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 Instructional Focus DocumentGrade 6 Mathematics
 TITLE : Unit 12: Essential Understanding of Proportionality SUGGESTED DURATION : 10 days

Unit Overview

Introduction
This unit bundles student expectations that address representing and solving problems with ratios and rates, including those involving percents and converting units within a measurement system using proportions and unit rates. According to the Texas Education Agency, mathematical process standards including application, a problem-solving model, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace. The introduction to the grade level standards state, “While the use of all types of technology is important, the emphasis on algebra readiness skills necessitates the implementation of graphing technology.”

Prior to this Unit
In Units 01 and 03 – 11, students generated equivalent forms of rational numbers, multiplied and divided positive rational numbers, and distinguished between and solved problems involving ratios and rates, including those involving converting units within a measurement system. Students used both qualitative and quantitative reasoning to make both predictions and comparisons in problem situations involving ratios and rates.

During this Unit
Students revisit and solidify essential understandings of proportionality. Students solve and represent problem situations involving ratios and rates with scale factors, tables, graphs, and proportions. They represent real-world problems involving ratios and rates, including unit rates, while converting units within a measurement system. Students use both qualitative and quantitative reasoning to make both predictions and comparisons in problem situations involving ratios and rates. They solve real-world 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.

After this Unit
In Grade 7, students will solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, as well as financial literacy problems. Students will also convert between measurement systems, using proportions and unit rates, as well as represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt.

In Grade 6, representing mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions is identified as Supporting Standard 6.5A. Applying qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates as well as real-world problems involving percents are described as Readiness Standard 6.4B and 6.5B. All of these standards are subsumed under the Grade 6 STAAR Reporting Category 2: Computations and Algebraic Relationships. Generating equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money is classified as Readiness Standard 6.4G. This standard is subsumed under the Grade 6 STAAR Reporting Category 1: Numerical Representations and Relationships. Readiness Standard 6.4H, convert units within a measurement system, including the use of proportions and unit rates, is part of the Grade 6 STAAR Reporting Category 3: Geometry and Measurement. All of the standards in this unit are subsumed under Grade 6 Texas Response to Curriculum Focal Points (TxRCFP): Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships. This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning, II. Algebraic Reasoning, IV. Measurement Reasoning, VIII. Problem Solving and Reasoning, IX. Communication and Representation, and X. Connections.

Research
According to Van De Walle (2014), “proportional reasoning goes well beyond the notion of setting up a proportion to solve a problem – it is a way of reasoning about multiplicative situations. Proportional reasoning, like equivalence, is considered a unifying theme in mathematics” (p. 198). The National Research Council (2001) adds that “research tracing the development of proportional reasoning shows that proficiency grows as students develop and connect different aspects of proportional reasoning. Further, the development of proportional reasoning can be supported by having students explore proportional situations in a variety of problem contexts using concrete materials or through data collection activities” (p. 417).

National Research Council. Adding It Up: Helping Children Learn Mathematics. Washington, DC: The National Academies Press, 2001.
Texas Education Agency & Texas Higher Education Coordinating Board. (2009). Texas college and career readiness standards. Retrieved from http://www.thecb.state.tx.us/index.cfm?objectid=E21AB9B0-2633-11E8-BC500050560100A9
Texas Education Agency. (2013). Texas response to curriculum focal points for kindergarten through grade 8 mathematics. Retrieved from https://www.texasgateway.org/resource/txrcfp-texas-response-curriculum-focal-points-k-8-mathematics-revised-2013
Van De Walle, J., Bay-Williams, J., Lovin, L., & Karp, K., (2014). Teaching student-centered mathematics: Developmentally Appropriate Instruction for Grades 6 - 8. (2nd ed., Vol. 3). Boston, MA: Pearson.

 Quantitative relationships model problem situations efficiently and can be used to make generalizations, predictions, and critical judgements in everyday life. What patterns exist within different types of quantitative relationships and where are they found in everyday life? Why is the ability to model quantitative relationships in a variety of ways essential to solving problems in everyday life?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• Understanding how two quantities can vary together and be reasoned up and down in situations involving invariant (constant) relationships builds flexible proportional reasoning.
• Ratios and rates are modeled and described to develop an understanding of proportional relationships and these relationships are applied to represent equivalence and solve problem situations involving ratios and rates.
• How can ratios and rates be described …
• qualitatively?
• quantitatively?
• How can …
• qualitative
• quantitative
… reasoning be used to make predictions and comparisons in problems involving ratios and rates?
• What is the difference between qualitative and quantitative reasoning?
• How can an equivalent …
• fraction be generated when given a decimal or percent?
• decimal be generated when given a fraction or percent?
• percent be generated when given a decimal or fraction?
• What types of models and strategies can be used to generate equivalent forms of fractions, decimals, and percents?
• Why is the ability to model numbers in a variety of ways essential to solving problems in everyday life?
• How can benchmark fractions and percents be used to solve problems involving money?
• How are …
• scale factors
• proportions
• unit rates
• conversion graphs
… used to convert within a measurement system?
• How can …
• scale factors
• tables
• graphs
• proportions
… be used to solve problems involving …
• ratios?
• rates?
• How can …
• concrete and pictorial models
• proportions or scale factors between ratios
… be used to determine the …
• whole when given a part and the percent?
• part when given the whole and the percent?
• percent when given the part and the whole?
• Proportionality
• Fractions and Decimals
• Percents
• Ratios and Rates
• Unit rates
• Scale factors
• Relationships and Generalizations
• Equivalence
• Qualitative and quantitative reasoning
• Proportions
• Representations
• Solution Strategies
• Systems of Measurement
• Customary
• Metric
• Associated Mathematical Processes
• Application
• Problem Solving Model
• Tools and Techniques
• Communication
• Representations
• Relationships
• Justification
 Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS

Underdeveloped Concepts:

• Some students may think that the order of the terms in a ratio or proportion is not important.
• Some students may think that generating an equivalent ratio is different from generating an equivalent fraction.
• Some students may think that all ratios are fractions rather than understanding that a ratio may represent a part-to-part or part-to-whole relationship.
• Some students may think that rates are not related to ratios.
• Some students may only use additive thinking rather than multiplicative thinking when solving proportions.
• Some students may think the value of 43% of 35 is the same value of 43% of 45 because the percents are the same rather than considering that the wholes of 35 and 45 are different, so 43% of each value will be different.
• Some students may believe every fraction relates to a different rational number instead of realizing equivalent fractions relate to the same relative amount.

Unit Vocabulary

• Percent – a part of a whole expressed in hundredths
• Positive rational numbers – the set of numbers that can be expressed as a fraction , where a and b are counting (natural) numbers
• Qualitative – a broad subjective description (e.g., The speed of car A is slower than the speed of car B.)
• 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.)
• Rate – a multiplicative comparison of two different quantities where the measuring unit is different for each quantity
• Ratio – a multiplicative comparison of two quantities
• Scale factor – the common multiplicative ratio between pairs of related data which may be represented as a unit rate
• Unit rate – a ratio between two different units where one of the terms is 1

Related Vocabulary:

 10 by 10 grid Area model Conversion graph Customary Decimal Denominator Equivalent Fraction Improper fraction Metric Mixed number Number line Numerator Proper fraction Proportion Proportion method Ratio table Strip diagram
Unit Assessment Items System Resources Other Resources

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Unit Assessment Items that have been published by your district may be accessed through Search All Components in the District Resources tab. Assessment items may also be found using the Assessment Center if your district has granted access to that tool.

System Resources may be accessed through Search All Components in the District Resources Tab.

Texas Higher Education Coordinating Board – Texas College and Career Readiness Standards

Texas Education Agency – Texas Response to Curriculum Focal Points for K-8 Mathematics Revised 2013

Texas Education Agency – Mathematics Curriculum

Texas Education Agency – STAAR Mathematics Resources

Texas Education Agency Texas Gateway – Revised Mathematics TEKS: Vertical Alignment Charts

Texas Education Agency Texas Gateway – Mathematics TEKS: Supporting Information

Texas Education Agency Texas Gateway – Interactive Mathematics Glossary

Texas Education Agency Texas Gateway – Resources Aligned to Grade 6 Mathematics TEKS

Texas Instruments – Graphing Calculator Tutorials

TAUGHT DIRECTLY TEKS

TEKS intended to be explicitly taught in this unit.

TEKS/SE 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 strike-through.

Specificity Legend:

• Supporting information / clarifications (specificity) written by TEKS Resource System are in blue text.
• Unit-specific 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.
TEKS# SE# TEKS SPECIFICITY
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:
• X. Connections
6.1B Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.
Process Standard

Use

A PROBLEM-SOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEM-SOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION

Including, but not limited to:

• Problem-solving model
• Analyze given information
• Formulate a plan or strategy
• Determine a solution
• Justify the solution
• Evaluate the problem-solving 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 non-examples, 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:
• X. Connections
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 real-world problems involving ratios and rates.

Apply

QUALITATIVE AND QUANTITATIVE REASONING TO SOLVE PREDICTION AND COMPARISON OF REAL-WORLD 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 real-world 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 real-world 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 6 introduces applying qualitative and quantitative reasoning to solve prediction and comparison of real-world 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
6.4G Generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money.

Generate

EQUIVALENT FORMS OF FRACTIONS, DECIMALS, AND PERCENTS USING REAL-WORLD 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 real-world 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 6 introduces generating equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money.
• Grade 6 introduces ordering a set of rational numbers arising from mathematical and real-world contexts.
• Grade 7 will solve problems involving ratios, rates, and percents, including multi-step 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.

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
• Customary
• Metric
• Unit rate – a ratio between two different units where one of the terms is 1
• Multiple solution strategies
• Dimensional analysis using unit rates
• Scale factor between ratios
• Proportion method
• Conversion graph

Note(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 real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions.
Supporting Standard

Represent

MATHEMATICAL AND REAL-WORLD 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 real-world 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 real-world problem situations
• Tables
• Graphs
• Proportions

Note(s):

• Grade 6 introduces representing mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions.
• Grade 7 will represent constant rates of change in mathematical an real-world 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 real-world 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.

Solve

REAL-WORLD 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 real-world 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 real-world 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 6 introduces solving real-world 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 multi-step 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 