GATEWAY REGIONAL HIGH SCHOOL

MATHEMATICS GEOMETRY

PACING GUIDE

# PURPOSE STATEMENT/PHILOSOPHY

The Geometry curriculum is composed of the same major concepts or ‘Big Ideas’ as Geometry, but on a more rigorous level. In addition, students are expected to do more in-depth geometric proofs. 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.  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 using EdConnect and Desmos.

PACING GUIDE

 Month # Days Standards Skills Activities Assessments September 22 G-CO.1G-CO-9C-CO.12 Know precise definitions of angle, line, parallel line, and line segment, based on the undefined notions of point, line, and distance along a line.  Prove theorems about lines and angles.Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Collaborative discussions CRP12Cooperative group work (eg. Placemat Activity, word sort)/ Differentiated group workCRP12Cooperative Team projects to discover relationships of undefined terms (points, lines, and planes) to defined terms (segments, surfaces, and solids).Analyzing questions8.1.8.A.2, CRP11Interactive Whiteboard Lessons based on student need Quiz- Intro to GeometryTest- Finding congruence, Distance, and Length October 12 G-CO.1G-CO-9C-CO.12 Know precise definitions of angle, line, parallel line, and line segment, based on the undefined notions of point, line, and distance along a line.  Prove theorems about parallel lines.Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Collaborative discussions CRP12Cooperative group work (eg. Placemat Activity)/ Differentiated group work 8.1.8.A.2, CRP11, CRP4Analyzing questions8.1.8.A.2, CRP11Interactive Whiteboard Lessons based on student need Quiz- Equivalent Ratios, Rates and Unit Rates, Unit Conversions, Proportionality in tables and GraphsQuick Checks-parallel lines. Test- Parallel Lines November/December 28 G-CO-8G-CO-9G-CO-10G-SRT.4G-SRT.5G.MG.3 Explain the criteria for triangle congruencePoints on a perpendicular bisector of a segment are exactly those equidistant from the segment’s endpoints.Prove theorems about triangles. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.Apply geometric methods to solve design problems. Foldable (converting fractions, decimals and percents) 8.1.8.A.2, CRP2Collaborative discussions Cooperative group work (eg. Placemat Activity)/ Differentiated group work8.1.8.A.2, CRP11Working with a typographic grid systems.   Analyzing questionsInteractive Whiteboard Lessons based on student need Quiz- perpendicular bisectorsQuick Checks-proving triangles theorems.  Test – Solve Design Problems. Lab: Angle-Angle Similarity LabLab: Side-Side-Side Similarity LabLab: Side-Angle-Side Similarity Lab December 18 G-C.1G-C.2G-C.3G-C.5 Prove that all circles are similar.Identify and describe relationships among inscribed angles, radii, and chords.Construct the inscribed and circumscribed circles of a triangle.Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius. Collaborative discussions Analyzing questionsInteractive Whiteboard Lessons based on student need Test- Prove all circles are similar. 12 G-CO.6G-CO.7G-CO.8 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Collaborative discussions Cooperative group work (eg. Placemat Activity)/ Differentiated group workAnalyzing questionsInteractive Whiteboard Lessons based on student needPick-Up Sticks activity (review) Quiz- TransformationsQuick Checks-CongruencePerformance Assessment – Transformations. January 12 G-CO.11G-GPE.4 Prove theorems about parallelograms.Use coordinates to prove simple geometric theorems algebraically Collaborative discussions Cooperative group work (eg. Placemat Activity)/ Differentiated group workAnalyzing questionsInteractive Whiteboard Lessons based on student need Quick Checks-QuadrilateralsTest- Proofs involving quadrilaterals 5 7.RP.A.37.EE.A.27.EE.B.37.NS.A.37.NS.1.d7.NS.2.c7.EE.17.EE.27.EE.4.a Benchmark Cooperative group work/ Differentiated group workAnalyzing questions Benchmark Assessment-Order of Operations, Solving 1 and 2-step equations February 8 7.NS.1.c7.NS.1.d7.NS.2.c7.EE.17.EE.27.E.E.4.b7.NS.1.c7.NS.1.d7.NS.2.c7.EE.17.EE.27.E.E.4.b Graphing InequalitiesWriting InequalitiesSolving 1-Step Inequalities Solving 2-Step InequalitiesReview Collaborative discussions Cooperative group work (eg. Placemat Activity)/ Differentiated group workAnalyzing questionsInteractive Whiteboard Lessons based on student need Quick Checks-Solving InequalitiesTest- Graphing Inequalities, Writing Inequalities, Solving 1-Step Inequalities , Solving 2-Step Inequalities 12 7.G.17.G.47.G.57.G.6 Angle RelationshipsComplementary and Supplementary AnglesClassifying Triangles by sides and anglesClassifying QuadrilateralsPerimeter and CircumferenceAreaPerimeter Collaborative discussions Cooperative group work (eg. Placemat Activity)/ Differentiated group workAnalyzing questionsInteractive Whiteboard Lessons based on student need Quiz- Angle Relationships, Complementary and Supplementary Angles, Classifying Triangles by sides and angles, Classifying QuadrilateralsQuick Checks-Classifying Triangles, Area March 8 7.G.17.G.47.G.57.G.6 Shaded areaProportions and Scale DrawingsReview Collaborative discussions Cooperative group work (eg. Placemat Activity)/ Differentiated group workAnalyzing questionsInteractive Whiteboard Lessons based on student need Quick Check-Shaded AreaTest- Angle Relationships, Complementary and Supplementary Angles, Classifying Triangles by sides and angles, Classifying QuadrilateralsPerimeter, CircumferenceArea, Shaded area, Proportions and Scale Drawings 4 7.NS.1.c7.NS.1.d7.NS.2.c7.EE.17.EE.27.E.E.4.b7.NS.1.c7.NS.1.d7.NS.2.c7.EE.17.EE.27.E.E.4.b7.G.17.G.47.G.57.G.67.G.17.G.47.G.57.G.6 Benchmark Cooperative group work/ Differentiated group workAnalyzing questions Benchmark Assessment-Solving Inequalities, 2-D Geometry 6 7.G.37.G.6 Identifying 3-D figuresCross SectionsVolumeReview Collaborative discussions Cooperative group work (eg. Placemat Activity)/ Differentiated group workAnalyzing questionsInteractive Whiteboard Lessons based on student need Quiz- Identifying 3-D figures, Cross Sections, VolumeQuick Checks-Volume April 12 7.G.37.G.6 Surface Area of PyramidsSurface Area of CylindersReview Collaborative discussions Cooperative group work (eg. Placemat Activity)/ Differentiated group workAnalyzing questionsInteractive Whiteboard Lessons based on student need Quick Check-Surface AreaTest- Identifying 3-D figures, Cross Sections, Volume, Surface Area of Pyramids, Surface Area of Cylinders 6 7.EE.4  8.EE.8  8.F.4 8.F.5 Analyze table and graphsMake tables and graphs Collaborative discussions Cooperative group work (eg. Placemat Activity)/ Differentiated group workAnalyzing questionsInteractive Whiteboard Lessons based on student need May 12 8.F.48.F.5 Writing Equations with 1 OperationsWriting Equations with 2 OperationsLinear Problem SolvingReviewGraphing Calculator Tables and Graphs Collaborative discussions Cooperative group work (eg. Placemat Activity)/ Differentiated group workAnalyzing questionsInteractive Whiteboard Lessons based on student need Quick CheckQuiz- Writing Equations with 1 Operations, Writing Equations with 2 Operations, Linear Problem SolvingTest- Writing Equations with 1 Operations, Writing Equations with 2 Operations, Linear Problem Solving 12 7.SP.37.SP.47.SP.57.SP.67.SP.7 Central TendenciesData AnaylsisBox-and-Whisker PlotSamplesSelecting SamplesReviewProbability and expected valueExperimental and Theoretical Probability Collaborative discussions Cooperative group work (eg. Placemat Activity)/ Differentiated group workAnalyzing questionsInteractive Whiteboard Lessons based on student needSpinner Activity Quick Check-Box-and Whisker, Theoretecial and ExperimentalQuiz- Central Tendencies, Data Anaylsis, Box-and-Whisker Plot, Samples, Selecting Samples June 6 7.SP.8 Counting Trees and ListsCounting Principle Collaborative discussions Cooperative group work (eg. Placemat Activity)/ Differentiated group workAnalyzing questionsInteractive Whiteboard Lessons based on student need 5 7.G.37.G.67.G.37.G.6 7.EE.4  8.EE.8  8.F.4 8.F.58.F.48.F.57.SP.37.SP.47.SP.57.SP.67.SP.77.SP.8 Benchmark Cooperative group work/ Differentiated group workAnalyzing questions Benchmark Assessment-Linear Functions, Probability, Data Analysis

 GATEWAY GROUP CURRICULUM UNIT PLAN Content Area:  Mathematics Unit Title: Points Lines, Planes and Angles 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 describe and identify points, lines, and planes.Students will be able to determine whether segments are congruent.Students will be able to apply the Ruler Postulate and the Segment Addition Postulate to calculate the length of a line segment.Students will be able to apply the Segment Addition Postulate and the rules of algebra to write and solve algebraic equations to find the value of a variable.Students will be able to construct congruent segments using a compass and straightedge, and/or dynamic geometry software.Students will be able to identify and classify angles based on its measurement and name them.Students will be able to apply the Angle Addition Postulate to calculate the measurement of angles and angle pair relationships.Students will be able to measure angles using a protractor.Students will be able to construct an angle congruent to any given angle using a compass and straightedge, and/or dynamic geometry software.Students will be able to construct the angle bisector of any given angle using a compass and straightedge, and/or dynamic geometry software.Students will be able to construct arguments to prove theorems about anglesStudents will be able to apply their knowledge of angle bisectors to calculate the measurements of angles. LEARNING TARGETS ESSENTIAL QUESTIONSHow do we develop an awareness of the structure of a mathematical system connecting definitions, postulates, and theorems? ENDURING UNDERSTANDINGS Understanding definitions of geometric figures.Understand congruence of segments and anglesUsing basic construction techniques to explore properties.

 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)Assessment- Congruence, Distance & Length of segments and angles.  Constructions – Angles, Locus, and Bisectors. 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 groupingsShortened assignments Assignment notebooksStudy sheets/summary sheets/outlines of most important factsSupplemental aids (vocabulary, summary cards, modern translation of original work, etc.)Visual demonstrationsPresentation of material in small stepsRead or paraphrase subject matterInstructions/directions given in different channels (written, spoken, demonstration)Visual or multisensory materialsFunctional level materialsMnemonic aids/devicesAdditional time for test preparationReview/testing matched to student paceTest directions read/explained thoroughlyOral, short-answer, modified testsEmphasis on successesGraphic OrganizersStudent choice of texts, projects, writing prompts, etc. Resources Provided:Textbook, Internet resources, graph paperG.CO.A.2 Horizontal Stretch of the PlaneG.CO.D.12 Bisecting an angleG.CO.D.12 Angle bisection and midpoints of line segments

 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: Parallel Lines Timeframe: 13 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 pairs of angles formed by two lines cut by a transversal.Students will be able to apply the properties of angles formed by parallel lines and a transversal.Students will be able to use information about angles to conclude whether or not lines are parallel/perpendicular. Students will be able to identify corresponding, alternate-interior, alternate-exterior, and same-side interior angles and then find the missing angles or solve for x.       Students will be able to construct parallel lines. LEARNING TARGETS ESSENTIAL QUESTIONSCan I logically communicate my mathematical reasoning in writing as well as orally?How do you prove that two lines are parallel? ENDURING UNDERSTANDINGS Not all lines and not all planes intersect. When a line intersects two or more lines, the angles formed at the intersection points create special angle pairs.The special angle pairs formed by parallel lines and a transversal are either congruent or supplementary.Certain angle pairs can be used to decide whether two lines are parallel/perpendicular. Use basic construction techniques to explore properties.

 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)Assessment- Apply theorems involving parallel and perpendicular lines to solve problems and construct proofs. 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 groupingsShortened assignments Assignment notebooksStudy sheets/summary sheets/outlines of most important factsSupplemental aids (vocabulary, summary cards, modern translation of original work, etc.)Visual demonstrationsPresentation of material in small stepsRead or paraphrase subject matterInstructions/directions given in different channels (written, spoken, demonstration)Visual or multisensory materialsFunctional level materialsMnemonic aids/devicesAdditional time for test preparationReview/testing matched to student paceTest directions read/explained thoroughlyOral, short-answer, modified testsEmphasis on successesGraphic OrganizersStudent choice of texts, projects, writing prompts, etc. Resources Provided:Textbook, Internet resources, graph paperG.CO.A.1 Defining Parallel LinesG.CO.A.1 Defining Perpendicular Lines

 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: Triangles Timeframe: 28 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 triangles by sides and anglesStudents will be able to write and solve algebraic equations to find the missing angle measurement, and/or the value of the variable using the Triangle Sum Theorem and Exterior Angles Theorem.Students will be able to identify which side of a triangle is the largest, knowing angle measure.Students will be able to identify which angle is the largest, knowing side lengths.Students will be able to write and solve proportions to find the missing side lengths in similar triangles.Students will be able to determine whether or not triangles are similar based on the given information.Students will be able to construct arguments and/or reasons to prove that triangles are similar.Students will be able to show triangles are congruent and solve problems based on that congruence.Students will be able state the congruence of corresponding parts knowing congruent triangles.Students will be able to complete and write proofs of triangles.Students will be able to find the congruent angles of an isosceles triangle given congruent sides.Students will be able to find the congruent sides of an isosceles triangle given congruent angles. LEARNING TARGETS ESSENTIAL QUESTIONSHow can statements about triangles be proven? ENDURING UNDERSTANDINGS Classifying triangles by sides and anglesThe sum of the angles of a triangle is 1800Triangle InequalitiesSimilarity statements for trianglesProofs involving similar triangles    Isosceles triangles have 2 congruent sides and two congruent angles  Congruence statements for triangles   CPCTC     Proofs involving triangles

 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)Benchmark Assessment- Classify triangles by their sides and angles, as well as the Triangle Sum Theorem.Assessment - Write triangle congruence statements and proofs involving triangle congruence 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 groupingsShortened assignments Assignment notebooksStudy sheets/summary sheets/outlines of most important factsSupplemental aids (vocabulary, summary cards, modern translation of original work, etc.)Visual demonstrationsPresentation of material in small stepsRead or paraphrase subject matterInstructions/directions given in different channels (written, spoken, demonstration)Visual or multisensory materialsFunctional level materialsMnemonic aids/devicesAdditional time for test preparationReview/testing matched to student paceTest directions read/explained thoroughlyOral, short-answer, modified testsEmphasis on successesGraphic OrganizersStudent choice of texts, projects, writing prompts, etc. Resources Provided:Textbook, Internet resources, graph paperG.CO.B.7 Properties of Congruent TrianglesG.CO.B.8 Why does SAS work?G.CO.B.8 Why does SSS work?G.CO.B.8 Why does ASA work?G.SRT.B.4 Joining two midpoints of sides of a triangle

 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: Circles Timeframe: 18 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 a circle.Students will be able to find the measure of angles given angles with vertices at the center, inside the circle, on the circle, or outside the circle.Students will be able to calculate the length of an arc in a circle.Students will be able to calculate the measurement of angles and arcs in radians.Students will be able to calculate the lengths of tangents, secant segments, and chords depending on the location of the intersection. LEARNING TARGETS ESSENTIAL QUESTIONSDo “how” and “where” a line(s) intersect a circle make a difference? ENDURING UNDERSTANDINGS Tangent lines intersect a circle at a single point.The angle measure of an angle that intersects a circle is related to the measure of the arc intersected.The power of a point depends on where the lines intersect in relationship to the circle.There is a relationship between central angles and arcs of a circleThere is relationship between a chord, its distance from the center of a circle, and the radius of the circle.

 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)Assessment- Explore parts of a circle and the relationships between intersecting lines and circles. 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 groupingsShortened assignments Assignment notebooksStudy sheets/summary sheets/outlines of most important factsSupplemental aids (vocabulary, summary cards, modern translation of original work, etc.)Visual demonstrationsPresentation of material in small stepsRead or paraphrase subject matterInstructions/directions given in different channels (written, spoken, demonstration)Visual or multisensory materialsFunctional level materialsMnemonic aids/devicesAdditional time for test preparationReview/testing matched to student paceTest directions read/explained thoroughlyOral, short-answer, modified testsEmphasis on successesGraphic OrganizersStudent choice of texts, projects, writing prompts, etc. Resources Provided:Textbook, Internet resources, graph paperG.SRT.B.5 Tangent Line to Two CirclesG.CO.A.3 Seven Circles II

 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: Transformations 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 identify rigid motions and images.Students will be able to describe transformations in the coordinate plane using function notation.  Students will be able to translate, reflect, rotate and dilate a figure using a variety of tools.Students will be able to identify line or rotational symmetry of a figure if it exists.  Students will be able to construct an equilateral triangle, square and regular hexagon using a variety of methods (compass & straightedge, string, and/or dynamic geometric software).Given congruent figures or similar figures, students will be able to find a sequence of transformations that moves one figure onto the other. LEARNING TARGETS ESSENTIAL QUESTIONSWhat types of transformations are rigid motions?How can you represent a transformation in the coordinate plane?How do recognize symmetry in a figure?What does it mean for two figures to be congruent? To be similar?Which sequence of transformations can map one figure onto the other? ENDURING UNDERSTANDINGS Rigid motions: translation, reflection, rotation and glide reflectionDilationsLine and rotational symmetryCompositions of TransformationsCongruence and Similarity Transformations

 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)Preformance Assessment- Identifying Symmetry with Transformations 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 groupingsShortened assignments Assignment notebooksStudy sheets/summary sheets/outlines of most important factsSupplemental aids (vocabulary, summary cards, modern translation of original work, etc.)Visual demonstrationsPresentation of material in small stepsRead or paraphrase subject matterInstructions/directions given in different channels (written, spoken, demonstration)Visual or multisensory materialsFunctional level materialsMnemonic aids/devicesAdditional time for test preparationReview/testing matched to student paceTest directions read/explained thoroughlyOral, short-answer, modified testsEmphasis on successesGraphic OrganizersStudent choice of texts, projects, writing prompts, etc. G.CO.A.3 Symmetries of rectanglesG.CO.A.4 Defining Rotations

 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: Quadrilaterals Timeframe: 12 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 find the measures of interior and exterior angles in polygonsStudents will be able to use the properties of quadrilaterals to find the measurements of angles and the lengths of sides.Students will be able to use the properties of quadrilaterals to write and solve algebraic equations.Students will be able to identify the members of the quadrilaterals family.Students will be able to construct quadrilaterals by applying sufficient conditions.Students will be able to construct arguments to write proofs involving quadrilaterals. LEARNING TARGETS ESSENTIAL QUESTIONSWhat are the similarities and differences between the different quadrilaterals?How do you graph a translation or reflection? ENDURING UNDERSTANDINGS Interior and Exterior Angles of PolygonsProperties of parallelograms, trapezoids, isosceles trapezoids, rectangles, kites, rhombi, and squaresApplying quadrilateral properties to coordinate proofsApplying quadrilateral properties to constructions

 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)Create the family tree of quadrilaterals.  Sufficient conditions and properties of the special triangles are explored and applied to problems.  Proofs involving quadrilaterals are also created. 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 groupingsShortened assignments Assignment notebooksStudy sheets/summary sheets/outlines of most important factsSupplemental aids (vocabulary, summary cards, modern translation of original work, etc.)Visual demonstrationsPresentation of material in small stepsRead or paraphrase subject matterInstructions/directions given in different channels (written, spoken, demonstration)Visual or multisensory materialsFunctional level materialsMnemonic aids/devicesAdditional time for test preparationReview/testing matched to student paceTest directions read/explained thoroughlyOral, short-answer, modified testsEmphasis on successesGraphic OrganizersStudent choice of texts, projects, writing prompts, etc. G.CO.C.11 Midpoints of the Sides of a ParallelogramG.CO.C.11 Is this a parallelogram?

 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.