# Geometry

Curriculum > High > Clark > Mathematics
• Syllabus
• Sample Lesson Plan
Course Description
Geometric concepts are given an analytical approach. This course will provide you with experiences that deepen the understanding of two‐ and three‐ dimensional properties. Inductive and deductive reasoning methods of proof are introduced and used in the process of studying about lines, angles triangles, polygons, circles, area, volume, similarity trigonometry, and transformations.
Students study Geometry as a mathematical system through the deductive development of relationships in the plane and space developed intuitively in previous years. Students study congruent segments and angles, circle chords, secants and tangent segments, parallel and perpendicular lines, angle measure in triangles, direct and indirect triangle congruence and similarity, proofs, solids of revolution, logic, similar triangles, transformations, the Pythagorean Theorem, geometric constructions, coordinate geometry, and surface area and volume of solids. Through these, students may develop their spatial skills and apply this to solve real‐world problems.
Course Standard
Students will:
1. Use the Pythagorean Theorem to solve problems involving right triangles and to find the distance between any two points in a coordinate system.
2. Understand and apply the relationships between the slopes of parallel lines and the slopes of perpendicular lines, reinforcing the idea of mathematics as a descriptive language rather than mere symbol manipulation.
3. Analyze polygons on a coordinate system by determining the slopes of their sides.
4. Determine the surface area and volume of pyramid, cones and spheres.
5. Compose and decompose two and three dimensional figures to determine the perimeter, area, surface area and volume of figures.
6. Understand and apply the effect of ‘k’ on length, area and volume.
7. Make reasonable estimate about the accuracy of values resulting from calculations involving measurements, reinforcing critical thinking skills.
8. Understand the roles of axioms, definitions, undefined terms and theorems in logical arguments, reinforcing critical thinking skills.
9. Accurately interpret and use words in geometric proofs, extending their English language vocabulary.
10. Construct logical arguments and write proofs of theorems, reinforcing critical thinking skills
11. Know and apply properties of parallel and perpendicular lines to solve problems.
12. Know and apply properties of angles to solve real world problems.
13. Know and apply properties of triangles to solve real world problems.
14. Apply the Pythagorean Theorem and its converse to solve real world problems.
15. Know and apply properties of right triangles to solve real world problems.
Textbook and Supplies
Weekly Course Plan
First Quarter
Week 1 – 2: Introduction of Geometry, definition of terms, e.g. point. Line, plane, segment, ray, theorem and postulate.
Week 3: Postulates 3‐6, Theorems 1 and 2, and congruent angles.
Week 4 – 5: Types of angles, e.g. acute, obtuse and right angles. This also includes applications.
Week 6: Polygons, definitions, types and parts of triangles, and their applications.
Week 7: Definition, types and parts of quadrilaterals, and their applications and sum of the measures of interior angles of polygons.
Week 8: Definition of circle and terms related to circle, and their applications.
Week 9: Review and Midterm Exams.
Second Quarter
Week 10: Pairs of angles such as complementary, supplementary, adjacent angles and linear pair with Algebra.
Week 11: Derivation and application of Pythagorean Theorem.
Week 12: Special right triangles – 30‐60‐90 and 45‐45‐90 right triangles.
Week 13 – 14: Definition of Area, derivation of formula and problems involving area of polygons and circle.
Week 15 – 17: Transversal, Remote‐interior angle, exterior angle, Two‐Column Proof – proving some postulates and theorems related to angles and polygons.
Week 18: Review and Final Exams.
Third Quarter
Week 1: Trapezoids
Week 2: Similarity and Proportions – Triangles.
Week 3: Symmetry, Tessellations, review about circles.
Week 4: Arcs and Central angles, and Arcs and chords, and inscribed polygons.
Week 5: Introduction to Solid Geometry, definition of Surface Area and Volume of Pyramid.
Week 6: Surface area and volume of cube and prism.
Week 7‐8: Surface area and volume of Cylinder and Sphere.
Week 9: Review and Midterm exams.
Fourth Quarter
Week 10: Introduction to Solving Right Triangle, and Tangent ratio.
Week 11: Sine and Cosine ratios.
Week 12 – 13: Inscribed Angles, and Tangent to a Circle.
Week 14: Secant Angles, Secant‐Tangent Angles, and Segment Measure.
Week 15: Equations and Graphs of Circles
Week 16 – 17: Translation, Reflection, Rotation, and Dilations
Week 18: Review and Final exams.
Evaluation
Homework Quiz – usually graded on a four point scale.
By Inspection During Class – Teacher will ask to see the work.
When Handed In – some homework assignments are to be turned in for grading.
Late work is discounted 10% first class period, 25% the next class period, and receives a zero if later than two class periods
A blank notebook receives an F for the homework and participation portions of the class.

 Quizzes 25% Seatwork 20% Homework 10% Class Standing 15% Examination 30%

 A+ 97 - 100 4 A 94 - 96.99 4 A- 90 - 93.99 3.7 B+ 87 - 89.99 3.3 B 84 - 86.99 3 B- 80 - 83.99 2.7 C+ 77 - 79.99 2.3 C 74 - 76.99 2 C- 70 - 73.99 1.7 D+ 67 - 69.99 1.3 D 64 - 66.99 1 D- 60 - 63.99 0.7 F 0 - 59.99 0
Course Requirement
Be prepared for class with pencil, notebook, and book.
Be on task at the appropriate times.
Work with others in an appropriate manner.
Your contribution to class discussions is expected and appreciated.
‐ Notebook
You need a notebook that is dedicated to math.
DO NOT PURCHASE A ‘FIVE SUBJECT’ NOTEBOOK. You will be handing in the notebook occasionally for the teacher to check homework, so it will not be available to you Notebooks should be handed in during every test. The teacher is looking for:
1. Organization
2. Homework (not just the answers but the WORK)
The notebook is graded on a 5 point scale.
5 points: organized, all sections clearly delineated, all homework attempted.
0 points: no work or notebook missing on the day requested or obviously copied.
‐ Homework
Like any new language, you have to practice math or you will not learn it. You can expect a homework assignment every day. Take notes, participate in class, the homework will be a breeze.
Homework is your chance to test out, solidify, or ‘come to grip[s’ with what we’ve talked about in class that day. It is graded when the teacher assess your notebook and in
homework quizzes.
2. Write each separate assignment on a new sheet in your notebook.
3. MAKE HOMEWORK CORRECTIONS. Write them next to the original work, in the margin, wherever. Try to underline your mistakes, so when you review for a test, you’ll know what kind of thinking to avoid.
4. You will generally have between 10 – 30 problems (or more) for homework.
‐ Homework quizzes
You will have many homework quizzes. This test is closed book. You will be expected to use your notebook. Problems are identified by page number, section number, and problem number. Copy the work from your notebook onto the quiz sheet. Occasionally there will be free response questions on these quizzes as well. On these quizzes, just writing down the answer (unless appropriate) is insufficient and will be counted as an incorrect response.
‐ Tests
1. Occur every two to three weeks.
2. Test will cover ANY MATERIAL WE HAVE DISCUSSE#D IN CLASS. Don’t just assume the test will only cover the ‘new’ material. Anything we’ve had thus far is fair game to be included. Unless otherwise indicated, tests are closed book.
4. Always round to two decimal places.(9.21; NOT 9.2)
5. Always show your work – if the answer is wrong you may still receive partial credit for the correct procedure.
6. No work shown usually results in a poorer grade
7. YOU MAY USE ELECTRONIC TRANSLATORS FOR A TEST. IF YOU HAVE TROUBLE WITH VOCABULARY ASK THE TEACHER FOR HELP
8. CHEATING ON A TEST (OR HOMEWORK) RESULTS IN A GRADE OF ZERO FOR THAT ASSIGNMENT FOR BOTH PARTIES.
‐ Calculators
1. You are expected to have a calculator. A TI‐83+ (or better) graphing calculator is used throughout the course. You should at the least have a scientific calculator to use on homework.
2. School calculators do not leave the classroom. UNLESS THEY ARE ASSIGNED OR RENTED TO YOU
3. If assigned, they are to be returned the NEXT DAY.
4. If the calculator is lost or broken while in your possession, you are responsible for replacing the calculator (cost \$100).
5. If you need a calculator for the year, see the office staff to arrange a possible rental.
Weekly Informational Knowledge Overview - (Students will know...)
Review of Algebra 1 materials in order to get them ready for the year ahead.
Weekly Procedural Knowledge Overview - (Students will be able to...)
interpret drawings, draw geometric figures, model points, lines, and planes
Monday
Tuesday
Wednesday
Thursday
Friday
***FIRST DAY OF CLASS***
Mon. Main Activity/Lesson:
Today is the introduction to the course. Distribute syllabus, calculators, and textbooks. Discuss at length the syllabus of the class and the class expectations.
Evaluation:
Vocabulary:
Homework:
Tues. Main Activity/Lesson:
Continue discussion of the course syllabus and discuss the fundamental question of the course, What is Geometry? We will review some basic ideas from Algebra 1 class.
Evaluation:
Vocabulary:
Homework:
Wed.Main Activity/Lesson:
Evaluation:
Vocabulary:
Homework:
Thurs.Main Activity/Lesson:
Points, Lines, and Planes, section 1‐1. Students will learn the vocabulary of the class today the significance of the terms will be emphasized.
Evaluation:
Seatwork
Vocabulary:
point, line, plane, collinear, coplanar, undefined terms, intersection, definitions, defined terms, space
Homework:
Section 1‐1: 1‐47 odds. Study for the quiz.
Fri.Main Activity/Lesson:
Review section 1‐1 and also algebra 1 information.
Evaluation:
Small Quiz Today
Vocabulary:
Homework:
Review section 1‐1
Materials / Resources (including technology)
Weekly Informational Knowledge Overview - (Students will know...)
the definition of some words in Geometry and how see how they are related from one another;
how to prove theorems;
how to name an angle, a ray and a segment;
how measure segment.
Weekly Procedural Knowledge Overview - (Students will be able to...)
draw, label and identify points, lines and planes in space.
name angles, segments and rays.
Monday
Tuesday
Wednesday
Thursday
Friday
Mon. Main Activity/Lesson:
Discussion and proving of theorems 1 and 2. Definition of terms related to the theorems.
Evaluation:
Seatwork – page 8
Vocabulary:
Collinear points, non‐collinear points, coplanar and noncoplanar points and lines.
Homework:
Workbook – Points, lines and planes. Page 2
Tues. Main Activity/Lesson:
Subsets of line – Segment and Ray
Linear Measure and betweenness
Evaluation:
Seatwork – #s 1‐9, page 18
Vocabulary:
Angle, betweenness, vertex, segment, and ray
Homework:
#s 14 – 32, Page 19
Weds. Main Activity/Lesson:
NO GEOMETRY
Evaluation:
Vocabulary:
Homework:
Thurs. Main Activity/Lesson:
Midpoint of a segment
Evaluation:
Seatwork ‐ #s 1 – 10, p. 30
Vocabulary:
Midpoint, average, irrational number
Homework:
Fri. Main Activity/Lesson:
QUIZ DAY
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology) View PDF
Weekly Informational Knowledge Overview - (Students will know...)
…the definition of angle, right angle, obtuse angle and acute angle;
…how to measure angle using protractor;
…how to classify angles.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…measure angles;
…name the different types of angles;
…draw right, obtuse and acute angles.
Monday
Tuesday
Wednesday
Thursday
Friday
Mon. Main Activity/Lesson:
Distance Formula – distance between two points
Evaluation:
seatwork ‐ #s 19‐24, p. 31
Vocabulary:
distance, coordinate plane
Homework:
Tues. Main Activity/Lesson:
Midpoint Formula ‐ Evaluation:
First 5, seatwork – #s 39‐46
Vocabulary:
Midpoint, average
Homework:
#s 47‐52
Wed. Main Activity/Lesson:
Evaluation:
Vocabulary:
Homework:
Thurs. Main Activity/Lesson:
ANGLES and its part and classification
Evaluation:
Seatwork ‐ #s 1‐11
Vocabulary:
Angle, right, obtuse, acute, vertex, side
Homework:
#s 12‐35
Fri. Main Activity/Lesson:
QUIZ #3
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
Weekly Informational Knowledge Overview - (Students will know...)
…how to measure angles;
…the different types/classifications of angles;
…how to use protractor;
…differentiate complementary from supplementary angles.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…determine the angle as vertical, adjacent or linear pair;
…draw and measure angles;
…apply the concept of angles in real world;
…use their knowledge in Algebra to solve some measures of angles involving Algebraic expressions.
Monday
Tuesday
Wednesday
Thursday
Friday
Mon. Main Activity/Lesson:
ANGLES and its part and classification
Evaluation:
Seatwork ‐ #s 1‐11
Vocabulary:
Angle, right, obtuse, acute, vertex, side
Homework:
#s 12‐35
Tues. Main Activity/Lesson:
Congruent Angles and Angle Bisector
Evaluation:
from the Workbook
Vocabulary:
angle bisector, congruent
Homework:
#s37‐43
Learning Objective:
Evaluation:
Vocabulary:
Homework:
Thurs. Main Activity/Lesson:
Angle Relationships – Adjacent angles, vertical angles, and linear pair.
Evaluation:
Seatwork ‐ #s 1‐18, p. 51
Vocabulary:
adjacent, linear pair, vertical, complementary, supplementary
Homework:
#s 20‐28, p. 51
Fri. Main Activity/Lesson:
QUIZ DAY
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology) View PDF
Weekly Informational Knowledge Overview - (Students will know...)
…the other facts about perpendicular lines;
…how the pairs of angles differ from one another;
…that the sum of the measures of angles in a linear pair is 180 degrees.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…draw perpendicular lines;
…solve problems involving perpendicular lines and pairs of angles;
…define each pair of angles;
…recall the meaning of interior and exterior points.
Monday
Tuesday
Wednesday
Thursday
Friday
Mon. Main Activity/Lesson: Angle Relationship ‐
***Please see lesson plan dated 26/9, Thursday***
Evaluation:
Vocabulary:
Homework:
Main Activity/Lesson:
Perpendicular Lines
Evaluation:
Vocabulary:
perpendicular lines
Homework:
Wed.Thurs. Main Activity/Lesson:
Evaluation:
Vocabulary:
Homework:
Thurs. Main Activity/Lesson:
Perpendicular lines – DAY 2
Evaluation:
Vocabulary:
Homework:
Fri. Main Activity/Lesson:
QUIZ DAY
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology) View PDF
Weekly Informational Knowledge Overview - (Students will know...)
…the different types of polygons;
…the parts of triangle;
…how is concave polygon different from convex polygon;
…the sum of the measures of interior angles of any polygon.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…find the sum of the measures of interior angles of polygons;
…construct triangles;
…name the parts of a triangle;
…enumerate the types of triangle.
Monday
Tuesday
Wednesday
Thursday
Friday
Learning Objective:
Definition of Polygon
Types of Polygons
Classification of Polygons
Evaluation:
Seatwork
Vocabulary:
concave, convex, polygon
Homework:
Learning Objective:
Triangle – Its parts and classification
Evaluation:
Seatwork/Group work
Vocabulary:
scalene, isosceles, equilateral
Homework:
Learning Objective:
Evaluation:
Vocabulary:
Homework:
Learning Objective:
Sum of the Measures of Interior Angles of Polygons
Evaluation:
Seatwork
Vocabulary:
interior angle, diagonal
Homework:
Review for the quiz
Learning Objective:
QUIZ DAY
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered View PDF
Weekly Informational Knowledge Overview - (Students will know...)
…that the sum of the measures of interior angles of a polygon is given by S = (n‐2)180;
…how to solve the measures of interior angles of a polygon algebraically;
…that the measures of each interior angle of a regular polygon are congruent.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…solve the measures of interior angles of a polygon using the formula S = (n‐2)180;
…apply algebra in solving problems involving the measures of interior angles of a triangle;
…count the number of triangles of other polygons.
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
QUIZ DAY
Evaluation:
Vocabulary:
Homework:
Main Activity:
Sum of the measures of interior angles of polygons
Evaluation:
Seatwork, first 7
Vocabulary:
diagonal
Homework:
Main Activity:
Sum of the measures of interior angles of a triangle ‐ ALGEBRA
Evaluation:
Seatwork
Vocabulary:
Homework:
Study QUADRILATERALS – Types, parts and classification
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…the definition of trapezoid and some other characteristics of parallelogram;
…the different terms related to circle;
…that arc is classified according to its measure.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…draw circle;
…define circle and other terms related to it;
…determine the relationship exists between radius and diameter.
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
Trapezoid – its parts and its diagonal
Other characteristics of Parallelogram
Evaluation:
Seatwork from the workbook
Vocabulary:
Legs, base angles, diagonal
Homework:
Main Activity:
Circle – definition and terms related to circle
Evaluation:
Seatwork
Vocabulary:
Radius, center, diameter, chord, tangent, secant, arc
Homework:
Answer the worksheet given by the teacher
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
ARC – its types
Evaluation:
Seatwork
Vocabulary:
semicircle, major and minor arc
Homework:
Main Activity:
QUIZ DAY
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
PLEASE SEE LESSON PLAN DATED October 21‐25
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
PLEASE SEE LESSON PLAN DATED October 21‐25
Evaluation:
Vocabulary:
Homework:
Main Activity:
QUIZ DAY
Evaluation:
Vocabulary:
Homework:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered View PDF
Weekly Informational Knowledge Overview - (Students will know...)
…the lessons covered by the exams.
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
***REVIEW FOR MIDTERM***
Evaluation:
Vocabulary:
Homework:
Main Activity:
MIDTERM EXAMINATION
Evaluation:
Vocabulary:
Homework:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
PREPARATION FOR NUMBO
Evaluation:
Vocabulary:
Homework:
Main Activity:
NUMBO GAME
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…how the formulae are derived;
…the definition of perimeter of a polygon and circumference of circle.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…define perimeter and circumference;
…use the formula to find the perimeter of polygons and circumference of circle;
…apply the concepts of perimeter and circumference to solve word problems.
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
Perimeter – The sum of the measures of all sides of a polygon.
Evaluation:
Drills
Vocabulary:
Perimeter
Homework:
Main Activity:
Perimeter – DAY 2
Circumference – the distance around a circle
Evaluation:
Seatwork – (from the workbook)
Vocabulary:
Homework:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
Problems involving PERIMETER of polygons and CIRCUMFERENCE of circle.
Evaluation:
Group activity
Vocabulary:
Homework:
Main Activity:
SCHOOL TRIP to Manila
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…how to solve 45‐45‐90 and 30‐60‐90 right triangles;
…how the formula of 30‐60‐90 right triangle was derived;
Weekly Procedural Knowledge Overview - (Students will be able to...)
…master the parts of special right triangles;
…solve special right triangle mentally;
…find enjoyment in the lesson.
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
(…continuation of SPECIAL RIGHT TRIANGLE – 45‐45‐90)
Evaluation:
seatwork from the workbook
Vocabulary:
Homework:
Answer problems left in the workbook
Main Activity:
SPECIAL RIGHT TRIANGLE – 60‐30‐90
Derivation, Discussion and Drills
Evaluation:
Exercises
Vocabulary:
Homework:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
(…continuation of 60‐30‐90 SPECIAL RIGHT TRIANGLE)
Evaluation:
seatwork
Vocabulary:
Homework:
Main Activity:
QUIZ # 1
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…what area is;
…the formula and units of area;
…how to apply the formula in solving word problems.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…find the area of something;
…solve real‐world problems involving area of rectangle.
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
(REVIEW)
Evaluation:
Seatwork
Vocabulary:
Homework:
Worksheet
Main Activity:
Area of Polygon – Area of Rectangle
Evaluation:
Seatwork, drills
Vocabulary:
Area, base, height
Homework:
Exercises from the book
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
Area of Rectangle (continuation)
Evaluation:
Seatwork
Vocabulary:
Homework:
Review for the quiz
Main Activity:
QUIZ # 2
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…the derivation of formula – Area of Trapezoid and Rhombus;
…that the formula for the area of trapezoid and rhombus are derived from the general formula A = bh.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…find areas and perimeter of trapezoid and rhombus;
…apply the formula in solving word problems.
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
Follow‐up discussion of the Area of Parallelogram and Triangle.
Discussion of answer in the quiz.
Evaluation:
Vocabulary:
Homework:
Main Activity:
Area of TRAPEZOID and RHOMBUS
Derivation of formulae and Introduction to problem solving
Evaluation:
Seatwork, drills
Vocabulary:
Homework:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
Area of Trapezoid and Rhombus DAY 2 – Word Problems
Evaluation:
Seatwork, First 6.
Vocabulary:
Homework:
Exercises from the book
Main Activity:
QUIZ # 3
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…the derivation of formula for the area of rhombus, kite and circle;
…how to apply the area of rhombus and circle to real world problems.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…solve or find the area of rhombus, kite and circle using the formula;
…derive the formula for rhombus and circle.
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
Area of RHOMBUS and KITE
Definition, Introduction and Derivation of formula
Evaluation:
Exercises from the book
Vocabulary:
Kite, Diagonals
Homework:
Exercises from the book
Main Activity:
Area of RHOMBUS and KITE
Definition, Introduction and Derivation of formula (DAY 2)
Evaluation:
Group Work
Vocabulary:
Homework:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
Area of Circle – A = ㅠr2 Definition, Introduction and Derivation of formula
Evaluation:
Exercises from the book
Vocabulary:
Homework:
Review for the quiz tomorrow
Main Activity:
QUIZ # 4
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
….the important vocabulary of the chapter.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…find the 3rd side of triangle using the pythagorea theorem.
….find the area of kite and other polygone.
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
Discuss 8‐2 The Pythagorean theorem and it’s converse.
Evaluation:
Vocab: Pythagorean Theorem, hypotenuse, Pythagorean triple.
Vocabulary:
Homework:
8‐2, 1‐33 ODDS
Main Activity:
Review the Pythagoream Theorem and do more examples on the board.
Evaluation:
Students will come to the board and do additional examples
Vocabulary:
converse
Homework:
Main Activity:
NO CLASS – BLOCK SCHEDULE
Evaluation:
Vocabulary:
Homework:
Main Activity:
Do section 8‐2 Coordinates in space, about ordered triples to show the hypotenuse how it can be found for such configurations
Evaluation:
Students come to the board to do the example problems. Vocab: Ordered triple.
Vocabulary:
Homework:
page 557#s 1‐19
Main Activity:
QUIZ DAY.
Evaluation:
After quiz, continue discussion of triangles in order to move to advanced work next week.
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…the three basic trigonometric functions;
…how to solve triangles using SOH‐CAH‐TOA.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…find the area of regular polygons using SOH‐CAH‐TOA;
…apply the SOH‐CAH‐TOA in solving for the area of regular polygons.
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
Short review about the area of regular polygons and special right triangles
Evaluation:
first 7
Vocabulary:
Homework:
Main Activity:
Trigonometric Ratios ‐ SOH‐CAH‐TOA
*short review of the parts of Rt. triangle
Evaluation:
exercises in the book
Vocabulary:
sine, cosine and tangent
Homework:
Exercises in the book
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
Finding the area of regular polygons involving trigonometric functions
Evaluation:
Seatwork
Vocabulary:
Homework:
Review for the quiz
Main Activity:
QUIZ # 5
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…how to apply SOH‐CAH‐TOA in finding the area of a regular polygons;
…how to find the area of composite polygons.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…find the area of regular polygons with SOHCAH‐ TOA;
...recall all the lessons in the quarter.
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
(continuation of area of regular polygons)
‐ With application of SOH‐CAH‐TOA.
Evaluation:
Exercises
Vocabulary:
Homework:
exercises from the book.
Main Activity:
AREA OF REGULAR POLYGONS –Composite Polygons
Evaluation:
Exercises from the book
Vocabulary:
Homework:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
Review for the final exams
Evaluation:
Vocabulary:
Homework:
Main Activity:
Review for the final exams
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…the students shall be able to recall all the lessons covered by the final exams;
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
TRIGONOMETRIC RATIOS –SOH‐CAH‐TOA
Evaluation:
Seatwork and Dri
Vocabulary:
Homework:
Main Activity:
Review for the Final Exams
Evaluation:
Vocabulary:
Homework:
Main Activity:
FINAL EXAMINATION – FIRST DAY
Evaluation:
Vocabulary:
Homework:
Main Activity:
FINAL EXAMINATION – SECOND DAY
Evaluation:
Vocabulary:
Homework:
Main Activity:
FINAL EXAMINATION – THIRD DAY
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…students shall be able to differentiate the angle of elevation from the angle of depression;
…the students shall be able to use the correct trigonometric ratio in solving realworld problems;
…the students shall be able to determine the relationship of angle of elevation and the angle of depression.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…define and name the angle of elevation and angle of depression in each given problem;
…illustrate the problem correctly;
…solve each real‐world problem with accuracy.
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
ANGLE OF ELEVATION – Introduction and Application
Word Problems
Evaluation:
Seatwork, drill
Vocabulary:
angle of elevation, line of sight
Homework:
exercises from the book
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
(continuation) ANGLE OF ELEVATION
ANGLE OF DEPRESSION – An Intro, Definition and discussion
Evaluation:
Drill
Vocabulary:
Homework:
Main Activity:
REAL‐WORLD PROBLEMS involving Angle of Depression and Angle of Elevation
Evaluation:
Vocabulary:
Homework:
Main Activity:
GROUP WORK/seatwork
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…students shall be able to answer the quiz very well;
…students shall be able to derive the formula for the law of sine;
…to remember that law of sine is only used to solve oblique triangles;
…to define oblique triangles.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…to apply the law of sine when the given are two angles and one side of an oblique triangle;
…to illustrate and to answer real‐world problems accurately.
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
‐ Continuation of the ANGLE OF ELEVATION AND ANGLE OF DEPRESSION due to some questions and clarifications from the students. Review for the quiz.
Evaluation:
Seatwork
Vocabulary:
Homework:
review for the quiz
Main Activity:
QUIZ # 1
Evaluation:
Vocabulary:
Homework:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
THE LAW OF SINES – this law is used to solve the missing parts of oblique Triangles. (SAA and ASA)
Evaluation:
Drill
Vocabulary:
included side and angle, non‐included side and angle.
Homework:
exercises from the book
Main Activity:
LAW OF SINE – Real‐world problems Application of the law of Sine
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…students shall be able to apply the law of sine and cosine in solving real‐world problems;
…students shall be able to derive the formula of the law of cosine;
…students shall be able to pass the quiz.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…to apply the laws of sine and cosine to solve real‐world problem;
…to derive the formula for the law of cosine.
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
LAW OF SINE – Application to Real‐World Problem (CONTINUATION from last week)
Evaluation:
Seatwork, drill
Vocabulary:
Homework:
Main Activity:
LAW OF COSINE – Definition and Derivation of formulas
***DISCUSSION FOR THE ENTIRE PERIOD***
Evaluation:
Vocabulary:
Homework:
exercises from the book
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
LAW OF COSINE – Definition and Derivation of formulas
***CONTINUATION***
Evaluation:
Seatwork and drills
Vocabulary:
Homework:
review for the quiz
Main Activity:
QUIZ # 2
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…students shall be able to derive the formula of the law of cosine;
Weekly Procedural Knowledge Overview - (Students will be able to...)
…to derive the formula for the law of cosine.
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
LAW OF SINE – Application to Real ‐ World Problem
Evaluation:
Vocabulary:
Homework:
Main Activity:
LAW OF COSINE – Definition and Derivation of formulas
Evaluation:
Vocabulary:
Homework:
Main Activity:
LAW OF COSINE – Definition and Derivation of formulas
Evaluation:
Vocabulary:
Homework:
Main Activity:
Seatwork and drills
Evaluation:
Vocabulary:
Homework:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…how to apply the lateral and surface area of right prism in word problems;
…how to derive the formula of the surface area of cube;
…the formula to find the surface area of a cube.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…to find the lateral and surface areas of prism and cube;
…to solve word problems involving lateral and surface areas of prism and cube.
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
NO CLASSES
Evaluation:
Vocabulary:
Homework:
Main Activity:
HOLIDAY – EDSA People Power
Evaluation:
Vocabulary:
Homework:
Main Activity:
SURFACE AREA AND LATERAL AREA OF RIGHT PRISM – Word problems
Evaluation:
seatwork, drills
Vocabulary:
surface area, lateral area
Homework:
Exercises from the book
Main Activity:
SURFACE AREA AND LATERAL AREA OF CUBE
Evaluation:
Seatwork, drills
Vocabulary:
Homework:
Exercises from the book
Main Activity:
QUIZ # 3
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…the definition of cylinder and the derivation of the formula of the surface area of cylinder;
…the real‐world application of the surface area of a cylinder.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…to derive the formula for the surface area of a cylinder;
…to solve real‐world problems involving surface area of cylinder.
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
CYLINDER‐ Definition and its Surface Area
Discussion and derivation of formula
Evaluation:
drill
Vocabulary:
Homework:
exercises from the book
Main Activity:
APPLICATION OF SURFACE AREA OF CYLINDER
Word problems– Real‐world problems
Evaluation:
seatwork
Vocabulary:
Homework:
Exercises from the book
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
SOLVING WORD PROBLEMS INVOLVING SURFACE AREA OF CYLINDER
Evaluation:
Group work
Vocabulary:
Homework:
Review for the quiz tomorrow
QUIZ # 4
Main Activity:
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…the formula to find the surface area of cone and sphere;
…how the surface area of cone and sphere differ from one another.
Weekly Procedural Knowledge Overview - (Students will be able to...)
…to solve problems involving surface area of cone and sphere.
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
SURFACE AREA OF CONE – Definition and parts Evaluation:
seatwork, drills
Vocabulary:
axis
Homework:
exercises from the book
Main Activity:
WORD PROBLEM INVOLVING SURFACE AREA OF CONE
Evaluation:
Group work
Vocabulary:
Homework:
Exercises from the book
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
SURFACE AREA OF SPHERE Evaluation:
seatwork, drills
Vocabulary:
Homework:
Main Activity:
PI DAY CELEBRATION
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…the derivation of the formula to fins the volume of sphere and prism;
…the definition of volume;
Weekly Procedural Knowledge Overview - (Students will be able to...)
…to find the volume of prism and sphere.
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
DEFINITION OF VOLUME ‐ VOLUME OF SPHERE Evaluation:
seatwork, drills
Vocabulary:
Homework:
Exercises from the book
Main Activity:
QUIZ # 5
Evaluation:
Vocabulary:
Homework:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
VOLUME OF RECTANGULAR PRISM
V= Bh or V = lwh
Evaluation:
seatwork
Vocabulary:
Homework:
exercises from the book
Main Activity:
VOLUME OF REGULAR PRISM Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…the formula for the volume of cube, cylinder, cone and pyramid;
…the real‐world application of the volume of cone, cylinder, cube and pyramid;
…the derivation of the formulas.
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
VOLUME OF CUBE AND CYLINDER Derivation of the formula and some Illustrative examples
Evaluation:
seatwork, drills
Vocabulary:
Homework:
exercises from the book
Main Activity:
VOLUME OF CONE AND PYRAMID Derivation of formula and some Illustrative examples
Evaluation:
seatwork, drills
Vocabulary:
Homework:
review for the quiz
Main Activity:
Evaluation:
Vocabulary:
Homework:
QUIZ # 6
Main Activity:
Evaluation:
Vocabulary:
Homework:
SPAS OLYMPICS
Main Activity:
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…MIDTEMR EXAMS
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
ACTIVITY – NUMBO GAME
Evaluation:
Vocabulary:
Homework:
Main Activity:
REVIEW FOR THE MIDTERM EXAMS
Evaluation:
Vocabulary:
Homework:
Main Activity:
MIDTERM EXAMS
Evaluation:
Vocabulary:
Homework:
Main Activity:
MIDTERM EXAMS
Evaluation:
Vocabulary:
Homework:
Main Activity:
MIDTERM EXAMS
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…how to write statement to if‐them form;
…how to write the converse of the given statement;
…recall the different properties of equality.
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
LOGIC – If‐Then form of Statement
Writing statements in the form of If‐Then statement
Evaluation:
seatwork and drills
Vocabulary:
Homework:
Main Activity:
(…continuation of) If‐Then Form of Statement
PROPERTIES OF EQUALITY
Evaluation:
seatwork and drills
Vocabulary:
Homework:
exercises from the book
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
APE, SPE, MPE, DPE, Symmetric, Reflexive, Transitive Property
Evaluation:
seatwork, drills
Vocabulary:
Homework:
Exercises from the book
Main Activity:
PROVING POSTULATE AND THEOREM Segment Addition Postulate
Evaluation:
seatwork and drills
Vocabulary:
Homework:
exercises from the book
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…use two‐column proof to prove theorems;
…that all right angles are congruent.
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
PROVING THEOREMS ‐ Right Angles Theorem
Evaluation:
seatwork
Vocabulary:
Homework:
review for the quiz
Main Activity:
QUIZ # 1
Evaluation:
Vocabulary:
Homework:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
HOLIDAY – Labor Day
Evaluation:
Vocabulary:
Homework:
Main Activity:
PROVING THEOREMS ‐ Congruent Triangles
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…prove SSS and SAS Congruence Postulates;
…apply the SSS and SAS Congruence Postulates in proving other postulates.
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
SSS Congruence Postulate ‐ If the three sides of a triangle are congruent respectively to the three corresponding sides of another triangle, then the two triangles are congruent.
Evaluation:
seatwork, group work
Vocabulary:
Homework:
proving using two‐column proof
Main Activity:
SAS Congruence Postulate ‐ If the two sides and an included angle of a triangle are congruent respectively to the corresponding two sides and an included angle of another triangle, then the two triangles are congruent. Evaluation: seatwork
Evaluation:
Vocabulary:
Homework:
exercise from the book
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
SAS Congruence Postulate
Evaluation:
seatwork
Vocabulary:
Homework:
review for the quiz
Main Activity:
QUIZ # 2
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…the proof of the ASA Congruence Postulate and the AAS;
…how to apply ASA postulate and AAS theorem in proving.
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
ASA Congruence Postulate: If the two angles and an included side of triangle are congruent respectively to the corresponding two angles and an included side of another triangle, then the two triangles are congruent.
Evaluation:
Vocabulary:
Homework:
Guided Practice in the book
Main Activity:
ASA Congruence Postulate ‐Application and proving
Evaluation:
seatwork, drills
Vocabulary:
Homework:
exercises from the book
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
AAS Theorem: If the two angles and a non‐included side of a triangle are congruent respectively to the corresponding two angles and a non‐included side of another triangle, then the two triangles are congruent.
Evaluation:
Vocabulary:
Homework:
Main Activity:
(continuation of the previous lesson) AAS Theorem
Evaluation:
seatwork, drills
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…how to make tessellations;
…how to apply CPCTC in proving theorems.
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
(…continuation of) CPCTC (PROVING THEOREMS)
Evaluation:
seatwork. Drills
Vocabulary:
Homework:
exercises from the book
QUIZ # 3
Main Activity:
Evaluation:
EXERCISES FROM THE BOOK
Vocabulary:
Homework:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
ACTIVITY ‐ TESSELLATIONS
Evaluation:
Vocabulary:
Homework:
Main Activity:
ACTIVITY ‐ TESSELLATIONS
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
…how to measure central angles;
…the different types of arcs;
…the definition of semi‐circle, minor and major arcs.
Weekly Procedural Knowledge Overview - (Students will be able to...)
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
CIRCLE – Central Angles and Arcs
Evaluation:
seatwork, drills
Vocabulary:
Homework:
Exercises from the book
Main Activity:
(continuation of the previous lesson) MEASURING CENTRAL ANGLES AND ARCS
Evaluation:
seatwork, drills
Vocabulary:
Homework:
exercises from the book
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
SCHOOL TRIP 2014
Evaluation:
Vocabulary:
Homework:
Main Activity:
SCHOOL TRIP 2014
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
The difference and importance of arcs and chords
Weekly Procedural Knowledge Overview - (Students will be able to...)
Use congruent chords to find arc measure
Use congruent arcs to find chord lengths
Use a radius perpendicular to a chor
Use a diameter perpendicular to a chord
Use inscripbed angles in proofs
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
Discuss 10‐3. Arcs and Chords.
Evaluation:
Vocabulary:
arcs and chords
Homework:
1‐33 ODDS
Main Activity:
Inscribed Angles, section 10‐4.
Evaluation:
Vocabulary:
Inscribed angle, intercepted arc,
Homework:
10‐4 #s 1‐33 ODDS
Main Activity:
NO CLASS – BLOCK SCHEDULE
Evaluation:
Vocabulary:
Homework:
Main Activity:
10‐5 calculating tangents to curves. Students will find the point of tangency and a common tangent. Students will identify a tangent.
Evaluation:
Vocabulary:
Point of tangency, common tangent, tangent
Homework:
10‐5, #s 1‐33 ODDS
Main Activity:
QUIZ DAY.
Begin preparing for the final exam.
Evaluation:
Vocabulary:
Homework:
Study for the coming exam.
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
#37. Review for exam Week #38. Exam Week, No Instruction~!
Weekly Procedural Knowledge Overview - (Students will be able to...)
….Review for exam.
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
BEGIN REVIEW FOR THE CHAPTER TEST
Evaluation:
Vocabulary:
Homework:
Main Activity:
GIVE CHAPTER TEST
Evaluation:
Vocabulary:
Homework:
Main Activity:
NO CLASS BLOCK SCHEDULE
Evaluation:
Vocabulary:
Homework:
Main Activity:
REVIEW FOR THE FINAL CUMULATIVE EXAM.
Evaluation:
Vocabulary:
Homework:
Main Activity:
REVIEW FOR THE FINAL CUMULATIVE EXAM.
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered
Weekly Informational Knowledge Overview - (Students will know...)
Exam Week, No Instruction~!
Weekly Procedural Knowledge Overview - (Students will be able to...)
Exam Week, No Instruction~!
Monday
Tuesday
Wednesday
Thursday
Friday
Main Activity:
Exam Week, No Instruction~!
Evaluation:
Vocabulary:
Homework:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Main Activity:
Evaluation:
Vocabulary:
Homework:
Materials / Resources (including technology)
State of Minnesota Standards Covered