Hughesville Junior/Senior High School



Danville Area School District

Course Overview

2017-2018

|Course: 8th Grade Geometry Teachers: Leslie / Michaels |

|Course Introduction: |Course Text or Student Materials: |

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|Course topics focus on the Pennsylvania state Keystone anchors and include, but are not limited to, |Geometry by Glencoe |

|angles and segments, an in-depth study of two-column proofs, parallel lines, triangles and their | |

|congruency and similarity, parallelograms and other polygons, circles, area and volume, | |

|transformations, and the application of basic trigonometric functions. Students will be required to | |

|complete honors level work at a pace designed to prepare them for additional honors caliber and | |

|advanced placement coursework. Enrichment will occur through in-depth analysis of all topics as well | |

|as acceleration towards trigonometric skills. | |

| | |

|Prerequisites: Successful completion of Keystone Algebra in 7th grade. Students must be proficient | |

|or advances on the Keystone Exam to move onto Geometry in 8th grade. | |

|Units of Study: |Student Objectives: |Standards/Anchors: |

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|1. Tools of Geometry |1. Tools of Geometry |G.1.1.1.1 Identify, determine, and/or use the radius, diameter, |

|Patterns and Inductive Reasoning |Use inductive reasoning to make conjectures |segment, and/or tangent of a circle. |

|Points, Lines and Planes |Know basic terms of geometry |G.1.1.1.2 Identify, determine, and/or use the arcs, semicircles, |

|Segments, Rays, Parallel Lines and Planes |Know, understand, and apply postulates of geometry |sectors, and/or angles of a circle. |

|Measuring Segments and Angles |Identify segments and rays |G.1.1.1.3 Use chords, tangents, and secants to find missing arc |

|The Coordinate Plane |Identify parallel lines and planes |measures or missing segment measures. |

| |Know and apply the ruler postulate and protractor postulate |G.1.1.1.4 Identify and/or use the properties of a sphere or cylinder. |

|2. Reasoning and Proofs |Know and apply the segment addition postulate and angle addition | |

|Reasoning in Algebra |postulate |G.1.2.1.1 Identify and/or use properties of triangles. |

|Proving Angles Congruent |Define perpendicular lines, perpendicular bisector and angle bisector | |

| |Know and apply the distance formula and midpoint formula |G.1.2.1.2 Identify and/or use properties of quadrilaterals |

|3. Parallel/Perpendicular Lines and Polygon Angles | | |

|Properties of Parallel Lines |2. Reasoning and Proofs |G.1.2.1.3 Identify and/or use properties of isosceles and equilateral |

|Proving Lines Parallel |Apply the properties of equality and congruence to prove statements |triangles. |

|Parallel Lines and the Triangle Angle-Sum Theorem |Identify angle pairs | |

|The Polygon Angle-Sum Theorem |Prove and apply theorems about angles |G.1.2.1.4 Identify and/or use properties of regular polygons. |

|Lines in the Coordinate Plane | | |

|Slopes of Parallel and Perpendicular Lines |3. Lines and Planes |G.1.2.1.5 Identify and/or use properties of pyramids and prisms. |

| |Identify angles formed by two lines and a transversal |G.1.3.1.1 Identify and/or use properties of congruent and similar |

|4. Congruent Triangles |Prove and use properties of parallel lines |polygons or solids. |

|Congruent Figures |Use a transversal in proving lines parallel |G.1.3.1.2 Identify and/or use proportional relationships in similar |

|Triangle Congruence by SSS and SAS |Relate and use properties of parallel and perpendicular lines |figures. |

|Triangle Congruence by ASA and AAS |Classify triangles and find the measures of their angles |G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., |

|Using Congruent Triangles: CPCTC |Apply the triangle angle-sum theorem |direct and/or indirect proofs/proofs by contradiction). |

|Isosceles and Equilateral Triangles |Use exterior angles of a triangle | |

|Congruence in Right Triangles |Apply the triangle exterior angle theorem |G.2.1.1.1 Use the Pythagorean theorem to write and/or solve problems |

|Using Corresponding Parts of Congruent Triangles |Classify polygons |involving right triangles. |

| |Find the measures of the interior and exterior angles of a polygon |G.2.1.1.2 Use trigonometric ratios to write and/or solve problems |

|5. Relationships Within Triangles |Recognize the equation for a line in slope-intercept form, standard |involving right triangles. |

|Midsegments of Triangles |form and point-slope form | |

|Bisectors in Triangles |Graph lines in slope-intercept form and point-slope form |G.2.1.2.1 Calculate the distance and/or midpoint between two points on |

|Concurrent Lines, Medians, and Altitudes |Graph lines in standard form by graphing the intercepts |a number line or on a coordinate plane. |

|Inequalities in Triangles |Write and transform lines to various forms | |

| |Identify the slopes of parallel and perpendicular lines |G.2.1.2.2 Relate slope to perpendicularity and/or parallelism (limit to|

|6. Quadrilaterals |Write the equations of lines parallel or perpendicular to a given line |linear algebraic equations). |

|Classify Quadrilaterals |through a given point | |

|Properties of Parallelograms | |G.2.1.2.3 Use slope, distance, and/or midpoint between two points on a |

|Proving that a Quadrilateral is a Parallelogram |4. Congruent Triangles |coordinate plane to establish properties of a 2-dimensional shape. |

|Special Parallelograms |Recognize congruent figures and their corresponding parts | |

|Trapezoids and Kites |Prove two triangles congruent by using SSS and SAS postulates |G.2.1.3.1 Apply the concept of the slope of a line to solve problems. |

|Placing Figures in the Coordinate Plane |Prove two triangles congruent by using ASA and AAS postulates | |

| |Use triangle congruence and CPCTC to prove that parts of two triangles |G.2.1.4.1 Solve or graph systems of equations or systems of |

|7. Area |are congruent |inequalities within a problem situation using coordinate geometry. |

|Areas of Parallelograms and Triangles |Apply properties of isosceles triangles | |

|The Pythagorean Theorem and Its Converse |Prove two right triangles congruent by HL |G.2.2.1.1 Use properties of angles formed by intersecting lines to find|

|Special Right Triangles |Identify congruent overlapping triangles |the measures of missing angles. |

|Area of Trapezoids, Rhombuses, and Kites |Prove two triangles are congruent by first proving two other triangles | |

|Areas of Regular Polygons |congruent, CPCTC |G.2.2.1.2 Use properties of angles formed when two parallel lines are |

|Circles and Arcs | |cut by a transversal to find the measures of missing angles. |

|Areas of Circles and Sectors |5. Relationships Within Triangles | |

|Geometric Probability |Identify and apply the midsegment of a triangle to solve problems |G.2.2.2.1 Estimate area, perimeter, or circumference of an irregular |

| |Apply properties of perpendicular bisectors and angle bisectors |figure. |

|8. Similarity |Identify and apply properties of perpendicular bisectors and angle | |

|Ratios and Proportions |bisectors |G.2.2.2.2 Find the measurement of a missing length, given the |

|Similar Polygons |Identify and apply properties of medians and altitudes of triangles |perimeter, circumference, or area. |

|Proving Triangles Similar |Apply properties of inequalities involving angles of triangles | |

|Similarity in Right Triangles |Apply properties of inequalities involving sides of triangles |G.2.2.2.3 Find the side lengths of a polygon with a given perimeter to |

|Proportions in Triangles | |maximize the area of the polygon. |

|Perimeters and Areas of Similar Figures |6. Quadrilaterals | |

| |Define and classify special types of quadrilaterals |G.2.2.2.4 Develop and/or use strategies to estimate the area of a |

|9. Right Triangle Trigonometry |Use relationships between angles and sides of parallelograms |compound/composite figure. |

|The Tangent Ratio |Use relationships involving diagonals of parallelograms or transversals| |

|Sine and Cosine Ratios |Determine whether a quadrilateral is a parallelogram |G.2.2.2.5 Find the area of a sector of a circle. |

|Angles of Elevation and Depression |Use properties of diagonals of rhombuses and rectangles | |

|Vectors |Determine whether a parallelogram is a rhombus or a rectangle |G.2.2.3.1 Describe how a change in the linear dimension of a figure |

| |Verify and use properties of trapezoids and kites |affects its perimeter, circumference, and area (e.g., How does changing|

|10. Area, Surface Area, and Volume |Name coordinates of special figures by using their properties |the length of the radius of a circle affect the circumference of the |

|Surface Areas of Prisms and Cylinders |Define and know the midsegment theorem of a trapezoid |circle?). |

|Surface Areas of Pyramids and Cones | | |

|Volumes of Prisms and Cylinders |7. Area |G.2.2.4.1 Use area models to find probabilities. |

|Volumes of Pyramids and Cones |Find the area of a parallelogram and triangle | |

|Surface Areas and Volumes of Spheres |Find the area of a composite figure comprised of parallelograms and |G.2.3.1.1 Calculate the surface area of prisms, cylinders, cones, |

|Areas and Volumes of Similar Solids |triangles |pyramids, and/or spheres. Formulas are provided on a reference sheet. |

| |Know and apply the Pythagorean Theorem to find the missing side of a | |

|11. Circles |right triangle |G.2.3.1.2 Calculate the volume of prisms, cylinders, cones, pyramids, |

|Tangent Lines |Know and apply the converse of the Pythagorean Theorem to identify if a|and/or spheres. Formulas are provided on a reference sheet. |

|Chords and Arcs |triangle is a right triangle | |

|Inscribed Angles |Use the properties of a 45-45-90 or 30-60-90 triangle |G.2.3.1.3 Find the measurement of a missing length, given the surface |

|Angle Measures and Segment Lengths |Find the area of a trapezoid, rhombus, or kite |area or volume. |

|Circles in the Coordinate Plane |Find the area of a regular polygon | |

| |Find the measures of central angles and arcs |G.2.3.2.1 Describe how a change in the linear dimension of a figure |

|12. Transformations |Find circumference and arc length |affects its surface area or volume (e.g., How does changing the length |

|Reflections |Find the areas of circles, sectors, and segments of circles |of the edge of a cube affect the volume of the cube?). |

|Translations |Find the area of shaded regions by applying the formulas of circles, | |

|Rotations |sectors, and segments of circles | |

|Dilations |Define and find geometric probabilities | |

|Symmetry | | |

| |8. Similarity | |

| |Write ratios and solve proportions | |

| |Identify similar polygons and apply their properties to solve | |

| |real-world problems | |

| |Use the AA similarity postulate to prove triangles similar | |

| |Use the SSS and SAS similarity theorems to prove triangles similar | |

| |Find and use similarities in right triangles | |

| |Find geometric mean | |

| |Use the side-splitter theorem | |

| |Use the triangle angle-bisector theorem | |

| |Find the perimeters and areas of similar figures | |

| | | |

| |9. Right Triangle Trigonometry | |

| |Use the tangent ratio to determine side lengths in triangles | |

| |Use the sine and cosine ratios to determine side lengths in triangles | |

| |Apply the tangent, sine, and cosine ratios to find areas of polygons | |

| |Apply the tangent, sine, and cosine ratios to solve real-world problems| |

| |Use angles of elevation and depression to solve real-world problems | |

| |Describe vectors | |

| |Find the x- and y- components of a vector | |

| |Solve problems that involve vector addition | |

| | | |

| |10. Area, Surface Area, and Volume | |

| |Find the SA of a prism and cylinder | |

| |Find the SA of a pyramid and cone | |

| |Find the SA of composite figures involving prisms, cylinders, pyramids,| |

| |or cones | |

| |Find the volume of a prism and cylinder | |

| |Find the volume of a pyramid and cone | |

| |Find the volume of composite figures involving prisms, cylinders, | |

| |pyramids, or cones | |

| |Find the SA and volume of a sphere | |

| |Find relationships between the ratios of the areas and volumes of | |

| |similar solids and then apply those to find SA and volume | |

| | | |

| |11. Circles | |

| |Use the relationship between a radius and a tangent | |

| |Use the relationship between two tangents from one point | |

| |Use congruent chords, arcs, and central angles | |

| |Recognize properties of lines through the center of a circle | |

| |Find the measure of an inscribed angle | |

| |Find the measure of an angle formed by a tangent and a chord | |

| |Find the measures of angles formed by chords, secants, and tangents | |

| |Find the lengths of segments associated with circles | |

| |Write the equation of a circle | |

| |Find the center and radius of a circle given its equation | |

| | | |

| |12. Transformations | |

| |Identify isometries | |

| |Identify images and pre-images | |

| |Identify reflections | |

| |Identify translations | |

| |Describe a translation using a vector | |

| |Identify rotations | |

| |Identify dilations | |

| |Identify scale factors | |

| |Identify symmetry as reflectional or rotational | |

|Instructional Plan: |

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|The instructional plan will be aligned with the Danville Area School District Instructional Model and may include the following: presentation of new material, checking homework, guided student practice, cooperative|

|learning, partnering, discussion, graphic organizers, projects and assignments involving applications of mathematical concepts. |

|Student Assistance: |

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|Students can request additional help during his/her advisory, before/after school, or at the beginning/end of class. Students can also seek help from other classmates and/or teachers (Mr. Leslie or Mrs. Michaels). |

|Assessments and Evaluation: |Grading: |Homework/Procedures: |

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|A formative assessment is typically given after every 2-3 sections of |Grades for this course are calculated by a weighted system. |Homework is assigned almost daily and should take a typical student less|

|book material. The assessment may contain multiple choice, short answer,| |than 20 minutes to complete. Assignments are given from the textbook or |

|and open–ended questions. |Calculations include: |worksheets, and occasionally online. Homework is not accepted late. |

| |Homework (checked for completion) –10% of marking period grade | |

|A summative assessment is typically given after the completion of each |Class Work – 10% of marking period grade |If a student needs help with an assignment, he/she should: |

|unit, or sub-unit. The assessment may contain multiple choice, short |Quizzes - 40% of marking period grade |Ask for help during class when the assignment is being reviewed. |

|answer, and/or short answer questions. |Unit Exams – 40% of marking period grade. |Visit the teacher during his/her advisory period. |

| |Final Exam - To be included in the 4th marking period grade |Schedule to meet with the teacher before or after school. |

|Other assessments include homework checks, weekly bell-ringers, and/or | | |

|projects. | | |

|Student and Parent Communication: |

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|Our middle school website contains a homework page, which contains daily/weekly assignments. The teacher may also share documents with students via the Google Drive. If a student or parent has a particular |

|question, he/she can contact the teacher through email (bleslie@danville.k12.pa.us or kmichaels@danville.k12.pa.us). Parents may call to schedule a meeting with his/her teacher during team time. Parents also have |

|the opportunity to meet with his/her teacher during open house and the scheduled parent-teacher conferences during the fall/spring semesters. |

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|Student Expectations and Classroom Rules of Conduct |

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|Students will appropriately participate and follow all policies as outlined in the Danville Student Handbook, which contains procedures regarding absences, classroom behavior, make-up of work, academic integrity and |

|all other student conduct guidelines. |

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|Materials Required: |

|3-ring Binder with loose paper |

|Pencil |

|Scientific Calculator |

|Textbook |

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|Expectations of the Student: |

|Report to class on time. |

|Attend each class and be prepared to learn every day. |

|Bring your notebook, textbook, assignment(s), calculator and pencil |

|Complete all given assignments. |

|Pay attention and take detailed and organized notes in class. |

|Respect fellow classmates. |

|Ask questions frequently. |

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|Makeup Policy: |

|If a student misses a day of class and the absence is excused, it is the student’s responsibility to request any work he or she missed. If an absence is not excused, the student will receive a grade of zero for any |

|assignment missed while absent. Makeup tests and quizzes are typically completed during advisory time. Individual accommodations can be made for extenuating circumstances. |

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|Cheating and Plagiarism: |

|Any evidence of cheating or plagiarism will result in a grade of zero for that assignment or assessment. Other disciplinary action will follow the plagiarism policy of Danville Middle School. Academic dishonesty is|

|not tolerated. |

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