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### GEOMETRY DOMAIN -February-March 2020

Posted on February 23, 2020

### January 2020

Posted on January 5, 2020
### SLOPE AND PROPORTIONAL RELATIONSHIPS

Posted on November 17, 2019
Posted on October 14, 2019
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ACCEPT

‘Arguably the largest highly successful Catholic elementary school in NYC’ – Former Pastor

Welcome to Mr. Competello’s 8th Grade Math class page!

FEBRUARY 23, 2020 All students should be familiar with the information below as it will be presented and discussed in class.

PERCENT APPLICATIONS……..A REVIEW OF THE APPLICATION OF PERCENTS IN CONSUMER MATH

After a major review of all the content of chapter 8 in FOUNDATIONS and an example of each problem put in your notes, you are to complete pp230 and 231 in Progress Purple text.

Each problem should have a rationale connected to a computation. This work will be due FEBRUARY 24.

IT WILL COUNT AS A MAJOR GRADE.

__INTRODUCTION TO GEOMETRY DOMAIN__

__Foundations Sourcebook __pp. 236, 237 After careful study of these pages and explanations in class, be sure to complete workbook pages 267 and 268.

A thorough explanation of these problems should be noted.

__Foundations Sourcebook __ pp. 238, 239 After careful study of these pages and explanations in class, as well as reviewing the Khan Academy YouTube presentation on parallel lines cut by a transversal, all of workbook pages 269 and 270 in Foundations should be completed and a thorough explanation of these problems should be noted.

__ Coach Book- __ Re-read, as discussed in class, lesson 28 on pp. 313 to 323. Complete all coached examples and lesson practices.

__Progress Book – __pp.264-265 Complete answers in the book and be sure to be able to explain your answers.

AT THIS POINT, AFTER COMPLETING THE ABOVE WORK, A TEST ON PARALLEL LINES CUT BY A TRANSVERSAL AND ALL THE CONTENT ON THE SUBJECT WILL BE GIVEN.

NEXT TOPIC WILL BE:

GEOMETRY DOMAIN

Topic one TRANSFORMATIONAL GEOMETRY

Review the Kahn Academy YouTube Introduction to transformational geometry.

Note the four types of transformations and describe each.

REFLECTIONS OR FLIP

TRANSLATIONS OR SLIDE

ROTATIONS OR TURN

DILATIONS OR ENLARGEMENT/REDUCTIONS

__COORDINATE PLANE: REFLECTIONS AND TRANSLATIONS__

Translations and reflections are geometric transformations that create images. __Foundations in Math __p. 315 – note well the information presented in the gray section. Be sure to note the rules for reflections and translations. Do # 1 to 3 at the bottom of p. 315, and # 4, 5, 6 at the top of p. 316. Study #10 at the bottom of p. 316 very carefully.

In __Finish Line __book, note well information presented on p. 104. Complete pp 105 to 111. All of the information on the above pages should present you with the ability to complete the following question: (In your notebooks) *describe how to reflect a figure over each axis. Use a triangle to illustrate your explanation. Also describe the effect of transposing the x and y coordinates of the vertices of a triangle. Again, use an illustration to demonstrate your answer. *

__VERIFYING PROPERTIES OF REFLECTIONS AND TRANSLATIONS:__

The essential question here is

**“What are the important properties of reflections and translations?” **

__Progress in Math – __After reading pp204-207, note well the questions from the guided practices pp.208 & 209.

Upon completion of all the above work go to pages directed by the teacher in __Practice Coach. __

** ROTATIONS** – Review and reinforce the information on rotations from the Khan Academy YouTube. Remember that in rotating a figure, we think of a rotation as clockwise or counterclockwise at 90 degrees, 180 degrees or 270 degrees. Remember to carefully note the rules presented for both clockwise and counterclockwise and the application of these rules. (Teacher presentation)

Using various “coached examples” from the handout complete all questions dealing with rotations.

From __Finish Line__ book review p. 112 and complete pp. 113 to 115.

__VERIFYING PROPERTIES OF ROTATIONS:__

__Progress in Math__ – p.212 and 213

__Foundations in Math__ – p.317 – note well rules presented in the gray section. Do #1-6 on p.317 and

# 7, 8, 9, 12, 13 on p.318

** DILATIONS – **Review and reinforce the information on dilations from the Khan Academy YouTube.

__Practice Coach Plus book__ – as directed by the teacher

__Finish Line Book__ – note well information on p.116 – Do pp. 117-118-119

__REVIEW INFORMATION ON COORDINATE GEOMETRY__

__Common Core Coach Book__ – as directed by the teacher

FOR THE WEEK OF MARCH 16 TO MARCH 20

Please follow the directions as outlined in class and repeated here for the week of March 16 through March 20. The following information can also be found on Mrs. Martinez’ Google classroom. Here is what was outlined in class:

- Complete review pages in Foundations on pp. 205, 206, 207, 208…Do only the marked questions and complete with an explanation on looseleaf.
- Refer to the class page above on transformational geometry. Do all outlined work except for work from the Finish Line Book.
- From Coach Book pp. 269 through 279…Do all practice pages.
- Coach book pp. 280 through 289 . Complete all exercises. Numbers 3 & 4 above can be done in the book.
- Review pages from Foundations pp. 105-106 # 1 to 24. These should also be done on loose-leaf. Remember multiple choice answers must be explained on loose-leaf.

ASSIGNMENT: Describe, in detail, each of the transformations. Illustrate each transformation giving **examples** (MORE THAN 1) of each. Be as creative as you wish in each illustration.

REFLECTION – TRANSLATION -ROTATION – DILATION

This work needs to be done with a ruler and graph paper. These assignments are due when classes resume and will graded.

PLEASE BE SURE TO LOGIN TO MY GOOGLE CLASSROOM PAGE. THE CLASS CODE FOR 8-1 IS ON MRS. MARTINEZ’ Google classroom page ….. FOR 8-2 CLASS CODE SEE MRS. FARON’s GOOGLE CLASSROOM PAGE

PLEASE VIEW THESE VIDEO PRESENTATIONS BECAUSE THEY WILL HELP YOU COMPLETE THE ASSIGNMENTS ON TRANSFORMATIONS. PLEASE KEEP ALL ASSIGNMENTS IN A FOLDER TO BE COLLECTED AND GRADED AS ALTERNATIVE ASSESSMENTS.

also the link below is for dilations

Good morning, Students,

As I do in class, going from group to group, giving helpful hints to solve problems before you work together, I am giving you hints today that may help you complete the assignments from the review pages. These hints are NOT for every problem but just for the ones that may pose a question for some of you. Do your best.

Here we go:

5- (-1) = 6 = 3x

2-0 2

To find a function rule : find the slope from the table in the book, substitute x/y values. Remember if x=0, you automatically have the y intercept.

Remember the slope formula: y²-y¹

x²-x¹

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a² + b² = c² Pythagorean theorem

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Use the Distributive Property/ Solving equations with variables on both sides.

Isolate the variables.

_________________________________________________________________________

When dividing and using the Rule of exponents, be sure to subtract the exponents.

_________________________________________________________________________

Point Slope formula: y-y₁ = m (x-x₁) This especially helpful for #8 on p.206.

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Applying the vertical line test .

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Solving Systems of equations can be done by substitution or elimination. You can refer to Foundations book pages 195-196.

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Repeating decimals

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Finding length of rectangle ( #3 on p.105)

3x

3x x is width

64=3x + 3x +x +x This should help you solve this problem Remember…you are looking for the LENGTH after you find x.

____________________________________________________________________________

This will help you with #9 on p.105

s ²

Looking at this rectangle whose width is 7, and Length is 28 you realize that the area is 196.

Finding the square root of 196 will help you find the side of the square.

__________________________________________________________________________

Please remember that these hints are only for some of the problems. You should be able to do other problems without hints. Also, the few questions on transformational Geometry posted yesterday are also due. Post all assignments in Google classroom. You can take pictures of your work if you want. BE SURE TO PRINT AND SAVE A HARD COPY OF EVERYTHING IN A FOLDER FOR REVIEW AT A LATER POINT.

Remember- as always- when assignments like this are done- the more effort shown , and knowledge is expressed in your work = better grade. Be safe. I miss seeing you all in class. Hope you and your families are well. Remember also to ask each other for help just as we do in our cooperative groups in school.

Best regards, Mr. Competello

****************************************************************************************************************************************

Monday, March 23, 2020

Good morning, Students,

Please be sure to complete the Foundations review pages ages listed on the Google class page to be submitted for a grade. Use the following as an example. You need to put only the answer and a BRIEF explanation of how you arrived at that answer.

Here is an example of how you would do a problem and show the answer and explanation:

What is the slope of a line that passes through (-2,-3) (-1, 4) ?

Answer : 7- I found this by using the slope formula.

Please be sure to submit the review page answers and explanations. Here are the pages:

FOUNDATIONS BOOK – pages 205,206,207,208 Do only the marked questions from our last class in school.

FOUNDATIONS BOOK- pages 105,106 – # 1 to 24

This is due March 25 by 3:00 P.M. for a grade. Please submit here and also please keep a hard copy in a folder to submit later.

*******************************************************************************************************************************************

WEDNESDAY, MARCH 25, 2020

Now that you have completed all the COACH BOOK pages, reviewed the YouTube videos and followed the directions, please answer these questions.

- Identify the coordinates of the images of the given points.

Example: (x,y) →(x+2) (y+4) – this is a translation

- (0,3) →a¹(2,7)
- (3,4) →b¹(5,8)
- (-6,-4) →c¹ (-4, 0)

Now you do this translation:

(x,y) →(x+1) (y-5)

- ( 4,5) →d¹ (____________)
- (-1,4) →e¹ (____________)
- (-9, -10) →f¹ (___________)

______________________________________________________________________________

State the new coordinates after a reflection over the x axis. You may want to refer to the sheet I gave out in class.

K (2,3)→k¹ (____________)

L (0,-5) →l¹ (____________)

M (-3,-7) →m¹ (____________)

______________________________________________________________________________

State the coordinates after a rotation of 180⁰ over the origin.

R (4,5) →r¹ (____________)

S (-2,5) →s¹ (____________)

T (7,-8) →t¹ (____________)

____________________________________________________________________________

State the coordinates of this figure after a dilation with a scale factor of ½.

H (-4,-6) →h¹ (____________)

J (4,2) →j¹ (____________)

K (4,-6) →k¹ (____________)

_____________________________________________________________________________

Please submit by Thursday, March 26 by 3:00 P.M. for a grade.

_____________________________________________________________________________

FRIDAY, MARCH 27, 2020

Use your class time today to fine-tune the assignment :

ASSIGNMENT: Describe, in detail, each of the transformations. Illustrate each transformation giving examples (MORE THAN 1) of each. Be as creative as you wish in each illustration.

Keep this in a folder as it will be checked for a grade in the future. I’ll let you know.

__________________________________________________________________________________________________

**************NEW MARCH 30 -APRIL 3, 2020

__MATH 8 WEEK OF MARCH 30- APRIL 3, 2020__

If you haven’t completed the assigned work from last week, March 23-27, or have only submitted part of the assignment, please complete and submit as soon as possible.

__Monday, March 30 – Tuesday, March 31__

Look carefully at the You tube presentations listed below. You should view them more than once. Please take notes on what is presented and write out an explanation of the Math concepts that are being taught.

I have provided “HELPFUL HINTS” in pictures to assist you in understanding the concept…

*“to find the sum of the measures of interior angles of a polygon”*

The focus of this lesson is only page 273 in __FOUNDATIONS__ book. Now, using my helpful hints, complete p273 – #1 to 16 – using #1 as the model problem.

PLEASE SUBMIT THE PARAGRAPH ASSIGNMENT FROM ABOVE AND WORK FROM page 273 BY WEDNESDAY, APRIL 1.

__Wednesday, April 1 – Thursday, April 2, 2020__

As part of our work at this point in the year, there are major review pages that need to be completed. These review pages are important for you to do and understand. They will help you in your future Math classes.

Assignment: __FOUNDATIONS__ book – pp 103-104 # 1 to 20 from practice Chapter test. Only do # 1to 20 for now.

__Helpful hints__ to help you complete this assignment:

- Sum – addition
- Product – multiplication
- “of” – times or multiplication
- √ – square root
- Quotient – divide

Use “n” to represent the missing number.

Here are some examples of answers.

Look at #2 on page 103. Look at #4

Answer is __½ n__ Answer is __4 + 3n__

0.012 2a

Look at #6 on page 103.

x² + x(x-y) + 10 xy

[Distribute x(x-y)] so the next line will look like this:

x² + x² -xy + 10 xy

Then combine like terms (x² + x² = 2x²) and (-xy + 10xy = 9xy)

Final answer is: 2 x² + 9xy

_{ }

Look at # 8 on page 103.

(r+3) – 2(r+9)

Distribute first so you get -2r-18

(r+3) – 2(r+9) = (r+3) -2r-18

Then combine like terms so you have: r-2r= -r and 3-18=-15

Answer: -r-15

Look at #13 on page 103.

(s-d)^{2} s=25, d=17

(25-17)^{2} =

8^{2}= 64

Friday, April 3, 2020

- Submit # 1 to 20 from
__FOUNDATIONS__book - Be sure you have a folder with all your work, including the description of transformations originally assigned last week as well as discussed the last time we were in class.

NOTE WELL: Questions may be submitted on Google Classroom. I will do my best to answer as quickly as possible. Be safe. Miss you all.

Mr. Competello

HELPFUL HINTS:

New Lesson – Week of January 6, 2020

__SUBSTITUTION AS WAY OF SOLVING SYSTEMS OF EQUATIONS__

- Complete
__Foundations In Algebra__book- page 196, # 1 to 16. These problems should be completed and were handed in for a test grade. These problems will be used for testing. __Progress In Math__book- pages 120 & 121 – read and be sure you understand the process required to solve systems of equations using substitution.- Complete the handout that will be given in solving systems of equations by substitution.

New Lesson – Week of January 6, 2020

__SOLVING SYSTEMS OF EQUATIONS USING THE ELIMINATION METHOD__

__Foundations in Math __ – p.196, # 17 to 34

__Progress In Math__ p. 124 to 127

Write several paragraphs describing the 3 ways to solve systems of linear equations.

__INTRODUCTION TO FUNCTIONS __

Use the Youtube presentations to note the important words that you need to ‘get the idea’

Be sure to fill in every example and do all the coached assignments.

What are the main characteristics of functions?

BE SURE TO NOTE THE SOLUTIONS AND WHAT STRATEGIES WERE APPLIED.

Write a paragraph describing what is needed for an equation to be a function.

What is meant by the vertical line test?

FOUNDATIONS IN ALGEBRA

KEY CONCEPTS TO REMEMBER

CHAPTER 6 PP175 /176 COMPLETE 1 TO 6. BE SURE TO DO THIS ON GRAPH PAPER FOR A HOMEWORK GRADE.

ALSO…….NUMBERS 7 to 16 (hint – use a mapping diagram to answer these questions).

On page 176….apply the vertical line test to answer questions 17 to 22.

Apply what you have learned to this point to answer numbers 23 and 24. IT IS NECESSARY TO WRITE WHAT YOUR RATIONALE IS IN ANSWERNG THESE PROBLEMS.

SOURCEBOOK SECTION 6/2 WRITING A FUNCTION RULE – COMPLETE THE “TRY THESE”, 1 TO 4

NOW… IN THE WORKBOOK COMPLETE ALL OF PAGES 177 AND 178.

SHORT QUIZ GIVEN AT THIS POINT.

Note well what content you are responsible for.

Be sure to complete:

— Coach pages as assigned

— Progress book pp 137 to 140 – this is lesson 13

—Progress book lesson 14 pages 149 to 153

AT THIS POINT THERE WILL BE REVIEW OF ALL WORK AND TEST DATE TO BE ANNOUNCED DEPENDING ON HOW QUICKLY WE COVER THIS INFORMATION.

** Early February:** AT THIS POINT WE WILL HAVE AN INTENSIVE REVIEW OF CONSUMER MATH

Looking at chapter 8 in the “old progress text 8”we will discuss all the content in consumer math.

After extended discussion of the content you are responsible for pages 230 and 231. These 27 problems cover all the computations. You should now be able to do the word problems.

All the problems will be done in our math groups. It is your responsibility to do the class work on loose leaf paper to be handed in with computation and explanations.

This will count for a major test grade.

Due date to be determined.

PROGRESS MONITOR QUESTIONS AS OUTLINED IN CLASS.

THESE ARE PROBLEMS COVERING ALL THE MAJOR MATH CONCEPTS YOU SHOULD KNOW.

Again, these answers must be explained.

Simply choosing a letter choice is not acceptable. You must support your choice with an explanation and/or a computation.

**SLOPE AND PROPORTIONAL RELATIONSHIPS**

Posted on November 17, 2019

Using the handout given in class explain what is meant by the relationship between the slope of a line and a proportional relationship. Review at home the YouTube presentations from Khan Academy on __Introduction to Slope__ and __ How to Find the__ __Slope of a Line.__

In Class – SOURCEBOOK pages 162 & 163…Do page 163 # 1 to 12.

Ongoing Assignment – __Foundations In Algebra Workbook __– pages 181 & 182 #1 to 30. Be sure to use the slope formula and also explain the problem -solving questions # 29 & 30.

In Class -SOURCEBOOK – pages 164 & 165 – Complete “Try These” on p. 165 # 1 to 8

__Foundations in Algebra Workbook__ p. 183 & 184..complete # 1 to 20

In class – __SOURCEBOOK __p. 166 & 167 – writing equations in slope-intercept form y=mx +b

__Foundations in Algebra Workbook – __p. 185 & 186 # 1 to 23. Be sure to use graph paper when directed. Be sure to graph the equations in slope-intercept form.

__Progress in Math Workbook __ – p. 96 to 111. Read for review. Be sure to complete the guided instruction and work through the guided practice and independent practices. Various problems will be highlighted for importance.

Lesson 12 on p. 92 – Do “Discuss” section and “Apply” section on p. 93 and complete p.94 to 99.

__GO MATH __ (Reference book to be used in class) – p. 83 to 87. Complete in your notebook.

__Common Core Coach 8__ – Read p. 40 to 43. Complete p. 44 & 45. Read p 46 & 47, then do p. 49 to 51.

The above assignments from __GO MATH__ and __Common Core Coach 8 __ will be done and reviewed in class.

The work from __Progress in Math Workbook, Foundations in Algebra Workbook, __and__ Practice Coach Plus__ will be completed in class and/or assigned for homework as we progress.

Complete assigned __Coach Book __pages.

**EXPRESSIONS AND EQUATIONS IN ALGEBRA**

Posted on October 14, 2019

*PARENTS- PLEASE NOTE – GRADED TESTS FROM LAST WEEK WILL BE GIVEN BACK THIS WEEK.

Simplifying and evaluating algebraic expressions–

Be sure to review the teaching display on page 73 in __Foundations__ following the initial presentation.

Ongoing assignment: Be sure to complete all ongoing assignments as the topics are presented in class. Assignments will be checked periodically and applied to your grade.

- Complete pp 73 & 74 — # 7 through 31. You have the option of the challenge question on p. 74 for additional credit.
- One-step addition and subtraction equations – Remember the subtraction property of equality and the addition property of equality. Be sure to note the various problems on pp 77 & 78 which incorporate fractions, decimals and integers. Do problems #5 -35 on pp 77 & 78 in
- One-step multiplication and division equations – Be sure you understand from the initial presentation, the division and multiplication properties of equality as explained on p. 79 in Remember multiplication and division are inverse operations as well as addition and subtraction. Complete pp 79 & 80 noting the use of fractions, decimals and integers.
- Two-step equations – pp 81 & 82 in
__Foundations –__Use #4 on p. 82 as a model problem. - THE SOURCE BOOK – pp. 76 & 77 – Be sure to understand all modeled problems after initial presentation is made. Complete # 1-5 from THE SOURCE BOOK p77, and in Foundations pp. 83 & 84.
- Multi-step equations with grouping symbols – THE SOURCE BOOK – pp 78 & 79 – Be sure to understand and be able to explain all the modeled problems. Complete p. 79 – # 1-9 and in Foundations Book -pp 85 & 86.
- Multi-step equations with variables on both sides – THE SOURCE BOOK – pp 80 & 81 – Be able to explain these examples after the initial presentation. Do p 81, #1-4 and in Foundations book pp 87 & 88.
- Coach Book – page 68 through 83 must be completed as a conclusion to this topic.
- TEST PREP QUESTIONS WILL BE PROVIDED FROM ADDITIONAL SOURCES TO BE USED AS A REVIEW AND REINFORCEMENT PRIOR TO THE SUMMATIVE TEST.