measurement systems, including the use of proportions and the use of unit rates.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 TxCCRS:
 I. Numeric Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation

6.4E 
Represent ratios and percents with concrete models, fractions, and decimals.
Supporting Standard

Represent
RATIOS AND PERCENTS WITH CONCRETE MODELS, FRACTIONS, AND DECIMALS
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
 Percent – a part of a whole expressed in hundredths
 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.)
 Concrete and pictorial models of ratios
 Objects
 Fraction circle
 Strip diagram – a linear model used to illustrate number relationships
 10 by 10 grid
 Number line
 Numeric representation of ratios
 Fraction notation
 Decimal notation
 Percent
 Numeric forms
 Concrete and pictorial models of percents
 Objects
 Fraction circle
 Strip diagram – a linear model used to illustrate number relationships
 10 by 10 grid
 Number line
 Numeric representation of percents
 Fraction notation
 Decimal notation
Note(s):
 Grade Level(s):
 Grade 6 introduces representing ratios and percents with concrete models, fractions, and decimals.
 Grade 7 will solve problems involving ratios, rates, and percents, including multistep problems involving percent increase and percent decrease, and financial literacy problems.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 TxCCRS:
 IX. Communication and Representation
 X. Connections

6.4G 
Generate equivalent forms of fractions, decimals, and percents using realworld problems, including problems that involve money.
Readiness Standard

Generate
EQUIVALENT FORMS OF FRACTIONS, DECIMALS, AND PERCENTS USING REALWORLD PROBLEMS, INCLUDING PROBLEMS THAT INVOLVE MONEY
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
 Percent – a part of a whole expressed in hundredths
 Equivalent forms of positive rational numbers in realworld problem situations, including money
 Given a fraction, generate a decimal and percent
 Given a decimal, generate a fraction and percent
 Given a percent, generate a fraction and decimal
Note(s):
 Grade Level(s):
 Grade 6 introduces generating equivalent forms of fractions, decimals, and percents using realworld problems, including problems that involve money.
 Grade 6 introduces ordering a set of rational numbers arising from mathematical and realworld contexts.
 Grade 7 will solve problems involving ratios, rates, and percents, including multistep problems involving percent increase and percent decrease, and financial literacy problems.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 TxCCRS:
 I. Numeric Reasoning
 IX. Communication and Representation
 X. Connections

6.4H 
Convert units within a measurement system, including the use of proportions and unit rates.
Readiness Standard

Convert
UNITS WITHIN A MEASUREMENT SYSTEM, INCLUDING THE USE OF PROPORTIONS AND 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
 Unit conversions within systems
 Unit rate – a ratio between two different units where one of the terms is 1
 Multiple solution strategies
 Scale factor between ratios
 Proportion method
Note(s):
 Grade Level(s):
 Grade 4 converted measurements within the same measurement system, customary or metric, from a smaller unit into a large unit or a large unit into a smaller unit when given other equivalent measures represented in a table.
 Grade 6 introduces using proportions and unit rates to convert units within a measurement system.
 Grade 7 will convert between measurement systems, including the use of proportions and the use of unit rates.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 TxCCRS:
 I. Numeric Reasoning
 IV. Measurement Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation

6.5 
Proportionality. The student applies mathematical process standards to solve problems involving proportional relationships. The student is expected to:


6.5A 
Represent mathematical and realworld problems involving ratios and rates using scale factors, tables, graphs, and proportions.
Supporting Standard

Represent
MATHEMATICAL AND REALWORLD PROBLEMS INVOLVING RATIOS AND RATES USING SCALE FACTORS, TABLES, GRAPHS, AND PROPORTIONS
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
 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.)
 Scale factor – the common multiplicative ratio between pairs of related data which may be represented as a unit rate
 Various representations of scale factor involving ratios in mathematical and realworld problem situations
 Tables
 Graphs
 Proportions
 Rate – a multiplicative comparison of two different quantities where the measuring unit is different for each quantity
 Various representations of scale factor involving rates in mathematical and realworld problem situations
 Tables
 Graphs
 Proportions
Note(s):
 Grade Level(s)
 Grade 6 introduces representing mathematical and realworld problems involving ratios and rates using scale factors, tables, graphs, and proportions.
 Grade 7 will represent constant rates of change in mathematical an realworld problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 TxCCRS:
 I. Numeric Reasoning
 II. Algebraic Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections

6.5B 
Solve 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.
Readiness Standard

Solve
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
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
 Percent – a part of a whole expressed in hundredths
 Relationship between part, whole, and percent
 Multiple methods for solving realworld problem situations involving percent
 Concrete and pictorial models (e.g., objects, area model, strip diagram, 10 by 10 grid, number line, etc.)
 Proportion method
 Scale factor between ratios
 Various types of realworld problem situations involving percent
 Limited to situations in which the parts and percents are less than the whole
 Finding the whole given a part and a percent
 Finding the part given the whole and a percent
 Finding the percent given the part and the whole
Note(s):
 Grade Level(s):
 Grade 6 introduces solving 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 7 will solve problems involving ratios, rates, and percents, including multistep problems involving percent increase and percent decrease, and financial literacy problems.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
 TxCCRS:
 I. Numeric Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections
