Units: When plan is complete, right click on the first entry to refresh the table of contents.

Unit 1 - Algebra Readiness

Unit 2 - Graphs, Functions and Models

Unit 3 - Polynomial and Rational Functions

Unit 4 - Exponential and Logarithmic Functions

Unit 5 - Rational Exponents and Functions

Unit 6 - Analytic Radical Functions

Unit Title

Unit 1 - Algebra Readiness

Timeframe 

3 weeks

Unit Summary

In order to progress in the study of College Algebra, students must have an understanding of the underlying algebraic topics such as linear functions, factoring, solving equations and solving inequalities.

Learning Targets

Essential Questions

• How is mathematics used to measure, model and calculate change?
• How are polynomials factoried?
• What is the relationship between factoring and solving polynomial equations?
• How are exponents and radicals related?

Enduring Understandings

Students will understand:

• The relationship between the algebraic and graphical representations of a function.
• How to solve and represent the solution sets of algebraic equations and inequalities. 

Know

By the end of this unit, students will know

• How to perform addition, subtraction, multiplication and division of polynomials
• How to factor polynomials
• How to solve and graph equations and inequalities
• How to simplify expressions with exponents and radicals

Do

By the end of this unit, students will be able to

• Perform operations on polynomials
• Factor polynomials
• Verbally, Algebraically, Graphically and Numerically represent equations and inequalities
• Perform operations with radicals and exponents

Evidence of Learning

Formative

• Person Puzzle: Eva Peron; Adding and Subtracting Polynomials
• Person Puzzle: Irena Sendler; Multiplying Monomials
• Person Puzzle: Stephanie Spielman; Multiplying Polynomials
• Person Puzzle: Wangari Maathai; Dividing Monomials and Negative Exponents
• Person Puzzle: Jaime Escalante; Factoring with a Greatest Common Factor
• Person Puzzle: Mother Theresa; Simple Factoring
• Person Puzzle: Muhammed Yunus; Advanced Factoring
• Person Puzzle: Grace Hopper; Quadratic Formula
• Person Puzzle: Maya Lin; Simplifying Rational Expressions
• Person Puzzle: Somaly Mam; Simplifying Radicals
• Person Puzzle: Hiroshi Yamauchi; Adding and Subtracting Rational Expressions
• Person Puzzle: Betty Mae Tiger Jumper; Multiplying and Dividing Rational Expressions
• Person Puzzle: Malala Yousafzai; Multiplying Radicals
• Person Puzzle: Desmond  Tutu; Multiplying Binomials with Radicals
• Person Puzzle: Ellen Degeneres; Rationalizing Denominators
• Person Puzzle: Hans Rosling; Solving Rational Equations

Summative/ Benchmark

• Unit Assessment: Monomial Boot Camp
• Unit Assessment: The relationship between the algebraic and graphical representations of a function.
• Unit Assessment:  How to solve and represent the solution sets of algebraic equations and inequalities

Alternative Assessments

• Mystery Adventure AND CSI Whodunnit: Adding and Subtracting Polynomials
• Mystery Adventure AND CSI Whodunnit: Multiplying Polynomials
• Mystery Adventure AND CSI Whodunnit: Dividing Monomials and Negative Exponents
• Mystery Adventure AND CSI Whodunnit: Factoring with GCF
• Mystery Adventure AND CSI Whodunnit: Simple Factoring
• Mystery Adventure AND CSI Whodunnit: Advanced Factoring
• Mystery Adventure AND CSI Whodunnit: Simplifying Radical Expressions
• Mystery Adventure AND CSI Whodunnit: Quadratic Formula
• Mystery Adventure AND CSI Whodunnit: Adding and Subtracting Rational Expressions
• Mystery Adventure AND CSI Whodunnit: Multiplying and Dividing Rational Expressions
• Mystery Adventure AND CSI Whodunnit: Multiplying Binomials with Radicals
• Mystery Adventure AND CSI Whodunnit: Rationalizing Denominators
• Mystery Adventure AND CSI Whodunnit: Solving Rational Equations

Learning Activities

• Group completion of graphic organizers involving equations, polynomials and inequalities
• Small group explorations involving equations, polynomials and inequalities
• Independent practice on algebra skills
• Using Kahoot to perform addition, subtraction, multiplication and division of polynomials
• Using Flipped Math to factor polynomials
• Graph equations and inequalities using Desmos
• Simplify expressions with exponents and radicals with Khan Academy.  
• Faceing Math Absolute Value and Inequalities
• Skill Practice Journey Game
• Writing Equations of Lines Jumble

Materials / Equipment / Resources

Core Instructional

Materials and Texts

Classroom Notes

Khan Academy

Flipped Math

Equipment

TI-83 Calculator

Chromebook - Desmos

Document Camera

LCD Projector

Supplemental Resources

Desmos

Faceing Math

Teachers Pay Teachers

Standards

Content Statement

Indicator

Create equations that describe numbers or relationships.

CCSS.MATH.CONTENT.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Represent and solve equations and inequalities graphically.

CCSS.MATH.CONTENT.HSA.REI.D.11

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions

Understand the relationship between zeros and factors of polynomials

CCSS.MATH.CONTENT.HSA.APR.B.2

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).

CCSS.MATH.CONTENT.HSA.APR.B.3

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Use polynomial identities to solve problems.

CCSS.MATH.CONTENT.HSA.APR.C.4

Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 - y2)2 + (2xy)2 can be used to generate Pythagorean triples.

Analyze functions using different representations.

CCSS.MATH.CONTENT.HSF.IF.C.7.C

Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

Use complex numbers in polynomial identities and equations.

CCSS.MATH.CONTENT.HSN.CN.C.9                                                                                                  Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

21st Century Skills and Themes

Interdisciplinary Connections

Career Ready Practices

9.2 Career Awareness, Exploration, and Preparation  

• Language Arts through open-ended questions and self-reflections.  
• Business through the use of excel and finance.
• Science through physics problems.

• CRP1. Act as a responsible and contributing citizen and employee.
• CRP2. Apply appropriate academic and technical skills.
• CRP4.Communicate clearly and effectively and with reason.
• CRP6.Demonstrate creativity and innovation.
• CRP8.Utilize critical thinking to make sense of problems and persevere in solving them.
• CRP9.Model integrity, ethical leadership and effective management.
• CRP11. Use technology to enhance productivity.
• CRP12.Work productively in teams while using cultural global competence.

By the end of 12th grade,

• 9.2.12.C.3 Identify transferable career skills and design alternate career plans.
• 9.2.12.C.4 Analyze how economic conditions and societal changes influence employment trends and

Technology Standards - 8.1

9-12th Grade

A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.

• Select and use applications effectively and productively.

8.1.12.A.2 Produce and edit a multi-page digital document for a commercial or professional audience and present it to peers and/or professionals in that related area for review.

8.1.12.A.4 Construct a spreadsheet workbook with multiple worksheets, rename tabs to reflect the data on the worksheet, and use mathematical or logical functions, charts and data from all worksheets to convey the results.

8.1.12.A.5 Create a report from a relational database consisting of at least two tables and describe the process, and explain the report results.

B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.

• Apply existing knowledge to generate new ideas, products, or processes.
• Create original works as a means of personal or group expression.

8.1.12.B.2 Apply previous content knowledge by creating and piloting a digital learning game or tutorial.

C. Communication and Collaboration: Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others.

• Interact, collaborate, and publish with peers, experts, or others by employing a variety of digital environments and media.
• Communicate information and ideas to multiple audiences using a variety of media and formats.
• Develop cultural understanding and global awareness by engaging with learners of other cultures.
• Contribute to project teams to produce original works or solve problems.

8.1.12.C.1 Develop an innovative solution to a real world problem or issue in collaboration with peers and experts, and present ideas for feedback through social media or in an online community.

D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

• Advocate and practice safe, legal, and responsible use of information and technology.

8.1.12.D.1 Demonstrate appropriate application of copyright, fair use and/or Creative Commons to an original work.

F: Critical thinking, problem solving, and decision making: Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources.

• Identify and define authentic problems and significant questions for investigation.
• Plan and manage activities to develop a solution or complete a project.
• Collect and analyze data to identify solutions and/or make informed decisions.
• Use multiple processes and diverse perspectives to explore alternative solutions.

8.1.12.F.1 Evaluate the strengths and limitations of emerging technologies and their impact on educational, career, personal and or social needs.

Modifications/Accommodations

IEPs

• preferential seating.
• extended time on tests and assignments.
• reduced homework or classwork.
• verbal, visual, or technology aids.
• modified textbooks or audio-video materials.
• behavior management support.
• adjusted class schedules or grading.
• verbal testing

504s

• preferential seating.
• extended time on tests and assignments.
• reduced homework or classwork.
• verbal, visual, or technology aids.
• modified textbooks or audio-video materials.
• behavior management support.
• adjusted class schedules or grading.
• verbal testing

ELLs

• modeling and using gestures to aid in understanding.
• simplify instructions

G/T

• provide learning centers where students are in charge of their learning.

Unit Title

Unit 2 - Graphs, Functions and Models

Timeframe 

5 weeks

Unit Summary

The concept of a function and function notation are central to modern mathematics and their applications.  This unit will develop skills in constructing and interpreting graphs of functions.  A “Real-life” situation in which one numerical quantity  depends on another is used to better understand the basic concepts of a function.  Graphs of many functions will be used to demonstrate characteristics of a function.

Learning Targets

Essential Questions

• How is mathematics used to measure, model and calculate change?
• How are functions and their graphs related?
• How can technology be used to investigate properties of families of functions and their graphs?
• What do effective problem solvers do, and what do they do when they get stuck?
•  How is mathematics used to quantify and compare situations, events and phenomena?

Enduring Understandings

Students will understand:

• Graphs and equations are alternative ways for depicting and analyzing patterns of linear and nonlinear change.
• Mathematical models can be used to describe physical relationships; these are often nonlinear.
• How different families of functions can be used to model real world situations.

Know

By the end of this unit, students will know

• How to graph a function with and without a graphing utility
• How to determine the domain and range of a function
• How to interpret the rate of change over an interval
• How to identify the characteristics and shape of various graphs
• How to graph the transformation of a function
• How to determine several ways in which given functions can be used to create new functions
• How to create functions based on a verbal description of real world situations

Do

By the end of this unit, students will be able to

• Determine if a relationship is a function
• Determine the inverse of a function and find the domain
• Determine if a function is 1 to 1
• Determine whether a function is odd, even or neither both algebraically and graphically
• Graph linear, absolute value, quadratic, square root, cube root, exponential, logarithmic and reciprocal functions with and without technology
• Identify the key characteristics of functions such as domain, range, maxima, minima, increasing intervals and decreasing intervals
• Analyze piece-wise functions
• Identify the vertex, intercepts, and axis of symmetry of a quadratic function
• Solve and model real-world problems using functions
• Transform functions
• Perform operations on functions

Evidence of Learning

Formative

• Person Puzzle: Serena Williams;  Identifying the Transformation
• Person Puzzle: Maria Montessori; Family of Functions with Transformations
• Working with Inverse Functions from a Table
• Inverse Functions Task Cards
• Analyzing Functions from Graphs and Tables group activity
• Write 5 higher order thinking questions and answer two.
• Tell me three things you know well and two things that confuse you.
• Play Kahoot.

Summative/ Benchmark

• Faceing Math: Operations with Functions
• Unit Assessment: Graph equations to depict and analyze patterns of linear and nonlinear change.
• Unit Assessment: Transforming and performing operations on functions.  

Alternative Assessments

• Domain and Range Maze
• Transformations of Functions Task Cards
• Superhero Transformations Game
• Transformation of Functions Task Cards
• Writing Equations for Piecewise Functions Scavenger Hunt
• Model relationships to describe non-linear relationships.
• Make a visual representations of the different families of functions.  
• Match, Pair and Share

Learning Activities

• Group completion of graphic organizers involving functions
• Small group explorations involving patterns of linear and nonlinear change
• Independent practice involving various types of functions
• Symmetry Jumble and Graphic Organizer
• Using Desmos to create functions from a real-world scenario
• Using Flipped Math to compare various types of functions
• Graph piece-wise functions using Desmos
• Identifying characteristics of functions through Khan Academy.  

Materials / Equipment / Resources

Core Instructional

Materials and Texts

Classroom Notes

Khan Academy

Flipped Math

Equipment

TI-83 Calculator

Chromebook - Desmos

Document Camera

LCD Projector

Supplemental Resources

Desmos

Faceing Math

Teachers Pay Teachers

Standards

Content Statement

Indicator

Understand the concept of a function and use function notation.

CCSS.MATH.CONTENT.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Interpret functions that arise in applications in terms of the context

CCSS.MATH.CONTENT.HSF.IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity

Analyze functions using different representations.

CCSS.MATH.CONTENT.HSF.IF.C.7

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

CCSS.MATH.CONTENT.HSF.IF.C.7.B

Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Build new functions from existing functions.

CCSS.MATH.CONTENT.HSF.BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Rewrite rational expressions.

CCSS.MATH.CONTENT.HSA.APR.D.6

Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

21st Century Skills and Themes

Interdisciplinary Connections

Career Ready Practices

9.2 Career Awareness, Exploration, and Preparation  

• Language Arts through open-ended questions and self-reflections.  
• Business through the use of excel and finance.
• Science through physics problems.

• CRP1. Act as a responsible and contributing citizen and employee.
• CRP2. Apply appropriate academic and technical skills.
• CRP4.Communicate clearly and effectively and with reason.
• CRP6.Demonstrate creativity and innovation.
• CRP8.Utilize critical thinking to make sense of problems and persevere in solving them.
• CRP9.Model integrity, ethical leadership and effective management.
• CRP11. Use technology to enhance productivity.
• CRP12.Work productively in teams while using cultural global competence.

By the end of 12th grade,

• 9.2.12.C.3 Identify transferable career skills and design alternate career plans.
• 9.2.12.C.4 Analyze how economic conditions and societal changes influence employment trends and

Technology Standards - 8.1

9-12th Grade

A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.

• Select and use applications effectively and productively.

8.1.12.A.2 Produce and edit a multi-page digital document for a commercial or professional audience and present it to peers and/or professionals in that related area for review.

8.1.12.A.4 Construct a spreadsheet workbook with multiple worksheets, rename tabs to reflect the data on the worksheet, and use mathematical or logical functions, charts and data from all worksheets to convey the results.

8.1.12.A.5 Create a report from a relational database consisting of at least two tables and describe the process, and explain the report results.

B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.

• Apply existing knowledge to generate new ideas, products, or processes.
• Create original works as a means of personal or group expression.

8.1.12.B.2 Apply previous content knowledge by creating and piloting a digital learning game or tutorial.

C. Communication and Collaboration: Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others.

• Interact, collaborate, and publish with peers, experts, or others by employing a variety of digital environments and media.
• Communicate information and ideas to multiple audiences using a variety of media and formats.
• Develop cultural understanding and global awareness by engaging with learners of other cultures.
• Contribute to project teams to produce original works or solve problems.

8.1.12.C.1 Develop an innovative solution to a real world problem or issue in collaboration with peers and experts, and present ideas for feedback through social media or in an online community.

D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

• Advocate and practice safe, legal, and responsible use of information and technology.

8.1.12.D.1 Demonstrate appropriate application of copyright, fair use and/or Creative Commons to an original work.

F: Critical thinking, problem solving, and decision making: Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources.

• Identify and define authentic problems and significant questions for investigation.
• Plan and manage activities to develop a solution or complete a project.
• Collect and analyze data to identify solutions and/or make informed decisions.
• Use multiple processes and diverse perspectives to explore alternative solutions.

8.1.12.F.1 Evaluate the strengths and limitations of emerging technologies and their impact on educational, career, personal and or social needs.

Modifications/Accommodations

IEPs

• preferential seating.
• extended time on tests and assignments.
• reduced homework or classwork.
• verbal, visual, or technology aids.
• modified textbooks or audio-video materials.
• behavior management support.
• adjusted class schedules or grading.
• verbal testing

504s

• preferential seating.
• extended time on tests and assignments.
• reduced homework or classwork.
• verbal, visual, or technology aids.
• modified textbooks or audio-video materials.
• behavior management support.
• adjusted class schedules or grading.
• verbal testing

ELLs

• modeling and using gestures to aid in understanding.
• simplify instructions

G/T

• provide learning centers where students are in charge of their learning.

Unit Title

Unit 3 - Polynomial and Rational Functions

Timeframe 

6 weeks

Unit Summary

Students will be able to examine different polynomial and rational functions that arise naturally in many applications.  More specifically, students will consider the degree, multiplicity, zeros, end behavior, and asymptotes when determining how a polynomial or rational function behaves.

Learning Targets

Essential Questions

• How do the characteristics of graphs relate to their corresponding equations?
• What are common characteristics of polynomial?
• What is the best method for graphing different polynomial and rational functions?

Enduring Understandings

Students will understand:

• Functions can be written in several ways
• Families of functions have common characteristics

Know

By the end of this unit, students will know

• Characteristics of polynomial and rational functions
• The relationship between zeros and factors of polynomials
• How to perform operations with complex numbers
• How to apply the Remainder and Factor Theorems
• How to find the degree, multiplicity, zeros, end behavior and asymptotes for polynomial and rational functions
• How to use the characteristics of polynomial and rational functions to create its’ graph
• How to use polynomial and rational functions to model real-world scenarios.
• How to identify common characteristics of families of functions

Do

By the end of this unit, students will be able to

Examine graphs to determine end behavior

Identify polynomial functions and find the degree given both factored and standard form

Identify the zeros of a polynomial function and its multiplicity

Investigate the role of multiplicity with regards to the graph of a polynomial function

Investigate the role of the degree of a polynomial with regards to the number of turns a graph takes

Factor polynomials of varying degrees

Divide polynomials using long and synthetic division

Apply the remainder and factor theorems

Find the real and complex zeros of a polynomial

Apply the conjugate pair theorem to help write a polynomial in standard form and find the zeros

Form a polynomial with specified zeros both real and complex

Solve polynomial equations for both real and complex zeros

Find the domain, range, and asymptotes for polynomial and rational functions and use the information to create its graph

Determine common characteristics of families of functions

Analyze real world scenarios using polynomial and rational functions

Evidence of Learning

Formative

• Factoring Maze
• Quadratic Equations Picture Puzzle
• Person Puzzle: Bob Marley; Graphing Quadratic Functions
• Career: Football Scout - STEMersion with Graphing Quadratic Equations
• Career: Marketing Director - STEMersion with Quadratic Functions
• Synthetic Division Task Cards
• Working With Complex Numbers Jumble
• Person Puzzle: Alicia Alonso; Introduction to Imaginary Numbers
• Person Puzzle: Yuri Gagarin; Operations with Complex Numbers
• Person Puzzle: Catalina Escobar; Rationalizing Imaginary Denominators
• Career: Anesthesiologist - Solving and Graphing Rational Functions
• Using Demos to find the real zeros
• Describe the common characteristics of polynomials and rational functions.
• Explain to a friend how to transform a polynomial.
• Complex Numbers Maze
• Rational Functions Stations

Summative/ Benchmark

• Faceing Math: Graphs of Quadratics
• Unit Assessment: Graphing, solving, and transforming polynomials.
• Unit Assessment:  Solving polynomial and rational functions.

Alternative Assessments

• Factoring Quadratic Equations Task Cards
• Quadratic Catapult
• CSI Whodunnit: Factoring and Quadratic Functions
• CSI Whodunnit: Graphing Quadratic Functions
• Choose Your Own Adventure: Operations with Complex Numbers
• Choose Your Own Adventure: Rationalizing Imaginary Denominators
• Career Exploration: Marketing Maverick
• The Remainder and Factor Theorem Partnership
• CSI Whodunnit: Polynomial Functions
• Angry Penguins Adventure with Functions
• CSI Whodunnit: Add & Subtract Rational Expressions
• CSI Whodunnit: Multiply & Divide Rational Expressions
• CSI Whodunnit: Solving  Rational Expressions
• Journey Game: Rational Functions
• Birthday Polynomial
• Desmos Activities

Learning Activities

• Group completion of graphic organizers involving polynomial and rational functions
• Small group explorations involving polynomial and rational functions
• Independent practice with polynomial and rational functions
• Finding the Vertex of a Parabola Jumble
• Parabolas Matching Task Cards
• Super Secret Number Puzzle: Synthetic Division
• Using Kahoot to reinforce the Remainder and Factor Theorems
• Color My Math: Working with Complex Numbers
• Using the Quadratic Formula with Complex Roots Task Cards
• Using Flipped Math to show the difference between real and complex zeros
• Graphing Rational Equations Card Sort
• Using Desmos to compare graphs of families of functions
• Using Khan Academy to investigate the role of degree and multiplicity in a function  

Materials / Equipment / Resources

Core Instructional

Materials and Texts

Classroom Notes

Khan Academy

Flipped Math

Equipment

TI-83 Calculator

Chromebook - Desmos

Document Camera

LCD Projector

Supplemental Resources

Desmos

Faceing Math

Teachers Pay Teachers

Standards

Content Statement

Indicator

Use complex numbers in polynomial identities and equations.

CCSS.MATH.CONTENT.HSN.CN.C.8

(+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x - 2i).

CCSS.MATH.CONTENT.HSN.CN.C.9

(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

Understand the relationship between zeros and factors of polynomials.

CCSS.MATH.CONTENT.HSA.APR.B.2

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).

CCSS.MATH.CONTENT.HSA.APR.B.3

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Rewrite rational expressions.

CCSS.MATH.CONTENT.HSA.APR.B.2

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).

CCSS.MATH.CONTENT.HSA.APR.B.3

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Analyze functions using different representations.

CCSS.MATH.CONTENT.HSF.IF.C.7

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*

CCSS.MATH.CONTENT.HSF.IF.C.7.C

Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

21st Century Skills and Themes

Interdisciplinary Connections

Career Ready Practices

9.2 Career Awareness, Exploration, and Preparation  

• Language Arts through open-ended questions and self-reflections.  
• Business through the use of excel and finance.
• Science through physics problems.

• CRP1. Act as a responsible and contributing citizen and employee.
• CRP2. Apply appropriate academic and technical skills.
• CRP4.Communicate clearly and effectively and with reason.
• CRP6.Demonstrate creativity and innovation.
• CRP8.Utilize critical thinking to make sense of problems and persevere in solving them.
• CRP9.Model integrity, ethical leadership and effective management.
• CRP11. Use technology to enhance productivity.
• CRP12.Work productively in teams while using cultural global competence.

By the end of 12th grade,

• 9.2.12.C.3 Identify transferable career skills and design alternate career plans.
• 9.2.12.C.4 Analyze how economic conditions and societal changes influence employment trends and

Technology Standards - 8.1

9-12th Grade

A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.

• Select and use applications effectively and productively.

8.1.12.A.2 Produce and edit a multi-page digital document for a commercial or professional audience and present it to peers and/or professionals in that related area for review.

8.1.12.A.4 Construct a spreadsheet workbook with multiple worksheets, rename tabs to reflect the data on the worksheet, and use mathematical or logical functions, charts and data from all worksheets to convey the results.

8.1.12.A.5 Create a report from a relational database consisting of at least two tables and describe the process, and explain the report results.

B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.

• Apply existing knowledge to generate new ideas, products, or processes.
• Create original works as a means of personal or group expression.

8.1.12.B.2 Apply previous content knowledge by creating and piloting a digital learning game or tutorial.

C. Communication and Collaboration: Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others.

• Interact, collaborate, and publish with peers, experts, or others by employing a variety of digital environments and media.
• Communicate information and ideas to multiple audiences using a variety of media and formats.
• Develop cultural understanding and global awareness by engaging with learners of other cultures.
• Contribute to project teams to produce original works or solve problems.

8.1.12.C.1 Develop an innovative solution to a real world problem or issue in collaboration with peers and experts, and present ideas for feedback through social media or in an online community.

D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

• Advocate and practice safe, legal, and responsible use of information and technology.

8.1.12.D.1 Demonstrate appropriate application of copyright, fair use and/or Creative Commons to an original work.

F: Critical thinking, problem solving, and decision making: Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources.

• Identify and define authentic problems and significant questions for investigation.
• Plan and manage activities to develop a solution or complete a project.
• Collect and analyze data to identify solutions and/or make informed decisions.
• Use multiple processes and diverse perspectives to explore alternative solutions.

8.1.12.F.1 Evaluate the strengths and limitations of emerging technologies and their impact on educational, career, personal and or social needs.

Modifications/Accommodations

IEPs

• preferential seating.
• extended time on tests and assignments.
• reduced homework or classwork.
• verbal, visual, or technology aids.
• modified textbooks or audio-video materials.
• behavior management support.
• adjusted class schedules or grading.
• verbal testing

504s

• preferential seating.
• extended time on tests and assignments.
• reduced homework or classwork.
• verbal, visual, or technology aids.
• modified textbooks or audio-video materials.
• behavior management support.
• adjusted class schedules or grading.
• verbal testing

ELLs

• modeling and using gestures to aid in understanding.
• simplify instructions

G/T

• provide learning centers where students are in charge of their learning.

Unit Title

Unit 4 - Exponential and Logarithmic Functions

Timeframe 

6 weeks

Unit Summary

This unit focuses on identifying and graphing exponential and logarithmic functions.  It is important to recognize that these functions are inverses of each other and have many applications in our world such as banking, medicine, growth and decay.

Learning Targets

Essential Questions

• What real-world scenarios can be represented by exponential and logarithmic functions?
• How can the properties of logarithms be used to solve equations?
• How can condensing and expanding exponents and logarithms be helpful in solving equations?

Enduring Understandings

Students will understand:

• The characteristics of exponential and logarithmic functions and their representations are useful in solving real-world problems
• Exponential and Logarithmic functions are closely related
• The importance of using exponential and logarithmic models to interpret real phenomena

Know

By the end of this unit, students will know

• The relationship between exponential and logarithmic functions
• How to simplify both exponential and logarithmic functions
• How to graph both exponential and logarithmic functions
• How to solve exponential and logarithmic equations
• How to apply exponential and logarithmic functions to real world situations

Do

By the end of this unit, students will be able to

• Evaluate exponential functions
• Graph exponential functions and their transformations
• Define the number e
• Solve exponential equations
• Change exponential expressions into logarithmic expressions and vice versa
• Evaluate logarithmic functions
• Graph logarithmic functions and their transformations
• Determine the domain and range of exponential and logarithmic functions
• Solve logarithmic equations
• Expand and condense logarithmic expressions
• Use the properties of exponents and logarithms to solve equations
• Use exponential and logarithmic functions to describe real world scenarios including growth and decay

Evidence of Learning

Formative

• Person Puzzle: Jesse Williams; Converting Exponents and Logarithms
• Person Puzzle: Tracy Chapman; Simplifying Logarithms
• Person Puzzle: Tony Dungy; Solving Exponential Equations without Logarithms
• Person Puzzle: Sonia Sotomayor; Solving Exponential Equations with Logarithms
• Person Puzzle: Millard Fuller; Solving Logarithmic Equations
• Career: Seismologist - STEMersion with Logarithmic Equations
• Career: Financial Advisor - STEMersion with Exponential Functions
• Using Demos to graph exponential and logarithmic functions.
• Describe the common characteristics of exponential and logarithmic function.
• Explain to a friend how to transform exponential and/or logarithmic function.

Summative/ Benchmark

• Faceing Math: Exponential Functions
• Exponential and Logarithmic Equations Card Sort
• Unit Assessment: Use exponential and logarithmic functions to describe real world scenarios including growth and decay
• Unit Assessment:  Evaluate exponential and logarithmic functions.  

Alternative Assessments

• CSI Whodunnit: Converting Between Exponents and Logarithms

• CSI Whodunnit: Simplifying Logarithms
• CSI Whodunnit: Exponential Equations with Logarithms
• CSI Whodunnit: Logarithmic Equations
• Color My Math: Solving Logarithmic and Exponential Equations
• Solving Exponential Equations Maze
• Solving Logarithmic Equations Maze
• Graph logarithmic functions and their transformations

Learning Activities

• Group completion of graphic organizers involving exponents and logarithms
• Small group explorations involving exponents and logarithms
• Independent practice on exponential and logarithmic functions
• Choose Your Own Adventure: Exponential Equations
• Choose Your Own Adventure: Simplifying Logarithms
• Simplifying Logarithms Card Sort
• Choose Your Own Adventure: Logarithmic Equations
• Exponential, Logistic, Logarithmic Lab Activity
• Using Kahoot to perform expanding and condensing logarithmic expressions
• Using Flipped Math to show the relationship between exponents and logarithms
• Graph exponential and logarithmic functions and their transformations using Desmos
• Solve exponential and logarithmic equations with Khan Academy.  

Materials / Equipment / Resources

Core Instructional

Materials and Texts

Classroom Notes

Khan Academy

Flipped Math

Equipment

TI-83 Calculator

Chromebook - Desmos

Document Camera

LCD Projector

Supplemental Resources

Desmos

Faceing Math

Teachers Pay Teachers

Standards

Content Statement

Indicator

Analyze functions using different representations.

CCSS.MATH.CONTENT.HSF.IF.C.7

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*

Analyze functions using different representations.

CCSS.MATH.CONTENT.HSF.IF.C.7.E

Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Construct and compare linear, quadratic, and exponential models and solve problems.

CCSS.MATH.CONTENT.HSF.LE.A.4

For exponential models, express as a logarithm the solution to abct = d where a, c, and dare numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

21st Century Skills and Themes

Interdisciplinary Connections

Career Ready Practices

9.2 Career Awareness, Exploration, and Preparation  

• Language Arts through open-ended questions and self-reflections.  
• Business through the use of excel and finance.
• Science through physics problems.

• CRP1. Act as a responsible and contributing citizen and employee.
• CRP2. Apply appropriate academic and technical skills.
• CRP4.Communicate clearly and effectively and with reason.
• CRP6.Demonstrate creativity and innovation.
• CRP8.Utilize critical thinking to make sense of problems and persevere in solving them.
• CRP9.Model integrity, ethical leadership and effective management.
• CRP11. Use technology to enhance productivity.
• CRP12.Work productively in teams while using cultural global competence.

By the end of 12th grade,

• 9.2.12.C.3 Identify transferable career skills and design alternate career plans.
• 9.2.12.C.4 Analyze how economic conditions and societal changes influence employment trends and

Technology Standards - 8.1

9-12th Grade

A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.

• Select and use applications effectively and productively.

8.1.12.A.2 Produce and edit a multi-page digital document for a commercial or professional audience and present it to peers and/or professionals in that related area for review.

8.1.12.A.4 Construct a spreadsheet workbook with multiple worksheets, rename tabs to reflect the data on the worksheet, and use mathematical or logical functions, charts and data from all worksheets to convey the results.

8.1.12.A.5 Create a report from a relational database consisting of at least two tables and describe the process, and explain the report results.

B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.

• Apply existing knowledge to generate new ideas, products, or processes.
• Create original works as a means of personal or group expression.

8.1.12.B.2 Apply previous content knowledge by creating and piloting a digital learning game or tutorial.

C. Communication and Collaboration: Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others.

• Interact, collaborate, and publish with peers, experts, or others by employing a variety of digital environments and media.
• Communicate information and ideas to multiple audiences using a variety of media and formats.
• Develop cultural understanding and global awareness by engaging with learners of other cultures.
• Contribute to project teams to produce original works or solve problems.

8.1.12.C.1 Develop an innovative solution to a real world problem or issue in collaboration with peers and experts, and present ideas for feedback through social media or in an online community.

D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

• Advocate and practice safe, legal, and responsible use of information and technology.

8.1.12.D.1 Demonstrate appropriate application of copyright, fair use and/or Creative Commons to an original work.

F: Critical thinking, problem solving, and decision making: Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources.

• Identify and define authentic problems and significant questions for investigation.
• Plan and manage activities to develop a solution or complete a project.
• Collect and analyze data to identify solutions and/or make informed decisions.
• Use multiple processes and diverse perspectives to explore alternative solutions.

8.1.12.F.1 Evaluate the strengths and limitations of emerging technologies and their impact on educational, career, personal and or social needs.

Modifications/Accommodations

IEPs

• preferential seating.
• extended time on tests and assignments.
• reduced homework or classwork.
• verbal, visual, or technology aids.
• modified textbooks or audio-video materials.
• behavior management support.
• adjusted class schedules or grading.
• verbal testing

504s

• preferential seating.
• extended time on tests and assignments.
• reduced homework or classwork.
• verbal, visual, or technology aids.
• modified textbooks or audio-video materials.
• behavior management support.
• adjusted class schedules or grading.
• verbal testing

ELLs

• modeling and using gestures to aid in understanding.
• simplify instructions

G/T

• provide learning centers where students are in charge of their learning.

Unit Title

Unit 5 - Rational Exponents  and Functions

Timeframe 

12 weeks

Unit Summary

Students will extend extend their knowledge of roots to include cube roots, fourth roots, fifth roots, and so on.  Students will learn to add, subtract, multiply, and divide radical expressions, including binomial radical expressions. Students will solve radical equations, and graph translations of radical functions and their inverses.  

Learning Targets

Essential Questions

• To simplify the nth root of an expression, what must be true about the expressions?
• When you square each side of an equation, is the resulting equation equivalent to the original?  
• How are the function and its inverse related.  

Enduring Understandings

Students will understand:

• A single quantity may be represented by many different expressions.  The facts about a quantity may be expressed by many different equations (or inequalities).
• Solving an equation is the process of rewriting the equation to make what it says about its variables as simple as possible.
• A Function is a relationship between variables in which each value of the input variable is associated with a unique value of the output variable.  

Know

By the end of this unit, students will know

• simplify nth roots
• multiply radical expressions
• divide radical expressions
• add and subtract radical expressions
• multiply and divide binomial expressions
• simplify expressions with rational exponents
• solve square root and other radical equations
• add, subtract, multiply, and divide functions
• find the composite of two functions
• find the inverse of a relation or function

Do

By the end of this unit, students will be able to

Evidence of Learning

Formative

• Rational Functions Special Values Puzzle
• Faceing Math: Basic Rational Functions
• Faceing Math: More Rational Functions

Summative/ Benchmark

• Rational Functions Basics Task Cards
• Unit Assessment: How to graph and solve Rational Functions
• Unit Assessment:  Use the rational functions to solve real world equations

Alternative Assessments

• Rational Functions Scavenger Hunt
• Rational Functions Matching Square
• Graph Matching Bingo
• Match, Pair and Share
• Create a Unit Circle using right triangle Rational Functions
• Use rational Functions to include real-life applications

Learning Activities

• Star Wars Jedi Academy: Applications of Rational Functions
• Rational Functions Convenient Values Flash Cards
• Rational Functions Jeopardy
• Digital Interactive Rational Functions Values Puzzle
• Inverse Trigonometric Functions Scavenger Hunt
• Using Kahoot to find coterminal and reference angles
• Using Flipped Math to solve r real-world scenarios
• Graph tunctions and their translations using Desmos

Materials / Equipment / Resources

Core Instructional

Materials and Texts

Classroom Notes

Khan Academy

Flipped Math

Equipment

TI-83 Calculator

Chromebook - Desmos

Document Camera

LCD Projector

Supplemental Resources

Desmos

Faceing Math

Teachers Pay Teachers

Standards

Content Statement

Indicator

Use complex numbers in polynomial identities and equations.

CCSS.MATH.CONTENT.HSN.CN.C.8

(+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x - 2i).

CCSS.MATH.CONTENT.HSN.CN.C.9

(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

Understand the relationship between zeros and factors of polynomials.

CCSS.MATH.CONTENT.HSA.APR.B.2

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).

CCSS.MATH.CONTENT.HSA.APR.B.3

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Rewrite rational expressions.

CCSS.MATH.CONTENT.HSA.APR.B.2

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).

CCSS.MATH.CONTENT.HSA.APR.B.3

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Analyze functions using different representations.

CCSS.MATH.CONTENT.HSF.IF.C.7

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*

CCSS.MATH.CONTENT.HSF.IF.C.7.C

Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

21st Century Skills and Themes

Interdisciplinary Connections

Career Ready Practices

9.2 Career Awareness, Exploration, and Preparation  

• Language Arts through open-ended questions and self-reflections.  
• Business through the use of excel and finance.
• Science through physics problems.

• CRP1. Act as a responsible and contributing citizen and employee.
• CRP2. Apply appropriate academic and technical skills.
• CRP4.Communicate clearly and effectively and with reason.
• CRP6.Demonstrate creativity and innovation.
• CRP8.Utilize critical thinking to make sense of problems and persevere in solving them.
• CRP9.Model integrity, ethical leadership and effective management.
• CRP11. Use technology to enhance productivity.
• CRP12.Work productively in teams while using cultural global competence.

By the end of 12th grade,

• 9.2.12.C.3 Identify transferable career skills and design alternate career plans.
• 9.2.12.C.4 Analyze how economic conditions and societal changes influence employment trends and

Technology Standards - 8.1

9-12th Grade

A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.

• Select and use applications effectively and productively.

8.1.12.A.2 Produce and edit a multi-page digital document for a commercial or professional audience and present it to peers and/or professionals in that related area for review.

8.1.12.A.4 Construct a spreadsheet workbook with multiple worksheets, rename tabs to reflect the data on the worksheet, and use mathematical or logical functions, charts and data from all worksheets to convey the results.

8.1.12.A.5 Create a report from a relational database consisting of at least two tables and describe the process, and explain the report results.

B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.

• Apply existing knowledge to generate new ideas, products, or processes.
• Create original works as a means of personal or group expression.

8.1.12.B.2 Apply previous content knowledge by creating and piloting a digital learning game or tutorial.

C. Communication and Collaboration: Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others.

• Interact, collaborate, and publish with peers, experts, or others by employing a variety of digital environments and media.
• Communicate information and ideas to multiple audiences using a variety of media and formats.
• Develop cultural understanding and global awareness by engaging with learners of other cultures.
• Contribute to project teams to produce original works or solve problems.

8.1.12.C.1 Develop an innovative solution to a real world problem or issue in collaboration with peers and experts, and present ideas for feedback through social media or in an online community.

D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

• Advocate and practice safe, legal, and responsible use of information and technology.

8.1.12.D.1 Demonstrate appropriate application of copyright, fair use and/or Creative Commons to an original work.

F: Critical thinking, problem solving, and decision making: Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources.

• Identify and define authentic problems and significant questions for investigation.
• Plan and manage activities to develop a solution or complete a project.
• Collect and analyze data to identify solutions and/or make informed decisions.
• Use multiple processes and diverse perspectives to explore alternative solutions.

8.1.12.F.1 Evaluate the strengths and limitations of emerging technologies and their impact on educational, career, personal and or social needs.

Modifications/Accommodations

IEPs

• preferential seating.
• extended time on tests and assignments.
• reduced homework or classwork.
• verbal, visual, or technology aids.
• modified textbooks or audio-video materials.
• behavior management support.
• adjusted class schedules or grading.
• verbal testing

504s

• preferential seating.
• extended time on tests and assignments.
• reduced homework or classwork.
• verbal, visual, or technology aids.
• modified textbooks or audio-video materials.
• behavior management support.
• adjusted class schedules or grading.
• verbal testing

ELLs

• modeling and using gestures to aid in understanding.
• simplify instructions

G/T

• provide learning centers where students are in charge of their learning.

Unit Title

Unit 6 - Analytic Radical Functions

Timeframe 

8 weeks

Unit Summary

Solving trigonometric equations can be helpful when trying to find the measure of an angle or the area of a triangle.  Students will prove the Pythagorean Identities and use them to establish new identities.  These identities will help them to solve for angles and sides in both right and oblique triangles.

Learning Targets

Essential Questions

• What does it mean to solve a radical equation?
• How are multiple solutions represented on a given domain?
• What does it mean to prove or verify a radical expression?

Enduring Understandings

Students will understand:

• Equivalent expressions can be written in infinite ways
• The solutions to a trigonometric equation can be represented algebraically and graphically
• Rational Functions can be used to solve oblique as well as right triangles
• Real-world phenomena can be modeled using trigonometric principles

Know

By the end of this unit, students will know

• How to use the radical equationsto simplify, verify and prove expressions
• How to solve radical equations

Do

By the end of this unit, students will be able to

Solve radical equations using algebraic and graphic techniques

Find the exact values of radicals.  

Evidence of Learning

Formative

• Radical Puzzles
• Faceing Math: Trigonometric Identities
• Solving Radical Equations Task Cards

Summative/ Benchmark

• Unit Assessment: Solving Trigonometric Equations using Identities
• Unit Assessment:  Solving and finding Area of Oblique Triangles

Alternative Assessments

Learning Activities

• Group completion of graphic organizers involving analytic Radical Functions
• Small group explorations involving analytic Radical Functions
• Independent practice involving analytic Radical Functions

Materials / Equipment / Resources

Core Instructional

Materials and Texts

Classroom Notes

Khan Academy

Flipped Math

Equipment

TI-83 Calculator

Chromebook - Desmos

Document Camera

LCD Projector

Supplemental Resources

Desmos

Faceing Math

Teachers Pay Teachers

Standards

Content Statement

Indicator

Use complex numbers in polynomial identities and equations.

CCSS.MATH.CONTENT.HSN.CN.C.8

(+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x - 2i).

CCSS.MATH.CONTENT.HSN.CN.C.9

(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

Understand the relationship between zeros and factors of polynomials.

CCSS.MATH.CONTENT.HSA.APR.B.2

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).

CCSS.MATH.CONTENT.HSA.APR.B.3

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Model periodic phenomena with trigonometric functions.

CCSS.MATH.CONTENT.HSF.TF.B.5

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.*

CCSS.MATH.CONTENT.HSF.TF.B.7

(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.*

Define trigonometric ratios and solve problems involving right triangles.

CCSS.MATH.CONTENT.HSG.SRT.C.8

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*

21st Century Skills and Themes

Interdisciplinary Connections

Career Ready Practices

9.2 Career Awareness, Exploration, and Preparation  

• Language Arts through open-ended questions and self-reflections.  
• Business through the use of excel and finance.
• Science through physics problems.

• CRP1. Act as a responsible and contributing citizen and employee.
• CRP2. Apply appropriate academic and technical skills.
• CRP4.Communicate clearly and effectively and with reason.
• CRP6.Demonstrate creativity and innovation.
• CRP8.Utilize critical thinking to make sense of problems and persevere in solving them.
• CRP9.Model integrity, ethical leadership and effective management.
• CRP11. Use technology to enhance productivity.
• CRP12.Work productively in teams while using cultural global competence.

By the end of 12th grade,

• 9.2.12.C.3 Identify transferable career skills and design alternate career plans.
• 9.2.12.C.4 Analyze how economic conditions and societal changes influence employment trends and

Technology Standards - 8.1

9-12th Grade

A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.

• Select and use applications effectively and productively.

8.1.12.A.2 Produce and edit a multi-page digital document for a commercial or professional audience and present it to peers and/or professionals in that related area for review.

8.1.12.A.4 Construct a spreadsheet workbook with multiple worksheets, rename tabs to reflect the data on the worksheet, and use mathematical or logical functions, charts and data from all worksheets to convey the results.

8.1.12.A.5 Create a report from a relational database consisting of at least two tables and describe the process, and explain the report results.

B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.

• Apply existing knowledge to generate new ideas, products, or processes.
• Create original works as a means of personal or group expression.

8.1.12.B.2 Apply previous content knowledge by creating and piloting a digital learning game or tutorial.

C. Communication and Collaboration: Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others.

• Interact, collaborate, and publish with peers, experts, or others by employing a variety of digital environments and media.
• Communicate information and ideas to multiple audiences using a variety of media and formats.
• Develop cultural understanding and global awareness by engaging with learners of other cultures.
• Contribute to project teams to produce original works or solve problems.

8.1.12.C.1 Develop an innovative solution to a real world problem or issue in collaboration with peers and experts, and present ideas for feedback through social media or in an online community.

D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

• Advocate and practice safe, legal, and responsible use of information and technology.

8.1.12.D.1 Demonstrate appropriate application of copyright, fair use and/or Creative Commons to an original work.

F: Critical thinking, problem solving, and decision making: Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources.

• Identify and define authentic problems and significant questions for investigation.
• Plan and manage activities to develop a solution or complete a project.
• Collect and analyze data to identify solutions and/or make informed decisions.
• Use multiple processes and diverse perspectives to explore alternative solutions.

8.1.12.F.1 Evaluate the strengths and limitations of emerging technologies and their impact on educational, career, personal and or social needs.

Modifications/Accommodations

IEPs

• preferential seating.
• extended time on tests and assignments.
• reduced homework or classwork.
• verbal, visual, or technology aids.
• modified textbooks or audio-video materials.
• behavior management support.
• adjusted class schedules or grading.
• verbal testing

504s

• preferential seating.
• extended time on tests and assignments.
• reduced homework or classwork.
• verbal, visual, or technology aids.
• modified textbooks or audio-video materials.
• behavior management support.
• adjusted class schedules or grading.
• verbal testing

ELLs

• modeling and using gestures to aid in understanding.
• simplify instructions

G/T

• provide learning centers where students are in charge of their learning.