COURSE OF STUDY UNIT PLANNING GUIDE

Transcription

1 COURSE OF STUDY UNIT PLANNING GUIDE FOR: GEOMETRY H 5 CREDITS GRADE LEVEL: 9 10 FULL-YEAR COURSE PREPARED BY: SUSAN EISEN GINA SULLIVAN CORINNE BRONDER SHANNON WARNOCK SUPERVISOR OF MATHEMATICS AND SCIENCE JULY 2018 BORN DATE: AUGUST 24, 2017 ALIGNED TO THE NJSLS AND B.O.E. ADOPTED AUGUST 23, 2018 DUMONT HIGH SCHOOL DUMONT, NEW JERSEY

2 Geometry Honors Grades 9-10 Full Year 5 Credits Geometry CP is offered to students who have successfully completed an Algebra 1 course. Topics covered include congruence, similarity, right triangles, trigonometry, circles, expressing geometric properties with equations, measurement, dimensions, and modeling. The deductive method of analysis and logical reasoning are used to solve problems, formulate proofs, and draw conclusions. COURSE REQUIREMENTS AND EXPECTATIONS A student will receive 5 credits for successfully completing course work. A grade of "D" or higher must be achieved in order to pass the course. The following criteria are used to determine the grade for the course: A B C D E Tests - 50% of the grade Tests will be given periodically. These may include alternative assessments that will count as tests. Quizzes - 35% of the grade Quizzes (announced and unannounced) based on class lessons or homework assignments will be given frequently to assess understanding of individual concepts. These may include alternative assessments that will count as quizzes. Homework - 10% of the grade Homework will be evaluated for completeness, neatness, and/or accuracy. Class Participation/Class Work - 5% of the grade Class Participation/Class Work will be evaluated a minimum of twice per marking period according to the departmental rubric (see page 3). The grade is based on the student's participation/work during class. Thus, consistent attendance is imperative. Final Examination Final examinations will count as follows: Full-Year Courses _ Weighting Semester Courses Weighting Quarter % of final grade Quarter 1 45% of final grade Quarter % of final grade Quarter 2 45% of final grade Quarter % of final grade Final Exam 10% of final grade Quarter % of final grade Final 10% of final grade Any work missed when the student has been absent is expected to be made up in a reasonable time. Usually one or two days are allowed for each day absent unless there are unusual circumstances, in which case the student is to request special arrangements with the teacher. Extra help is available. Ask your teacher where he/she will be when you are planning to come in for extra help.

3 High School Mathematics Participation Rubric Attendance Preparedness Oral Participation 1(60) Inadequate -Almost never with attendance policies and/or punctuality -Almost never makes up work in timely fashion -Almost never has pencil, books, calculators, and/or notebooks -Almost never has assignments on time -Almost never asks & answers questions without prompting 2(70) Limited -Rarely abides by attendance policies and/or punctuality -Rarely makes up work in timely fashion -Rarely has pencil, books, calculators, and/or notebooks -Rarely has assignments on time -Rarely asks & answers questions without prompting 3(80) Partial -Sometimes struggles with attendance policies and/or punctuality -Sometimes makes up work in timely fashion -Sometimes has pencil, books, calculators, and/or notebooks -Sometimes has assignments on time -Sometimes asks & answers questions without prompting 4(90) Adequate -Almost always punctual -Almost always makes up work in timely fashion -Not disruptive when tardy -Almost always has pencil, books, calculators, and/or notebooks -Almost always has assignments on time -Almost always asks & answers questions without prompting 5(100) Superior -Always punctual -Always makes up work in a timely fashion -Always has pencil, books, calculators, and/or notebooks -Always has assignments on time -Always asks & answers questions without prompting (daily) Written Participation Cooperative Learning -Almost never takes notes -Almost never makes corrections on homework/ class work and/or applies teacher recommendations to writing -Almost never provides meaningful input -Almost never focused on the assignment -Almost never assumes a leadership role -Rarely takes notes -Rarely makes corrections on homework/ class work and/or applies teacher recommendations to writing -Rarely provides meaningful input -Rarely focused on the assignment -Rarely assumes a leadership role -Sometimes takes notes -Sometimes makes corrections on homework/ class work and/or applies teacher recommendations to writing -Sometimes provides meaningful input -Sometimes focused on the assignment -Sometimes assumes a leadership role -Almost always takes notes -Almost always makes corrections on homework/ class work and applies teacher recommendations to writing -Almost always provides meaningful input -Almost always focused on the assignment -Almost always assumes a leadership role -Always takes notes -Always makes corrections on homework/ classwork and applies teacher recommendations to writing -Always provides meaningful input -Always focused on the assignment -Usually assumes a leadership role General Behavior -Almost never shows respect for peers and teacher -Almost never remains focused on assignments -Almost never abides by all class & school rules -ALMOST NEVER HAS CELL PHONE/IPOD -Rarely shows respect for peers and teacher -Rarely remains focused on assignments -Rarely abides by all class & school rules -Sometimes shows respect for peers and teacher -Sometimes remains focused on assignments -Sometimes abides by all class & school rules -Almost always shows respect for peers and teacher -Almost always remains focused on assignments -Almost always abides by all class & school rules -ALMOST NEVER HAS CELL -NEVER HAS CELL -NEVER HAS CELL PHONE/IPOD PHONE/IPOD PHONE/IPOD *Score of Zero Results from Limited or No Response to Class Participation/Class Work -Always shows respect for peers and teacher -Always remains focused on assignments -Always abides by all class & school rules -NEVER HAS CELL PHONE/IPOD

4 Number of Days 11 Unit 1: Basics of Geometry NJSLS-M A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. G-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G-CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. Standards for Mathematical Practices Science and Engineering Practices (SEP) NJSLS for ELA Companion Standards for Science: RST NJSLS for ELA Companion Standards for Science: WHST MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. SEP.1 Asking Questions and Defining Problems RST Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9-10 texts and topics. WHST Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. Career Ready CRP1. Act as a responsible and contributing citizen and employee.

5 Practices (CRPs) CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason. CRP5. Consider the environmental, social and economic impacts of decisions. CRP6. Demonstrate creativity and innovation. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP10. Plan education and career paths aligned to personal goals. CRP11. Use technology to enhance productivity. 21st Century: Personal Financial Literacy (9.1) 21st Century: Career Awareness, Exploration, and Preparation (9.2) Educational Technology (8.1) Technology Education, Engineering, Design, and Computational Thinking - Programming (8.2) Students will be able to... NA C.1 Review career goals and determine steps necessary for attainment A.3 Collaborate in online courses, learning communities, social networks or virtual worlds to discuss a resolution to a problem or issue. NA Find and describe patterns Understand and use the basic undefined terms and defined terms of geometry Sketch the intersections of lines and planes Use segment postulates Use the Distance Formula Use angle postulates Classify angles as acute, right, obtuse, or straight Bisect segments and angles Identify vertical angles, linear pairs, complementary, and supplementary pairs Find the perimeter, circumference, and area of common plane figures

6 Essential Questions What is the Pythagorean Theorem? What are points, lines, and planes? How do I determine segment and angle measures? What are the distance formula and midpoint formula and how can they be used? Activities Group Work (Challenge Problems) Patterns Sketching Points, Lines, and Planes Graphic Organizers on: Conjectures Counterexamples Segment and Angle Measures Segment and Angle Bisectors Angle Pair Relationships Distance Formula and Midpoint Formula Discovery Activities Distance Formula Midpoint Formula Constructions Angle Bisector Segment Bisector Copying a Segment and/or Angle Project Line Design Resources McDougal Littell Geometry Warm-Up/Daily Homework Quiz Worksheets Practice A-C Worksheets Kutasoftware.com Pearsonsuccessnet.com Khanacademy.com Vocabulary Conjecture Inductive Reasoning Counterexample

7 Definition/Undefined Point/Line/Plane Collinear Coplanar Line Segment Endpoints Ray Initial Point Opposite Rays Intersect/Intersection Postulates/Axioms Theorem Distance/Length Congruent Segments Angle Vertex of an Angle Congruent Angles Measure of an Angle Interior/Exterior of an Angle Acute/Obtuse Angle Right/Straight Angle Adjacent Angles Midpoint Bisect Segment Bisector Compass/Straightedge Construct/Construction Angle Bisector Vertical Angles Linear Pair Complementary Angles Supplementary Angles Technology/GAFE PARCC Practice on the basics of geometry SMART Board on the basics of geometry Graphing Calculator on the basics of geometry Other Graphing technologies on the basics of geometry

8 ipads on the basics of geometry SMART Response Technology on the basics of geometry Quizlet on the basics of geometry Socrative on the basics of geometry Kahoot on the basics of geometry Flubaroo on the basics of geometry Google Drive on the basics of geometry Study Island on the basics of geometry Special Education/504 Providing Notes/Modified Notes on the basics of geometry PowerPoints SMART Board Notes Guided Notes on the basics of geometry Highlighting Underlining Providing Definitions Modeling on the basics of geometry Chunking on the basics of geometry Scaffolding on the basics of geometry Repeat/Rephrase on the basics of geometry Manipulatives/Visuals on the basics of geometry Graphic Organizers on the basics of geometry Study Guides on the basics of geometry Portfolios on the basics of geometry Modified Texts on the basics of geometry Conferencing on the basics of geometry Student Parent Guidance Administration CST Tutoring/Extra Help on the basics of geometry ELL (SEI) Bilingual Math Dictionaries on the basics of geometry Total Physical Response on the basics of geometry Native/Non-Native Speaker Groupings on the basics of geometry Providing Notes/Modified Notes on the basics of geometry

9 PowerPoints SMART Board Notes Include native language in guided notes Guided Notes on the basics of geometry Highlighting Underlining Providing Definitions in English and native language Modeling on the basics of geometry Chunking on the basics of geometry Scaffolding on the basics of geometry Repeat/Rephrase on the basics of geometry Manipulatives/Visuals on the basics of geometry Graphic Organizers on the basics of geometry Study Guides on the basics of geometry Portfolios on the basics of geometry Modified Texts on the basics of geometry Conferencing on the basics of geometry Student Parent Guidance Administration CST Tutoring/Extra Help on the basics of geometry At Risk of School Failure Providing Notes/Modified Notes on the basics of geometry PowerPoints SMART Board Notes Guided Reading on the basics of geometry Highlighting Underlining Providing Definitions Modeling on the basics of geometry Chunking on the basics of geometry Scaffolding on the basics of geometry Repeat/Rephrase on the basics of geometry Manipulatives/Visuals on the basics of geometry Study Guides on the basics of geometry

10 Portfolios on the basics of geometry Modified Texts on the basics of geometry Priority Seating on the basics of geometry Checking Assignments Pads on the basics of geometry Conferencing on the basics of geometry Student Parent Guidance Administration CST Tutoring/Extra Help on the basics of geometry Gifted & Talented Self-Directed Learning on the basics of geometry Independent Research on the basics of geometry Individualized Pacing on the basics of geometry Supplemental Challenge Problems on the basics of geometry Virtual High School on the basics of geometry Formative, Summative, Benchmark, and Alternative Assessments Benchmark Algebra 1 Competency Assessment Study Island Geometry Benchmark #1 Formative Ask and answer questions on the basics of geometry Post-lesson exit slips on the basics of geometry Homework on the basics of geometry Summative Quiz on patterns, segments and their measures, and distance formula Test on the basics of geometry Alternative Assessments Line Design Project

11 Number of Days 10 Unit 2: Reasoning and Proof NJSLS-M A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. G-CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment s endpoints. Standards for Mathematical Practices Science and Engineering Practices (SEP) NJSLS for ELA Companion Standards for Science: RST NJSLS for ELA Companion Standards for Science: WHST Career Ready Practices (CRPs) MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. SEP.1 Asking Questions and Defining Problems RST Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text. RST Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9-10 texts and topics. WHST Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. CRP1. Act as a responsible and contributing citizen and employee. CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason. CRP5. Consider the environmental, social and economic impacts of decisions.

12 CRP6. Demonstrate creativity and innovation. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP10. Plan education and career paths aligned to personal goals. CRP11. Use technology to enhance productivity. 21st Century: Personal Financial Literacy (9.1) 21st Century: Career Awareness, Exploration, and Preparation (9.2) Educational Technology (8.1) Technology Education, Engineering, Design, and Computational Thinking - Programming (8.2) Students will be able to... NA C.1 Review career goals and determine steps necessary for attainment A.3 Collaborate in online courses, learning communities, social networks or virtual worlds to discuss a resolution to a problem or issue. NA Recognize and analyze a conditional statement Recognize and use definitions and biconditional statements Use symbolic notation to represent logical statements Form conclusions by applying the laws of logic to true statements Use properties from algebra Use properties of length and measure to justify segment and angle relationships Justify statements about congruent segments Write reasons for steps in a proof Use angle congruence properties Prove properties about special pairs of angles Essential Questions How do I use logic to reason through problems and puzzles?

13 How can I use algebraic and geometric properties, theorems, and postulates to prove properties of segments and angles? Activities Graphic Organizers Reasoning with properties of algebra Reasoning with properties and theorems about segments Reasoning with properties and theorems about angles Introductory Activity for Proofs Resources McDougal Littell Geometry Warm-Up/Daily Homework Quiz Worksheets Practice A-C Worksheets Kutasoftware.com pearsonsuccessnet.com standardsolutions.com Vocabulary If-Then Form Hypothesis Conclusion Converse Equivalent Statement Perpendicular Lines Logical Argument Two-Column Proof Paragraph Proof Technology/GAFE PARCC Practice on reasoning and proof SMART Board on reasoning and proof Graphing Calculator on reasoning and proof Other Graphing technologies on reasoning and proof ipads on reasoning and proof SMART Response Technology on reasoning and proof Quizlet on reasoning and proof Socrative on reasoning and proof Kahoot on reasoning and proof Flubaroo on reasoning and proof Google Drive on reasoning and proof

14 Study Island on reasoning and proof Special Education/504 Providing Notes/Modified Notes on reasoning and proof PowerPoints SMART Board Notes Guided Notes on reasoning and proof Highlighting Underlining Providing Definitions Modeling on reasoning and proof Chunking on reasoning and proof Scaffolding on reasoning and proof Repeat/Rephrase on reasoning and proof Manipulatives/Visuals on reasoning and proof Graphic Organizers on reasoning and proof Study Guides on reasoning and proof Portfolios on reasoning and proof Modified Texts on reasoning and proof Conferencing on reasoning and proof Student Parent Guidance Administration CST Tutoring/Extra Help on reasoning and proof ELL (SEI) Bilingual Math Dictionaries on reasoning and proof Total Physical Response on reasoning and proof Native/Non-Native Speaker Groupings on reasoning and proof Providing Notes/Modified Notes on reasoning and proof PowerPoints SMART Board Notes Include native language in guided notes Guided Notes on reasoning and proof Highlighting Underlining Providing Definitions in English and native language

15 Modeling on reasoning and proof Chunking on reasoning and proof Scaffolding on reasoning and proof Repeat/Rephrase on reasoning and proof Manipulatives/Visuals on reasoning and proof Graphic Organizers on reasoning and proof Study Guides on reasoning and proof Portfolios on reasoning and proof Modified Texts on reasoning and proof Conferencing on reasoning and proof Student Parent Guidance Administration CST Tutoring/Extra Help on reasoning and proof At Risk of School Failure Providing Notes/Modified Notes on reasoning and proof PowerPoints SMART Board Notes Guided Reading on reasoning and proof Highlighting Underlining Providing Definitions Modeling on reasoning and proof Chunking on reasoning and proof Scaffolding on reasoning and proof Repeat/Rephrase on reasoning and proof Manipulatives/Visuals on reasoning and proof Study Guides on reasoning and proof Portfolios on reasoning and proof Modified Texts on reasoning and proof Priority Seating on reasoning and proof Checking Assignments Pads on reasoning and proof Conferencing on reasoning and proof Student Parent

16 Guidance Administration CST Tutoring/Extra Help on reasoning and proof Gifted & Talented Self-Directed Learning on reasoning and proof Independent Research on reasoning and proof Individualized Pacing on reasoning and proof Supplemental Challenge Problems on reasoning and proof Virtual High School on reasoning and proof Formative, Summative, Benchmark, and Alternative Assessments Formative Ask and answer questions on reasoning and proof Post-lesson exit slips on reasoning and proof Homework on reasoning and proof Summative Quiz on reasoning with algebra, segment addition postulate, and angle addition postulate Test on reasoning and proof

17 Number of Days 12 Unit 3: Parallel and Perpendicular Lines NJSLS-M A -CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A -REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. G-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G-CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment s endpoints. G-CO.C.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. G-GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Standards for Mathematical Practices Science and Engineering Practices (SEP) NJSLS for ELA Companion Standards for Science: RST MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. SEP.1 Asking Questions and Defining Problems RST Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9-10 texts and topics.

18 NJSLS for ELA Companion Standards for Science: WHST Career Ready Practices (CRPs) 21st Century: Personal Financial Literacy (9.1) 21st Century: Career Awareness, Exploration, and Preparation (9.2) Educational Technology (8.1) Technology Education, Engineering, Design, and Computational Thinking - Programming (8.2) Students will be able to... WHST Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. CRP1. Act as a responsible and contributing citizen and employee. CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason. CRP5. Consider the environmental, social and economic impacts of decisions. CRP6. Demonstrate creativity and innovation. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP10. Plan education and career paths aligned to personal goals. CRP11. Use technology to enhance productivity. NA C.1 Review career goals and determine steps necessary for attainment A.3 Collaborate in online courses, learning communities, social networks or virtual worlds to discuss a resolution to a problem or issue. NA Identify relationships between lines Identify angles formed by transversals Prove that lines are parallel

19 Use properties of parallel lines Write equations of parallel and perpendicular lines Essential Questions What are relationships between lines? What angles are formed by transversals? What are properties of parallel and perpendicular lines? Activities Group Work (Challenge Problems) Lines and Angles - Map Reading Activity Parallel Lines and Transversals Graphic Organizers Proving Lines are Parallel Using Properties of Parallel Lines Using Properties of Perpendicular Lines Constructions Parallel Line Through a Point Perpendicular Line Through a Point Perpendicular Bisector Resources McDougal Littell Geometry Warm-Up/Daily Homework Quiz Worksheets Practice A-C Worksheets Parallel and Perpendicular lines Activity Kutasoftware.com pearsonsuccessnet.com standardsolutions.com Vocabulary Parallel Lines Skew Lines Parallel Planes Transversal Corresponding Angles Alternate Interior Angles Alternate Exterior Angles Consecutive Interior Angles Same Side Interior Angles Flow Proof

20 Technology/GAFE PARCC Practice on parallel and perpendicular lines SMART Board on parallel and perpendicular lines Graphing Calculator on parallel and perpendicular lines Other Graphing technologies on parallel and perpendicular lines ipads on parallel and perpendicular lines SMART Response Technology on parallel and perpendicular lines Quizlet on parallel and perpendicular lines Socrative on parallel and perpendicular lines Kahoot on parallel and perpendicular lines Flubaroo on parallel and perpendicular lines Google Drive on parallel and perpendicular lines Study Island on parallel and perpendicular lines Special Education/504 Providing Notes/Modified Notes on parallel and perpendicular lines PowerPoints SMART Board Notes Guided Notes on parallel and perpendicular lines Highlighting Underlining Providing Definitions Modeling on parallel and perpendicular lines Chunking on parallel and perpendicular lines Scaffolding on parallel and perpendicular lines Repeat/Rephrase on parallel and perpendicular lines Manipulatives/Visuals on parallel and perpendicular lines Graphic Organizers on parallel and perpendicular lines Study Guides on parallel and perpendicular lines Portfolios on parallel and perpendicular lines Modified Texts on parallel and perpendicular lines Conferencing on parallel and perpendicular lines Student Parent Guidance Administration CST Tutoring/Extra Help on parallel and perpendicular lines

21 ELL (SEI) Bilingual Math Dictionaries on parallel and perpendicular lines Total Physical Response on parallel and perpendicular lines Native/Non-Native Speaker Groupings on parallel and perpendicular lines Providing Notes/Modified Notes on parallel and perpendicular lines PowerPoints SMART Board Notes Include native language in guided notes Guided Notes on parallel and perpendicular lines Highlighting Underlining Providing Definitions in English and native language Modeling on parallel and perpendicular lines Chunking on parallel and perpendicular lines Scaffolding on parallel and perpendicular lines Repeat/Rephrase on parallel and perpendicular lines Manipulatives/Visuals on parallel and perpendicular lines Graphic Organizers on parallel and perpendicular lines Study Guides on parallel and perpendicular lines Portfolios on parallel and perpendicular lines Modified Texts on parallel and perpendicular lines Conferencing on parallel and perpendicular lines Student Parent Guidance Administration CST Tutoring/Extra Help on parallel and perpendicular lines At Risk of School Failure Providing Notes/Modified Notes on parallel and perpendicular lines PowerPoints SMART Board Notes Guided Reading on parallel and perpendicular lines Highlighting Underlining Providing Definitions Modeling on parallel and perpendicular lines Chunking on parallel and perpendicular lines

22 Scaffolding on parallel and perpendicular lines Repeat/Rephrase on parallel and perpendicular lines Manipulatives/Visuals on parallel and perpendicular lines Study Guides on parallel and perpendicular lines Portfolios on parallel and perpendicular lines Modified Texts on parallel and perpendicular lines Priority Seating on parallel and perpendicular lines Checking Assignments Pads on parallel and perpendicular lines Conferencing on parallel and perpendicular lines Student Parent Guidance Administration CST Tutoring/Extra Help on parallel and perpendicular lines Gifted & Talented Self-Directed Learning on parallel and perpendicular lines Independent Research on parallel and perpendicular lines Individualized Pacing on parallel and perpendicular lines Supplemental Challenge Problems on parallel and perpendicular lines Formative, Summative, Benchmark, and Alternative Assessments Formative Ask and answer questions on parallel and perpendicular lines Post-lesson exit slips on parallel and perpendicular lines Homework on parallel and perpendicular lines Summative Quiz on lines, angles, parallel lines and transversals, properties of parallel lines, proving lines are parallel Test on parallel and perpendicular lines

23 Number of Days 10 Unit 4: Transformations NJSLS-M G.CO. A.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). G.CO.A.3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. G.CO.A. 4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G.CO.A.5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. G.CO.B.6. 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. G.CO.B.7. 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. Standards for Mathematical Practices Science and Engineering Practices (SEP) NJSLS for ELA Companion Standards for Science: RST MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. SEP.1 Asking Questions and Defining Problems RST Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9-10 texts and topics.

24 NJSLS for ELA Companion Standards for Science: WHST Career Ready Practices (CRPs) 21st Century: Personal Financial Literacy (9.1) 21st Century: Career Awareness, Exploration, and Preparation (9.2) Educational Technology (8.1) Technology Education, Engineering, Design, and Computational Thinking - Programming (8.2) Students will be able to... WHST Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. CRP1. Act as a responsible and contributing citizen and employee. CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason. CRP5. Consider the environmental, social and economic impacts of decisions. CRP6. Demonstrate creativity and innovation. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP10. Plan education and career paths aligned to personal goals. CRP11. Use technology to enhance productivity. NA C.1 Review career goals and determine steps necessary for attainment A.3 Collaborate in online courses, learning communities, social networks or virtual worlds to discuss a resolution to a problem or issue. NA Identify and name the different types of transformations Perform reflections in a line Perform rotations about a point

25 Identify line and rotational symmetry of shapes Perform translations on a coordinate grid Use words, vectors, component form, and coordinate notation to describe translations Perform glide reflections and compositions of transformations Describe transformations that occurred based on a diagram Essential Questions What are types of transformations? How do I perform reflections and determine line symmetry? How do I perform rotations and determine rotational symmetry? How do I perform and describe translations? Activities Discovery Activities Reflections Rotations Graphic Organizers Rigid Motion in a Plane Translations Glide Reflections and Compositions SmartBoard Activities Line Symmetry Rotational Symmetry Resources McDougal Littell Geometry Warm-Up/Daily Homework Quiz Worksheets Practice A-C Worksheets Kutasoftware.com pearsonsuccessnet.com standardsolutions.com Vocabulary Image/Preimage Transformation Isometry Reflection Line of Reflection Line of Symmetry Rotation Center of Rotation

26 Angle of Rotation Rotational Symmetry Translation Vector Initial Point Terminal Point Coordinate Notation Component Form Glide Reflection Composition Technology/GAFE PARCC Practice on transformations SMART Board on transformations Graphing Calculator on transformations Other Graphing technologies on transformations ipads on transformations SMART Response Technology on transformations Quizlet on transformations Socrative on transformations Kahoot on transformations Flubaroo on transformations Google Drive on transformations Study Island on transformations Special Education/504 Providing Notes/Modified Notes on transformations PowerPoints SMART Board Notes Guided Notes on transformations Highlighting Underlining Providing Definitions Modeling on transformations Chunking on transformations Scaffolding on transformations Repeat/Rephrase on transformations Manipulatives/Visuals on transformations Graphic Organizers on transformations

27 Study Guides on transformations Portfolios on transformations Modified Texts on transformations Conferencing on transformations Student Parent Guidance Administration CST Tutoring/Extra Help on transformations ELL (SEI) Bilingual Math Dictionaries on transformations Total Physical Response on transformations Native/Non-Native Speaker Groupings on transformations Providing Notes/Modified Notes on transformations PowerPoints SMART Board Notes Include native language in guided notes Guided Notes on transformations Highlighting Underlining Providing Definitions in English and native language Modeling on transformations Chunking on transformations Scaffolding on transformations Repeat/Rephrase on transformations Manipulatives/Visuals on transformations Graphic Organizers on transformations Study Guides on transformations Portfolios on transformations Modified Texts on transformations Conferencing on transformations Student Parent Guidance Administration CST

28 Tutoring/Extra Help on transformations At Risk of School Failure Providing Notes/Modified Notes on transformations PowerPoints SMART Board Notes Guided Reading on transformations Highlighting Underlining Providing Definitions Modeling on transformations Chunking on transformations Scaffolding on transformations Repeat/Rephrase on transformations Manipulatives/Visuals on transformations Study Guides on transformations Portfolios on transformations Modified Texts on transformations Priority Seating on transformations Checking Assignments Pads on transformations Conferencing on transformations Student Parent Guidance Administration CST Tutoring/Extra Help on transformations Gifted & Talented Self-Directed Learning on transformations Independent Research on transformations Individualized Pacing on transformations Supplemental Challenge Problems on transformations Formative, Summative, Benchmark, and Alternative Assessments Formative Ask and answer questions on transformations Post-lesson exit slips on transformations Homework on transformations Summative

29 Quiz on types of transformations, reflections, rotations, symmetry Test on transformations Alternative Assessment Signature Reflection Project Tessellation Project

30 Number of Days 14 Unit 5: Triangles NJSLS-M A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. G.CO.A.2. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). G.CO.B.7. 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. G.CO.B.8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Standards for Mathematical Practices Science and Engineering Practices (SEP) NJSLS for ELA Companion Standards for Science: RST NJSLS for ELA Companion Standards for Science: WHST MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. SEP.1 Asking Questions and Defining Problems RST Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9-10 texts and topics. WHST Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

31 Career Ready Practices (CRPs) 21st Century: Personal Financial Literacy (9.1) 21st Century: Career Awareness, Exploration, and Preparation (9.2) Educational Technology (8.1) CRP1. Act as a responsible and contributing citizen and employee. CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason. CRP5. Consider the environmental, social and economic impacts of decisions. CRP6. Demonstrate creativity and innovation. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP10. Plan education and career paths aligned to personal goals. CRP11. Use technology to enhance productivity. NA C.1 Review career goals and determine steps necessary for attainment A.3 Collaborate in online courses, learning communities, social networks or virtual worlds to discuss a resolution to a problem or issue. Technology Education, Engineering, Design, and Computational Thinking - Programming (8.2) Students will be able to D.1 Design and create a prototype to solve a real world problem using a design process, identify constraints addressed during the creation of the prototype, identify trade-offs made, and present the solution for peer review. Classify triangles by their sides and angles Find angle measurements in triangles Find angle and side measurements in congruent figures Prove that triangles are congruent using SSS, SAS, ASA, and AAS Use congruent triangles to write proofs Use congruent triangles to prove constructions are valid (if time) Use properties of isosceles and equilateral triangles Use properties of right triangles

32 Identify and use properties of perpendicular bisectors and angle bisectors of segments Identify and use properties of perpendicular bisectors, angle bisectors, medians, and altitudes of triangles Identify and use properties of midsegments of a triangle Use triangle measurements to decide which side is longest/shortest, and which angle is largest/smallest Use the Triangle Inequality Theorem Read and write indirect proofs Essential Questions How do I classify triangles? What is the sum of the interior angles of a triangle? What are methods used to prove that triangles are congruent? What are specific characteristics of isosceles and right triangles? What are the properties of perpendicular bisectors and angle bisectors of segments? What are the properties of perpendicular bisectors, angle bisectors, medians, and altitudes of triangles? What are the properties of midsegments of a triangle? How are the angles and sides of triangles related? What is the Triangle Inequality Theorem? What is an indirect proof? Activities Graphic Organizers: Types of Triangles Using Congruent Triangles Isosceles, Equilateral, and Right Triangles Midsegment Theorem Inequalities in One Triangle (Hinge Theorem) Discovery Activity Methods for Proving Triangles Congruent Triangle Inequality Theorem Challenge Problems (Group Work) Isosceles, Equilateral, and Right Triangles Projects Popsicle Stick Bridge Resources McDougal Littell Geometry Warm-Up/Daily Homework Quiz Worksheets Practice A-C Worksheets Constructions Kutasoftware.com

33 pearsonsuccessnet.com standardsolutions.com Vocabulary Equilateral Triangle Isosceles Triangle Scalene Triangle Acute Triangle Equiangular Triangle Right Triangle Obtuse Triangle Vertex of a Triangle Adjacent Sides of a Triangle Legs of a Right Triangle Hypotenuse Legs of an Isosceles Triangle Base of an Isosceles Triangle Interior Angle Exterior Angle Congruent Figures Congruent Triangles Corresponding Angles Corresponding Sides Base Angles Vertex Angle Perpendicular Bisector Equidistant Altitude of a Triangle Midsegment of a Triangle Technology/GAFE PARCC Practice on triangles SMART Board on triangles Graphing Calculator on triangles Other Graphing technologies on triangles ipads on triangles SMART Response Technology on triangles Quizlet on triangles Socrative on triangles

34 Kahoot on triangles Flubaroo on triangles Google Drive on triangles Study Island on triangles Special Education/504 Providing Notes/Modified Notes on triangles PowerPoints SMART Board Notes Guided Notes on triangles Highlighting Underlining Providing Definitions Modeling on triangles Chunking on triangles Scaffolding on triangles Repeat/Rephrase on triangles Manipulatives/Visuals on triangles Graphic Organizers on triangles Study Guides on triangles Portfolios on triangles Modified Texts on triangles Conferencing on triangles Student Parent Guidance Administration CST Tutoring/Extra Help on triangles ELL (SEI) Bilingual Math Dictionaries on triangles Total Physical Response on triangles Native/Non-Native Speaker Groupings on triangles Providing Notes/Modified Notes on triangles PowerPoints SMART Board Notes Include native language in guided notes Guided Notes on triangles

35 Highlighting Underlining Providing Definitions in English and native language Modeling on triangles Chunking on triangles Scaffolding on triangles Repeat/Rephrase on triangles Manipulatives/Visuals on triangles Graphic Organizers on triangles Study Guides on triangles Portfolios on triangles Modified Texts on triangles Conferencing on triangles Student Parent Guidance Administration CST Tutoring/Extra Help on triangles At Risk of School Failure Providing Notes/Modified Notes on triangles PowerPoints SMART Board Notes Guided Reading on triangles Highlighting Underlining Providing Definitions Modeling on triangles Chunking on triangles Scaffolding on triangles Repeat/Rephrase on triangles Manipulatives/Visuals on triangles Study Guides on triangles Portfolios on triangles Modified Texts on triangles Priority Seating on triangles Checking Assignments Pads on triangles

36 Conferencing on triangles Student Parent Guidance Administration CST Tutoring/Extra Help on triangles Gifted & Talented Self-Directed Learning on triangles Independent Research on triangles Individualized Pacing on triangles Supplemental Challenge Problems on triangles Formative, Summative, Benchmark, and Alternative Assessments Formative Ask and answer questions on triangles Post-lesson exit slips on triangles Homework on triangles Summative Quiz on types of triangles, properties of triangles, congruent figures Quiz on proving triangles are congruent and using congruent triangles Test on triangles Alternative Assessments Popsicle Stick Bridge Project

37 Number of Days 11 Unit 6: Polygons NJSLS-M A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. G-CO.C.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. G-GPE.B.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the origin and containing the point (0, 2). G-GPE.B.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. Standards for Mathematical Practices Science and Engineering Practices (SEP) NJSLS for ELA Companion Standards for Science: RST NJSLS for ELA Companion Standards for MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. SEP.1 Asking Questions and Defining Problems RST Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9-10 texts and topics. WHST Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

38 Science: WHST Career Ready Practices (CRPs) 21st Century: Personal Financial Literacy (9.1) 21st Century: Career Awareness, Exploration, and Preparation (9.2) Educational Technology (8.1) Technology Education, Engineering, Design, and Computational Thinking - Programming (8.2) Students will be able to... CRP1. Act as a responsible and contributing citizen and employee. CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason. CRP5. Consider the environmental, social and economic impacts of decisions. CRP6. Demonstrate creativity and innovation. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP10. Plan education and career paths aligned to personal goals. CRP11. Use technology to enhance productivity. NA C.1 Review career goals and determine steps necessary for attainment A.3 Collaborate in online courses, learning communities, social networks or virtual worlds to discuss a resolution to a problem or issue. NA Identify and classify polygons Use properties of parallelograms Prove that a quadrilateral is a parallelogram Use properties of quadrilaterals including rhombi, rectangles, squares, trapezoids, and kites Find the area of triangles and quadrilaterals

39 Essential Questions What are polygons and how do I classify them? What are properties of parallelograms? How do I prove a quadrilateral is a parallelogram? How are various quadrilaterals related? How do I find the area of triangles and quadrilaterals? Activities Graphic Organizers: Types of Polygons Properties of Parallelograms Proving Quadrilaterals are Parallelograms Family Tree of Quadrilaterals Parallelograms (Rectangles, Rhombi, Squares) Trapezoids (Isosceles Trapezoids) Kites Properties of Quadrilaterals Coordinate Proofs Discovery Activities Sum of Interior Angles of Polygons Sum of Exterior Angles of Polygons Challenge Problems (Group Work) Areas of Composite Figures Projects Storage Space Facility Blueprint Resources McDougal Littell Geometry Warm-Up/Daily Homework Quiz Worksheets Practice A-C Worksheets Kutasoftware.com pearsonsuccessnet.com standardsolutions.com Vocabulary Polygon Sides of a Polygon Vertex/Vertices Convex Concave/Nonconvex Equilateral Polygon