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DESCRIPTION OF COURSE
In Geometry you will study the concepts and applications of Geometry. We will complete the majority of the text consisting of topics such as properties of triangles, circles, parallelograms, squares, rectangles, and other shapes, constructions, trigonometry, theorems, postulates, and proofs. You will also become very comfortable working with formulas in this course. This course is semi project and activity driven to help deepen understanding of the application of Geometry. *In Honors Geometry you will delve deeper into the world of proofs as well a little deeper into all of the content covered in each unit.
MAJOR CONCEPTS
Essentials of Geometry
Reasoning and Proof
Parallel and Perpendicular Lines
Congruent Triangles
Relationships within Triangles
Similarity
Right Triangles and Trigonometry
Quadrilaterals
Properties of Transformations
Properties of Circles
Measuring Length and Area
Surface Area and Volume of Solids
DISCIPLINE COURSE COMPETENCIES
Mathematical Communication
Mathematical Application
Mathematical Modeling
Mathematical Process
COURSE CONTENT LEARNING TARGETS
Students will know and apply the essentials of geometry to understand problems when notation is used for lines, rays, points, segments, angles, etc.
Students will be able to reason/prove geometrically and algebraically using postulates and theorems, as well as conditional statements
Students will know the relationships formed with parallel and perpendicular lines and write equations for them.
Students will be able to prove two triangles congruent using SSS, SAS, ASA, AAS, and HL.
Students will be able to solve for parts of triangles using relationships within a triangle
Students will be able to use proportions to solve real-world problems involving similar figures.
Students will be able to use trigonometry to solve right triangle problems.
Students will be able to use properties of special quadrilaterals to solve the quadrilaterals.
Students will be able to use properties of transformations to move shapes around a plane as well as create similar figures in a plane.
Students will know and apply properties of angles and segments within circles to solve circles.
Students will be able apply formulas to calculate perimeter, lengths, and areas of two-dimensional shapes
Students will be able to apply formulas to calculate surface are and volume of solids
Common Core State Standards
Experiment with transformations in the plane
G.CO.1,G.CO.2, G.CO.3, G.CO.4, G.CO.5
I can know precise definitions of angle, circle, perpendicular and parallel lines, and line segment in terms of the undefined terms of point, line and plane, and develop definitions of rotations, reflections and translations in terms of angles, circles, line segments, and perpendicular and parallel lines.
I can represent transformations in the plane, compare transformations that preserve distance and angle to those that do not, and given a geometric figure and a rotation, reflection or translation, draw the transformed figure, and given a rectangle, parallelogram, trapezoid or regular polygon, describe the rotations and reflections that carry it onto itself
Understand congruence in terms of rigid motions
G.CO.6, G.CO.7, G.CO.8
I can use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure, and use the definition of congruence in terms of rigid motions to decide if they are congruent
I can use the definition of congruence in terms of rigid motions to show that two triangles are congruent and explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions
Prove geometric theorems
G.CO.9, G.CO.10, G.CO.11
I can prove theorems about lines, angles, triangles, and parallelograms
Make geometric constructions
G.CO.12, G.CO.13
I can make formal geometric constructions with a variety of tools and methods
Similarity, Right Triangles, and Trigonometry
Understand similarity in terms of similarity transformations
G.SRT.1a,G.SRT.1b, G.SRT.2,G.SRT.3
I can verify experimentally the properties of dilations given by a center and a scale factor
I can, given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar, and use the properties of similarity transformations to establish the AA criterion for two triangles to be similar
Prove theorems involving similarity
G.SRT.4, G.SRT.5
I can prove theorems about triangles and use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures
Define trigonometric ratios and solve problems involving right triangles
G.SRT.6, G.SRT.7, G.SRT.8
I can show by similarity that side ratios in right triangles are properties of the angles in the triangle, leading to the definitions of the trig ratios for acute angles
I can explain and use the relationship between the sine and cosine of complementary angles, and use trig ratios and the Pythagorean Theorem to solve right triangles in applied problems
Apply trigonometry to general triangles
G.SRT.9, G.SRT.10, G.SRT.11
I can derive the formula A=(1/2)ab sin(c) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side, prove the Laws of Sines and Cosines and use them to solve problems, and apply the Laws to find unknown measurements in right and non-right triangles
Circles
Understand and apply theorems about circles
G.C.1, G.C.2,G.C.3,G.C.4+
I can prove that all circles are similar
I can identify and describe relationships among inscribed angles, radii, and chords
I can construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle
I can construct a tangent line from a point outside a given circle to the circle
Find arc lengths and areas of sectors of circles
G.C.5
I can derive the fact that the length of the arc intercepted by an angle is proportional to the radius, and derive the formula for the area of a sector
Expressing Geometric Properties with Equations
Translate between the geometric description and the equation for a conic section
G.GPE.1, G.GPE.2
I can derive the equation of a circle given the radius and center, and derive the equation of a parabola given a focus and directrix
Use coordinates to prove simple geometric theorems algebraically
G.GPE.4, G.GPE.5. G.GPE.6, G.GPE.7
I can prove or disprove things like a figure defined by four given points is the coordinate plane is a rectangle, prove or disprove that a point in on a circle knowing the center and radius, prove the slope criteria for parallel and perpendicular lines, find the point on a directed line segment between two given points that partitions the segment in a given ratio, and use coordinates to compute perimeters of polygons and areas of triangles and rectangles
Geometric Measurement and Dimensions
Explain volume formulas and use them to solve problems
G.GMD.1,G.GMD.3
I can give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid and cone, and use those formulas to solve problems.
Visualize relationships between two-dimensional and three-dimensional objects
G.GMD.4
I can identify the shapes of two-dimensional cross-sections of three-dimensional objects and identify three-dimensional objects generated by rotations of two-dimensional objects
Modeling with Geometry
Apply geometric concepts in modeling situations
G.GMD.1, G.GMD.2, G.GMD.3
I can use measures and properties of geometric shapes to describe objects, apply concepts of density based on area and volume in modeling situations, and apply geometric methods to solve design problems
Competency 1: Mathematical Communication (MC)
The student can use the language of mathematics, either written and/or orally, to express their ideas precisely, coherently and clearly. This competency is assessed in all of the course content learning targets.Sample Performance Assessment (SPA #1) Erin wants to cut down a dead tree in her yard.
a.) On a sunny day Erin measured the trees shadow and found it was 20 feet long. She also measured the shadow cast by an 8 foot lamppost and found that that shadow was 5 feet long. Sketch the tree, the lamppost, and their shadows. Label your sketch with the appropriate lengths.
b.) If the base of the tree is 25 feet from Erins house, is it possible for the tree to hit the house when it falls? Justify your answer. Explain or show how you determined the height of the tree.
(The part of the question that is assessing Mathematical Communication is the justification and explaining)SPA #1 RubricProficient with Distinction
Uses sophisticated mathematical terminology or vocabulary in order to construct viable arguments and critique the reasoning of others
Uses relevant mathematical facts to justify conclusions
Uses correct grammar, punctuation and spellingProficient
Uses mathematical terminology or vocabulary in order to construct viable arguments and critique the reasoning of others
Uses relevant mathematical facts to justify conclusions
Grammatical, punctuation and spelling errors do not detract from the meaningPartially Proficient
Can construct viable arguments and critique the reasoning of others, with some evidence of relevant vocabulary
Minimal use of mathematical facts to justify conclusions
Several grammatical, punctuation and/or spelling errors detract from the meaningNot Proficient
Argument does not support the conclusion or is incomplete
Inaccurate or no mathematical facts used to justify conclusions
Several grammatical, punctuation and/or spelling errors detract from the meaning
Competency 2: Mathematical Application (MA)
Students will recognize, explore and develop mathematical connections and transfer those skills and concepts to solve real-world scenarios. This competency is assessed in all of the course content learning targets.Sample Performance Assessment (SPA #2)Erin wants to cut down a dead tree in her yard.
a.) On a sunny day Erin measured the trees shadow and found it was 20 feet long. She also measured the shadow cast by an 8 foot lamppost and found that that shadow was 5 feet long. Sketch the tree, the lamppost, and their shadows. Label your sketch with the appropriate lengths.
b.) If the base of the tree is 25 feet from Erins house, is it possible for the tree to hit the house when it falls? Justify your answer. Explain or show how you determined the height of the tree.
(The part of this question that is assessing Mathematical Application is knowing the correct equation to set up based on the information given in the question)SPA #2 RubricProficient with Distinction
Accurately and efficiently transfers content knowledge to correctly solve unfamiliar real-world scenariosProficient
Accurately transfers content knowledge to correctly solve real-world scenariosPartially Proficient
Can transfer content knowledge to correctly solve real-world scenarios, with minimal assistanceNot Proficient
Cannot transfer content knowledge to correctly solve real-world scenarios, with minimal assistance
Competency 3: Mathematical Modeling (MM)
The student is able to represent a problem using graphs, diagrams, expressions, equations and/or inequalities. This competency is assessed in all of the course content learning targets.Sample Performance Assessment (SPA #3)Erin wants to cut down a dead tree in her yard.
a.) On a sunny day Erin measured the trees shadow and found it was 20 feet long. She also measured the shadow cast by an 8 foot lamppost and found that that shadow was 5 feet long. Sketch the tree, the lamppost, and their shadows. Label your sketch with the appropriate lengths.
b.) If the base of the tree is 25 feet from Erins house, is it possible for the tree to hit the house when it falls? Justify your answer. Explain or show how you determined the height of the tree.
(the part of the question that is assessing Mathematical Modeling is when they are asked to make a sketch and label it correctly)SPA #3 RubricProficient with Distinction
Correctly represents a real world situation in the form of a picture, diagram, graph, equation, inequality or expression
Uses correct labels with units when appropriate or declares all variablesProficient
Correctly represents a real world situation in the form of a picture, diagram, graph, equation, inequality or expression
Uses correct labels when appropriate
Partially Proficient
Represents a real world situation in the form of a picture, diagram, graph, equation, inequality or expression with minor errors
Not Proficient
Represents a real world situation in the form of a picture, diagram, graph, equation, inequality or expression with major errors
Competency 4: Mathematical Process (MP)
In order to solve a problem, the student is able to follow a logical mathematical sequence, concluding with the correct answer. This competency is assessed in all of the course content learning targets.Sample Performance Assessment (SPA #4)Erin wants to cut down a dead tree in her yard.
a.) On a sunny day Erin measured the trees shadow and found it was 20 feet long. She also measured the shadow cast by an 8 foot lamppost and found that that shadow was 5 feet long. Sketch the tree, the lamppost, and their shadows. Label your sketch with the appropriate lengths.
b.) If the base of the tree is 25 feet from Erins house, is it possible for the tree to hit the house when it falls? Justify your answer. Explain or show how you determined the height of the tree.
(The part of the problem that is assessing Mathematical Process is when they need to solve for the height of the tree)SPA #4 RubricProficient with Distinction
Follows correct process/sequence
Shows all relevant work
Where appropriate, chooses more sophisticated and/or efficient processes
Contains no mathematical errors
Arrives at correct answerProficient
Follows correct process/sequence
Shows all relevant work
Completes task with minimal mathematical errorsPartially Proficient
Errors in process/sequence
Shows all relevant work
Task is mostly completeNot Proficient
No evidence of proper process/sequence
Does not complete task
Geometry
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