Download File - Kirksey`s K`NECTD MATHEMATICS

Northeast Prep Academy
Course Syllabus
Instructor: Martin Kirksey
[email protected]
Course Title: Unified Geometry
Term: Fall 2013 (August 5, 2013 – December 20, 2013)
(901) 416-2132
Ext.51421
Course Description: This standard first course in geometry covers the required concepts
of Euclidean geometry including definitions, postulates, and theorems. Areas of study
include angles, parallel lines, congruent and similar triangles, rectilinear figures, polygons,
circles and arc, and the Pythagorean Theorem. Special topics covered include coordinate
and spatial geometry, introductory trigonometry, and constructions and loci. In addition to
including problems which serve to review algebra, the process of “proving” theorems is
introduced.
Course Objectives:
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Use the term equidistant.
Use the terms point, line, plane, collinear, coplanar, and intersection. Draw
representations of points, lines, and planes.
Use symbols for lines, segments, rays, and distances; find distances. Use the
Segment Addition Postulate.
Name angles and find their measures. Use the Angle Addition Postulate.
Use postulates and theorems relating points, lines, and planes.
Solve algebraic problems using segments and angles.
Write a statement in if-then form.
Write the converse of an if-then statement.
Recognize hypotheses and conclusions.
Use counterexamples.
Use properties of equality in algebraic and geometric
proofs.
Use properties of congruence.
Examine proofs involving segment theorems and postulates.
Examine proofs involving angle theorems and postulates.
Identify and use the terms complementary and supplementary.
Determine what information can and cannot be assumed from a diagram.
Solve algebraic problems involving systems of equations.
Distinguish between intersecting lines, parallel lines, and skew lines. Identify parallel
lanes.
Identify the angles formed when two lines are cut by a transversal.
State and apply postulates and theorems about parallel lines.
Classify triangles according to sides and angles.
Apply the theorem about the sum of the measures of the angles of a triangle.
Apply the theorem about the measure of an exterior angle of a triangle.
Recognize and name convex polygons and regular polygons.
Find the measure of the interior and exterior angles of polygons.
Understand and use inductive reasoning.
Identify the corresponding parts of congruent triangles.
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Prove two triangles congruent using the SSS Postulate, the SAS Postulate, and the
ASA Postulate.
Deduce information about segments and angles after proving that two triangles are
congruent.
Apply the theorems about isosceles triangles.
Use the AAS Theorem and the HL Theorem to prove two triangles congruent.
Apply the definitions of the median and the altitude of a triangle and the perpendicular
bisector of a segment. Apply the theorem about a point on a perpendicular bisector of
a segment, and the converse. Apply the theorem about a point on the bisector of an
angle, and the converse.
Perform constructions such as copy a segment, copy an angle, construct an angle
bisector, construct a perpendicular bisector.
State and apply theorems involving concurrent lines.
Apply the definition of a parallelogram and the theorems about properties of a
parallelogram.
Prove that certain quadrilaterals are parallelograms.
Apply theorems about parallel lines and the segment that joins the midpoints of two
sides of a triangle.
Apply the definitions and identify the special properties of a rectangle, a rhombus, and
a square.
Apply the definitions and identify the properties of a trapezoid and an isosceles
trapezoid.
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Apply properties of inequalities to positive numbers.
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State the contrapositive and inverse of an if-then statement. Understand the
relationship between logically equivalent statements.
Write indirect proofs in paragraph form.
State and apply the inequality theorems for one triangle.
State and apply the inequality theorems for two triangles.
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Express a ratio in simplest form.
Solve for an unknown term in a given proportion. Express a given proportion in
an equivalent form.
State and apply the properties of similar polygons.
Use the AA Similarity Postulate to prove triangles similar. Use similar triangles
to deduce information about segments or angles.
Use the SAS Similarity Theorem and the SSS Similarity Theorem to prove
triangles similar.
Apply the Triangle Proportionality Theorem and its corollary. Apply the Triangle
Angle-Bisector Theorem.
Determine the geometric mean between two numbers. Apply the relationships
that exist when the altitude is drawn to the hypotenuse of a right triangle.
State and apply the Pythagorean Theorem.
State and apply the converse of the Pythagorean Theorem and related
theorems about obtuse and acute triangles.
Determine the lengths of two sides of a 45º-45º-90º or a 30º-60º-90º triangle
when the length of the third side is known.
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Define the tangent, sine, and cosine ratios for an acute angle. Solve right
triangle problems by correct selection of the sine, cosine and tangent ratios.
Use trigonometry to solve problems involving angles of elevation or depression.
Define a circle, a sphere, and terms related to them. Recognize circumscribed
circles and inscribed polygons.
Apply theorems that relate tangents and radii. Recognize circumscribed
polygons and inscribed circles.
Define and apply properties of arcs and central angles.
Apply theorems about the chords of a circle.
Solve problems involving inscribed angles and angles formed by chords and
tangents.
Solve problems involving angles formed by chords, secants, and tangents.
Solve problems involving lengths of chords, secant segments, and tangent
segments.
Understand the area postulates. Know and use the formula for the areas of
rectangles.
Know and use the formulas for the areas of parallelograms, triangles, and
rhombuses.
Know and use the formulas for the areas of trapezoids.
Know and use the formula for the area of regular polygons.
Know and use the formulas for circumference and areas of circles.
Know and use the formulas for arc lengths and the areas of sectors of circles.
Find the ratio of the areas of two triangles. Understand and apply the
relationships between scale factors, perimeters, and areas of similar figures.
Use lengths and areas to solve problems involving geometric probability.
Identify the parts of prisms. Find the lateral areas, total areas, and volumes of
right prisms.
Identify the parts of pyramids. Find the lateral area, total area and volumes of
regular pyramids.
Identify the parts of cylinders and cones. Find the lateral area, total area and
volumes of right cylinders and right cones.
Find the area and volume of a sphere.
Apply the properties of similar solids.
Apply the distance formula. Apply the general equation of a circle.
State and apply the slope formula.
Determine whether two lines are parallel, perpendicular, or neither.
Understand the basic properties of vectors.
State and apply the midpoint formula.
Identify the slope and y-intercept of the line specified by a given equation.
Draw the graph of the line specified by a given equation. Determine the
intersection of two lines.
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Write an equation of a line when given either one point and the slope of the line
or two points on the line.
Prove theorems of geometry using coordinate methods.
Student Learning Outcomes:
Upon successful completion of this course, the student will be able to:
Quarter 1
1. Students will learn the foundation blocks for the structure of geometry
Students will:
•learn to use inductive reasoning to make conjectures.
•understand basic terms: points, lines, planes, segments, rays, and parallel lines
and parallel planes, perpendicular.
•measure segments and angles.
•use the distance and midpoint formulas.
•determine perimeter, circumference, and area.
2. Students will develop skills involving reasoning and proof.
Students will:
•recognize and write conditional and corresponding converse statements.
•distinguish between the Law of Detachment and Law of Syllogism and how they
apply to various situations.
•connect reasoning in algebra and geometry by use of properties.
•recognize and apply appropriate theorems to prove congruency of angles.
3. Students will prove and use properties of parallel lines and learn about angle
measures in triangles and other polygons.
Students will:
•identify angles formed by two lines and a transversal and use properties of
parallel lines.
•apply appropriate theorems and postulates to prove parallel lines given a
transversal.
•understand the relationships between parallel and perpendicular lines.
•classify triangles and find the measures and sums of their interior and exterior
angles.
•write and graph the equation of a line.
•use slope to determine when lines are parallel, perpendicular or intersecting.
Quarter 2
4. Students will learn how to prove that triangles are congruent
Students will:
•recognize congruent figures and their corresponding parts.
•prove triangles are congruent using the SSS, SAS and ASA postulates as well as
the AAS and HL theorems.
•use CPCTC to prove that corresponding parts of congruent triangles are
congruent.
•apply properties of isosceles and equilateral triangles.
5. Students will learn about geometric relationships within triangles
Students will:
•use properties of midsegments of triangles to solve problems.
•apply properties of perpendicular bisectors, angle bisectors, medians and
altitudes.
•write the inverse and contrapositive of a conditional statement.
•use indirect reasoning.
•apply triangle inequalities.
6. Students will classify and use properties of quadrilaterals.
Students will:
•define and classify special types of quadrilaterals.
•use relationships among sides, angles, diagonals and transversals of
parallelograms.
•be able to determine whether a quadrilateral is a parallelogram.
•work with properties of rhombi.
•verify and use properties of trapezoids and kites.
Quarter 3
7. Students will learn how to find the area of geometric figures.
Students will:
•find the areas of parallelograms, triangles, trapezoids, rhombuses, kites, and
regular polygons.
•learn to use the Pythagorean Theorem and its converse.
•use the properties of special triangles: 45°-45°-90° and 30°-60°-90°.
•use CPCTC to prove that corresponding parts of congruent triangles are
congruent.
•find the measures of central angles and arcs of circles.
•find the circumference and arc lengths of circles.
•find the areas of circles, sectors, and segment of circles.
8. Students will learn and use to apply the properties of similar polygons
Students will:
•write ratios and solve proportions.
•use proportions to identify similar polygons.
•use and apply AA, SAS, and SSS similarity statements.
•find and use relationships in similar right triangles.
•use the Side-Splitter Theorem and the Triangle-Angle Bisector Theorem.
•find perimeters and areas of similar figures.
9. Students will learn the basics of right-angle trigonometry
Students will:
•use the sine, cosine, and tangent ratios to determine side and angle measurements in right triangles.
•use Angle of Elevation and Angle of Depression to solve problems.
•learn the Pythagorean Identity.
•use trigonometry to find the area of a regular polygon and any triangle.
Quarter 4
10. Students will learn about Surface Area and Volume
Students will
•be able to recognize the parts of a polyhedron (i.e. faces, edges, vertices).
•find the surface area of a prism, cylinder, pyramid, cone, and sphere.
•find the volume of a prism, cylinder, pyramid, cone, and sphere.
•find relationships between the ratios of the areas and volumes of similar solids.
11. Students will learn Circles
Students will:
•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.
•calculate the measure of an inscribed angle.
•calculate 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.
•be able to write an equation of a circle.
•find the center and radius of a circle.
12. Students will learn to use Transformations for relating two given congruent shapes to each other
Students will:
•be able to find reflection images of figures.
•identify isometries.
•find translation images.
•draw and identify rotation images of figures.
•use composition of reflections.
•identify glide reflections.
•identify the type of symmetry in a figure.
•identify transformations and tessellations and figures that will tessellate.
•identify symmetries in tessellations.
•locate dilation images in figures.
Student Expectations:
1. Students are encouraged to attend every class with the desire to gain, grow, and develop the necessary
concepts, skills and understanding needed to successfully pass.
2. Students are expected to be in class on time ready to work and participate in activities and provide input. 1
3. Students are expected to complete all assignments and homework. Assignments, tests, or quizzes
completed in ink will NOT be accepted – NO EXCEPTIONS.
4. Attendance Policy:
a) Each student is required to attend school on regular basis. Students must provide the necessary
paperwork for absences. If students are absent on multiple days or class meetings, students are required to
check with the school. Attendance will be factored in the grading process. Students with 10 or more
unexcused absences will be dropped from the roster immediately.
b) Students are expected to be in class by the posted starting time of the class. Late arrivals can be a distraction and
should be kept to a minimum. Three (3) late arrivals will be counted as one absence.
5. MAKEUP POLICY
IT IS THE STUDENT’S RESPONSIBILITY TO CONTACT THE INSTRUCTOR TO DISCUSS/RECEIVE ANY WORK
MISSED.
Students are expected to be present for all exams. If a verifiable emergency arises which prevents you from taking an inclass exam at the regularly scheduled time, you must notify the instructor as soon as possible, and in any case, prior to
the next regularly scheduled class. Make-up exams will cover the same material as a regular exam but may be slightly
harder than the regularly schedule in-class exam AND will be administered only at the discretion of the instructor. IF a
student is allowed to make up a missed exam, he/she must: (1) provide documentation of the absence and (2)
arrange to take the exam at a mutually agreeable time. No further opportunities will be extended. Failure to contact
the instructor as stated above or inability to produce sufficient evidence of a real emergency will result in a grade of zero
on the exam.
EXCESSIVE ABSENCES – Being absent does not excuse you from completing and understanding any material
you missed!
 All assignments will be clearly posted on the board(s).
 Daily classwork may be completed for credit (You are allowed one day for every day absent to make up daily
work). Late homework will not be accepted without approval from the instructor.
 It is YOUR responsibility to find out what you missed!!!!!!!
 Quizzes cannot be made up and no test (makeup's, IF permitted) will be given during class time. It is YOUR
responsibility to make an appointment during my office hours.
 BEING ABSENT FOR THE DAY OF REVIEW DOES NOT EXCUSE YOU FROM TAKING THE TEST IF THAT IS
THE ONLY TIME YOU WERE GONE.
6. Treat everyone with respect.
Evaluation Methods:
1. Beginning Assessment
2. Daily Warm-Ups
3. Daily Work (including Exit Tickets)
4. Homework & Homework Policy (10%)
Homework Policy:
Homework is an important part of learning mathematics and will be assigned daily. Students will be required to
participate in regular homework or out of class assignments. The assignments will explained by the instructor.
Each student is responsible for his/her own work unless a group project is assigned by instructor. Homework
should be done in pencil in order to allow you to easily fix any mistakes that you have made. Every assigned
problem should be tried and the answer checked. It is permissible to discuss problems with other students or
relatives. It is not permissible to copy another student's work. Do your best to think through the problems and
understand why things work the way they do.
Because this is an upper level math course, I may assign odd problems from the book in order for you to check
your answers before you come to class. When I check your homework, I expect to see all of the work for the
problem, not just the answer. The problem, the work, and the answer should all be shown neatly together. You
will not receive credit for homework that is turned in without work for EVERY problem.
There may be problems that are unusually difficult that I have not prepared you for. Doing
homework may make you frustrated. That is ok. I am hoping that the homework will challenge
you to think. Thinking is part of learning! If you are having difficulty with your homework, keep
the following in mind:
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Write down what you know.
Write down what the problem is asking you to do.
Look through your notes for examples.
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Re-READ the current section of your textbook, your notes and possibly other sections. This implies that
you are already reading each section. THE EXAMPLES IN OUR TEXTBOOK ARE EXTREMELY
GOOD. USE THEM AS A GUIDE.
Get familiar with the glossary and index of a book -- these can come in handy when you are searching
the book for a topic.
It you are still lost, please come and ask questions.
Working together on classwork and homework is encouraged but copying is prohibited. Be
careful when you ask another student for help. Make sure that YOU UNDERSTAND the
solution. Putting an answer on your paper means that YOU understood that problem and could
explain it to the entire class. Remember that there are school policies about copying.
All homework must be done on loose-leaf paper. Please label your homework with your
name, the date, page # and problem #’s in the top right hand corner of each assignment.
Homework should take anywhere from 20 minutes to 30 minutes, depending on the type of
assignment. Homework will be checked on a regular basis as you enter the class. You will not be allowed
to complete homework at the beginning of class! All homework assignments that are complete will receive a
checkmark. Homework should be corrected and added to as the material is better understood. Completeness,
accuracy, and effort will all be considered.
5. Quizzes (NO make-ups on quizzes) (30%)
 Work, if needed, must always be shown to get full credit, even if you use a calculator. I generally award
partial credit on tests and quizzes for correct work even if the final answer is incorrect. Please use a
pencil on all quizzes.
 Quizzes will be given throughout each chapter based on instructor discretion. Quizzes will usually
consist of 5-6 questions (20-30 minutes) covering the material that we’re currently studying.
6. Chapter Exams (40%)
 There will be an exam at the end of each chapter. Test will be cumulative in nature so be sure that you
keep reviewing prior topics that have been covered. Exams will be announced AT LEAST a week
ahead of time. We will review based on material from warm-ups, quizzes, and class assignments. I will
not answer questions during the test!
 Work, if needed, must always be shown to get full credit, even if you use a calculator. I generally award
partial credit on tests and quizzes for correct work even if the final answer is incorrect. Please use a
pencil on all exams.
7. Final exam (Post-Assessment – 20%)
GRADING
I do not grade on a “curve”. Under no circumstances will your grade directly depend on how your fellow students do. If
you do a good job of learning the material, you will receive a good grade, regardless of how well the other members of the
class perform. Don’t forget that the reverse is also true: If you do a poor job of learning the material, you will receive a
poor grade, regardless of how poorly everyone else does. I will assign both numerical grades and checks. I will use the
following grading scale:
Percentage Range
93 – 100
85 – 92
75 – 84
74 – 69
< 69
Letter Grade
A
B
C
D
F
Late or Missing Work Policy
Students are expected to turn in assignments as they are due. Late assignments will be given on a case-bycase basis. Missing work will eventually turn into zero credit.
MISUSE OF COMPUTERS
Computers in Northeast Prep’s classrooms, computer labs, and library are to be used for educational purposes only.
Web-based resources:
www.interactmath.com
www.mathisfun.com
www.purplemath.com
http://mathbits.com/MathBits/StudentResources/GraphPaper/GraphPaper.htm
http://www.mrlarkins.com/
www.education.ti.com/calculators/products/US/home/
www.khanacademy.com
YOUTube
Search: shaunteaches
Search: yourteachermathhelp
Supplies and Supplementary Materials: Handouts and other math manipulatives as needed.
Topical Outline/Course Pacing Guide
Chapter 1
1.1
Points, Lines & Planes
1.2
Linear Measure & Precision
1.3
Distance & Midpoints
1.4
Angle Measure
1.5
Angle Relationships
1.6
Polygons
*Geometric constructions
Chapter 2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
Inductive Reasoning & Conjecture
Logic
Conditional Statements
Deductive Reasoning
Postulates & Paragraph Proofs
Algebraic Proof
Proving Segment Relationships
Proving Angle Relationships
Chapter 3
3.1
Parallel Lines & Transversals
3.2
Angles & Parallel Lines
3.3
Slopes of Lines
3.5
Proving Lines Parallel
3.6
Perpendiculars & Distance
Chapter 4
4.1
Classifying Triangles
4.2
Angles of Triangles
4.3
Congruent Triangles
4.4
Proving Congruence - SSS, SAS
4.5
Proving Congruence - ASA, AAS
4.6
Isosceles Triangles
4.7
Triangles & Coordinate Proof
Chapter 5
5.1
Bisectors, Medians & Altitudes
5.2
Inequalities & Triangles
5.3
Indirect Proof
5.4
The Triangle Inequality
5.5
Inequalities Involving Two Triangles
Chapter 6
6.1
Proportions
6.2
Similar Polygons
6.3
Similar Triangles
6.4
Parallel Lines & Proportional Parts
6.5
Parts of Similar Triangles
CHAPTER 7 (SECT. 7.1-7.3 only)
7.1
Geometric Mean
7.2
The Pythagorean Theorem & Its
Converse
7.3
Special Right Triangles
7.4
Trigonometry
7.5
Angles of Elevation & Depression
7.6
The Law of Sines
7.7
The Law of Cosines
CHAPTER 8
8.1
Angles of Polygons
8.2
Parallelograms
8.3
Tests for Parallelograms
8.4
Rectangles
8.5
Rhombi & Squares
8.6
Trapezoids
8.7
Coordinate Proof with Quadrilaterals
CHAPTER 9
9.1
Reflections
9.2
Translations
9.3
Rotations
9.4
Tessellations
9.5
Dilations
(Optional)
CHAPTER 10
10.1
10.2
10.3
10.4
10.5
10.6
Circles & Circumference
Angles & Arcs
Arcs & Chords
Inscribed Angles
Tangents
Secants, Tangents & Angle Measures
10.7 Special Segments in a Circle
10.8 Equations of Circles
CHAPTER 11
11.1
11.2
Areas of Parallelograms
Areas of Triangles, Trapezoids & Rhombi
11.3 Areas of Regular Polygons & Circles
11.4 Areas of Irregular Figures
11.5 Geometric Prob (Sectors, Segments,
Annuli)
CHAPTER 12
12.1
12.2
12.3
12.4
12.5
12.6
12.7
Three-Dimensional Figures
Nets & Surface Area
Surface Areas of Prisms
Surface Areas of Cylinders
Surface Areas of Pyramids
Surface Areas of Cones
Surface Areas of Spheres
CHAPTER 13
13.1
13.2
13.3
13.4
Volumes of Prisms & Cylinders
Volumes of Pyramids & Cones
Volumes of Spheres
Congruent & Similar Solids
Student Outline borrowed from:
http://www.augusta.k12.va.us/Page/2846, 8/5/2013
Student Learning Outcomes borrowed from:
http://www.rockwood.k12.mo.us/lafayette/departments/Mathematics%20Department%20Learning%20Targets
%20and%20Standa/Geometry.pdf, 8/5/2013
*PROCEDURES AND EXPECTATIONS MAY BE CHANGED TO MEET THE TEACHER’S REQUIREMENTS AND
OTHERS MAY ALSO BE ADDED.