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

 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.

 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.

 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

 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.

 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