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GATEWAY REGIONAL HIGH SCHOOL

ALGEBRA I

PACING GUIDE

PURPOSE STATEMENT/PHILOSOPHY

The Algebra I curriculum is comprised of the following major concepts or ‘Big Ideas’:  (1) tools of algebra; (2) equations and inequalities; (3) rational and irrational numbers;  (4) polynomials;  (5) functional and relations; and (6) linear systems (7) exponential functions.  While knowledge of content is being developed students are engaged in hands-on and cooperative activities that encourage mathematical reasoning, problem solving, communicating and making connections. Through these activities students utilize technology such as graphing calculators, computers, and calculator-based lab equipment. In addition they are encouraged to think more critically through activities that involve investigations, explorations, and discovery. Finally, evaluation appears in several formats: tests, performance tasks, and long- and short-term projects.

PACING GUIDE

Month

# Days

Standards

Skills

Activities

Assessments

September

Number, Operations, and Expressions

6

A-SSE.A.1a

A-CED.A.1

Review simplifying expressions by evaluating absolute value, using the order of operations, comparing rational numbers, and graphing in the coordinate plane.

Collaborative discussions

Stations Activities – Absolute Value, Order of Operations, Variables & Expressions, Evaluating Expressions, Coordinate Plane, Comparing Values.

Three Act videos:  http://www.101qs.com/2859

Kahn Academy:  The coordinate plane.  

Number and Expression Lab:

https://njctl.org/courses/math/algebra-i/numbers-operations-and-expressions-algebra-1/attachments/numbers-operations-and-expressions-labs-algebra-1/

Assessment Questions from Stations- Absolute Value, Order of Operations, Variables & Expressions, Evaluating Expressions, Coordinate Plane, Comparing Values.

Unit Test- Absolute Value, Order of Operations, Variables & Expressions, Evaluating Expressions, Coordinate Plane, Comparing Values.  

Performance Assessments:

A.SSE.A.1 Kitchen Floor Tiles

A.CED.A.1 Planes and wheat        

A-CED.A.1 Paying the rent

Properties of Real Numbers

10

A-SSE.A.1a

A-CED.A.1

A-REI.B.3

Properties of Real Numbers

Simplifying Expressions with the Distributive Property and by Combining Like Terms

Analyzing questions

Interactive Whiteboard Lessons based on student need

Modeling Expressions with Algebra Tiles

Three Act Video:  

Quick Check – Properties of Real Numbers and Simplifying Expressions

Quiz – Properties of Numbers and Simplifying Expressions

Performance Assessment:

A.REI.A.1 Zero Product Property 1

A.CED.A.2 Clea on an Escalator

S.ID.B.6,S.ID.C.7-9 Coffee and Crime

October

Solving and Graphing Equations and Inequalities

18

A-SSE.A.1a

A-CED.A.1

A-CED.A.4

A-REI.B.3

Solving Equations

Solving Inequalities

Graphing Inequalities on a Number Line

Collaborative discussions

Cooperative group work (eg. Placemat Activity)/ Differentiated group work

Analyzing questions

Interactive Whiteboard Lessons based on student need

Quick Check – Solving One and Two Step Equations

Quick Check- Solving Equations

Quiz- Solving Inequalities

Unit Test- Properties of Real Numbers, Simplifying Expressions, Solving Equations and Inequalities

4

A-SSE.A.1a

A-CED.A.1

A-CED.A.4

A-REI.B.3

1st Marking Period Benchmark

Cooperative Group Work

Analyzing questions

Benchmark – Create and Solve an Equation to Budget for a Desired Item; Create Puzzle Worksheet

November

Functions

14

  • F-IF.B.4
  • A.REI.D.10
  • F-IF.B.5
  • N-Q.A.2
  • F-IF.A.1
  • F-IF.A.1.b
  • F-IF.C.7a
  • A.SSE.1.a
  • A.CED.2
  • F.IF.LE.2
  • F.IF.7.a

Properties of Functions

Linear Functions

Writing Linear Equations

Graphing Linear Equations

Collaborative discussions

Analyzing questions

Interactive Whiteboard Lessons based on student need

Card Sorts – Linear/Non-Linear; Function/Not a Function

Tech Lab – Determining if an equation’s graph is linear or non-linear

Quick Check- Slope

Quick Check- Create an Equation, Table & Graph for a Pattern

Quiz – Functions, Create an Equation, Table & Graph for a Pattern, Determine if a Representation is Linear or Nonlinear, Write and Graph Linear Equations

December

Patterns and Functions

8

  • F-IF.B.4
  • A.REI.D.10
  • F-IF.B.5
  • N-Q.A.2
  • F-IF.A.1
  • F-IF.A.1.b
  • F-IF.C.7a
  • A.SSE.1.a
  • A.CED.2
  • F.IF.LE.2

F.IF.7.a

S.ID.6.a

S.ID.6b

S.ID.7

Writing Linear Equations in Different Forms

Scatter Plots & Trend Lines

Patterns & Non-Linear Functions

Collaborative discussions

Analyzing questions

Interactive Whiteboard Lessons based on student need

Data Collection for Scatter Plot – Measuring foot length and height and graphing data as class

Unit Test – Properties of Functions, Linear Functions

Writing Linear Equations,

Graphing Linear Equations,

Writing Linear Equations in Different Forms; Scatter Plots and Trend Lines; Patterns & Non-Linear Functions

Systems of Equations

8

A.CED.A.3

A.REI.C.6

Parallel & Perpendicular Lines

Solve Systems of Equations by Graphing

Collaborative discussions

Analyzing questions

Desmos Polygraph Activity

Quick Check – Solve Systems of Equations by Graphing

Quiz – Parallel & Perpendicular Lines; Solve Systems of Equations by Graphing

January

Graphings systems

7

A.CED.A.3

A.REI.D.12

A.REI.C.6

Graphing Linear Inequalities

Graphing a System of Linear Inequalities

Collaborative discussions

Analyzing questions

Interactive Whiteboard Lessons based on student need

Desmos Putt-Pott Golf Activity

Unit Test – Parallel & Perpendicular Lines; Solve Systems of Equations by Graphing; Graph Linear Inequalities and Graph Systems of Linear Inequalities

Benchmark

5

A.CED.A.3

A.REI.D.12

F-IF.B.4

A.REI.D.10

F-IF-A.1.b

F-IF-C.7a

A.SSE.1a

A.CED.2

2nd Marking Period Benchmark

Cooperative group work

Desmos online graphing calculator

Benchmark – Graphing Linear Inequalities; Graphing and Writing Linear Equations

February

Polynomials

14

N-RN.A.1

A-APR.A.1

Exponent Rules

Scientific Notation

Introduction to Polynomials

Adding and Subtracting Polynomials

Collaborative discussions

Cooperative activities (eg. Exponent Block Game, Exponent Rule Jeopardy)

Analyzing questions

Interactive Whiteboard Lessons based on student need

Quick Check – Introduction to Exponent Rules

Quick Check – Scientific Notation

Quick Check – Simplifying Expressions with Negative Exponents

Quiz – Scientific Notation and Exponent Rules

Quick Check – Polynomials

Unit Test – Exponent Rules, Scientific Notation, Introduction to Polynomials, Adding & Subtracting Polynomials

Quadratic Functions

7

A-APR.A.1

A-SSE.A.1a

A-SSE.2

F-IF.B4

F-IF.B5

F-IF.C.7a

Quadratic Functions & Their Graphs

Multiplying a Monomial

Factoring out a Common Monomial

Collaborative discussions

Exploratory Activity: Relating traits of quadratic graphs to their equations by exploring graphs on Desmos

Analyzing questions

Interactive Whiteboard Lessons based on student need

Quick Check – Quadratic Graphs

Quick Check – Multiplying a Monomial and a Polynomial

Quiz – Attributes of Quadratic Graphs; Multiplying a Monomial; Factoring out a Common Monomial

March

Multiplying and Factoring Trinomials

13

A-APR.A.1

A-SSE.A.1a

A-SSE.2

F-IF.B4

F-IF.B5

F-IF.C.7a

Multiplying Two Binomials

Factoring Trinomials

Collaborative discussions

Analyzing questions

Interactive Whiteboard Lessons based on student need

Differentiated Practice Problems

Quick Check – Multiplying Two Binomials

Quick Check – Factor Quadratic Expressions

Unit Test – Attributes of Quadratic Graphs; Multiplying a Monomial; Factoring out a Common Monomial, Multiplying Two Binomials, Factoring Trinomials

Benchmark

4

N-RN.A.1

A-APR.A.1

F-IF.B4

F-IF.B5

F-IF.C.7a

A-SSE.A.1a

A-SSE.2

3rd Marking Period Benchmark

Cooperative group work

Analyzing Questions

Benchmark – Creating Polynomials, Writing Expressions for Area & Perimeter, Matching Graphs and Attributes to Quadratic Equations

April

Solving Quadratics

10

A.CED.2

A.APR.B.3

A.REI.B.4b

A-SSE.C.3a

F-IF.B.4

F-IF.C.7a

F-IF.C.8a

Forms of Quadratic Functions

Solving Quadratics by Factoring

Rational and Irrational Numbers

Simplifying Radical Expressions

Solving Quadratics by the Square Root Method

Collaborative discussions

Exploratory Activity: Relating traits of quadratic graphs to the different forms of their equations by exploring graphs on graphing calculators

Analyzing questions

Interactive Whiteboard Lessons based on student need

Quick Check – Solve by Factoring

Quiz – Forms of Quadratic Equations; Solving Quadratic Equations by Factoring

Quick Check – Rational and Irrational Numbers

May

Pythagorean Theorem

9

A.CED.2

A.APR.B.3

A.REI.B.4b

A-SSE.C.3a

F-IF.B.4

F-IF.C.7a

F-IF.C.8a

Pythagorean Theorem and its Converse

Solving Quadratics Using the Quadratic Formula

Collaborative discussions

Cooperative group activity – Pick Up Sticks

Analyzing questions

Interactive Whiteboard Lessons based on student need

Review Booklet – Methods of Solving Quadratics; Properties of Quadratic Functions and the Different Forms of Quadratic Equations; Pythagorean Theorem and its Converse

Unit Test- Solving Quadratic Equations; Different Forms of Quadratic Equations & their Properties; Pythagorean Theorem and its Converse

Exponential Growth

10

A.SSE.A.1b

A.SSE.B.3c

A-CED.A.1

A-CED.A.2

A-CED.A.3

A-CED.A.4

A-REI.D.10

A-REI.D.11

F-IF-B.4

F-IF.B.5

Exponential Growth and Decay

Vertical Motion

Collaborative discussions

Analyzing questions

Interactive Whiteboard Lessons based on student need

Quick Check – Exponential Growth and Decay

Quiz – Exponential Growth and Decay

Quick Check – Vertical Motion

June

Modeling

4

A.SSE.A.1b

A.SSE.B.3c

A-CED.A.1

A-CED.A.2

A-CED.A.3

A-CED.A.4

A-REI.D.10

A-REI.D.11

F-IF-B.4

F-IF.B.5

Modeling Data with Linear, Quadratic or Exponential Functions

Cooperative Group Activities – Testing Bridge Thickness; Testing Bridge Length

Analyzing questions

Interactive Whiteboard Lessons based on student need

Unit Test – Exponential Growth and Decay

Vertical Motion

Modeling Data with Linear, Quadratic or Exponential Functions

Benchmark

5

A.SSE.A.1b

A.SSE.B.3c

A-CED.A.1

A-CED.A.2

A-CED.A.3

A-CED.A.4

A-REI.D.10

A-REI.D.11

F-IF-B.4

F-IF.B.5

4th Marking Period Benchmark

Cooperative group work – data collection for all tasks

Analyzing Questions

Benchmark – Collecting Data for a Linear, Exponential and Quadratic Model

 GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area:  Mathematics

Unit Title: Number, Operations, and Expressions

Timeframe: 6 Days

Lesson Components

UNIT SUMMARY

A summary of what the unit will contain and the learning students will be engaged in.

Students will be able to classify numbers in the real number system.

Students will be able to identify and combine like terms.

Students will be able to evaluate an expression for given values.

Students will be able to put terms in order by the degree of a variable.

LEARNING TARGETS

ESSENTIAL QUESTION:

What are the basic skills needed for Algebra I?

ENDURING UNDERSTANDINGS

What are irrational numbers?

What are like terms and how to combine them.

Using substitution to evaluate an expression for a value.

21st Century Themes/Career Readiness Practices

Global Awareness:  Students will analyze and synthesize information from multiple news sources relating to current events/global issues.  Students will explore stereotypes and understand other cultures through class readings and writing prompts.

Creativity and Innovation: Students will brainstorm and produce original narratives/arguments inspired from the texts read.  Students will analyze texts for discussion and for developing a written response.  Students will be open and responsive to new and diverse perspectives and develop arguments relating to the risks and rewards of undertaking bold actions.  

Critical Thinking and Problem Solving:  Students will use various types of reasoning as appropriate to the situation.  Students will analyze how parts of a text interact to produce the overall theme or purpose.  Students will effectively analyze and evaluate evidence, arguments, claims, beliefs, and alternate points of view.  Students will synthesize and make connections between information and arguments.  Students will interpret information and draw conclusions based on analysis.

Communication and Collaboration: Students will articulate thoughts and ideas effectively using oral, written, and nonverbal communication skills in a variety of contexts. Students will use various media to communicate.  Students will demonstrate ability to work effectively and respectfully with diverse teams and work to accomplish a common goal.

Information Literacy: Students will critically evaluate information from the internet in short research projects to assess its credibility for research purposes and use the information to accomplish a task. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information.

Media Literacy: Students will interpret and analyze a variety of media sources to better understand the unit theme.  This includes how media can influence beliefs and behaviors.  Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of media. Students will create media products.

ICT Literacy-Information, Communications and Technology:  Students will use technology as a tool to research, organize, evaluate, and communicate information. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information technologies.

Life and Career Skills/Standards/Practices: Students will interact with others through listening and speaking in a respectable and professional manner, manage goals, work independently and be self-directed.

EVIDENCE OF LEARNING

  • Unit Test - Absolute Value, Order of Operations, Variables & Expressions, Evaluating Expressions, Coordinate Plane, Comparing Values.

Differentiation/Adaptations/Modifications:

The curriculum has a strong foundation of differentiated instruction. Differentiated instruction or modifications for all students, special education, ELL, and gifted & talented students include but not limited to learning environment, scheduling of learning tasks, materials and procedures. The classroom teacher often makes these modifications as appropriate to each child’s developmental and academic needs and/or directed by a child’s IEP or 504 plans. Gifted & talented students as well as all students are given choice of learning activities, assessments and projects as appropriate to the unit of study or lesson to meet their intellectual and academic differences.

  • Projects are designed so teacher may add or omit criteria based on student needs.
  • Extended time is allotted for students when directed by IEP’s or 504 plans.
  • Modification of project dimensions or materials for students with special needs.
  • Small groups/Flexible groupings
  • Shortened assignments
  • Assignment notebooks
  • Study sheets/summary sheets/outlines of most important facts
  • Supplemental aids (vocabulary, summary cards, modern translation of original work, etc.)
  • Visual demonstrations
  • Presentation of material in small steps
  • Read or paraphrase subject matter
  • Instructions/directions given in different channels (written, spoken, demonstration)
  • Visual or multisensory materials
  • Functional level materials
  • Mnemonic aids/devices
  • Additional time for test preparation
  • Review/testing matched to student pace
  • Test directions read/explained thoroughly
  • Oral, short-answer, modified tests
  • Emphasis on successes
  • Graphic Organizers
  • Student choice of texts, projects, writing prompts, etc.

Resources Provided:

Textbook, Internet resources, graph paper

A.SSE.A.1 Kitchen Floor Tiles

A.CED.A.1 Planes and wheat        

A-CED.A.1 Paying the rent

A.REI.A.1 Zero Product Property 1

A.CED.A.2 Clea on an Escalator

S.ID.B.6,S.ID.C.7-9 Coffee and Crime


Technology Standards:
(See Pacing Guide for Specific Integration)

Career Ready Practices:

(See Pacing Guide for Specific Integration)

Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.

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

  • 8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.

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

  • 8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).

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

  • 8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.
  • 8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.
  • 8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.
  • 8.1.8.D.4 Assess the credibility and accuracy of digital content.
  • 8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.

E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.

  • 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem.

CRP2. Apply appropriate academic and technical skills.

CRP4. Communicate clearly and effectively and with reason.

CRP6. Demonstrate creativity and innovation.

CRP7. Employ valid and reliable research strategies.

CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.

CRP11. Use technology to enhance productivity.

CRP12. Work productively in teams while using cultural global competence.


 GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area:  Mathematics

Unit Title: Equations and Inequalities

Timeframe: 32 Days

Lesson Components

UNIT SUMMARY

A summary of what the unit will contain and the learning students will be engaged in.

Students will be able to solve equations that contain the same variable on both sides.

Students will be able transform a formula to a different form of that equation.

Students will be able to find the value of unknown quantities using Literal Equations and Substitution.

Students will be able to classify numbers in the real number system.

Students will be able to identify and combine like terms.

Students will be able to evaluate an expression for given values.

Students will be able to put terms in order by the degree of a variable.

Students will be able to write an inequality.

Students will be able to solve one-step inequalities.

Students will be able to solve two-step and multiple step inequalities.

Students will be able to graph a single inequality on a number line.

Students will be able to solve compound inequalities and graph them on a number line.

LEARNING TARGETS

ESSENTIAL QUESTIONS

How do we represent unknown quantities?

How can the value of an unknown variable be

How can related values that are not equivalent be represented?

How do we solve for a variable in an inequality?

ENDURING UNDERSTANDINGS

How to solve an equation in one variable.

How can an equation be solved for a variable in the equation.

The vocabulary associated with inequalities.

Steps used to solve inequalities.

The difference between and & or statements.

21st Century Themes/Career Readiness Practices

Global Awareness:  Students will analyze and synthesize information from multiple news sources relating to current events/global issues.  Students will explore stereotypes and understand other cultures through class readings and writing prompts.

Creativity and Innovation: Students will brainstorm and produce original narratives/arguments inspired from the texts read.  Students will analyze texts for discussion and for developing a written response.  Students will be open and responsive to new and diverse perspectives and develop arguments relating to the risks and rewards of undertaking bold actions.  

Critical Thinking and Problem Solving:  Students will use various types of reasoning as appropriate to the situation.  Students will analyze how parts of a text interact to produce the overall theme or purpose.  Students will effectively analyze and evaluate evidence, arguments, claims, beliefs, and alternate points of view.  Students will synthesize and make connections between information and arguments.  Students will interpret information and draw conclusions based on analysis.

Communication and Collaboration: Students will articulate thoughts and ideas effectively using oral, written, and nonverbal communication skills in a variety of contexts. Students will use various media to communicate.  Students will demonstrate ability to work effectively and respectfully with diverse teams and work to accomplish a common goal.

Information Literacy: Students will critically evaluate information from the internet in short research projects to assess its credibility for research purposes and use the information to accomplish a task. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information.

Media Literacy: Students will interpret and analyze a variety of media sources to better understand the unit theme.  This includes how media can influence beliefs and behaviors.  Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of media. Students will create media products.

ICT Literacy-Information, Communications and Technology:  Students will use technology as a tool to research, organize, evaluate, and communicate information. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information technologies.

Life and Career Skills/Standards/Practices: Students will interact with others through listening and speaking in a respectable and professional manner, manage goals, work independently and be self-directed.

EVIDENCE OF LEARNING

 Assessment (attach benchmarks/unit tests)

  • Unit Test- Properties of Real Numbers, Simplifying Expressions, Solving Equations and Inequalities
  • Benchmark – Create and Solve an Equation to Budget for a Desired Item

Materials/Equipment:

Calculator, Interactive White Board, graph paper, ChromeBooks 

Differentiation/Adaptations/Modifications:

The curriculum has a strong foundation of differentiated instruction. Differentiated instruction or modifications for all students, special education, ELL, and gifted & talented students include but not limited to learning environment, scheduling of learning tasks, materials and procedures. The classroom teacher often makes these modifications as appropriate to each child’s developmental and academic needs and/or directed by a child’s IEP or 504 plans. Gifted & talented students as well as all students are given choice of learning activities, assessments and projects as appropriate to the unit of study or lesson to meet their intellectual and academic differences.

  • Projects are designed so teacher may add or omit criteria based on student needs.
  • Extended time is allotted for students when directed by IEP’s or 504 plans.
  • Modification of project dimensions or materials for students with special needs.
  • Small groups/Flexible groupings
  • Shortened assignments
  • Assignment notebooks
  • Study sheets/summary sheets/outlines of most important facts
  • Supplemental aids (vocabulary, summary cards, modern translation of original work, etc.)
  • Visual demonstrations
  • Presentation of material in small steps
  • Read or paraphrase subject matter
  • Instructions/directions given in different channels (written, spoken, demonstration)
  • Visual or multisensory materials
  • Functional level materials
  • Mnemonic aids/devices
  • Additional time for test preparation
  • Review/testing matched to student pace
  • Test directions read/explained thoroughly
  • Oral, short-answer, modified tests
  • Emphasis on successes
  • Graphic Organizers
  • Student choice of texts, projects, writing prompts, etc.

Resources Provided:

Textbook, Internet resources, graph paper

N.Q.A.1 Runners' World

N.Q.A.2 Giving Raises

N.Q.A.3 Calories in a Sports Drink

A.REI.B.3, A.REI.A.1 Reasoning with linear inequalities

A.CED.A.4 Equations and Formulas


Technology Standards:
(See Pacing Guide for Specific Integration)

Career Ready Practices:

(See Pacing Guide for Specific Integration)

Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.

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

  • 8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.

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

  • 8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).

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

  • 8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.
  • 8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.
  • 8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.
  • 8.1.8.D.4 Assess the credibility and accuracy of digital content.
  • 8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.

E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.

  • 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem.

CRP2. Apply appropriate academic and technical skills.

CRP4. Communicate clearly and effectively and with reason.

CRP6. Demonstrate creativity and innovation.

CRP7. Employ valid and reliable research strategies.

CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.

CRP11. Use technology to enhance productivity.

CRP12. Work productively in teams while using cultural global competence.

 GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area:  Mathematics

Unit Title: Functions

Timeframe: 22 Days

Lesson Components

UNIT SUMMARY

A summary of what the unit will contain and the learning students will be engaged in.

Students will be able to define a function and identify its domain and range.

Students will be able to evaluate functions.

Students will be able to write recursive and explicit formulas.

Students will be able to compare the rate of change of multiple representations of functions.

Students will be able to write a linear function after a given transformation.

Students will be able to determine the transformation(s) that occur between 2 linear functions.

LEARNING TARGETS

ESSENTIAL QUESTIONS

How do you use a formula to identify the terms of a sequence?

What are the multiple ways a function can be represented?

How do you write a linear function after a given transformation?

ENDURING UNDERSTANDINGS

The definition of a function.

The difference between the domain and range.

Know how to evaluate functions.

How to generate explicit and recursive formulas.

Know how to find the rate of change.

21st Century Themes/Career Readiness Practices

Global Awareness:  Students will analyze and synthesize information from multiple news sources relating to current events/global issues.  Students will explore stereotypes and understand other cultures through class readings and writing prompts.

Creativity and Innovation: Students will brainstorm and produce original narratives/arguments inspired from the texts read.  Students will analyze texts for discussion and for developing a written response.  Students will be open and responsive to new and diverse perspectives and develop arguments relating to the risks and rewards of undertaking bold actions.  

Critical Thinking and Problem Solving:  Students will use various types of reasoning as appropriate to the situation.  Students will analyze how parts of a text interact to produce the overall theme or purpose.  Students will effectively analyze and evaluate evidence, arguments, claims, beliefs, and alternate points of view.  Students will synthesize and make connections between information and arguments.  Students will interpret information and draw conclusions based on analysis.

Communication and Collaboration: Students will articulate thoughts and ideas effectively using oral, written, and nonverbal communication skills in a variety of contexts. Students will use various media to communicate.  Students will demonstrate ability to work effectively and respectfully with diverse teams and work to accomplish a common goal.

Information Literacy: Students will critically evaluate information from the internet in short research projects to assess its credibility for research purposes and use the information to accomplish a task. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information.

Media Literacy: Students will interpret and analyze a variety of media sources to better understand the unit theme.  This includes how media can influence beliefs and behaviors.  Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of media. Students will create media products.

ICT Literacy-Information, Communications and Technology:  Students will use technology as a tool to research, organize, evaluate, and communicate information. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information technologies.

Life and Career Skills/Standards/Practices: Students will interact with others through listening and speaking in a respectable and professional manner, manage goals, work independently and be self-directed.

EVIDENCE OF LEARNING

 Assessment (attach benchmarks/unit tests)

Functions, Create an Equation, Table & Graph for a Pattern, Determine if a Representation is Linear or Nonlinear, Write and Graph Linear Equations

Materials/Equipment:

Calculator, Interactive White Board, graph paper, ChromeBooks 

Differentiation/Adaptations/Modifications:

The curriculum has a strong foundation of differentiated instruction. Differentiated instruction or modifications for all students, special education, ELL, and gifted & talented students include but not limited to learning environment, scheduling of learning tasks, materials and procedures. The classroom teacher often makes these modifications as appropriate to each child’s developmental and academic needs and/or directed by a child’s IEP or 504 plans. Gifted & talented students as well as all students are given choice of learning activities, assessments and projects as appropriate to the unit of study or lesson to meet their intellectual and academic differences.

  • Projects are designed so teacher may add or omit criteria based on student needs.
  • Extended time is allotted for students when directed by IEP’s or 504 plans.
  • Modification of project dimensions or materials for students with special needs.
  • Small groups/Flexible groupings
  • Shortened assignments
  • Assignment notebooks
  • Study sheets/summary sheets/outlines of most important facts
  • Supplemental aids (vocabulary, summary cards, modern translation of original work, etc.)
  • Visual demonstrations
  • Presentation of material in small steps
  • Read or paraphrase subject matter
  • Instructions/directions given in different channels (written, spoken, demonstration)
  • Visual or multisensory materials
  • Functional level materials
  • Mnemonic aids/devices
  • Additional time for test preparation
  • Review/testing matched to student pace
  • Test directions read/explained thoroughly
  • Oral, short-answer, modified tests
  • Emphasis on successes
  • Graphic Organizers
  • Student choice of texts, projects, writing prompts, etc.

Resources Provided:

Textbook, Internet resources, graph paper

A.REI.C.6 Cash Box

A.CED.A.3 Dimes and Quarters

A.REI.C.5 Solving Two Equations in Two Unknowns

A.REI.D.12 Fishing Adventures 3

F.IF.A.1 The Parking Lot

F.IF.A.2 Yam in the Oven

F.LE.A.1 Finding Linear and Exponential Models

F.LE.A.2 Interesting Interest Rates


Technology Standards:
(See Pacing Guide for Specific Integration)

Career Ready Practices:

(See Pacing Guide for Specific Integration)

Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.

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

  • 8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.

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

  • 8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).

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

  • 8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.
  • 8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.
  • 8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.
  • 8.1.8.D.4 Assess the credibility and accuracy of digital content.
  • 8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.

E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.

  • 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem.

CRP2. Apply appropriate academic and technical skills.

CRP4. Communicate clearly and effectively and with reason.

CRP6. Demonstrate creativity and innovation.

CRP7. Employ valid and reliable research strategies.

CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.

CRP11. Use technology to enhance productivity.

CRP12. Work productively in teams while using cultural global competence.

 GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area:  Mathematics

Unit Title: Systems of Equations and Inequalities

Timeframe: 20 Days

Lesson Components

UNIT SUMMARY

A summary of what the unit will contain and the learning students will be engaged in.

Students will be able to graph systems of linear equations to find a solution.

Students will be able to solve a system of equations by using substitution and elimination.

Students will be able to graph systems of linear inequalities to find a solution.

Students will be able to solve a system of inequalities by using substitution and elimination.

Students will be able to translate real world problem into a system.

LEARNING TARGETS

ESSENTIAL QUESTIONS

How can real world situations be modeled by systems?  

How can solutions be found to a system?

ENDURING UNDERSTANDINGS

The point at which lines intersect is the solution to the system with those lines.

The area at which shading intersect is the solution to the system of those inequalities.

21st Century Themes/Career Readiness Practices

Global Awareness:  Students will analyze and synthesize information from multiple news sources relating to current events/global issues.  Students will explore stereotypes and understand other cultures through class readings and writing prompts.

Creativity and Innovation: Students will brainstorm and produce original narratives/arguments inspired from the texts read.  Students will analyze texts for discussion and for developing a written response.  Students will be open and responsive to new and diverse perspectives and develop arguments relating to the risks and rewards of undertaking bold actions.  

Critical Thinking and Problem Solving:  Students will use various types of reasoning as appropriate to the situation.  Students will analyze how parts of a text interact to produce the overall theme or purpose.  Students will effectively analyze and evaluate evidence, arguments, claims, beliefs, and alternate points of view.  Students will synthesize and make connections between information and arguments.  Students will interpret information and draw conclusions based on analysis.

Communication and Collaboration: Students will articulate thoughts and ideas effectively using oral, written, and nonverbal communication skills in a variety of contexts. Students will use various media to communicate.  Students will demonstrate ability to work effectively and respectfully with diverse teams and work to accomplish a common goal.

Information Literacy: Students will critically evaluate information from the internet in short research projects to assess its credibility for research purposes and use the information to accomplish a task. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information.

Media Literacy: Students will interpret and analyze a variety of media sources to better understand the unit theme.  This includes how media can influence beliefs and behaviors.  Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of media. Students will create media products.

ICT Literacy-Information, Communications and Technology:  Students will use technology as a tool to research, organize, evaluate, and communicate information. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information technologies.

Life and Career Skills/Standards/Practices: Students will interact with others through listening and speaking in a respectable and professional manner, manage goals, work independently and be self-directed.

EVIDENCE OF LEARNING

 Assessment (attach benchmarks/unit tests)

Unit Test – Parallel & Perpendicular Lines; Solve Systems of Equations by Graphing;

Unit Test -Graph Linear Inequalities and Graph Systems of Linear Inequalities

Benchmark – Graphing Linear Inequalities; Graphing and Writing Linear Equations

Materials/Equipment:

Calculator, Interactive White Board, graph paper, ChromeBooks 

Differentiation/Adaptations/Modifications:

The curriculum has a strong foundation of differentiated instruction. Differentiated instruction or modifications for all students, special education, ELL, and gifted & talented students include but not limited to learning environment, scheduling of learning tasks, materials and procedures. The classroom teacher often makes these modifications as appropriate to each child’s developmental and academic needs and/or directed by a child’s IEP or 504 plans. Gifted & talented students as well as all students are given choice of learning activities, assessments and projects as appropriate to the unit of study or lesson to meet their intellectual and academic differences.

  • Projects are designed so teacher may add or omit criteria based on student needs.
  • Extended time is allotted for students when directed by IEP’s or 504 plans.
  • Modification of project dimensions or materials for students with special needs.
  • Small groups/Flexible groupings
  • Shortened assignments
  • Assignment notebooks
  • Study sheets/summary sheets/outlines of most important facts
  • Supplemental aids (vocabulary, summary cards, modern translation of original work, etc.)
  • Visual demonstrations
  • Presentation of material in small steps
  • Read or paraphrase subject matter
  • Instructions/directions given in different channels (written, spoken, demonstration)
  • Visual or multisensory materials
  • Functional level materials
  • Mnemonic aids/devices
  • Additional time for test preparation
  • Review/testing matched to student pace
  • Test directions read/explained thoroughly
  • Oral, short-answer, modified tests
  • Emphasis on successes
  • Graphic Organizers
  • Student choice of texts, projects, writing prompts, etc.

Resources Provided:

Textbook, Internet resources, graph paper

F.BF.A.1a Skeleton Tower

A.SSE.A.1 Mixing Candies

F.IF.B.4 Warming and Cooling

F.IF.B.4, F.IF.B.5 Average Cost

F.LE.B.5 US Population 1982-1988

F.IF.B.6 Temperature Change

F.IF.C.7b Bank Account Balance


Technology Standards:
(See Pacing Guide for Specific Integration)

Career Ready Practices:

(See Pacing Guide for Specific Integration)

Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.

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

  • 8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.

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

  • 8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).

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

  • 8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.
  • 8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.
  • 8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.
  • 8.1.8.D.4 Assess the credibility and accuracy of digital content.
  • 8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.

E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.

  • 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem.

CRP2. Apply appropriate academic and technical skills.

CRP4. Communicate clearly and effectively and with reason.

CRP6. Demonstrate creativity and innovation.

CRP7. Employ valid and reliable research strategies.

CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.

CRP11. Use technology to enhance productivity.

CRP12. Work productively in teams while using cultural global competence.

 GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area:  Mathematics

Unit Title: Polynomials

Timeframe: 14 Days

Lesson Components

UNIT SUMMARY

A summary of what the unit will contain and the learning students will be engaged in.

Students will be able to describe and identify monomials, polynomials, and degrees.

Students will be able to add and subtract polynomials.

Students will be able to multiply a polynomial by a monomial.

Students will be able to multiply two polynomials.

Students will be able to recognize and factor monomials out of a polynomial.

Students will be able to factor trinomials.

Students will be able to factor a polynomial with 4 terms using the grouping method.

LEARNING TARGETS

ESSENTIAL QUESTIONS

How can factoring help to simplify a polynomial?

ENDURING UNDERSTANDINGS

To add or subtract polynomials, only like terms can be combined.

To multiply polynomials, each term of the terms of one polynomial is multiplied to each term of the second polynomial.

Factoring is another way of rewriting a polynomial.

21st Century Themes/Career Readiness Practices

Global Awareness:  Students will analyze and synthesize information from multiple news sources relating to current events/global issues.  Students will explore stereotypes and understand other cultures through class readings and writing prompts.

Creativity and Innovation: Students will brainstorm and produce original narratives/arguments inspired from the texts read.  Students will analyze texts for discussion and for developing a written response.  Students will be open and responsive to new and diverse perspectives and develop arguments relating to the risks and rewards of undertaking bold actions.  

Critical Thinking and Problem Solving:  Students will use various types of reasoning as appropriate to the situation.  Students will analyze how parts of a text interact to produce the overall theme or purpose.  Students will effectively analyze and evaluate evidence, arguments, claims, beliefs, and alternate points of view.  Students will synthesize and make connections between information and arguments.  Students will interpret information and draw conclusions based on analysis.

Communication and Collaboration: Students will articulate thoughts and ideas effectively using oral, written, and nonverbal communication skills in a variety of contexts. Students will use various media to communicate.  Students will demonstrate ability to work effectively and respectfully with diverse teams and work to accomplish a common goal.

Information Literacy: Students will critically evaluate information from the internet in short research projects to assess its credibility for research purposes and use the information to accomplish a task. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information.

Media Literacy: Students will interpret and analyze a variety of media sources to better understand the unit theme.  This includes how media can influence beliefs and behaviors.  Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of media. Students will create media products.

ICT Literacy-Information, Communications and Technology:  Students will use technology as a tool to research, organize, evaluate, and communicate information. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information technologies.

Life and Career Skills/Standards/Practices: Students will interact with others through listening and speaking in a respectable and professional manner, manage goals, work independently and be self-directed.

EVIDENCE OF LEARNING

 Assessment (attach benchmarks/unit tests)

  • Unit Test – Exponent Rules, Scientific Notation, Introduction to Polynomials, Adding & Subtracting Polynomials

Materials/Equipment:

Calculator, Interactive White Board, graph paper, ChromeBooks 

Differentiation/Adaptations/Modifications:

The curriculum has a strong foundation of differentiated instruction. Differentiated instruction or modifications for all students, special education, ELL, and gifted & talented students include but not limited to learning environment, scheduling of learning tasks, materials and procedures. The classroom teacher often makes these modifications as appropriate to each child’s developmental and academic needs and/or directed by a child’s IEP or 504 plans. Gifted & talented students as well as all students are given choice of learning activities, assessments and projects as appropriate to the unit of study or lesson to meet their intellectual and academic differences.

  • Projects are designed so teacher may add or omit criteria based on student needs.
  • Extended time is allotted for students when directed by IEP’s or 504 plans.
  • Modification of project dimensions or materials for students with special needs.
  • Small groups/Flexible groupings
  • Shortened assignments
  • Assignment notebooks
  • Study sheets/summary sheets/outlines of most important facts
  • Supplemental aids (vocabulary, summary cards, modern translation of original work, etc.)
  • Visual demonstrations
  • Presentation of material in small steps
  • Read or paraphrase subject matter
  • Instructions/directions given in different channels (written, spoken, demonstration)
  • Visual or multisensory materials
  • Functional level materials
  • Mnemonic aids/devices
  • Additional time for test preparation
  • Review/testing matched to student pace
  • Test directions read/explained thoroughly
  • Oral, short-answer, modified tests
  • Emphasis on successes
  • Graphic Organizers
  • Student choice of texts, projects, writing prompts, etc.

A.APR.A.1 Powers of 11

A.SSE.A.2 Equivalent Expressions

A.REI.B.4 Visualizing Completing the Square

A.REI.B.4 Braking Distance

A.REI.B.4 Two Squares are Equal

F.IF.B.4 Words – Tables - Graphs

F.IF.B.5 The restaurant

A.SSE.B.3 Profit of a company


Technology Standards:
(See Pacing Guide for Specific Integration)

Career Ready Practices:

(See Pacing Guide for Specific Integration)

Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.

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

  • 8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.

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

  • 8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).

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

  • 8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.
  • 8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.
  • 8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.
  • 8.1.8.D.4 Assess the credibility and accuracy of digital content.
  • 8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.

E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.

  • 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem.

CRP2. Apply appropriate academic and technical skills.

CRP4. Communicate clearly and effectively and with reason.

CRP6. Demonstrate creativity and innovation.

CRP7. Employ valid and reliable research strategies.

CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.

CRP11. Use technology to enhance productivity.

CRP12. Work productively in teams while using cultural global competence.

 GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area:  Mathematics

Unit Title: Quadratic Functions

Timeframe: 34 Days

Lesson Components

UNIT SUMMARY

A summary of what the unit will contain and the learning students will be engaged in.

Students will be able to identify the parts of quadratics.

Students will be able to calculate the axis of symmetry and vertex of a quadratic function when it is in standard form.

Students will be able to find the zeros of a quadratic function by graphing it in a coordinate plane.

Students will be able to solve quadratic equations using the zero product property.

Students will be able to solve quadratic equations and polynomials by factoring.

Students will be able to solve quadratic equations using square roots.

Students will be able to solve quadratic equations by completing the square.

Students will be able to identify the nature of the roots of a quadratic using the discriminant.

Students will be able to solve quadratic equations using the quadratic formula.

Students will be able to solve polynomial equations using u-substitution.

Students will be able to solve application problem using methods for solving quadratic equations.

LEARNING TARGETS

ESSENTIAL QUESTIONS

How can factoring help to solve an equation?

In what ways can the zeros of a quadratic be found and can this help us find when an object is in free fall.  

ENDURING UNDERSTANDINGS

The characteristics and properties of a graph of a quadratic (parabola)

What it means to solve a quadratic.

If the product of two factors is zero, one of the factors is zero.

The quadratic formula and the discriminant.

21st Century Themes/Career Readiness Practices

Global Awareness:  Students will analyze and synthesize information from multiple news sources relating to current events/global issues.  Students will explore stereotypes and understand other cultures through class readings and writing prompts.

Creativity and Innovation: Students will brainstorm and produce original narratives/arguments inspired from the texts read.  Students will analyze texts for discussion and for developing a written response.  Students will be open and responsive to new and diverse perspectives and develop arguments relating to the risks and rewards of undertaking bold actions.  

Critical Thinking and Problem Solving:  Students will use various types of reasoning as appropriate to the situation.  Students will analyze how parts of a text interact to produce the overall theme or purpose.  Students will effectively analyze and evaluate evidence, arguments, claims, beliefs, and alternate points of view.  Students will synthesize and make connections between information and arguments.  Students will interpret information and draw conclusions based on analysis.

Communication and Collaboration: Students will articulate thoughts and ideas effectively using oral, written, and nonverbal communication skills in a variety of contexts. Students will use various media to communicate.  Students will demonstrate ability to work effectively and respectfully with diverse teams and work to accomplish a common goal.

Information Literacy: Students will critically evaluate information from the internet in short research projects to assess its credibility for research purposes and use the information to accomplish a task. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information.

Media Literacy: Students will interpret and analyze a variety of media sources to better understand the unit theme.  This includes how media can influence beliefs and behaviors.  Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of media. Students will create media products.

ICT Literacy-Information, Communications and Technology:  Students will use technology as a tool to research, organize, evaluate, and communicate information. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information technologies.

Life and Career Skills/Standards/Practices: Students will interact with others through listening and speaking in a respectable and professional manner, manage goals, work independently and be self-directed.

EVIDENCE OF LEARNING

 Assessment (attach benchmarks/unit tests)

  • Unit Test – Attributes of Quadratic Graphs; Multiplying a Monomial; Factoring out a Common Monomial, Multiplying Two Binomials, Factoring Trinomials

Materials/Equipment:

Calculator, Interactive White Board, graph paper, ChromeBooks 

Differentiation/Adaptations/Modifications:

The curriculum has a strong foundation of differentiated instruction. Differentiated instruction or modifications for all students, special education, ELL, and gifted & talented students include but not limited to learning environment, scheduling of learning tasks, materials and procedures. The classroom teacher often makes these modifications as appropriate to each child’s developmental and academic needs and/or directed by a child’s IEP or 504 plans. Gifted & talented students as well as all students are given choice of learning activities, assessments and projects as appropriate to the unit of study or lesson to meet their intellectual and academic differences.

  • Projects are designed so teacher may add or omit criteria based on student needs.
  • Extended time is allotted for students when directed by IEP’s or 504 plans.
  • Modification of project dimensions or materials for students with special needs.
  • Small groups/Flexible groupings
  • Shortened assignments
  • Assignment notebooks
  • Study sheets/summary sheets/outlines of most important facts
  • Supplemental aids (vocabulary, summary cards, modern translation of original work, etc.)
  • Visual demonstrations
  • Presentation of material in small steps
  • Read or paraphrase subject matter
  • Instructions/directions given in different channels (written, spoken, demonstration)
  • Visual or multisensory materials
  • Functional level materials
  • Mnemonic aids/devices
  • Additional time for test preparation
  • Review/testing matched to student pace
  • Test directions read/explained thoroughly
  • Oral, short-answer, modified tests
  • Emphasis on successes
  • Graphic Organizers
  • Student choice of texts, projects, writing prompts, etc.

F.IF.B.4 Words – Tables - Graphs

F.IF.B.5 The restaurant

A.SSE.B.3 Profit of a company

A.SSE.B.3 Rewriting a Quadratic Expression

F.IF.C.7a Graphs of Quadratic Functions

F.IF.C.8a Springboard Dive

F.IF.C.8a Which Function?

F.IF.B.9 Throwing Baseballs

F.IF.B.6 Mathemafish Population


Technology Standards:
(See Pacing Guide for Specific Integration)

Career Ready Practices:

(See Pacing Guide for Specific Integration)

Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.

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

  • 8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.

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

  • 8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).

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

  • 8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.
  • 8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.
  • 8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.
  • 8.1.8.D.4 Assess the credibility and accuracy of digital content.
  • 8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.

E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.

  • 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem.

CRP2. Apply appropriate academic and technical skills.

CRP4. Communicate clearly and effectively and with reason.

CRP6. Demonstrate creativity and innovation.

CRP7. Employ valid and reliable research strategies.

CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.

CRP11. Use technology to enhance productivity.

CRP12. Work productively in teams while using cultural global competence.

 GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area:  Mathematics

Unit Title: Non-Linear Functions

Timeframe: 23 Days

Lesson Components

UNIT SUMMARY

A summary of what the unit will contain and the learning students will be engaged in.

Students will be to identify exponential relationships from fro a table, a graph, and an equation.

Students will be able to calculate growth rates and factors.

Students will be able identify exponential decay.

Students will be able to simplify expressions using rules of exponents.

Students will be able to identify the key features of a parabola.

Students will be able to graph a parabola when the equation is in standard form.

Students will be able to graph a quadratic function using intercept form.

Students will be able to graph a quadratic function using vertex form

Students will be able to solve application problems by writing a quadratic function in its desired form.

Students will be able to calculate the roots of a quadratic equation when it is in vertex form.

Students will be able to determine the transformations of a parabola from its parent function.

Students will be able to determine the equation of a new function after its parent function went through a transformation.

Students will be able to graphically analyze the behavior of non-linear functions.

Students will be able to compare key features of linear, quadratic, and exponential functions.

LEARNING TARGETS

ESSENTIAL QUESTIONS

How do exponential functions differ from linear functions?

What are the key features of a quadratic equation? How do you graph a quadratic function in standard form, vertex form, and intercept form?

ENDURING UNDERSTANDINGS

Know what exponential growth is.

The difference between growth rate and a growth factor.

Know what exponential decay is.

The parts of a parabola.

Know how to graph a quadratic function.

How to determine and write the transformations of a parabola.

How to compare features of functions.

21st Century Themes/Career Readiness Practices

Global Awareness:  Students will analyze and synthesize information from multiple news sources relating to current events/global issues.  Students will explore stereotypes and understand other cultures through class readings and writing prompts.

Creativity and Innovation: Students will brainstorm and produce original narratives/arguments inspired from the texts read.  Students will analyze texts for discussion and for developing a written response.  Students will be open and responsive to new and diverse perspectives and develop arguments relating to the risks and rewards of undertaking bold actions.  

Critical Thinking and Problem Solving:  Students will use various types of reasoning as appropriate to the situation.  Students will analyze how parts of a text interact to produce the overall theme or purpose.  Students will effectively analyze and evaluate evidence, arguments, claims, beliefs, and alternate points of view.  Students will synthesize and make connections between information and arguments.  Students will interpret information and draw conclusions based on analysis.

Communication and Collaboration: Students will articulate thoughts and ideas effectively using oral, written, and nonverbal communication skills in a variety of contexts. Students will use various media to communicate.  Students will demonstrate ability to work effectively and respectfully with diverse teams and work to accomplish a common goal.

Information Literacy: Students will critically evaluate information from the internet in short research projects to assess its credibility for research purposes and use the information to accomplish a task. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information.

Media Literacy: Students will interpret and analyze a variety of media sources to better understand the unit theme.  This includes how media can influence beliefs and behaviors.  Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of media. Students will create media products.

ICT Literacy-Information, Communications and Technology:  Students will use technology as a tool to research, organize, evaluate, and communicate information. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information technologies.

Life and Career Skills/Standards/Practices: Students will interact with others through listening and speaking in a respectable and professional manner, manage goals, work independently and be self-directed.

EVIDENCE OF LEARNING

 Assessment (attach benchmarks/unit tests)

Unit Test – Exponential Growth and Decay

Vertical Motion

Modeling Data with Linear, Quadratic or Exponential Functions

Benchmark – Collecting Data for a Linear, Exponential and Quadratic Model

Unit Test- Solving Quadratic Equations; Different Forms of Quadratic Equations & their Properties; Pythagorean Theorem and its Converse.

Materials/Equipment:

Calculator, Interactive White Board, graph paper, ChromeBooks 

Differentiation/Adaptations/Modifications:

The curriculum has a strong foundation of differentiated instruction. Differentiated instruction or modifications for all students, special education, ELL, and gifted & talented students include but not limited to learning environment, scheduling of learning tasks, materials and procedures. The classroom teacher often makes these modifications as appropriate to each child’s developmental and academic needs and/or directed by a child’s IEP or 504 plans. Gifted & talented students as well as all students are given choice of learning activities, assessments and projects as appropriate to the unit of study or lesson to meet their intellectual and academic differences.

  • Projects are designed so teacher may add or omit criteria based on student needs.
  • Extended time is allotted for students when directed by IEP’s or 504 plans.
  • Modification of project dimensions or materials for students with special needs.
  • Small groups/Flexible groupings
  • Shortened assignments
  • Assignment notebooks
  • Study sheets/summary sheets/outlines of most important facts
  • Supplemental aids (vocabulary, summary cards, modern translation of original work, etc.)
  • Visual demonstrations
  • Presentation of material in small steps
  • Read or paraphrase subject matter
  • Instructions/directions given in different channels (written, spoken, demonstration)
  • Visual or multisensory materials
  • Functional level materials
  • Mnemonic aids/devices
  • Additional time for test preparation
  • Review/testing matched to student pace
  • Test directions read/explained thoroughly
  • Oral, short-answer, modified tests
  • Emphasis on successes
  • Graphic Organizers
  • Student choice of texts, projects, writing prompts, etc.

S.ID.A.1-3 Haircut Costs

S.ID.A.1-3 Speed Trap

S.ID.A.2-3 Measuring Variability in a Data Set

S.ID.A.3 Identifying Outliers

S.ID.B.5 Support for a Longer School Day?

S.ID.B.6 Laptop Battery Charge 2

F.IF.B.4 The Aquarium

F.IF.B.4 Containers        


Technology Standards:
(See Pacing Guide for Specific Integration)

Career Ready Practices:

(See Pacing Guide for Specific Integration)

Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.

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

  • 8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.

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

  • 8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).

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

  • 8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.
  • 8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.
  • 8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.
  • 8.1.8.D.4 Assess the credibility and accuracy of digital content.
  • 8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.

E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.

  • 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem.

CRP2. Apply appropriate academic and technical skills.

CRP4. Communicate clearly and effectively and with reason.

CRP6. Demonstrate creativity and innovation.

CRP7. Employ valid and reliable research strategies.

CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.

CRP11. Use technology to enhance productivity.

CRP12. Work productively in teams while using cultural global competence.