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The resources included here provide teaching examples and/or meaningful learning experiences to address the District Curriculum. In order to address the TEKS to the proper depth and complexity, teachers are encouraged to use resources to the degree that they are congruent with the TEKS and research-based best practices. Teaching using only the suggested resources does not guarantee student mastery of all standards. Teachers must use professional judgment to select among these and/or other resources to teach the district curriculum. Some resources are protected by copyright. A username and password is required to view the copyrighted material. District Specificity/Examples TEKS clarifying examples are a product of the Austin Area Math Supervisors TEKS Clarifying Documents.

Title Suggested Time Frame Absolute Value – Functions, Equations, and Inequalities *CISD Safety Net Standards: 2A.2A

1st Six Weeks Suggested Duration: 16 Days

Big Ideas/Enduring Understandings Guiding Questions • Functions can be used to show various forms of information,

both conceptual and real world, to help understand what is being expressed.

• Absolute value expresses the distance between two points and is the same no matter from which direction the information is viewed.

• Why would one choose to use an equation, a graph, or a table to solve a problem?

• If a person was to drive their car in reverse, would they remove miles from their odometer? Why or why not?

Vertical Alignment Expectations

TEA Vertical Alignment Document

Sample Assessment Question COMING SOON………………………………….

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Ongoing TEKS

Mathematical Process Standards - The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: 1A apply mathematics to problems arising in everyday life, society, and the workplace; Apply

Mathematical Practices 1) Make sense of problems and persevere in

solving them. 2) Reason abstractly and quantitatively. 3) Construct viable arguments and critique

the reasoning of others. 4) Model with mathematics. 5) Use appropriate tools strategically. 6) Attend to precision. 7) Look for and make use of structure. 8) Look for and express regularity in repeated

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

Communicate: Have the students: 1) Keep a journal 2) Participate in online forums for the classroom like Schoology or Edmoto. 3) Write a summary of their daily notes as

part of the assignments. 1E Create and use representations to organize, record, and communicate mathematical ideas;

Create, Use The students can: 1) Create and use graphic organizers for things such as parent functions. This organizer can have a column for a) the name of the functions, b) the parent function equation, c) the graph, d) the domain, e) the range, f) any asymptotes.

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This organizer can be filled out all at once, or as you go through the lessons. They could even use this on assessments at the

teacher’s discretion. 1F analyze mathematical relationships to connect and communicate mathematical ideas;

ANALYZE

Knowledge and Skills

with Student Expectations

District Specificity/ Examples

Vocabulary

Suggested Resources

Resources listed and categorized to indicate suggested uses. Any additional resources

must be aligned with the TEKS.

2A.6E 2A.2A

2A.6C 2A.6D 2A.6F

Major Points • Analyzing Functions • Absolute Value Functions and Equations

• Coefficient • Domain • Function • Interval • Quadratic

Function • Range • Transformation

Text Resources • HMH Algebra II Text Book Lessons: • Domain, Range, and End

Behavior • Characteristics of

Functions • Transformations of

Function Graphs • Inverses of Functions • Graphing Absolute Value

Functions • Solving Absolute Value

Equations

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2A.2 Linear Functions, Equations, and Inequalities The student applies mathematical processes to understand that functions have distinct key attributes and understand the relationship between a function and its inverse. The student is expected to: *CISD Safety Net* 2A.2A graph the functions , f (x) = √x, f (x) = 1/x f(x) = x3 , f(x) = 3√x , f(x) = xb , f(x) = |x| , and f(x) = logbx where b is 2, 10, and e, and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval

2A.2A Graph * This could work here as well as in the example above. The graphs would be stressed at this standard. The students can: 1) Create and use graphic organizers for things such as parent functions. This organizer can have a column for a) the name of the functions, b) the parent function equation, c) the graph, d) the domain, e) the range, f) any asymptotes. This organizer can be filled out all at once, or as you go through the lessons. They could even use is on assessments at the teacher’s discretion.

Websites: • https://my.hrw.com • https://www.khanacadem

y.org/ • http://illuminations.nctm.

org/ • Region XI: Livebinder Parent Functions Chart

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2A.2B graph and write the inverse of a function using notation such as f -1 (x); 2A.2D use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each other.

2A.2B Graph, Write The students should be given several graphs that may or may not be “functions”. In teams, the students will: a) identify points on the given graph, b) identify the domain and range of the given graphs, c) switch the x and y values, d) graph the results using the “new” points, e) write the domain and range of the result. The teacher can guide them to the idea that the inverse is the original graph reflected about the line y = x. 2A.2D Use, Determine Remind the students of composition of functions from Algebra 1. Explain what composition of functions is and how to do the work. Then give them several examples grouped into two groups: 1) These functions are inverses of each other, and 2) these functions are not inverses of each other. Ask them to determine what the inverses have in common that the non-inverse functions do not have in common. Lead them to the understanding that if two functions are inverses of each other, then f(g(x)) = x and g(f(x)) = x. If there is any other result, than the functions are not inverses of each other.

Finding the Inverse Algebraically See A&M Consolidated 05-06 Spring Unit 1 Topic 1-1 and 1-2 Verifying Inverses See A&M Consolidated 05-06 Spring Unit 1 Topic 1-3

2A.6 Cubic, Cube Root, Absolute Value and Rational Functions, Equations, and Inequalities.

2A.6E Solving an Absolute Value Equation

See A&M Consolidated 05-06 Fall Unit 1 Topic 1-5

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The student applies mathematical processes to understand that cubic, cube root, absolute value and rational functions, equations, and inequalities can be used to model situations, solve problems, and make predictions. The student is expected to 2A.6E solve absolute value linear equations;

Solve and graph: |2x − 1| = 5

Solving a Multi-Step Absolute Value Equation Solve and graph: 3|x + 2| - 1 = 8

Solving Absolute Value Equations Practice Solving Absolute Value Equations Graphically Khan Academy Tutorial

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2A.6C analyze the effect on the graphs of f(x) = |x| when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d;

Extraneous Solutions What is the solution |3x + 2| = 4x + 5 Check for extraneous solutions.

2A.6C Analyze Example 1: Vertical and Horizontal Transformations of Absolute Value functions Use the graph of f (x) = |x| to graph g (x) = |x + 3| and h(x) = |x| + 2 . The graph of h(x) = |x| + 2 is the graph of f (x) = |x| shifted up 2 units. The graph of g (x) = |x + 3| is the graph of f (x) = |x| shifted 3 units to the left.

Transformations Tutorial Transformations of Absolute Value Functions Practice

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2A.6D formulate absolute value linear equations; 2A.6F solve absolute value linear inequalities;

2A.6D

Example: The solutions of =|x| 3 are the two points that are 3 units from zero. The solution is a disjunctions: x = 3 or x = − 3 .

2A.6F

Solving Absolute Value Inequality |x| < a x > − a and x < a or

See A&M Consolidated 05-06 Fall Unit 1 Topic 1-5 and Topic 1-7

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− a < x < a Example: The solutions of |x| < 3 are the points that are less than 3 units from zero. The solution is the conjunction: − 3 < x < 3.

Solving the Absolute Value Inequality ( |x| < a)

Solve and Graph:

Solving Absolute Value Inequality |x| > a

x < − a OR x > a Example: The solutions of |x| > 3 are the points that are more than 3 units from zero.

Absolute Value Inequalities Tutorial from Khan Academy

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The solution is the disjunction: x <− 3 OR x > 3.

Solving the Absolute Value Inequality ( |x| > a ) Solve and graph:

2A.7 Number and Algebraic Methods The student applies mathematical processes to simplify and perform operations on

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expressions and to solve equations. The student is expected to: 2A.7I write the domain and range of a function in interval notation, inequalities, and set notation.

2A.7I Students should know: Set Notation :

Interval Notation:

Example:

Domain and Range Matching Activity What is domain and range? Domain and Range of a graph Interval Notation Tutorial Set Builder Notation

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Write the domain and range in interval notation, inequalities and set notation.

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.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;

2A.8B

How to do linear regression on the graphing calculator video Printable Calculator Instructions Linear Regression Activity Linear Regression Activities

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From the graphs, it looks like the quadratic functions is the best fit for the data set.

Quadratic Regression Tutorial Pass the ball activity Exponential Worksheet with Answers Step by Step Exponential Regression Steps M&M's and Rhinos More M&M's NSA Exponential Growth and Decay Activities