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: |
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 |
| 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.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 | ||
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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.
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Resources Provided: Textbook, Internet resources, graph paper 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: | 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.
B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.
D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.
E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.
| 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)
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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.
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Resources Provided: Textbook, Internet resources, graph paper 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: | 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.
B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.
D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.
E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.
| 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.
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Resources Provided: Textbook, Internet resources, graph paper A.REI.C.5 Solving Two Equations in Two Unknowns A.REI.D.12 Fishing Adventures 3 F.LE.A.1 Finding Linear and Exponential Models F.LE.A.2 Interesting Interest Rates | ||
Technology Standards: | 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.
B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.
D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.
E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.
| 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.
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Resources Provided: Textbook, Internet resources, graph paper F.IF.B.4, F.IF.B.5 Average Cost F.LE.B.5 US Population 1982-1988 F.IF.C.7b Bank Account Balance | ||
Technology Standards: | 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.
B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.
D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.
E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.
| 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)
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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.
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A.SSE.A.2 Equivalent Expressions A.REI.B.4 Visualizing Completing the Square A.REI.B.4 Two Squares are Equal F.IF.B.4 Words – Tables - Graphs | ||
Technology Standards: | 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.
B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.
D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.
E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.
| 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)
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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.
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F.IF.B.4 Words – Tables - Graphs A.SSE.B.3 Rewriting a Quadratic Expression F.IF.C.7a Graphs of Quadratic Functions F.IF.B.6 Mathemafish Population | ||
Technology Standards: | 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.
B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.
D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.
E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.
| 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.
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S.ID.A.2-3 Measuring Variability in a Data Set S.ID.B.5 Support for a Longer School Day? S.ID.B.6 Laptop Battery Charge 2 | ||
Technology Standards: | 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.
B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.
D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.
E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.
| 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. |