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 Instructional Focus DocumentAlgebra II
 TITLE : Unit 11: Linear, Quadratic, and Exponential Data Models SUGGESTED DURATION : 5 days

#### Unit Overview

Introduction
This unit bundles student expectations that address analyzing sets of data using technology to determine if the data is best represented using linear, quadratic, or exponential models and applying the selected models to make predictions and critical judgments in terms of the data. Concepts are incorporated into both mathematical and real-world problem situations. According to the Texas Education Agency, mathematical process standards including application, 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.

Prior to this Unit
In Algebra I Units 03, 08, and 09, students were introduced to linear, quadratic, and exponential functions. In Algebra II Units 05 and 09, students analyzed quadratic and exponential functions. Linear functions were interspersed throughout Algebra II.

During this Unit
Students analyze and compare linear, quadratic, and exponential data sets using graphs, tables, verbal descriptions, and technology to determine which function can be selected to best model the data. Students use regression methods available through technology to write the appropriate regression function (linear, quadratic, or exponential) to model the data. Students apply the regression model to predict and make decisions and critical judgments in terms of the data.

Other considerations: Reference the Mathematics COVID-19 Gap Implementation Tool HS Algebra II

After this Unit
In Units 12 and 13, students will review and continue to apply linear, quadratic, and exponential functions. In subsequent mathematics courses, students will also continue to apply these concepts when linear, quadratic, and exponential functions and equations arise in problem situations.

In Algebra II, analysis of sets of data to select an appropriate regression equation and application of that regression equation to make predictions and critical judgments are identified as STAAR Readiness Standard 2A.8C and STAAR Supporting Standards 2A.8A and 2A.8B. These standards are subsumed under STAAR Reporting Category 2: Describing and Graphing Functions and Their Inverses. This unit is supporting the development of Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning B1; II. Algebraic Reasoning D1, D2; III. Geometric and Spatial Reasoning C2; V. Statistical Reasoning A1, B4, C1, C2; VI. Functions A2, C1, C2; VII. Problem Solving and Reasoning A1, A2, A3, A4, A5, B1, C1, D1, D2; VIII. Communication and Representation A1, A2, A3, B1, B2, C1, C2, C3; IX. Connections A1, A2, B1, B2, B3.

Research
According to the National Council of Teachers of Mathematics (2011), Developing Essential Understanding of Functions, Grades 9-12, understanding of the function concept is essential to describing and analyzing quantities which vary with respect to one another. According to research from the National Council of Teachers of Mathematics (2000), Principles And Standards For School Mathematics, high school algebra should provide students with insights into mathematical abstraction and structure. High school students’ algebra experience should enable them to create and use tabular, symbolic, graphical, and verbal representations and to analyze and understand patterns, relations, and functions with a higher degree of sophistication. Students should develop an understanding of the algebraic properties that govern manipulation of symbols in expressions, equations, and inequalities.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics, Inc.
National Council of Teachers of Mathematics. (2011). Developing essential understanding of expressions, equations, and functions, grades 9-12. Reston, VA: National Council of Teachers of Mathematics, Inc.
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

 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? Statistical displays often reveal patterns within data that can be analyzed to interpret information, inform understanding, make predictions, influence decisions, and solve problems in everyday life with degrees of confidence. How does society use or make sense of the enormous amount of data in our world available at our fingertips? How can data and data displays be purposeful and powerful? Why is it important to be aware of factors that may influence conclusions, predictions, and/or decisions derived from data?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• Understanding how two quantities vary together (covariation) builds flexible functional reasoning in order to make predictions and critical judgments about the relationship.
• What are the strengths and limitations of a particular function model for a problem situation?
• How can functions be used to model problem situations efficiently?
• How can it be determined if a relationship between two variables can be represented by a function?
• How is function notation used to define and describe a function rule?
• How is function notation used to make predictions and critical judgements about the relationship?
• How can the most appropriate function model be determined for a set of data?
• Different families of functions, each with their own unique characteristics, can be used to model problem situations to make predictions and critical judgments.
• Linear functions are characterized by a constant rate of change and can be used to describe, model, and make predictions about situations.
• Quadratic functions are characterized by a rate of change that changes at a constant rate and can be used to describe, model, and make predictions about problem situations.
• Exponential functions are characterized by a rate of change that is proportional to the value of the function and can be used to describe, model, and make predictions about problem situations.
• What kinds of mathematical and real-world situations can be modeled by …
• linear functions?
• exponential functions?
• What graphs, key attributes, and characteristics are unique to …
• linear functions?
• exponential functions?
• What patterns of covariation are associated with …
• linear functions?
• exponential functions?
• How can the key attributes of linear, quadratic, and exponential functions be …
• determined?
• analyzed?
• described?
• How can key attributes be used to describe the behavior of linear, quadratic, and exponential functions?
• What are the real-world meanings of the key attributes of linear, quadratic, and exponential function models?
• How can key attributes be used to make predictions and critical judgments about the problem situation?
• Functions can be represented in various ways with different representations of the function highlighting different characteristics and being more useful than other representations depending on the context.
• How can functions be represented?
• What is the purpose of representing functions in various ways?
• How are function characteristics highlighted in different representations of the function?
• What are the limitations of different function representations?
• What connections can be made between multiple representations of a function?
• Data
• Data and Statistics
• Data
• Models
• Conclusions and predictions
• Regression methods
• 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

Misconceptions:

• Some students may think a scatterplot is linear because the points appear to be almost a line, rather than doing a regression analysis and comparing correlation coefficients. Parts of a quadratic relationship and parts of an exponential relationship may appear linear without in-depth analysis.
• Some students may fail to put data in sequential order before checking first and second differences and common ratios.
• Some students may check on first and second differences and fail to check common ratios when analyzing sequential data.
• Some students may not put values in the correct order when calculating first and second differences (not y1y2, but y2y1).
• Some students may not put values in the correct order when calculating the common ratio (not , but ).

#### Unit Vocabulary

• Coefficient of determination (r2-value) – representation of the percent of data closest to the regression line and used to measure how well the regression line can be used as a prediction model
• Correlation coefficient (r-value) – numeric value that assesses the strength of the linear relationship between two quantitative variables in a set of bivariate data
• Regression equation – line of best fit representing a set of bivariate data

Related Vocabulary:

 Common ratio Exponential First differences Linear Quadratic Rate of change Regression Regression equation Second differences Sequential data
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 – 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 Algebra II 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.
• 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
2A.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
2A.1A Apply mathematics to problems arising in everyday life, society, and the workplace.

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.
• TxCCRS:
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.1. Interpret results of the mathematical problem in terms of the original real-world 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, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world 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.
2A.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.

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.
• 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 problem-solving process.
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.2. Evaluate the problem-solving process.
2A.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.

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.
• 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.
2A.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

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.
• 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, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
2A.1E Create and use representations to organize, record, and communicate mathematical ideas.

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.
• 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.
2A.1F Analyze mathematical relationships to connect and communicate mathematical ideas.

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.
• 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.
2A.1G Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

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.
• 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.
2A.8 Data. The student applies mathematical processes to analyze data, select appropriate models, write corresponding functions, and make predictions. The student is expected to:
2A.8A Analyze data to select the appropriate model from among linear, quadratic, and exponential models.
Supporting Standard

Analyze

DATA

Including, but not limited to:

• Data collected from data collection devices
• Data given in mathematical problem situations
• Types of data
• Linear
• Constant rate of change (slope)
• If independent values change sequentially, the dependent values have a common first difference.
• Non-constant rate of change
• If independent values change sequentially the dependent values have a common second difference.
• Exponential
• Non-constant rate of change
• If independent values change sequentially the dependent values have a common ratio, .
• Comparisons between sequential data as linear, quadratic, and exponential

To Select

THE APPROPRIATE MODEL FROM AMONG LINEAR, QUADRATIC, AND EXPONENTIAL MODELS

Including, but not limited to:

• Data collected from data collection devices
• Data given in real-world problem situations
• Data relationships
• Linear
• Exponential
• Data representations
• Data tables
• Graphs/scatterplots
• Verbal descriptions
• Algebraic generalizations

Note(s):

• Algebra I introduced the linear, quadratic, and exponential functions.
• Algebra II expands on transformations and applications of exponential functions.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxCCRS:
• III.C. Geometric and Spatial Reasoning – Connections between geometry and other mathematical content strands
• III.C.2. Make connections between geometry, statistics, and probability.
• V.B. Statistical Reasoning – Describe data
• V.B.4. Describe patterns and departure from patterns in the study of data.
• V.C. Statistical Reasoning – Analyze, interpret, and draw conclusions from data
• V.C.1. Analyze data sets using graphs and summary statistics.
• V.C.2. Analyze relationships between paired data using spreadsheets, graphing calculators, or statistical software.
• VI.A. Functions – Recognition and representation of functions
• VI.A.2. Recognize and distinguish between different types of functions.
• VI.C. Functions – Model real-world situations with functions
• VI.C.1. Apply known functions to model real-world situations.
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.1. Analyze given information.
• 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.2. Create and use representations to organize, record, and communicate mathematical ideas.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
2A.8B Use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data.
Supporting Standard

Use

REGRESSION METHODS AVAILABLE THROUGH TECHNOLOGY TO WRITE A LINEAR FUNCTION, A QUADRATIC FUNCTION, AND AN EXPONENTIAL FUNCTION FROM A GIVEN SET OF DATA

Including, but not limited to:

• Data collected from data collection devices
• Data given in mathematical and real-world problem situations
• Data relationships
• Linear
• Exponential
• Regression equation – line of best fit representing a set of bivariate data
• Correlation coefficient (r-value) – numeric value that assesses the strength of the linear relationship between two quantitative variables in a set of bivariate data
• When the correlation coefficient, r, is given in regression calculations, it can be used to determine the strength of the regression model as a representation of mathematical and real-world problem situations.
• The correlation coefficient, r, can only be used to analyze linear relationships or relationships that can be linearized such as exponential
• Correlation coefficients closest to ±1 indicate the best model for mathematical and real-world problem situations.
• Value of the correlation coefficient, –1 ≤ r ≤ 1
• Perfect correlation, r = 1 or –1
• Strong correlation, 0.68 < |r| < 1.00
• Moderate correlation, 0.34 ≤ |r| ≤ 0.68
• Weak, 0 < |r| < 0.34
• No correlation, r = 0
• Coefficient of determination (r2-value) – representation of the percent of data closest to the regression line and used to measure how well the regression line can be used as a prediction model
• When the coefficient of determination, r2, is given in regression calculations, it can be used to determine the strength of the regression model to represent and make predictions in mathematical and real-world problem situations.
• The coefficient of determination, r2, can be used to analyze and compare all types of relationships such as linear, quadratic, and exponential

Note(s):

• Algebra I introduced the linear, quadratic, and exponential functions.
• Algebra I calculated, using technology, the correlation coefficient between two quantitative variables and interpreted this quantity as a measure of the strength of association.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxCCRS:
• II.D. Algebraic Reasoning – Representing relationships
• II.D.2. Convert among multiple representations of equations, inequalities, and relationships.
• III.C. Geometric and Spatial Reasoning – Connections between geometry and other mathematical content strands
• III.C.2. Make connections between geometry, statistics, and probability.
• VI.A. Functions – Recognition and representation of functions
• VI.A.2. Recognize and distinguish between different types of functions.
• VI.C. Functions – Model real-world situations with functions
• VI.C.2. Develop a function to model a situation.
• 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.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
2A.8C Predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models.

Predict, Make

DECISIONS AND CRITICAL JUDGMENTS FROM A GIVEN SET OF DATA USING LINEAR, QUADRATIC, AND EXPONENTIAL MODELS

Including, but not limited to:

• Mathematical and real-world problem situations modeled by linear, quadratic, and exponential functions and equations
• Predictions, decisions, and critical judgments from function models
• Justification of reasonableness of solutions in terms of mathematical and real-world problem situations
• Mathematical justification
• Substitution in original problem
• Justification for predictions using the coefficient of determination, r2

Note(s):

• Algebra I introduced the linear, quadratic, and exponential functions.
• Algebra I introduced the correlation coefficient as a measure of the strength of linear association.
• Algebra I applied linear, quadratic, and exponential functions to model and make predictions in real-world problem situations.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxCCRS:
• III.C. Geometric and Spatial Reasoning – Connections between geometry and other mathematical content strands
• III.C.2. Make connections between geometry, statistics, and probability.
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.4. Justify the solution.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations. 