Geometry Handbook - Tumwater School District



Geometry Handbook 2012-13

Mrs. Joelle King Ph: 709-7863

Joelle.king@tumwater.k12.wa.us

Contents

Introduction & Welcome ……………………………………………………………………….. 1

Textbook information ……………………………………………………………………………. 1

Online resources and Login information ….…………………………………………… 1

Required Materials …………………………………………………………………………………… 2

Grades ………………….…………………………………………………………………………………… 2

Graduation Requirements ………………………………………………………………………. 3

General Classroom Responsibilities ……………………………………………………… 3

Absences …………………………………………………………………………………………………… 4

Homework policies ……………………………….…………………………………………………4

Testing …………………………………………………………………………………………………….. 5

Extra Help ………………………………………………………………………………………………… 6

7 Habits ……………………………………………………………………………………………………… 7

EOC allowed formulas …………………………………………………………………………… 8

Formulas you will need to memorize .................................................... 10

Postulates, Properties, and Theorems

Chapter 1 ……………………………………………………………………………………… 11

Chapter 2 ……….……………………………………………………………………………. 12

Chapter 3 ……………………………………………………………………………………… 14

Chapter 4 ……………………..……………………………………………………………… 15

Chapter 5 ……………………………………………………………………………………… 16

Chapter 6 ……………………………………………………………………………………… 17 Right Triangles>……………………………………………………………………………… 20

EOC Standards Checklist ………………………………………………………………………. 21 CHAMPS………………………………………………………………………………….………..……… 24

Classroom Meetings…………………………………………………………………………………25

Mistaken Goals of Misbehavior…………………………………………..………………….26

This handbook belongs to__________________________________ Period______

If found, please return to room 203.

Introduction & Welcome

Welcome to Geometry! I am looking forward working with you and hope that your year is both fun and challenging. This handbook contains almost everything you need to know about this class and my expectations. Please keep it with your math notebook at all times so that you can review classroom information regularly.

Geometry is one of the most useful and relevant math courses you will take in high school. We are surrounded by geometric ideas every day. Through the study of lines, polygons, circles, and solids, you will learn to apply geometry to your world. Though you will not be asked to draw on your Algebra skills every day, the ability to solve simple equations is expected regularly. Please ask for help if this is a weakness for you.

Textbook information

Burger, Edward, et al. Geometry. Holt, Rinehart and Winston, 2007

Home Book number __________

Online resources and Login information

Holt online access login: bhhsgeometry2 password: wolves

my.

Skyward Family Access login:__________________ password__________________

BHHS web page link

Catchup Math login: bhhswolfpack password__________________



bhhsmathstandards. (access reteach, practice B, and reading strategies for each section)

login: bhhswolfpack password: wolves

Mrs. King's webpage (no login necessary)

or follow the links on school website.

Other useful sites for independent study and tutoring

•

• (khan academy)

• (Interactive Math; pick a topic and explore!)

• (Investigating Geometry)

Required Materials

Please have the following materials with you every day.

• Geometry and vocabulary handbooks

• Composition Notebook (Notes)

• Filler notebook paper OR spiral notebook (assignments)

• Graph Paper (will not need much)

• Pencils

• Colored pencils or pens (Corrections and/or notes)

• Highlighter (optional)

• Scientific Calculator (needs sin, cos, tan buttons --should be around $8-$12)

➢ cell phone and ipod calculators will not be allowed.

➢ Students without a calculator will be asked to check one out through the library.

• Ruler (6 inch okay)

• Compass

• Section in 3-ring binder or a pocket folder for math

• box of kleenex (optional)

Note: The calculator is not intended to replace your thinking. You should be doing most simple calculations in your head. However, the calculator is a critical tool when decimal solutions are necessary and when numbers are large.

A calculator is required on the Geometry EOC. Though a graphing calculator is acceptable,

it is not necessary at this level.

All About Grades

A 93%

A- 90%

B+ 87%

B 83%

B- 80%

C+ 77%

C 73%

C- 68%

D* 65%

*A D is not sufficient for advancement to Algebra 2

Daily Work (preparation) 10% of the grade

• warm ups

• classroom and home practice

• lesson notes & activities

• homework quizzes

Assessment (performance) 90% of the grade

• section quizzes

• unit tests

• final exam

Graduation Requirements

End of Course Assessment (EOC)

All current 9th and 10th graders are required to pass both the Algebra 1 and Geometry EOCs in order to graduate. If you did not pass the Algebra EOC, then you will be offered intervention this fall and a retest in January. The Geometry EOC will be given in late May or early June.

|Algebra EOC |May 2012 score |January 2013 score |Standard Met |

| | | | |

High School Math Credit

BHHS students are required to earn 3 full years of math to graduate. This most likely includes Algebra 1, Geometry, and Algebra 2. Financial Literacy may replace Algebra 2 if taken in the senior year.

Four-Year College Entrance

Four year colleges and universities in Washington State require completion of Algebra 2 for entrance. Taking 4 full years of math, however, will improve your chances of college acceptance at competitive institutions.

General Classroom responsibilities

Be Here

Please take responsibility and be here every day. Absences in math class are the number one reason students struggle.

Be prompt

You are expected to arrive to class on time each day, ready to begin class at the bell. Losing class time at the beginning of the period is disrespectful to those who are ready and translates into less learning time for everyone.

Be Prepared

Have required materials with you every day.

Be Willing to Try

By completing your assigned practice every day, you will learn Geometry quickly and will minimize the need for extra help. If you get behind, get help immediately.

Be Honest

You have a right to get credit for your own work. Please do not share your papers with other students so that they can copy what you spent your valuable time doing. If a friend asks you if he/she can copy your paper, try this:

“I can’t let you copy my paper, but I’d be happy to help you with your assignment.” (

Be Helpful

We’re in this together. Please be willing to help those around you when necessary and appropriate.

Be Neat

According to school policy, food and drink are not allowed in the classrooms or pods of the B building. In this room, I allow drinks with lids only.

➢ Always pick up after yourself before leaving class.

Be Respectful

Cell phones and portable listening devices must be out of sight and sound at all times. Please check your texts and other messages during passing time or lunch. If your parents must reach you during class time, please have them call the front office to have a message delivered to you.

➢ Students using a cell phone in class can expect to have the phone taken and held for the remainder of the period

Be Informed

Make it a habit to regularly check your Geometry status using Skyward and let me know if you find any errors. I expect you to take responsibility for and ownership of your progress. Please let me know if you need help with this.

Absences

Whenever possible, please avoid scheduling appointments during math class. In the event of an unavoidable absence, however, please do the following:

On the day(s) of the absence:

❑ Check Mrs. King’s webpage to find out what we did in class that day.

❑ Add the assignment (if any) to your assignment sheet.

❑ If you feel well enough and have the time, try to do the assignment from that day using the Holt online lessons for help.

When you return to school:

❑ Use the notebook in the back of the classroom to correct your assignment that was due on the day of the absence. Take a moment to fix any mistakes you made.

❑ Make sure that your paper has the correct heading and turn in to the in-tray on my desk.

❑ Make arrangements with Mrs. King to get extra help on what you missed, if needed.

Homework procedures and policies

How much homework should I expect?

The purpose of homework is to give you practice to learn and reinforce concepts taught in class. Research shows that the best way to learn something is to teach someone else. The second most effective way to learn something is practice, practice, practice! You should expect to be assigned Geometry for home practice every day. However, many weeks will have only 4 assignments. Your homework should take 20-30 minutes.

Assignments are worth 4 points. To receive full credit you must have attempted each problem and all work must be shown. No work, no credit!

Correcting your homework

Any odd problems from the textbook need to be corrected using the back of your book, prior to coming to class. Even answers will be corrected in class immediately after the warm-up. You are responsible for correcting your own paper and fixing your mistakes. Please work with a neighbor to clean up your errors before we discuss the assignment as a class.

Format and Heading

Name

SCORE Date, period (target) 3.1

Warm-up:

1. 2. 3.

p. 32 #1 - 1999 odds

------------------------------------------------------------------------------

Original Work Corrections

1.

3.

5.

Late Work

Late work will be accepted for partial credit

until the day of the unit test.

If you have work to turn in late, please correct

it, fix your mistakes, score it, and place it

in the tray on the bookshelf by the door.

Testing

Quizzes

I will be giving quizzes regularly throughout a unit to check that you are learning the targets identified in a timely manner. Scores will be recorded in the grade book. If you score higher on the unit test, then your quiz score will be dropped. If your unit test score is lower than the quiz score, then both scores will be kept.

Testing

A unit test will be given at the end of each chapter or unit of study. In order to show mastery on each section of the unit test, students must score at least 80%. Classroom theorem sheets are always allowed on the unit tests.

Retesting

Students will be expected to retest for every section score below 80%. The retest will be given in class and students must have completed the required retest preparation in order to be eligible.

❑ Print the Reading Strategies and Reteach handouts from each section you plan to retest.

❑ Complete all handouts.

❑ Correct the handouts using the answer keys provided in the classroom.

A retest will not be offered to students who did not complete the required preparation.

Extra Help Resources

Your online textbook has many additional resources available for students. You can view video lessons, see worked-out problems from homework, take interactive practice tests and quizzes, play games, and much more!



If you would like additional practice on a particular unit or would like to review Algebra or Geometry, see Mrs. King for a free Catchup math account.

Math Center

Student and teacher tutors will be available in the math center on Tuesday and Thursday, 2:15 - 3:15. No appointment is necessary. Come as you are!

After-school with Mrs. King

See the schedule on the front board indicating which days each week that Mrs. King will be here after school. Let me know you're coming or just drop in!

PACK time

I am only here part time, so I will be unavailable for help during PACK. Please plan to use your PACK time in your 2nd period class as a study hall.

Do you enjoy math and like helping others? Maybe you’d like to volunteer as a tutor! If you are interested in helping out, see Mrs. King

about working with Algebra and Geometry students after school or during PACK time. Community service hours are available.

“No one is useless in this world who lightens the burdens of another.”

- Charles Dickens

7 Habits of Highly Effective Math Students (as penned by Mrs. Mulcahy ()

Throughout the year, you will be given several opportunities to reflect on and assess your progress in class. Though grades will inform you of your learning, you may use the following “habits” to assess your behaviors that contribute to learning.

Preparation

❑ Come to class on time, with all required materials.

❑ Complete your assignments on time, ready to be turned in at the beginning of the period on the day they are due.

Engagement

❑ Use your class time productively. Wasted time is wasted learning.

❑ When doing an assignment, do more than write down answers to problems; work to understand the concepts that are being studied.

❑ Take careful notes in class.

❑ Get actively involved in the lessons, both orally and mentally.

Practice

❑ Complete your assignments on time, ready to be turned in at the beginning of the period on the day they are due.

❑ Get actively involved in the lessons, both orally and mentally.

Follow-through

❑ When having trouble with an assignment, seek help from a friend, a teacher, the solution book, or hotmath.

Feedback

❑ Always correct your assignments using the resources provided.

Communication

❑ Ask questions of a neighbor or the teacher when you have a question during the lesson.

❑ Have someone that you can work on math with outside of class.

Names and Phone numbers of friends to work with:

___________________________ ______________________________

___________________________ ______________________________

Praise

❑ Support your friends and neighbors.

❑ Congratulate others on a job well done.

❑ Celebrate your own successes.

EOC allowed formulas

[pic]

Formulas you will need to memorize

|Distance between 2 points: |[pic] |

|Midpoint of a segment: |[pic] |

|Slope of a line, given 2 points: |[pic] |

|The Pythagorean Theorem: |[pic] |

|Equation of a Line: |[pic] |

| |[pic] |

|Circumference of a Circle: |[pic] |

|Area of common 2-dimensional figures |

|Rectangle |[pic] |

|Triangle |[pic] |

|Parallelogram |[pic] |

|Rhombus / kite |[pic] |

|Trapezoid |[pic] |

|Circle |[pic] |

|Common Unit Conversions |

|1 foot = 12 inches |1 meter = 100 centimeters |

|1 yard = 3 feet |1 inch = 2.54 centimeters |

|1 miles = 5,280 feet | |

Chapter 1 Properties, Postulates and Theorems

Points, Lines, and Planes

|Name or Number |What is Says |Picture |

|1-1-1 |Through any two points there is exactly one line. | |

|1-1-2 |Through any three noncollinear points there is exactly one plane | |

| |containing them. | |

|1-1-3 |If two points lie in a plane, then the line containing those points | |

| |lies in the plane. | |

|1-1-4 |If two lines intersect, then they intersect in exactly one point. | |

|1-1-5 |If two planes intersect, then they intersect in exactly one line. | |

|Segment Addition |If B is between A and C, then [pic] | |

|Postulate | | |

|Angle Addition Postulate |If S is in the interior of [pic], then [pic] | |

Chapter 2 Properties, Postulates and Theorems

Geometric Reasoning

| | |

|Addition Property of Equality |If [pic], then [pic] |

|Subtraction Property of Equality |If [pic], then [pic] |

|Multiplication Property of Equality |If [pic], then [pic] |

|Division Property of Equality |If [pic] and [pic], then [pic] |

|Reflexive Property of Equality |[pic] |

|Symmetric Property of Equality |If [pic], then [pic]. |

|Transitive Property of Equality |If [pic] and [pic], then [pic] |

|Substitution Property of Equality |If [pic], then [pic] can be substituted for [pic] in any expression. |

|Reflexive Property of Congruence: |[pic] |

| | |

|figure A ( figure A | |

|Symmetric Property of Congruence: |If [pic], then [pic]. |

| | |

|If figure A ( figure B, then figure B ( figure A. | |

|Transitive Property of Congruence |If [pic] and [pic], then [pic]. |

| | |

|If figure A ( figure B and figure B ( figure C, then figure A ( figure C. | |

Chapter 2 Properties, Postulates and Theorems

Geometric Reasoning

|Theorem Name |What it says… |Key Words |Picture |

|Linear Pair Theorem |If two angles form a linear pair, then they are |Two angles | |

|2-6-1 |supplementary. | | |

| | |Linear pair | |

| | | | |

| | |Supplementary | |

| |If two angles are supplementary to the same angle (or to two|Two angles | |

|Congruent Supplements Theorem|congruent angles), then the two angles are congruent. | | |

| | |Supplementary | |

|2-6-2 | | | |

| | |Congruent | |

|Right Angle Congruence |All right angles are congruent. |Right angle | |

|Theorem | | | |

|2-6-3 | |Congruent | |

|Congruent Complements Theorem|If two angles are complementary to the same angle (or to two|Two angles | |

|2-6-4 |congruent angles), then the two angles are congruent. | | |

| | |Complementary | |

| | | | |

| | |Congruent | |

|Common Segments Theorem |Given collinear points A, B, C and D arranged as shown, if |Collinear | |

|2-7-1 |[pic], then [pic]. | | |

| | |Congruent | |

|Vertical Angles Theorem |Vertical angles are congruent. |Vertical Angles | |

|2-7-2 | | | |

| | |Congruent | |

|2-7-3 |If two congruent angles are supplementary, then each angle |Congruent angles | |

| |is a right angle. | | |

| | |Supplementary | |

| | | | |

| | |Right angle | |

Chapter 3 Properties, Postulates and Theorems

Parallel and Perpendicular Lines

|Postulate or Theorem Name |What it says |Key Words |Picture |

|If 2 parallel lines are cut by a transversal, then… |

|Corresponding Angles |…the corresponding angles are congruent. |Parallel lines | |

|Postulate | | | |

| | |Transversal | |

| | | | |

| | |Corresponding angles | |

|Alternate Interior Angles |…the alternate interior angles are congruent. |Parallel lines | |

|Theorem | | | |

| | |Transversal | |

| | | | |

| | |Alternate interior angles | |

|Alternate Exterior Angles |…the alternate exterior angles are congruent. |Parallel lines | |

|Theorem | | | |

| | |Transversal | |

| | | | |

| | |Alternate exterior angles | |

|Same-side Interior Angles |…the same-side interior angles are |Parallel lines | |

|Theorem |supplementary. | | |

| | |Transversal | |

| | | | |

| | |Same-side interior angles | |

| | | | |

| | |Supplementary | |

|Proving lines are parallel |

|Corresponding Angles |If 2 coplanar lines are cut by a transversal |Transversal | |

|CONVERSE |so that a pair of corresponding angles are |Corresponding angles | |

| |congruent, THEN THE LINES ARE PARALLEL. |parallel | |

|Alternate Interior Angles |If 2 coplanar lines are cut by a transversal |Transversal | |

|CONVERSE |so that a pair of alternate interior angles | | |

| |are congruent, THEN THE LINES ARE PARALLEL. |Alternate interior angles | |

| | | | |

| | |parallel | |

|Alternate Exterior Angles |If 2 coplanar lines are cut by a transversal |Transversal | |

|CONVERSE |so that a pair of alternate exterior angles |Alternate exterior angles | |

| |are congruent, THEN THE LINES ARE PARALLEL. |parallel | |

|Same-side Interior Angles |If 2 coplanar lines are cut by a transversal |Transversal | |

|CONVERSE |so that a pair of same-side interior angles |Same-side interior angles | |

| |are supplementary, THEN THE LINES ARE |Supplementary | |

| |PARALLEL. |parallel | |

|Theorems about perpendicular lines |

|3-4-1 |If intersecting lines form a congruent linear|Linear Pair | |

| |pair, then the lines are perpendicular. | | |

| | |Perpendicular | |

| | | | |

| | | | |

| | | | |

|Perpendicular Transversal |In a plane, if a transversal is perpendicular|Perpendicular | |

|Theorem |to one of 2 parallel lines, then it is | | |

| |perpendicular to the other. |Transversal | |

| | | | |

| | |Parallel | |

| | | | |

|3-4-3 |If 2 coplanar lines are perpendicular to the |Perpendicular | |

| |same line, then the 2 lines are parallel to | | |

| |each other. |Parallel | |

| | | | |

Chapter 4 Properties, Postulates and Theorems

Congruent Triangles

| |Postulate or Theorem Name |What it says |Sketch |

|4-2 | | | |

| | | | |

| |Triangle Sum Theorem |The sum of the angle measures of | |

| |(4-2-1) |a triangle is 180°. | |

| | | | |

| |Exterior Angle Theorem |The measure of an exterior angle is equal to the sum of its 2 | |

| | |remote interior angles. | |

| | | | |

| |Third Angles Theorem |If two angles of one triangle are congruent to two angles of | |

| |(4-2-5) |another triangle, then the third pair of angles are congruent. | |

| | | | |

|Ways to prove that 2 triangles are congruent |

|4-4 |Side-Side-Side (SSS) |If three sides of one triangle are congruent to three sides of | |

| |Congruence |another triangle, THEN THE TRIANGLES ARE CONGRENT. | |

| | | | |

| |Side-Angle-Side (SAS) |If two sides and the included angle of one triangle are congruent | |

| |Congruence |to two sides and the included angle of another triangle, THEN THE | |

| | |TRIANGLES ARE CONGRENT. | |

|4-5 |Angle-Side-Angle (ASA) |If two angles and the included side of one triangle are congruent | |

| |Congruence |to two angles and the included side of another triangle,THEN THE | |

| | |TRIANGLES ARE CONGRENT. | |

| | | | |

| |Angle-Angle-Side (AAS) |If two angles and the NON-included side of one triangle are | |

| |Congruence |congruent to two angles and the NON-included side of another | |

| | |triangle, THEN THE TRIANGLES ARE CONGRENT. | |

| | | | |

| |Hypotenuse-Leg (HL) |If the hypotenuse and a leg of a right triangle are congruent to | |

| |Congruence |the same parts of another, THEN THE TRIANGLES ARE CONGRENT. | |

| | | | |

| | | | |

|4-6 |CPCTC |The corresponding parts (sides and angles) of congruent triangles | |

| |(or Definition of congruent |are congruent. | |

| |triangles) | | |

| | | | |

| | | | |

| | | | |

|4-8 |Isosceles Triangles Theorem |If 2 sides of a triangle are congruent, then the angles opposite | |

| | |them (base angles) are congruent. | |

| | | | |

| | | | |

| | | | |

| | | | |

| |Isosceles Triangles Converse |If 2 angles of a triangle are congruent, then the sides opposite | |

| | |them are congruent. | |

| | | | |

| | | | |

| | | | |

| | | | |

Chapter 5 Properties, Postulates and Theorems

Special Segments in Triangles

See Foldable!

Chapter 6 Properties, Postulates and Theorems

Polygons and Quadrilaterals

|Angle measures of a convex polygon with n sides |

| |Interior Angles |Exterior Angles |

|Sum of all angles |[pic] |[pic] |

|Measure of one if the polygon is REGULAR! |[pic] |[pic] |

|All About a Parallelogram! |

|Characteristics of ... |Proving that it is one ... |

| | |

|Definition: Both pairs of opposite sides are parallel. |Definition: Both pairs of opposite sides are parallel. |

| | |

|6-2-1: Both pairs of opposite sides are congruent. |6-3-1: One pair of opposite sides are parallel and congruent. |

| | |

|6-2-2: Both pairs of opposite angles are congruent |6-3-2: Both pairs of opposite sides are congruent |

| | |

|6-2-3: Pairs of same-side interior angles are supplementary. |6-3-3: Both pairs of opposite angles are congruent. |

| | |

|6-2-4: The diagonals bisect each other. |6-3-4: One angle is supplementary to both consecutive angles. |

| | |

| |6-3-5: The diagonals bisect each other. |

| | |

Special Parallelograms

|All About a Rectangle! |

|Characteristics of ... |Proving that it is one ... |

| | |

|Definition: An equiangular quadrilateral |6-5-1: A parallelogram with one right angle |

| | |

|6-4-1: All rectangles are parallelograms. |6-5-2: A parallelogram with congruent diagonals |

| | |

|6-4-2: Diagonals are congruent. | |

| | |

| | |

|All About a Rhombus! |

|Characteristics of ... |Proving that it is one ... |

| | |

|Definition: An equilateral quadrilateral |6-5-3: A parallelogram with one pair of consecutive congruent sides |

| | |

|6-4-3: All rhombuses are parallelograms. |6-5-4: A parallelogram with perpendicular diagonals |

| | |

|6-4-4: Its diagonals are perpendicular. |6-5-5: A parallelogram whose diagonal bisects a pair of opposite angles |

| | |

|6-4-5: Each diagonal bisects a pair of opposite angles. | |

| | |

| | |

| | |

| | |

| | |

|All About a Square! |

|Characteristics of ... |Proving that it is one ... |

| | |

|Definition: An equiangular quadrilateral |Prove that the quadrilateral is both a rectangle and a rhombus! |

| | |

|6-4-1: All rectangles are parallelograms. | |

| | |

|6-4-2: Diagonals are congruent. | |

Other Special Quadrilaterals

|Kite |Trapezoid |Isosceles Trapezoid |

|Definition: A quadrilateral with exactly two |Definition: A quadrilateral with exactly one |Definition: A trapezoid whose non-parallel sides|

|pairs of consecutive, congruent sides. |pair of parallel sides. |are congruent. |

| | | |

|6-6-1: Its diagonals are perpendicular. |Consecutive angles between the bases are |Base angles are congruent. |

| |supplementary. | |

|6-6-2: Non-vertex angles are congruent. | |Diagonals are congruent. |

| |The length of the midsegment is the average of | |

|One diagonal is the |the lengths of the two bases. | |

|perpendicular bisector of the other. | | |

| | | |

|One diagonal bisects each vertex angle. | | |

Chapter 5/8 Properties, Postulates and Theorems

Right Triangles

Pythagorean Theorem Special Right Triangles

45(-45(-90( 30(-60(-90(

Trigonometry (SOH-CAH-TOA)

Chapter 9 Properties, Postulates and Theorems

Extending Perimeter and Area

See “Formulas you will need to memorize” on page 11

Chapter 10 Properties, Postulates and Theorems

Spatial Reasoning

See “EOC Allowed formulas” on page 9

EOC Standards Checklist

The standards listed below are those that you will see tested on the EOC at the end of the year. These state requirements, however, do not make up your entire Geometry course. Additional topics are necessary as preparation for Algebra 2.

|Performance Expectation |Tested, but doesn’t |Record here your performance on |

| |count for graduation|each assessment. |

| | | | | | | |

|G.1.A. Distinguish between inductive and deductive reasoning. |x | | | | | |

|G.1.C. Use deductive reasoning to prove that a valid geometric statement is true. | | | | | | |

|G.1.D. Write the converse, inverse, and contrapositive of a valid proposition and determine | | | | | | |

|their validity. | | | | | | |

|G.1.E. Identify errors or gaps in a mathematical argument and develop counterexamples to | | | | | | |

|refute invalid statements about geometric relationships. | | | | | | |

|G.1.F. Distinguish between definitions and undefined geometric terms and explain the role of | | | | | | |

|definitions, undefined terms, postulates (axioms), and theorems. | | | | | | |

|G.2.A. Know, prove, and apply theorems about parallel and perpendicular lines. |x | | | | | |

|G.2.B. Know, prove, and apply theorems about angles, including angles that arise from parallel|x | | | | | |

|lines intersected by a transversal. | | | | | | |

|G.2.C. Explain and perform basic compass and straightedge constructions related to parallel |x | | | | | |

|and perpendicular lines. | | | | | | |

|G.2.D. Describe the intersections of lines in the plane and in space, of lines and planes, and|x | | | | | |

|of planes in space. | | | | | | |

|G.3.A. Know, explain, and apply basic postulates and theorems about triangles and the special | | | | | | |

|lines, line segments, and rays associated with a triangle. | | | | | | |

|G.3.B. Determine and prove triangle congruence, triangle similarity, and other properties of | | | | | | |

|triangles. | | | | | | |

|G.3.C. Use the properties of special right triangles (30°–60°–90° and 45°–45°–90°) to solve | | | | | | |

|problems. | | | | | | |

|G.3.D. Know, prove, and apply the Pythagorean Theorem and its converse. | | | | | | |

|Performance Expectation |Tested, but doesn’t |Record here your performance on |

| |count for graduation|each assessment. |

| | | | | | | |

|G.3.E. Solve problems involving the basic trigonometric ratios of sine, cosine, and tangent. | | | | | | |

|G.3.F. Know, prove, and apply basic theorems about parallelograms. | | | | | | |

|G.3.G. Know, prove, and apply theorems about properties of quadrilaterals and other polygons. | | | | | | |

|G.3.H. Know, prove, and apply basic theorems relating circles to tangents, chords, radii, |x | | | | | |

|secants, and inscribed angles. | | | | | | |

| |x | | | | | |

|G.3.I. Explain and perform constructions related to the circle. | | | | | | |

|G.3.J. Describe prisms, pyramids, parallelepipeds, tetrahedra, and regular polyhedra in terms |x | | | | | |

|of their faces, edges, vertices, and properties. | | | | | | |

|G.3.K. Analyze cross-sections of cubes, prisms, pyramids, and spheres and identify the |x | | | | | |

|resulting shapes. | | | | | | |

|G.4.A. Determine the equation of a line in the coordinate plane that is described |x | | | | | |

|geometrically, including a line through two given points, a line through a given point parallel| | | | | | |

|to a given line, and a line through a given point perpendicular to a given line. | | | | | | |

|G.4.B. Determine the coordinates of a point that is described geometrically. | | | | | | |

|G.4.C. Verify and apply properties of triangles and quadrilaterals in the coordinate plane. | | | | | | |

|G.4.D. Determine the equation of a circle that is described geometrically in the coordinate |x | | | | | |

|plane and, given equations for a circle and a line, determine the coordinates of their | | | | | | |

|intersection(s). | | | | | | |

|G.5.A. Sketch results of transformations and compositions of transformations for a given |x | | | | | |

|two-dimensional figure on the coordinate plane, and describe the rule(s) for performing | | | | | | |

|translations or for performing reflections about the coordinate axes or the line y = x. | | | | | | |

| |x | | | | | |

|G.5.B. Determine and apply properties of transformations. | | | | | | |

|Performance Expectation |Tested, but doesn’t |Record here your performance on |

| |count for graduation|each assessment. |

| | | | | | | |

|G.5.C. Given two congruent or similar figures in a coordinate plane, describe a composition of|x | | | | | |

|translations, reflections, rotations, and dilations that superimposes one figure on the other. | | | | | | |

|G.5.D. Describe the symmetries of two-dimensional figures and describe transformations, |x | | | | | |

|including reflections across a line and rotations about a point. | | | | | | |

|G.6.A. Derive and apply formulas for arc length and area of a sector of a circle. |x | | | | | |

|G.6.C. Apply formulas for surface area and volume of three-dimensional figures to solve |x | | | | | |

|problems. | | | | | | |

|G.6.D. Predict and verify the effect that changing one, two, or three linear dimensions has on|x | | | | | |

|perimeter, area, volume, or surface area of two- and three-dimensional figures. | | | | | | |

|G.6.E. Use different degrees of precision in measurement, explain the reason for using a | | | | | | |

|certain degree of precision, and apply estimation strategies to obtain reasonable measurements | | | | | | |

|with appropriate precision for a given purpose. | | | | | | |

|G.6.F. Solve problems involving measurement conversions within and between systems, including | | | | | | |

|those involving derived units, and analyze solutions in terms of reasonableness of solutions | | | | | | |

|and appropriate units. | | | | | | |

|G.7.A. Analyze a problem situation and represent it mathematically. | | | | | | |

|G.7.B. Select and apply strategies to solve problems. | | | | | | |

|G.7.C. Evaluate a solution for reasonableness, verify its accuracy, and interpret the solution| | | | | | |

|in the context of the original problem. | | | | | | |

|G.7.E. Read and interpret diagrams, graphs, and text containing the symbols, language, and | | | | | | |

|conventions of mathematics. | | | | | | |

|G.7.G. Synthesize information to draw conclusions and evaluate the arguments and conclusions | | | | | | |

|of others. | | | | | | |

Classroom Procedures & Expectations / CHAMPS

Transitions (time between activities) are opportunities for wasted time. The less time we waste in class, the more time you will have for practice assignments, student interviews, and other engaging activities. By learning these routines and expectations, we will cut down on lost class time and complete our “jobs” more quickly.

|[pic] |Teacher-Directed |Collaboration Time |Independent Assessment |

| |Instruction |Warm-up | |

| | |Working in Pairs | |

| | |Work time | |

| | |Group Activity | |

|C |No Conversation unrelated to the lesson. |Conversation allowed |No Conversation |

| |Voice Level – 0, 1 |Voice Level – 2 |Voice Level – 0 |

| | |Speaking with partner about activity. | |

|H |Raise your hand. |Ask your partner / group. |Raise your hand. |

| |Keep it raised until acknowledged. |If none of you know the answer, raise your hand. |Keep it raised until acknowledged. |

| | |Go on to the next question or step until the teacher | |

| | |can help. | |

|A |Take notes. |Read directions on activity and complete each task |Work on Assessment. |

| |Work on tasks. |defined. |Show all necessary work. |

| |Give verbal or written responses to |When finished, wait quietly for the next set of | |

| |teacher-presented tasks. |instructions. | |

|M |Permission needed to leave your seat. |Permission needed for the restroom (10/10). |Permission needed to leave your seat. |

| |Restroom only if emergency (10/10). |Permission needed to go for a drink (10/10). |No Restroom. |

| |Wait to use the pencil sharpener. |Pencil sharpener – Yes |Pencil sharpener – with permission. |

| |Please wait to get a drink. |Movement must be assignment related. |Finish assessment before getting a drink.|

|P |Looks like … |Looks like … |Looks like … |

| | | | |

| |Students are on task. |Pairs or groups are helping each other. |Students are working entirely alone. |

| |Students give attention to the speaker. |100% participation. |Eyes are on own papers. |

| |Whole-class engagement. |Electronic devices are out of sight and sound. |Electronic devices are out of sight and |

| |Electronic devices are out of sight and | |sound. |

| |sound. | | |

|S | “Success is simple. Do what's right, the right way, |

| |at the right time.” Arnold H. Glasow |

Class Meeting Protocol:

▪ Everyone sits in a circle at the same height.

▪ You only bring yourself to the meeting, not something else to work on.

▪ You only talk when you have the orb or while brainstorming.

▪ Compliments and appreciation

▪ Follow up on prior solutions

▪ Agenda items

o Share feelings while others listen

o Discuss without fixing

o Ask for problem-solving help

▪ Future plans

Problem-solving guidelines:

▪ Try to determine the underlying reason for misbehavior –see mistaken goals chart.

▪ Brainstorm and/or role play

▪ Make sure the 4 Rs are applied:

o Related: The solution is directly related to the behavior. For example, when students don’t do their homework, sending them to the office is not related to missed homework. A related solution would be for them to make up the homework or not get points for that assignment.

o Respectful: Teacher and students maintain a respectful attitude in their manner and tone of voice. It also means following up on the solutions with dignity and respect: “Would you like to make up the homework assignment during lunch or right after school?

o Reasonable: Don’t add punishment. For example, don’t say something like, “Now you’ll have to do twice as much.”

o Revealed: Students should know in advance that if they don’t do their work, they’ll need to make it up or else risk getting a poor grade.

▪ Select appropriate solution that person(s) are willing to try.

|The Student’s Goal is… |If the teacher feels… |And tends to react by… |And if the student’s response|The belief behind the behavior|Coded Message |Teacher proactive and empowering responses include |

| | | |is… |is… | | |

|Undue Attention |Annoyed |Reminding |Stops temporarily, but later |I count (belong) only when I |Notice me |I care about you and…(Example: “I care about you and|

|(to keep others busy or to |Irritated |Coaxing |resumes same or another |am being noticed or getting |Involve me |will spend time with you later.” Redirect by |

|get special services) |Worried |Doing things for the student |disturbing behavior |special service. | |assigning a task so student can gain useful |

| |Guilty |(s)he could do for | |I’m only important when I am | |attention, avoid special service, plan special time,|

| | |himself/herself. | |keeping you busy with me. | |set up routines, use problem solving, encourage, use|

| | | | | | |class meetings, touch without words, ignore, set up |

| | | | | | |nonverbal signals. |

|Misguided Power |Angry |Fighting |Intensifies behavior |I belong only when I am boss, |Let me help. |Redirect to positive power by asking for help; offer|

|(to be boss) |Challenged |Giving in |Defiance |in control or proving no one |Give me choices. |limited choices; don’t fight or give in; withdraw |

| |Threatened |Thinking “You can’t get away |Compliance |can boss me. | |from conflict; be firm and kind; act, don’t talk; |

| |Defected |with it” or “I’ll make you” |Feels (s)he has won when |You can’t make me. | |decide what you will do; let routines be the boss; |

| | |Wanting to be right |parent/teacher is upset. | | |leave and calm down; develop mutual respect; set a |

| | | |Passive power | | |few reasonable limits; practice follow-through; |

| | | | | | |encourage, use class meetings. |

|Revenge |Hurt |Retaliating |Retaliates |I don’t think I belong so I |Help me: I’m |Acknowledge hurt feelings; avoid feeling hurt; avoid|

|(to get even) |Disappointed |Getting even |Intensifies |will hurt others as I feel |hurting. |punishment and retaliation; build trust; use |

| |Disbelieving |Thinking, “How could you do |Escalates the same behavior |hurt. |Acknowledge my |reflective listening; share your feelings; make |

| |Disgusted |this to me?” |or chooses another weapon. |I can’t be liked or loved. |feelings. |amends; show you care; encourage strengths; don’t |

| | | | | | |take sides; use class meetings. |

|Assumed Inadequacy |Despair |Giving up |Retreats further |I can’t belong because I am |Show me |Break task down into small steps; stop all |

|(to give up and be left |Hopeless | | |not perfect, so I’ll convince | |criticism; encourage any positive attempt; have |

|alone) |Helpless |Doing for |Passive |others not to expect anything |Small steps |faith in student’s abilities; focus on assets; don’t|

| |Inadequate | | |of me. | |pity; don’t give up; set up opportunities for |

| | |Over-helping |No Improvement | |Celebrate my |success; teach skills/show how, but don’t do for; |

| | | | |I am helpless and unable. |successes |enjoy the student; build on his/her interests; |

| | | |No Response | | |encourage; use class meetings. |

| | | | |It’s no use trying because I | | |

| | | | |won’t do it right. | | |

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“An error doesn’t become a mistake until you refuse to correct it.”

A. Battista

“Success is the sum of small efforts, repeated day in and day out.”

Robert Collier ~ Robert Collier

Properties of Equality

Properties of Congruence

(

(

A

B

C

D

You don’t have to feel worse to do better.

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