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- 1. A variety of templates, organizers and other resources that can be used for interactivenotebooks. This is a combination of resources I found while searching the web and I am inno way representing these resources as my original creations.
- 2. Sherry OlivaresRegion 4 Education Service Centerwww.theansweris4.netsolivares@esc4.net713.744.6330Permission to copy classroom-ready materials grantedto attendees of this session.© 2011 Region 4 Education Service CenterAll rights reserved.Using Interactive Notebooks in theMathematics Classroom
- 3. Handouts will be available online until 3 weeks after workshophttp://www.theansweris4.net-Click on Services-Click on Academic Services-Click on Mathematics-Click on Professional Development Materialshttp://www.twitter.com/R4math
- 4. " " ""Interactive Notebooks are characterized byRIGHT SIDE Input and LEFT SIDE Output!An Interactive Notebook gives students a place to:Ü Set GoalsÜ Plan Study StrategiesÜ Document LearningÜ Track SuccessLeft Side Examples Right Side ExamplesPoemsVocabulary CartoonsWord PuzzlesAnalogiesGraphicsSketchesPractice problems or examplesParaphrasesPicturesArticlesLyrics to a songWeb informationMemory tips and techniquesBrainstormingConcept maps/flow chartsStudy planReflectionsGoal settingCommunication with parent/teacherLecture NotesDaily and homework assignmentsTestsQuizzesLab activitiesHand outsVocabulary AssignmentsFocus or warm-up activitiesFoldablesPre-lab notesBook notesGraphic organizersFilm notesLeft Side CharacteristicsColorful, creative, unique to student,demonstrates understanding, entered oneven numbered pages, date and subjecttitle at top of each pageRight Side CharacteristicsContent and concepts of curriculum, notesin Cornell style, teacher or text driven,entered on odd numbered pages, date andsubject title at top of page
- 5. " " ""Interactive Notebook and Parent CommunicationMath Student: Each 6 weeks, schedule a time to meet with your parent or significantadult. Show them your INB and let them know what is going on in class. Write down afew comments made.Dear Parent or Significant Adult,Your student is keeping an Interactive Notebook in Mathematics. Please look through itand respond to the following questions. Thank you for supporting our science program.1) The work I found most interesting was…….. because…….2) What does the notebook tell you about your student’s learning habits?3) Do you have any comments, questions, or concerns?Print Name_______________________________Signature_________________________________Student’s Name____________________________Date_______________________________
- 6. " " ""Suggested First PagesTitle Page (1stactual page)‚ Name‚ Course‚ Class period‚ Year‚ InstructorTable of contents‚ Have students draw their own TOC chart‚ Start on the front of the 2ndactual page‚ First entry is a right side Content‚ Student use three consecutive pages front and backThe following documents may be entered on the front and back of the next few pages.Have the students use staples or tape.Handouts‚ Course syllabus‚ Expectations/norms‚ Honor code‚ OtherGoal Page‚ Students write goals stating what they want to accomplish or gain from thecourse‚ May be written in process or performance terms‚ Goals should be revisited/rewritten when analyzing grade reports/test scoresPlanning page‚ Students state the strategies needed to accomplish their goals‚ Strategies should be revisited/rewritten when analyzing grade reports/test scoresTracking Page‚ Students create data table for grade reports or exam grades‚ Students graph their progressFirst Content Page‚ Page one on the next available right side.
- 7. " " ""Table of ContentsPage # Left Side Page # Right SideThis Table of Content is designed to fit a standard composition book.Cut along the dottedlines.
- 8. " " ""Table of ContentsPage # Date Left Side Page # Date Right Side
- 9. My Math Interactive NotebookYou are a mathematician. Mathematicians use notebooks andjournals to record data, illustrations, charts, graphs, and theirthinking. You can also use it to record your questions and ides.We will follow guidelines when using our notebooks to make theminformative and interesting. Your notebook should reflect yourexperiences, your thinking, and your creativity, but it should beeasily understood by others.Guidelines:‚ Write neatly and legibly – across out mistakes with a singleline or carefully erase‚ Do not tear out pages‚ Create a title page‚ Number each page‚ Create a table of contents‚ Title each activity and add to the table of contents‚ Label drawings, graphs, and charts‚ Use sentences to communicate observations, plans,explanations, conclusions, and applicationsGetting Started with Writing:‚ This reminds me of . . .‚ I see a pattern . . .‚ What would happen . . .‚ I observed that . . .‚ This problem . . .‚ How many . . .
- 10. INTERACTIVE CAFÉDAILY SPECIALSThis Interactive Café is designed to fit a standard compositionbook.APPETIZERS– EASY PICKINGSDigital photos Magazine picturesWeb information Research notesArticles News feeds0.00ENTRÉES– MEATY MATTERSGraphic organizer Thinking mapsReal world applications Career connectionsGoal setting Study plan0.00SIDES– CROSS-CURRICULARPractice problems Historical connectionsAcrostics AcronymsAnalogies Sketch0.00DESSERTS– CREATIVE FLAIRNonlinguistic representation Innovative applicationCartoon GameSong Folding model0.00BEVERAGES– THE FLOWReflectionSummary of UnderstandingAHAs!Where meetings of the mind are always thespecial of the day!0.00Cut along the dottedlines.
- 11. INTERACTIVE CAFÉDAILY SPECIALSINTERACTIVE CAFEWhere meetings of the mind are always the special of the day!APPETIZERS– EASY PICKINGSDigital photos Magazine picturesWeb information Research notesArticles News feeds0.00ENTRÉES– MEATY MATTERSGraphic organizer Thinking mapsReal world applications Career connectionsGoal setting Study plan0.00SIDES– CROSS-CURRICULARPractice problems Historical connectionsAcrostics AcronymsAnalogies Sketch0.00DESSERTS– CREATIVE FLAIRNonlinguistic representation Innovative applicationCartoon GameSong Folding model0.00BEVERAGES– THE FLOWReflectionSummary of UnderstandingAHAs!0.00
- 12. ""Authors PageName: ________________________________Nickname: _____________________________Birthday: ______________________________Food: ____________________Music: ___________________Sport: ___________________Color: ___________________Movie: ___________________Book: ___________________Place: ___________________Three words I would use to describe myself are:I would like to take a vacation to:In the future I would like to be a(n):
- 13. Authors PageName: __________________________Nickname: _______________________Birthday: ________________________Food: ____________________Music: ___________________Sport: ___________________Color: ___________________Movie: ___________________Book: ___________________Place: ___________________Three words I would use to describemyself are:I would like to take a vacation to:In the future I would like to be a(n):
- 14. Notebook"Labels""Name: _________________Please return to_________________________Room: __________"Name: _________________Please return to_________________________Room: __________"Name: _________________Please return to_________________________Room: __________"Name: _________________Please return to_________________________Room: __________"Name: _________________Please return to_________________________Room: __________"Name: _________________Please return to_________________________Room: __________"Name: _________________Please return to_________________________Room: __________"Name: _________________Please return to_________________________Room: __________"""
- 15. Interactive Notebook Rubric6 Excellent¬ Notebook contents are complete, dated, and labeled¬ Pages are numbered (odd: Right side, even: Left-side)¬ Right-side/Left-side topic are correct and organized¬ Notes and writing go beyond basic requirements¬ Uses color and effective diagrams¬ Notebook is neat and shows attention to detail¬ Shows impressive and in-depth self-reflection about work5 Above Average¬ Notebook contents are complete, dated, and labeled¬ Pages are numbered (odd: Right side, even: Left-side)¬ Right-side/Left-side topic are correct and organized¬ Most areas meet requirement but don’t go beyond¬ Uses color and effective diagrams¬ Includes traits of a six, but lacks excellence¬ Shows in-depth self-reflection4 Average¬ Notebook contents are 90% complete, dated, and labeled¬ Pages are numbered (odd: Right side, even: Left-side)¬ Right-side/Left-side topic are correct and organized¬ Information shows a basic understanding of content and topics¬ Uses color and some diagrams¬ Some areas meet requirements but don’t go beyond¬ Shows limited but real self-reflection3 Below Average¬ Notebook contents are 80% complete, dated, and labeled¬ Pages are numbered (odd: Right side, even: Left-side)¬ Right-side/Left-side topic are somewhat organized¬ Information shows limited understanding of content and topics¬ Uses minimal color and few diagrams¬ Few areas meet all requirements¬ Shows some real self-reflection2 Inadequate¬ Contents are incomplete¬ Some attempt at dating an labeling is evident¬ R side/L side inconsistent an unorganized¬ Information shows superficial understanding and inaccuracies¬ Sloppiness prevails¬ Shows little self reflection1 Incomplete¬ Too incomplete to gradeThis Interactive Notebook Rubric is designed to fit a standard composition book.Cut along the dottedlines.
- 16. " " ""Interactive Notebook Rubric6 Excellent¬ Notebook contents are complete, dated, and labeled¬ Pages are numbered (odd: Right side, even: Left-side)¬ Right-side/Left-side topic are correct and organized¬ Notes and writing go beyond basic requirements¬ Uses color and effective diagrams¬ Notebook is neat and shows attention to detail¬ Shows impressive and in-depth self-reflection about work5 Above Average¬ Notebook contents are complete, dated, and labeled¬ Pages are numbered (odd: Right side, even: Left-side)¬ Right-side/Left-side topic are correct and organized¬ Most areas meet requirement but don’t go beyond¬ Uses color and effective diagrams¬ Includes traits of a six, but lacks excellence¬ Shows in-depth self-reflection4 Average¬ Notebook contents are 90% complete, dated, and labeled¬ Pages are numbered (odd: Right side, even: Left-side)¬ Right-side/Left-side topic are correct and organized¬ Information shows a basic understanding of content and topics¬ Uses color and some diagrams¬ Some areas meet requirements but don’t go beyond¬ Shows limited but real self-reflection3 Below Average¬ Notebook contents are 80% complete, dated, and labeled¬ Pages are numbered (odd: Right side, even: Left-side)¬ Right-side/Left-side topic are somewhat organized¬ Information shows limited understanding of content and topics¬ Uses minimal color and few diagrams¬ Few areas meet all requirements¬ Shows some real self-reflection2 Inadequate¬ Contents are incomplete¬ Some attempt at dating an labeling is evident¬ R side/L side inconsistent an unorganized¬ Information shows superficial understanding and inaccuracies¬ Sloppiness prevails¬ Shows little self reflection1 Incomplete¬ Too incomplete to grade
- 17. " " ""Interactive Notebook RubricExcellent SatisfactoryNeedImprovementWeakOutputAll work is:, Finished, Thoughtful, Makingconnections, Clear, CreativeMajority of work is:, Finished, Thoughtful, Makingconnections, Clear, CreativeSome work is:, Finished, Thoughtful, Makingconnections, Clear, CreativeLittle/No work is:, Finished, Thoughtful, Makingconnections, Clear, CreativePoints 20 15 10 5InputAll work is:, Finished, Thoughtful, Thorough, Consistentlydone with goodeffortMajority of work is:, Finished, Thoughtful, Thorough, Consistentlydone with goodeffortSome work is:, Finished, Thoughtful, Thorough, Consistentlydone withgood effortLittle/No work is:, Finished, Thoughtful, Thorough, Consistentlydone with goodeffortPoints 20 15 10 5Organizationand Neatness, Pages arenumbered, Table ofContentscomplete withtitles, Work is neat andlegible, Contents isorganized and inits proper placeLess than 4 itemsare missing.Five to Eightitems are missing.Nine or more itemsare missing.Points 10 8 6 4Teacher Comments:_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Score:Rubric Points: ________50? %
- 18. Interactive Notebook Rubric"" " ""Excellent Satisfactory Need Improvement WeakOutputAll work is:, Finished, Thoughtful, Making connections, Clear, CreativeMajority of work is:, Finished, Thoughtful, Making connections, Clear, CreativeSome work is:, Finished, Thoughtful, Making connections, Clear, CreativeLittle/No work is:, Finished, Thoughtful, Making connections, Clear, CreativePoints 20 15 10 5InputAll work is:, Finished, Thoughtful, Thorough, Consistently done withgood effortMajority of work is:, Finished, Thoughtful, Thorough, Consistently donewith good effortSome work is:, Finished, Thoughtful, Thorough, Consistently done withgood effortLittle/No work is:, Finished, Thoughtful, Thorough, Consistently done withgood effortPoints 20 15 10 5Organization andNeatness, Pages are numbered, Table of Contentscomplete with titles, Work is neat and legible, Contents is organizedand in its proper placeLess than 4 items aremissing.Five to Eight items aremissing.Nine or more items aremissing.Points 10 8 6 4Teacher Comments:__________________________________________________________________________________________________Score:Rubric Points: ________50? %
- 19. "" " ""Name:___________________________Interactive Notebook RubricTitle Page: 5 pts. ______Student Name, Course,Period, Year, TeacherTable of Contents: 15 pts. ______LS/RS correct designation,entries completeGrade Sheet/GraphUpdated: 5 pts. ______Pages Titled: 5 pts. ______Pages Numbered: 10 pts. ______Entries Secure: 5 pts. ______Daily Focus: 15 pts. ______All AssignmentsEntered: 10 pts. ______L Sides: 30 pts. ______Appropriate, colorful, creative,shows interaction with contentExtra Credit: 5 pts. ______Work is neat and organizedTotal points: ______Teacher Comments:"Name:___________________________Interactive Notebook RubricTitle Page: 5 pts. ______Student Name, Course,Period, Year, TeacherTable of Contents: 15 pts. ______LS/RS correct designation,entries completeGrade Sheet/GraphUpdated: 5 pts. ______Pages Titled: 5 pts. ______Pages Numbered: 10 pts. ______Entries Secure: 5 pts. ______Daily Focus: 15 pts. ______All AssignmentsEntered: 10 pts. ______L Sides: 30 pts. ______Appropriate, colorful, creative,shows interaction with contentExtra Credit: 5 pts. ______Work is neat and organizedTotal points: ______Teacher Comments:"
- 20. Algebra 1 Course Syllabus and ExpectationsTeacher: XXXXXXXXXXXX Room XXXXXXXX Middle School School Phone: XXX-XXX ext: XXXHome Phone: XXX-XXXX email: XXXXXXXXXXXXXXXCourse Description:Algebra 1 is a required yearlong course for advanced middle school students. It is the study ofexpressions, equations, functions and inequalities. Students will solve linear equation, use proportionalreasoning, graph relations and functions, analyze linear equations solve linear inequalities and systems oflinear equations and inequalities, explore polynomials and quadratic/exponential functions. They will alsoexplore rational and radical expressions and equations.Credit:Students successfully completing this course are eligible for one high school credit.Classroom Instruction and group work:Students will work in collaborative groups on a regular basis and approach problems conceptually. Theonly way students will master the concepts is by being actively involved in their learning. I will beresponsible for guiding, supporting and summarizing at all times.Daily assignments will be given to practice and master the skills we have learned in class.Student Assessments will be given at the end of each chapter and may include multiple choice, shortanswer and extended response questions. This is a balanced program where skill development is basedupon problem solving and understanding. Most of the 8th grade student expectations (TEKS) areembedded in the curriculum but some are not because it is a high school curriculum. Any 8th grade SEsnot covered by the high school Algebra 1 curriculum will be included in some other manner throughout theschool year.Parent Involvement:Parents, the following suggestions will help students be successful and have a positive experience inAlgebra 1.• Encourage and support risk taking on homework and while working in groups.• Talk on a regular basis about the concepts being taught.• Read and discuss student toolkit and journal entries on occasion.• Create an atmosphere at home where there is a designated study space and study time.• Be open to math groups working together at homes in evenings and weekends.• When students are asked to teach new concept to parents, be enthusiastic and attentive.• Offer help with homework and suggest that students get help at school when necessary.• Look through the geometry binder on occasion and ask about organizational strategies.• If your student needs help, start by asking them to read the problem out loud.Textbook:College Preparatory Mathematics (CPM) Algebra Connections: www.cpm.org. This web site has all of theproblems from the student textbook as well as solutions to the out-of class portion of each assignment forAlgebra Connections. Any resource pages that we have used in class are also available for the studentsthat have been sick or have missed class.
- 21. Classroom Supplies:Students will need these materials for math by Friday of the first week of school.1. 5-Star Notebook (college rule)2. Pencil pouch with two pencils, one red pen for correcting, colored pencils, eraser, six-inch ruler.3. A scientific calculator in pencil pouch. (TI 30xa is the least expensive and is excellent.)4. A bound quad rule notebook (with holes punched in it) of graph paper. We have asked the officesupply stores to have these books available for the high school and the middle school mathstudents.Attendance:Attendance is required in accordance with XXXXs Policy (see XXXX Handbook in the “Planner”. A studentwill not be successful without regular attendance.Classroom Management:“Make Your Day” is a citizenship program that encourages students to “Do what is expected” and “Do theirbest” each period of the day. Students have an opportunity to earn points, which enables them to “MYD”each school day.Assessments and Evaluation:Grades will be given at the end of each quarter. Grades will be updated weekly on line at:http://fms.wsd.wednet.edu. Please check student grades on line regularly.Assessments: Team and Individual exams 65%Daily Assignments and group presentations 25%Performance Expectations 5%Parent signatures and attendance at open house 5%The only extra credit will be applied from the bathroom passes and it will not exceed 1% of total grade.Grading Scale:A 93-100 C+ 76-79A- 90-92 C 73-75B+ 86-89 C- 70-72B 83-85 D+ 66-69B- 80-82 D 60-65F 0-59------------------------------------------------------------------------------------------------------------Please sign and return this section of the Algebra 1 Syllabus to school with you student. Keep the syllabusas a reference. Thank you!Student Signature: ______________________________ _________________________________(Please print and sign clearly.)Parent signature: ______________________________ Home or Cell Phone # __________________Please clearly print email address below.
- 22. Clock Partners Clock Partners
- 23. My Clock Partners My Clock Partners
- 24. Concept Definition MapProvided by Region 4 Education Service CenterConceptDefinitionAttributesExamples
- 25. My Concept Map: _____________________My definition:Important facts to remember:______________My example:_____________My example:______________My example:
- 26. My Concept Map: ________________________________My example:___________My example:____________My example:Important facts to remember:
- 27. My Concept Map: ____________________My example: My example:My example:Attributes:Category:Another work in theCategory:Another work in theCategory:
- 28. " " ""Title:Questions NotesSummary:
- 29. " " ""Title:Questions NotesSummary:Cornell Note Taking(Content title here)Questions Notes
- 30. " " ""Questions, comments,thoughts about contentnotesFold at line or cover notesand use questions as astudy toolStudents take notes in the style you model or in thestyle that makes sense to themSummary: Students summarize concepts and content and/or connect to real world ortheir own experiences. Can use as a checkpoint for understanding.
- 31. """"
- 32. Provided byDefinition (in your own words) Facts/CharacteristicsExamples Non-ExamplesDefinition (in your own words) Facts/CharacteristicsExamples Non-Examples
- 33. Lesson 2Grade 9© 2007 Region 4 Education Service Center Closing the Distance: A Flexible Tutorial for TAKS™All Rights Reserved 31Transparency: Posing the ProblemKim is standing by her desk. She startswalking away from her desk at a rate of 2feet per second and walks for 10 seconds.
- 34. 1TEXTEAMS Rethinking Middle School Mathematics: Algebraic ReasoningMovin on Down the LineInstitute NotesConcept: Use a graph to explore relationships between thequantities time and distance.Overview: Participants actively collect distance data in relation totime and graph it. Through questioning and richdiscussion, participants make the connection betweenthe motions observed during the activity and therelationship shown in the graph. This activity requiresextra physical space and can be done in a hallway orgym but gives the perfect opportunity to go outdoorson a day that weather permits.TEKS Focus: 6.13— The student uses logical reasoning to makeconjectures and verify conclusions.7.15— The student uses logical reasoning to makeconjectures and verify conclusions.8.16— The student uses logical reasoning to makeconjectures and verify conclusions.Materials: Stop watches or watches with a second hand (one pergroup), 100’ or 150’ Measuring tapes (one per group),Data Collection Cards, Secret Instruction Cards, 1”grid wall charts, Peel-and-stick dots or markersProcedure: 1. To prepare for this activity make a copy of the DataCollection Cards and Secret Instruction Cardssheets for each group and cut the cards apart.You may wish to laminate the cards.2. Go over the directions on a transparency ofActivity 1 - Instruction Sheet with the whole group.Do a quick demonstration and allow participants toask questions about the procedure.3. Divide the participants into groups of 12, distributesupplies, and have them complete Activity 1 byrecording the distance data for the five movers.4. Once the participants return to the room, havethem complete Activity 1 by compiling their datainto the tables and graphing the data on the grids.Also:Grade 64A, 7, 8B, 10D, 12A, 13AGrade 72G, 4B, 7A, 11B, 14A, 15AGrade 84, 5A, 12B, 15A, 16AAlgebra Ib.1A, 1D, 1E, b.2C, 2D,c.1B, c.2B, 2F
- 35. 2TEXTEAMS Rethinking Middle School Mathematics: Algebraic ReasoningMovin on Down the Line5. Have participants do Activity 2 by graphing the dataon 1” grid wall charts. Label each graph with thename and number of the mover. You may wish toassign a mover (1 – 5) to each group so that thedata for each mover is graphed only once.6. When all graphs are completed, use the Reason andCommunicate questions to discuss the informationyou can determine from the graphs.7. Have participants work in their groups of twelve todiscuss the graphs and determine the writteninstructions that each mover was given.8. With the whole group, use a transparency of theSecret Instruction Card sheet to compare theinstructions written by the groups to the actual secretinstructions given to each mover.9. Have participants reverse the process by doingActivity 2. Discuss using the Reason and Communi-cate questions.10.Have participants use the rules they have formed toanalyze the graphs in Activity 3. Discuss using theReason and Communicate questions.Extensions: Write a story about a person or some people moving.Draw a graph to illustrate it. The graph should showthe relationship between the distances of the personor people from some fixed place at different times.Exchange graphs with another group. Write a story togo with the graph drawn by the other group. Compareyour story with the other group’s story.Select a straight line section of one of the “Movin’ onDown the Line” graphs and determine the speed ofthe mover and the direction in which he or she wasmoving. Repeat for several different sections. Write abrief description explaining how you determined thespeed and direction.Graph the data in both inches and feet and comparethe graphs.
- 36. 3TEXTEAMS Rethinking Middle School Mathematics: Algebraic ReasoningMovin on Down the LineAssessment: Illustrate the following situation with a graph thatshows distance from the bus stop in relation to time:Ann was walking toward the bus stop when shesaw the bus coming. She ran as fast as she couldtoward the bus stop, but the bus left before she gotthere. She walked slowly the rest of the way to thestop and sat down to wait for the next bus.Write a brief statement describing how you can deter-mine the following when looking at a graph of distancefrom a fixed place over time.• How can you tell when the mover is travelingfast, slow, or standing still?• How can you tell if the mover is traveling towardor away from the beginning of the measuringtape?Notes:
- 37. TEXTEAMS Rethinking Middle School Mathematics: Algebraic Reasoning Activity-4Movin on Down the LineSecret Instruction CardsMovin’ on Down the LineSecret Instruction Card for Mover 1Do not show this card to anyone.Start at the beginning of the measuringtape. Walk forward slowly at a constantrate. When the timekeeper calls the10thsecond, stand still. When youhear 16, walk at a faster rate until timeruns out.Movin’ on Down the LineSecret Instruction Card for Mover 4Do not show this card to anyone.Start at the far end of the measuringtape. Walk fast toward the beginningof the measuring tape. Keep yourspeed as constant as you can. Whenthe timekeeper says 10, walk veryslowly. Continue to walk very slowlytoward the beginning of the tape.Movin’ on Down the LineSecret Instruction Card for Mover 5Do not show this card to anyone.Start at the 10 foot mark of the mea-suring tape. Walk very, very slowly atfirst. Then very gradually increaseyour speed until you are running.When you reach the end of the tape,stop running and stand still.Movin’ on Down the LineSecret Instruction Card for Mover 3Do not show this card to anyone.Start at the 25 foot mark of themeasuring tape, facing the beginningof the measuring tape. Stand still for 6seconds. When the timekeeper callsthe 6thsecond, walk along the tapetoward the beginning of the tape at aconstant speed. When you hear 12,stand still. When the timekeeper says18, walk again until time runs out.Movin’ on Down the LineSecret Instruction Card for Mover 2Do not show this card to anyone.Start at the beginning of the measuringtape. Jog along the tape at a moder-ate speed for 10 seconds, keepingyour speed as constant as you can.When the timekeeper calls the 10thsecond, walk back toward the startingpoint at a slow, steady pace until timeruns out.
- 38. TEXTEAMS Rethinking Middle School Mathematics: Algebraic Reasoning Activity-5Movin on Down the LineData Collection CardsMover12345Position at:Mover12345Position at:Mover12345Position at:Mover12345Position at:Mover12345Position at:Mover12345Position at:0 seconds 2 seconds 4 seconds 6 seconds8 seconds 10 seconds 12 seconds 14 seconds16 seconds 18 seconds 20 seconds 22 seconds
- 39. TEXTEAMS Rethinking Middle School Mathematics: Algebraic Reasoning Activity-6Movin on Down the LineActivity 1 - Instruction SheetPurpose: Collect data about the relationship between the distance of a personfrom the beginning of a measuring tape and the elapsed time.In each group identify: 1 Timekeeper with a stopwatch or a watch with asecond hand5 Movers, each with a different Secret Instruction Card6 Data collectors, each with a Data Collection CardDescription of the activity:Each data collector will be given a Data Collection Card with two times writtenon the top. Each is responsible for recording the position of the mover at eachtime on his or her card. For example, if your card has 4 and 6 seconds on it,you are responsible for recording the position of each mover when the time-keeper calls 4 seconds and 6 seconds.Each mover will be given a Secret Instruction Card. One at a time, follow thesecret instructions on your card without showing others your card. The time-keeper will give the start signal and then call out each second for 22 seconds.(“Go,…1,…2,...”)First, mover 1 will practice moving down the line to give the data collectors theopportunity to position themselves where the mover will be at their assignedtime. The second time Mover 1 moves down the line, each data collector willrecord the position of the BACK of the mover’s back foot at his or her assignedtime, rounding to the nearest foot.Repeat this procedure for each mover.Once all of the data is collected, return to the classroom.
- 40. 7TEXTEAMS Rethinking Middle School Mathematics: Algebraic ReasoningMovin on Down the LineMath Notes:In this activity, participants have recorded movers distances at certaintimes, organized this data into a table, and then represented the data witha graph. From the data and graphs, they made conjectures about themovers’ instructions. In the next activity, they will reverse the process.We call this habit of mathematical (algebraic) thinking doing andundoing. One of the processes we want to help develop during theinstitute and in our students is this notion of reversibility. That is, once wedo something, often we can work backwards and gain new insight, abetter understanding of what we have done, and a concrete knowledge ofthe concepts.Also, one goal of this activity is for participants to form ideas about howthe graph of a mover’s movement looks for different instructions. Ineffect, we are building intuition for what motion looks like graphically as arelationship between distance and time. This is the first step towarddeveloping algebraic reasoning by generalizing rules from data. We havenot moved to a symbolic form with variables and equations yet, but wehave begun to move from one representation to another. We call thishabit of mathematical (algebraic) thinking patterns to rules (Driscoll).Reason and Communicate:• What does the ordered pair (x,y)mean in these graphs? (time,distance)• In which graphs did the moverstand still for some period of time?How can you tell? Graphs 1, 3, and5. They have a horizontal line,which indicates that for more thanone second the mover was at thesame distance from the beginning ofthe tape.• In which graphs did the moverstart at the beginning of the tape?Graphs 1 and 2.• If the mover starts at the beginningof the tape, at what point does thegraph start? (0,0)• If the mover did not start at thebeginning of the tape, where did heor she start? In Graph 3, the moverstarted 25 feet from the beginning ofthe tape since the distance at t=0 is25 feet (300 in.). In Graph 4, themover started at the end of the tapesince the distance from the begin-ning of the tape at t=0 is equal to thelength of the tape. In Graph 5, themover started 10 feet (120 in.) fromthe beginning of the tape since thedistance at t=0 is 10 feet.• In which graphs is the movermoving away from the beginning ofthe tape? How can you tell? InGraphs 1 and 5, the mover movesaway from the beginning of the tapesince the distance from the begin-ning of the tape is increasing overtime. In Graph 2, the mover ismoving away from the beginning ofthe tape at first.• In which graphs is the movermoving toward the beginning of thetape? How can you tell? In Graphs3 and 4, the mover is moving towardthe beginning of the tape since thedistance from the beginning of thetape is decreasing over time. InGraph 2, the mover moves towardthe beginning of the tape in thesecond part.
- 41. TEXTEAMS Rethinking Middle School Mathematics: Algebraic Reasoning Activity-8Movin on Down the LineActivity 1, cont.Enter the data for each mover into the tables below. Graph the data on the corre-sponding grids below and then transfer to the 1" grids to display on the wall.Based on each graph, write a description of the instructions the mover followed.DistanceDistanceTimeTimeMover 2Time DistanceMover 1Time Distance
- 42. 9TEXTEAMS Rethinking Middle School Mathematics: Algebraic ReasoningMovin on Down the LineReason and Communicate, cont:• What does the graph look like ifthe mover moves away from thebeginning of the tape? The graphrises from left to right.• What does the graph look like ifthe mover moves toward thebeginning of the tape? The graphfalls from left to right.• In Graph 1, during which part isthe mover moving the fastest? Themover is moving fastest in the thirdsection of the walk because then thechange in his or her distance overone second is the greatest .• In Graph 2, when is the movermoving the slowest? The mover ismoving the slowest in the secondsection because the change in his orher distance over one second is theleast then.• Comparing all five graphs, inwhich one is the mover moving thefastest? How can you tell? Look forthe steepest segment.• Comparing all five graphs, inwhich one is the mover moving theslowest? How can you tell? Lookfor the most shallow segment.• Which graph does not look similarto the others? Why? Graph 5 has acurved line instead of a straight line.The mover’s rate is changing.• Should you connect the datapoints? Is the data discrete orcontinuous? Discuss that the onlyway you would have a break in thegraph is if the mover left the courseand then came back.• The graph represents a relation-ship between what two quantities?Elapsed time and distance from thebeginning of the measuring tape.
- 43. TEXTEAMS Rethinking Middle School Mathematics: Algebraic Reasoning Activity-10Movin on Down the LineActivity 1, cont.DistanceTimeTimeMover 3Time DistanceMover 4Time DistanceDistance
- 44. 11TEXTEAMS Rethinking Middle School Mathematics: Algebraic ReasoningMovin on Down the Line
- 45. TEXTEAMS Rethinking Middle School Mathematics: Algebraic Reasoning Activity-12DistanceTimeMovin on Down the LineActivity 1, cont.Mover 5Time Distance
- 46. 13TEXTEAMS Rethinking Middle School Mathematics: Algebraic ReasoningMovin on Down the LineMath Notes:Point out that in Activity 1 participants recorded movers distances atcertain times, organized the data into a table, and represented the data ona graph. From the data and graphs, we made conjectures about themovers’ instructions. Now in Activity 2, we have reversed the process.We are undoing by taking the verbal description of a movers walk andrepresenting it with a graph.Also, we used the algebraic thinking skill of patterns to rules by applyingthe rules we found in Activity 1. For example, a faster pace is representedby a steeper line.Reason and Communicate:• How are the graphs alike? Howare they different?• Which graph has a horizontalsection? Graph 1• How do you represent on thegraph a mover standing still? Ex-plain why. By drawing a horizontalline to show that the distance isstaying the same as the timechanges.• Which graph slopes down from leftto right? Why does it slope thatway? Graph 2 slopes down from leftto right because the mover started atthe end and walked toward thebeginning. Thus, the distance fromthe beginning of the tape decreasedin relation to time. Also, Graphs 3and 4 had segments where themover turned around and walkedtoward the beginning, so they havesegments that slope down from leftto right.• Which graph has the steepestsegment? Why? Graph 3, becausethe mover ran and there was agreater change in distance persecond.• How did you represent a moverwalking at a slow pace? Why? Bydrawing a shallow line to show asmall change in distance for eachsecond of time.• Does it matter how shallow youdraw the line? At this point, we arenot overly concerned with findingspecific rates of change. We justwant participants to draw things slowand fast relative to one another.
- 47. TEXTEAMS Rethinking Middle School Mathematics: Algebraic Reasoning Activity-14Movin on Down the LineActivity 2Some students in another class were given different Secret Instruction Cards for“Movin on Down the Line.” Data was collected for 20 seconds. Below is a list ofwhat was on their cards. Draw a sketch of what you think the graph should looklike for each one.1. Start at the beginning of themeasuring tape. Walk forward at asteady, slow pace for 5 seconds.Then stand still for the next 5 sec-onds. Repeat these steps until timeruns out.2. Start at the end of the tape andwalk towards the beginning of thetape at a steady pace.3. Start at the beginning of themeasuring tape and walk slowly for8 seconds then run for 8seconds. Then turn around andwalk slowly back towards the begin-ning of the tape.4. Start at the 50 foot mark on themeasuring tape. Walk forwardquickly for 7 seconds. Then turnaround and walk slowly backtoward the beginning of the tape for7 seconds. Turn around again andwalk away at a medium rate fromthe beginning of the tape until timeruns out.
- 48. 15TEXTEAMS Rethinking Middle School Mathematics: Algebraic ReasoningAnswers:1. Start about in the middle of the tape measure, walk further away for ashort while, and then stand still for the remainder of the time.2. Start at the beginning of the tape measure and stand still for a fourthof the time. Then walk away from the beginning of the tape measure untiltime runs out.3. This graph is not possible for this activity. At one time, the mover isthree different distances from the beginning of the tape. This implies thatthe walker was in three places at once. Note that Exercises 1 and 2 arefunctions and Exercise 3 is not a function.Math Notes:Remember that we are looking atthe relationship between the twoquantities time and distance fromthe beginning of the tape. Thegraphs represent these relation-ships. The graphs do not representa picture of the path taken. Themover did not walk a course thatlooks like the graph.In Activity 2, we went from a descrip-tion to a graph. In Activity 3, wemove from a graph to a description.This idea of going back and forthbetween representations, doing andundoing, is a major mathematicalhabit of thinking that builds algebraicreasoning. Keep looking for itthroughout the institute.In Activity 3, we build intuition for thealgebraic concept of function.Algebra students will need todifferentiate between relations thatare functions and relations that arenot functions.Reason and Communicate:• Which graphs are possible graphsfor Secret Instruction Cards? Why?Graphs 1 and 2 show that eachmoment the mover is only at onedistance from the beginning of themeasuring tape.• Which graph is not a possiblegraph of distance from the beginningof the measuring tape in relation toelapsed time? Why? Graph 3 is notpossible because to produce thisgraph, the mover would have to bein up to three places at the samemoment in time.• What do we mean by doing andundoing? Doing and undoing is amathematical (algebraic) habit ofmind. It is the idea of reversibility,strengthening of mathematicalconnections by going backwards.Activity 2 reverses Activity 1. Activ-ity 3 reverses Activities 1 and 2.Movin on Down the Line
- 49. TEXTEAMS Rethinking Middle School Mathematics: Algebraic Reasoning Activity-16Movin on Down the LineActivity 3Study the graphs below made by a group of students in another class. Are thesegraphs possible graphs for other Secret Instruction Cards for “Movin’ on Downthe Line”? If not, explain why. If possible, write a description of how the personwas moving.1.2.3.
- 50. Movin’"on"Down"the"Line"Adapted"for"Interactive"Notebook""Cut"along"the"dotted"lines,"and"then"fold"along"the"solid"line."Attach"to"your"notebook."Then"draw"a"sketch"of"what"you"think"the"graph"should"look"like"for"each"scenario.""" Adapted"from"TEXTEAMS"(Movin’"on"Down"the"Line)""Start at the beginning of themeasuring tape. Walk forward at asteady, slow pace for 5 seconds. Thenstand still for the next 5 seconds.Repeat these steps until time runsout."Start at the end of the tape and walktowards the beginning of the tape at asteady pace."Start at the beginning of themeasuring tape and walk slowly for8 seconds then run for 8 seconds.Then turn around and walk slowlyback towards the beginning of thetape."Start at the 50 foot mark on themeasuring tape. Walk forward quicklyfor 7 seconds. Then turn around andwalk slowly back toward the beginningof the tape for 7 seconds. Turn aroundagain and walk at a medium rate fromthe beginning of the tape until timeruns out."
- 51. ""Plot"each"point.""On"what"part"of"the"coordinate"plane"does"each"point"fall?""A"(2,2)" B"( 3,1)/ "C"( 4, 5)/ / " D"(2, 3)/ "E"(0, 3)/ " F"(5,0)""
- 52. Rectangular Prism MatchEngaging Mathematics © Region 4 Education Service CenterGrade 4 314 All rights reserved.Answer (continued):Cards not used:
- 53. Engaging Mathematics:Algebra I TEKS-Based Activities© Region 4 Education Service CenterAll rights reserved.Linear Relationship CardsCut along the dotted lines. Four sets of cards are provided.The graph of the line passesthrough the origin.Equation is not of theform y = kx.The video game rental fee is$15 plus $3 per day.There is a constant rateof change.The cell phone rate is $9.99each month and 3 cents aminute.The graph does not passthrough the origin.Angelica earns $6 an hourbabysitting.The graph is a line. Equations fit the form y = kx.The graph of the line passesthrough the origin.Equation is not of theform y = kx.The video game rental fee is$15 plus $3 per day.There is a constant rateof change.The cell phone rate is $9.99each month and 3 cents aminute.The graph does not passthrough the origin.Angelica earns $6 an hourbabysitting.The graph is a line. Equations fit the form y = kx.The graph of the line passesthrough the origin.Equation is not of theform y = kx.The video game rental fee is$15 plus $3 per day.There is a constant rateof change.The cell phone rate is $9.99each month and 3 cents aminute.The graph does not passthrough the origin.Angelica earns $6 an hourbabysitting.The graph is a line. Equations fit the form y = kx.The graph of the line passesthrough the origin.Equation is not of theform y = kx.The video game rental fee is$15 plus $3 per day.There is a constant rateof change.The cell phone rate is $9.99each month and 3 cents aminute.The graph does not passthrough the origin.Angelica earns $6 an hourbabysitting.The graph is a line. Equations fit the form y = kx.26
- 54. ProportionalA candy necklace costs $1.20.Jaiden wants to buy candynecklaces for all of her friends,but only has $15.00 to spend.How many necklaces can Jaidenpurchase with $15?A health club charges $30 permonth as a membership fee.Members can enroll in fitnessclasses for $10 per class. Howmany classes could Monica takein one month for $100?Non-Proportional"
- 55. Table A Table BNumber ofBooksHeight of Stack ofBooks From Floor (in.)Number ofBooksHeight of Stack ofBooks From Floor (in.)1 1.25 1 9.52 2.5 2 10.753 3 125 6.25 410 1710 9x xTable A Table BNumber ofBooksHeight of Stack ofBooks From Floor (in.)Number ofBooksHeight of Stack ofBooks From Floor (in.)1 1.25 1 9.52 2.5 2 10.753 3 125 6.25 410 1710 9x xTable A Table BNumber ofBooksHeight of Stack ofBooks From Floor (in.)Number ofBooksHeight of Stack ofBooks From Floor (in.)1 1.25 1 9.52 2.5 2 10.753 3 125 6.25 410 1710 9x x
- 56. Engaging Mathematics:Algebra I TEKS-Based Activities© Region 4 Education Service CenterAll rights reserved.Quilt PiecesCut along the bold lines.2x3x–2xxx+1x + 22x – 25 – x21x+22164
- 57. Engaging Mathematics:Algebra I TEKS-Based Activities© Region 4 Education Service CenterAll rights reserved.Student Name: ________________________________________ Date: ________________Technology and ScatterplotsEnter the data below into ̊ and æ of your graphing calculator to create a scatterplot.Miles DrivenGallons ofGasoline Used285 8.9378 11.8341 10.7454 14.2272 8.5422 13.2319 101. Determine an appropriate viewing window.Record your window settings.2. View the graph and sketch the scatterplot that appears. Determine the trend.Trend: _______________________Communicating About MathematicsInterpret the meaning of the trend in the problem above.___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________MilesGallonsofGas49
- 58. Star"Coordinates"–"one"per"student" Point A (2, 0) Point B (3, 4) Point C (0, 6) Point D (4, 6) Point E (5, 10) Point F (6, 6) Point G (10, 6) Point H (7, 4) Point I (8, 0) Point J (5, 3)" Point A (2, 0) Point B (3, 4) Point C (0, 6) Point D (4, 6) Point E (5, 10) Point F (6, 6) Point G (10, 6) Point H (7, 4) Point I (8, 0) Point J (5, 3)" Point A (2, 0) Point B (3, 4) Point C (0, 6) Point D (4, 6) Point E (5, 10) Point F (6, 6) Point G (10, 6) Point H (7, 4) Point I (8, 0) Point J (5, 3)" Point A (2, 0) Point B (3, 4) Point C (0, 6) Point D (4, 6) Point E (5, 10) Point F (6, 6) Point G (10, 6) Point H (7, 4) Point I (8, 0) Point J (5, 3)" Point A (2, 0) Point B (3, 4) Point C (0, 6) Point D (4, 6) Point E (5, 10) Point F (6, 6) Point G (10, 6) Point H (7, 4) Point I (8, 0) Point J (5, 3) Point A (2, 0) Point B (3, 4) Point C (0, 6) Point D (4, 6) Point E (5, 10) Point F (6, 6) Point G (10, 6) Point H (7, 4) Point I (8, 0) Point J (5, 3)) Point A (2, 0) Point B (3, 4) Point C (0, 6) Point D (4, 6) Point E (5, 10) Point F (6, 6) Point G (10, 6) Point H (7, 4) Point I (8, 0) Point J (5, 3) Point A (2, 0) Point B (3, 4) Point C (0, 6) Point D (4, 6) Point E (5, 10) Point F (6, 6) Point G (10, 6) Point H (7, 4) Point I (8, 0) Point J (5, 3) Point A (2, 0) Point B (3, 4) Point C (0, 6) Point D (4, 6) Point E (5, 10) Point F (6, 6) Point G (10, 6) Point H (7, 4) Point I (8, 0) Point J (5, 3) Point A (2, 0) Point B (3, 4) Point C (0, 6) Point D (4, 6) Point E (5, 10) Point F (6, 6) Point G (10, 6) Point H (7, 4) Point I (8, 0) Point J (5, 3) Point A (2, 0) Point B (3, 4) Point C (0, 6) Point D (4, 6) Point E (5, 10) Point F (6, 6) Point G (10, 6) Point H (7, 4) Point I (8, 0) Point J (5, 3) Point A (2, 0) Point B (3, 4) Point C (0, 6) Point D (4, 6) Point E (5, 10) Point F (6, 6) Point G (10, 6) Point H (7, 4) Point I (8, 0) Point J (5, 3)"
- 59. Vocabulary List:‚ Acute‚ Angle‚ Degree‚ Obtuse‚ Protractor‚ Rightan angle with ameasure between0° and 90°an angle with ameasure between90° and 180°an angle with ameasureof 90°a unit of measure the symbol H a tool used tomeasure degrees
- 60. Vocabulary Word Question Vocabulary WordWhich word goes with____________________________________________?Which word goes with____________________________________________?Which word goes with____________________________________________?Which word goes with____________________________________________?Which word goes with____________________________________________?Which word goes with____________________________________________?
- 61. Vocabulary Word Question Vocabulary WordWhich word goes with . . .Which word goes with . . .Which word goes with . . .Which word goes with . . .Which word goes with . . .Which word goes with . . ."
- 62. Engaging Mathematics:Algebra I TEKS-Based Activities© Region 4 Education Service CenterAll rights reserved.Information CardsCut along the dotted lines. Two sets of cards are provided.Data that is onlydefined for the givenvalues. The values inbetween are notincluded (usuallybecause fractionaldata is not possible).Data that is definedfor given values andthe interval betweenthe values‚ Graphs asseparate points‚ Usually thingsyou count (ex:number of booksor people)‚ Graphs as a line orcurve‚ Usually things youmeasure (ex: time,temperature)This spaceintentionally leftblank.Data that is onlydefined for the givenvalues. The values inbetween are notincluded (usuallybecause fractionaldata is not possible).Data that is definedfor given values andthe interval betweenthe values‚ Graphs asseparate points‚ Usually thingsyou count (ex:number of booksor people)‚ Graphs as a line orcurve‚ Usually things youmeasure (ex: time,temperature)This spaceintentionally leftblank.36
- 63. Engaging Mathematics:Algebra I TEKS-Based Activities© Region 4 Education Service CenterAll rights reserved.Student Name: ________________________________________ Date: ________________Vocabulary OrganizerCut apart the Information Cards and paste the items in the appropriate box in the vocabularyorganizer.Definition CharacteristicsExample NonexampleCommunicating About MathematicsGive an example of continuous data and explain why it is continuous.Definition CharacteristicsExample NonexampleDiscrete DataContinuous Data___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________35
- 64. Math Interactive Student NotebookYour notebook will…Be a way to organize your notesWill more class notes easier to understandAllow you to be more successful in classBecome a personalized textbookWhat makes the ISN different than a regular notebook?Many traditional notebooks have a tendency to get disorganized easily. Papersfall out and get lost. Notes can be boring and hard to understand. Manystudents do not take pride in their notebook and consequently do not use it tohelp them.Your interactive notebook will be your most valuable tool this year. Notes andnew ideas will be presented in a clear manner that you will be able to use asyour own personal “how-to guide” to pre-algebra.You will need the skills you learn this year when you take algebra next year.If maintained well, the ISN will travel with you to 9thgrade and be anextremely useful guide as you review topics that we learn this year.This side will have newideas and skills. Youshould look at right sidepages when you need helpremembering how to dosomething or to study.This side is where youwill process and practicenew skills.Right SideLeft Sideinput______________output______________IN ORDER TO BE SUCCESSFUL, YOUR NOTEBOOK MUST BEBROUGHT TO CLASS EVERYDAY AND SHOULD BE BROUGHTHOME TO STUDY AND HELP WITH HOMEWORK.
- 65. What goes in the ISN?Personalized CoverTable of ContentsCourse Guide and ExpectationsWords Worth Knowing (vocabulary)Class NotesPractice ActivitiesNJASK Formula SheetGrade Record SheetsLearning Style & MultipleIntelligences ProfilesSCORING CRITERIAYour notebook will be collected frequently and graded on the following:• TABLE OF CONTENTS IS COMPLETE• ALL RIGHT SIDE ENTRIES ARE PRESENT AND COMPLETE• ENTRIES ARE DATED• PAGES ARE NUMBERED• HEADINGS ARE LABELED• WORDS WORTH KNOWING (WWK) IS COMPLETE• WRITING IS NEAT, CLEAR, AND LEGIBLE• LEFT SIDE WORK IS COMPLETEDYou will also be occasionally permitted to use your ISN’s on quizzes.
- 66. Ğƚ ŽƌŐĂŶŝǌĞĚ ǁŝƚŚ DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ >> ƐĞĂƐŽŶƐ͊DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ >> ƐĞĂƐŽŶƐ ;ƉĚĨ ĨŝůĞ Θ ŵĞŵďĞƌƐŚŝƉ ƐŝƚĞͿ ŚĞůƉƐǇŽƵ ŐĞƚ Ă ŐƌŝƉ ŽŶ Ăůů ƚŚĞ ĂƌĞĂƐ ŽĨ ǇŽƵƌ ůŝĨĞ ďĞĨŽƌĞ ƚŚĞǇ ŐĞƚ Ă ŐƌŝƉ ŽŶ ǇŽƵ͊ĞĂƵƚŝĨƵů ĂƌƚǁŽƌŬ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶ ďƌĞĂƚŚĞƐ ŶĞǁ ůŝĨĞ ŝŶƚŽ ǇŽƵƌ ũŽƵƌŶĂů ;ŽƌũŽƵƌŶĂůƐͿ ĞǀĞƌǇ ƚŚƌĞĞ ŵŽŶƚŚƐ͘zŽƵƌ ƉƵƌĐŚĂƐĞ ŽĨ DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ƐĞĂƐŽŶƐ ĂůƐŽ ĐŽŵĞƐ ǁŝƚŚ ĂŽŶĞͲǇĞĂƌ ŵĞŵďĞƌƐŚŝƉ ƚŽ ŽƵƌ DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů DĞŵďĞƌƐŚŝƉ ^ŝƚĞ͘ ĂĐŚŵŽŶƚŚ͕ ƚŚŝƐ ƐŝƚĞ ŝƐ ƵƉĚĂƚĞĚ ǁŝƚŚ ŶĞǁ ĂŶĚ ƵƉĚĂƚĞĚ ĨŽƌŵƐ͕ ƚĞŵƉůĂƚĞƐ͕ƚŚĞŵĞƐ͕ ĞƚĐ͘^Ž ǁŚĂƚ͛Ɛ ŝŶĐůƵĚĞĚ ŝŶ ƚŚĞ ũŽƵƌŶĂů ͘ ͘ ͘ ƐŽ ĨĂƌ͍x ďĞĂƵƚŝĨƵů ĐŽǀĞƌ Θ ƐƉŝŶĞƐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ĞŵĞƌŐĞŶĐǇ Θ ĐŽŶƚĂĐƚ ŝŶĨŽ ƉĂŐĞƐx ǇĞĂƌ ĂƚͲĂͲŐůĂŶĐĞ͕ ǁĞĞŬͲĂƚͲĂͲŐůĂŶĐĞ͕ ĂŶĚ ŽƚŚĞƌ ͞ĂƚͲĂͲŐůĂŶĐĞ͟ ƉůĂŶŶŝŶŐ ƉĂŐĞƐx ĚŝǀŝĚĞƌ ƉĂŐĞƐ ;ĐŽƵůĚ ĂůƐŽ ďĞ ƵƐĞĚ ĂƐ ĐŽǀĞƌ ƉĂŐĞƐ ĨŽƌ ŝŶĚŝǀŝĚƵĂů ũŽƵƌŶĂůƐ ʹ ůŝŬĞ Ă ƌĞĐŝƉĞ ďŽŽŬͿ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ĐĂůĞŶĚĂƌƐ ĨŽƌ ϮϬϭϭ ;ĞŝŐŚƚ ƐƚǇůĞƐ ĨŽƌ ĞĂĐŚ ŵŽŶƚŚ͕ Ϯ ƉĂŐĞͲƐƉƌĞĂĚ͕ ĂŶĚ ŵŽƌĞ͊Ϳx ůŝƐƚƐ͗ ƐŚŽƉƉŝŶŐ͕ ŐŝĨƚ ƉůĂŶŶŝŶŐ͕ ŐŽĂů ƐĞƚƚŝŶŐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx Ă ǀĂƌŝĞƚǇ ŽĨ ƚŽͲĚŽ ůŝƐƚ ƉĂŐĞƐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ŚŽƵƐĞŚŽůĚ ĨŽƌŵƐ ĨŽƌ ŵĞŶƵ ƉůĂŶŶŝŶŐ͕ ŚŽƵƐĞĐůĞĂŶŝŶŐ͕ Θ ĨŝŶĂŶĐŝĂů ǁŽƌŬ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ƉĂŐĞƐ ƚŽ ďƵŝůĚ ĂŶĚ ƉůĂŶ ǇŽƵƌ ƌŽƵƚŝŶĞƐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx Ă ǀĂƌŝĞƚǇ ŽĨ ũŽƵƌŶĂůŝŶŐ ƉĂŐĞƐ ;ƐŽŵĞ ǁŝƚŚ ͞ŶŽƚĞďŽŽŬŝŶŐ ĨůĂŝƌ͟Ϳ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ŚŽŵĞƐĐŚŽŽů ƉůĂŶŶĞƌ ƉĂŐĞƐx ƌĞĐŝƉĞ ŶŽƚĞďŽŽŬ ƉĂŐĞƐΘ ŵƵĐŚ ŵŽƌĞ ƚŽ ĐŽŵĞ ʹ Ͳ ŶĞǁ ĐŽŶƚĞŶƚ ŝƐ ĂĚĚĞĚ ĞĂĐŚ ŵŽŶƚŚ͊ŚĞĐŬ ŝƚ ŽƵƚ ŽŶůŝŶĞ͗ŚƚƚƉ͗ͬͬŵŽŵƐƚŽŽůďĞůƚ͘ĐŽŵͬŵŽŵƐͲŚŽŵĞͲũŽƵƌŶĂůtĞ ŚŽƉĞ ǇŽƵ ĞŶũŽǇ ƚŚŝƐ ĨƌĞĞďŝĞ ĨƌŽŵ EŽƚĞďŽŽŬŝŶŐWĂŐĞƐ͘ĐŽŵ͊Ğ ƐƵƌĞ ƚŽ ĐŚĞĐŬ ŽƵƚ ŽƵƌ ǁĞďƐŝƚĞ ĨŽƌ Ă ĨƵůů ĂŶĚ ŐƌŽǁŝŶŐ ĐŽůůĞĐƚŝŽŶŽĨ ŶŽƚĞďŽŽŬŝŶŐ ƉĂŐĞƐ ĂŶĚ ŚŽŵĞƐĐŚŽŽůŝŶŐ ƌĞƐŽƵƌĐĞƐ ĂƐ ǁĞůů ĂƐŽƵƌ ŶĞǁ ŵĞŵďĞƌƐŚŝƉ ƉƌŽŐƌĂŵ͗dŚĞ EŽƚĞďŽŽŬŝŶŐ WĂŐĞƐ dƌĞĂƐƵƌǇ͘/Ĩ ǇŽƵ ĂƌĞ ůŽŽŬŝŶŐ ĨŽƌ Ă ĨĂŶƚĂƐƚŝĐ ǁĂǇ ƚŽ ŐĞƚ ŽƌŐĂŶŝǌĞĚ͕ ĐŽŶƐŝĚĞƌǀŝƐŝƚŝŶŐ ŽƵƌ ŶĞǁĞƐƚ ƐŝƚĞ͗ ŚƚƚƉ͗ͬͬŵŽŵƐƚŽŽůďĞůƚ͘ĐŽŵ ĂŶĚ ŽƵƌDŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ůů ^ĞĂƐŽŶƐ ;ĚĞƚĂŝůƐ ďĞůŽǁ͊Ϳ͘ůĞƐƐŝŶŐƐ͕ĞďƌĂ ZĞĞĚŚƚƚƉ͗ͬͬŶŽƚĞďŽŽŬŝŶŐƉĂŐĞƐ͘ĐŽŵŚƚƚƉ͗ͬͬŵŽŵƐƚŽŽůďĞůƚ͘ĐŽŵ
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- 81. Ğƚ ŽƌŐĂŶŝǌĞĚ ǁŝƚŚ DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ƐĞĂƐŽŶƐ͊DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ƐĞĂƐŽŶƐ ;ƉĚĨ ĨŝůĞ Θ ŵĞŵďĞƌƐŚŝƉ ƐŝƚĞͿ ŚĞůƉƐǇŽƵ ŐĞƚ Ă ŐƌŝƉ ŽŶ Ăůů ƚŚĞ ĂƌĞĂƐ ŽĨ ǇŽƵƌ ůŝĨĞ ďĞĨŽƌĞ ƚŚĞǇ ŐĞƚ Ă ŐƌŝƉ ŽŶ ǇŽƵ͊ĞĂƵƚŝĨƵů ĂƌƚǁŽƌŬ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶ ďƌĞĂƚŚĞƐ ŶĞǁ ůŝĨĞ ŝŶƚŽ ǇŽƵƌ ũŽƵƌŶĂů ;ŽƌũŽƵƌŶĂůƐͿ ĞǀĞƌǇ ƚŚƌĞĞ ŵŽŶƚŚƐ͘zŽƵƌ ƉƵƌĐŚĂƐĞ ŽĨ DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ƐĞĂƐŽŶƐ ĂůƐŽ ĐŽŵĞƐ ǁŝƚŚ ĂŽŶĞͲǇĞĂƌ ŵĞŵďĞƌƐŚŝƉ ƚŽ ŽƵƌ DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů DĞŵďĞƌƐŚŝƉ ^ŝƚĞ͘ ĂĐŚŵŽŶƚŚ͕ ƚŚŝƐ ƐŝƚĞ ŝƐ ƵƉĚĂƚĞĚ ǁŝƚŚ ŶĞǁ ĂŶĚ ƵƉĚĂƚĞĚ ĨŽƌŵƐ͕ ƚĞŵƉůĂƚĞƐ͕ƚŚĞŵĞƐ͕ ĞƚĐ͘^Ž ǁŚĂƚ͛Ɛ ŝŶĐůƵĚĞĚ ŝŶ ƚŚĞ ũŽƵƌŶĂů ͘ ͘ ͘ ƐŽ ĨĂƌ͍x ďĞĂƵƚŝĨƵů ĐŽǀĞƌ Θ ƐƉŝŶĞƐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ĞŵĞƌŐĞŶĐǇ Θ ĐŽŶƚĂĐƚ ŝŶĨŽ ƉĂŐĞƐx ǇĞĂƌ ĂƚͲĂͲŐůĂŶĐĞ͕ ǁĞĞŬͲĂƚͲĂͲŐůĂŶĐĞ͕ ĂŶĚ ŽƚŚĞƌ ͞ĂƚͲĂͲŐůĂŶĐĞ͟ ƉůĂŶŶŝŶŐ ƉĂŐĞƐx ĚŝǀŝĚĞƌ ƉĂŐĞƐ ;ĐŽƵůĚ ĂůƐŽ ďĞ ƵƐĞĚ ĂƐ ĐŽǀĞƌ ƉĂŐĞƐ ĨŽƌ ŝŶĚŝǀŝĚƵĂů ũŽƵƌŶĂůƐ ʹ ůŝŬĞ Ă ƌĞĐŝƉĞ ďŽŽŬͿ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ĐĂůĞŶĚĂƌƐ ĨŽƌ ϮϬϭϭ ;ĞŝŐŚƚ ƐƚǇůĞƐ ĨŽƌ ĞĂĐŚ ŵŽŶƚŚ͕ Ϯ ƉĂŐĞͲƐƉƌĞĂĚ͕ ĂŶĚ ŵŽƌĞ͊Ϳx ůŝƐƚƐ͗ ƐŚŽƉƉŝŶŐ͕ ŐŝĨƚ ƉůĂŶŶŝŶŐ͕ ŐŽĂů ƐĞƚƚŝŶŐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx Ă ǀĂƌŝĞƚǇ ŽĨ ƚŽͲĚŽ ůŝƐƚ ƉĂŐĞƐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ŚŽƵƐĞŚŽůĚ ĨŽƌŵƐ ĨŽƌ ŵĞŶƵ ƉůĂŶŶŝŶŐ͕ ŚŽƵƐĞĐůĞĂŶŝŶŐ͕ Θ ĨŝŶĂŶĐŝĂů ǁŽƌŬ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ƉĂŐĞƐ ƚŽ ďƵŝůĚ ĂŶĚ ƉůĂŶ ǇŽƵƌ ƌŽƵƚŝŶĞƐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx Ă ǀĂƌŝĞƚǇ ŽĨ ũŽƵƌŶĂůŝŶŐ ƉĂŐĞƐ ;ƐŽŵĞ ǁŝƚŚ ͞ŶŽƚĞďŽŽŬŝŶŐ ĨůĂŝƌ͟Ϳ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ŚŽŵĞƐĐŚŽŽů ƉůĂŶŶĞƌ ƉĂŐĞƐx ƌĞĐŝƉĞ ŶŽƚĞďŽŽŬ ƉĂŐĞƐΘ ŵƵĐŚ ŵŽƌĞ ƚŽ ĐŽŵĞ ʹ Ͳ ŶĞǁ ĐŽŶƚĞŶƚ ŝƐ ĂĚĚĞĚ ĞĂĐŚ ŵŽŶƚŚ͊ŚĞĐŬ ŝƚ ŽƵƚ ŽŶůŝŶĞ͗ŚƚƚƉ͗ͬͬŵŽŵƐƚŽŽůďĞůƚ͘ĐŽŵͬŵŽŵƐͲŚŽŵĞͲũŽƵƌŶĂůtĞ ŚŽƉĞ ǇŽƵ ĞŶũŽǇ ƚŚŝƐ ĨƌĞĞďŝĞ ĨƌŽŵ EŽƚĞďŽŽŬŝŶŐWĂŐĞƐ͘ĐŽŵ͊Ğ ƐƵƌĞ ƚŽ ĐŚĞĐŬ ŽƵƚ ŽƵƌ ǁĞďƐŝƚĞ ĨŽƌ Ă ĨƵůů ĂŶĚ ŐƌŽǁŝŶŐ ĐŽůůĞĐƚŝŽŶŽĨ ŶŽƚĞďŽŽŬŝŶŐ ƉĂŐĞƐ ĂŶĚ ŚŽŵĞƐĐŚŽŽůŝŶŐ ƌĞƐŽƵƌĐĞƐ ĂƐ ǁĞůů ĂƐŽƵƌ ŶĞǁ ŵĞŵďĞƌƐŚŝƉ ƉƌŽŐƌĂŵ͗dŚĞ EŽƚĞďŽŽŬŝŶŐ WĂŐĞƐ dƌĞĂƐƵƌǇ͘/Ĩ ǇŽƵ ĂƌĞ ůŽŽŬŝŶŐ ĨŽƌ Ă ĨĂŶƚĂƐƚŝĐ ǁĂǇ ƚŽ ŐĞƚ ŽƌŐĂŶŝǌĞĚ͕ ĐŽŶƐŝĚĞƌǀŝƐŝƚŝŶŐ ŽƵƌ ŶĞǁĞƐƚ ƐŝƚĞ͗ ŚƚƚƉ͗ͬͬŵŽŵƐƚŽŽůďĞůƚ͘ĐŽŵ ĂŶĚ ŽƵƌDŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ůů ^ĞĂƐŽŶƐ ;ĚĞƚĂŝůƐ ďĞůŽǁ͊Ϳ͘ůĞƐƐŝŶŐƐ͕ĞďƌĂ ZĞĞĚŚƚƚƉ͗ͬͬŶŽƚĞďŽŽŬŝŶŐƉĂŐĞƐ͘ĐŽŵŚƚƚƉ͗ͬͬŵŽŵƐƚŽŽůďĞůƚ͘ĐŽŵ
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- 99. Ğƚ ŽƌŐĂŶŝǌĞĚ ǁŝƚŚ DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ƐĞĂƐŽŶƐ͊DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ƐĞĂƐŽŶƐ ;ƉĚĨ ĨŝůĞ Θ ŵĞŵďĞƌƐŚŝƉ ƐŝƚĞͿ ŚĞůƉƐǇŽƵ ŐĞƚ Ă ŐƌŝƉ ŽŶ Ăůů ƚŚĞ ĂƌĞĂƐ ŽĨ ǇŽƵƌ ůŝĨĞ ďĞĨŽƌĞ ƚŚĞǇ ŐĞƚ Ă ŐƌŝƉ ŽŶ ǇŽƵ͊ĞĂƵƚŝĨƵů ĂƌƚǁŽƌŬ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶ ďƌĞĂƚŚĞƐ ŶĞǁ ůŝĨĞ ŝŶƚŽ ǇŽƵƌ ũŽƵƌŶĂů ;ŽƌũŽƵƌŶĂůƐͿ ĞǀĞƌǇ ƚŚƌĞĞ ŵŽŶƚŚƐ͘zŽƵƌ ƉƵƌĐŚĂƐĞ ŽĨ DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ƐĞĂƐŽŶƐ ĂůƐŽ ĐŽŵĞƐ ǁŝƚŚ ĂŽŶĞͲǇĞĂƌ ŵĞŵďĞƌƐŚŝƉ ƚŽ ŽƵƌ DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů DĞŵďĞƌƐŚŝƉ ^ŝƚĞ͘ ĂĐŚŵŽŶƚŚ͕ ƚŚŝƐ ƐŝƚĞ ŝƐ ƵƉĚĂƚĞĚ ǁŝƚŚ ŶĞǁ ĂŶĚ ƵƉĚĂƚĞĚ ĨŽƌŵƐ͕ ƚĞŵƉůĂƚĞƐ͕ƚŚĞŵĞƐ͕ ĞƚĐ͘^Ž ǁŚĂƚ͛Ɛ ŝŶĐůƵĚĞĚ ŝŶ ƚŚĞ ũŽƵƌŶĂů ͘ ͘ ͘ ƐŽ ĨĂƌ͍x ďĞĂƵƚŝĨƵů ĐŽǀĞƌ Θ ƐƉŝŶĞƐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ĞŵĞƌŐĞŶĐǇ Θ ĐŽŶƚĂĐƚ ŝŶĨŽ ƉĂŐĞƐx ǇĞĂƌ ĂƚͲĂͲŐůĂŶĐĞ͕ ǁĞĞŬͲĂƚͲĂͲŐůĂŶĐĞ͕ ĂŶĚ ŽƚŚĞƌ ͞ĂƚͲĂͲŐůĂŶĐĞ͟ ƉůĂŶŶŝŶŐ ƉĂŐĞƐx ĚŝǀŝĚĞƌ ƉĂŐĞƐ ;ĐŽƵůĚ ĂůƐŽ ďĞ ƵƐĞĚ ĂƐ ĐŽǀĞƌ ƉĂŐĞƐ ĨŽƌ ŝŶĚŝǀŝĚƵĂů ũŽƵƌŶĂůƐ ʹ ůŝŬĞ Ă ƌĞĐŝƉĞ ďŽŽŬͿ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ĐĂůĞŶĚĂƌƐ ĨŽƌ ϮϬϭϭ ;ĞŝŐŚƚ ƐƚǇůĞƐ ĨŽƌ ĞĂĐŚ ŵŽŶƚŚ͕ Ϯ ƉĂŐĞͲƐƉƌĞĂĚ͕ ĂŶĚ ŵŽƌĞ͊Ϳx ůŝƐƚƐ͗ ƐŚŽƉƉŝŶŐ͕ ŐŝĨƚ ƉůĂŶŶŝŶŐ͕ ŐŽĂů ƐĞƚƚŝŶŐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx Ă ǀĂƌŝĞƚǇ ŽĨ ƚŽͲĚŽ ůŝƐƚ ƉĂŐĞƐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ŚŽƵƐĞŚŽůĚ ĨŽƌŵƐ ĨŽƌ ŵĞŶƵ ƉůĂŶŶŝŶŐ͕ ŚŽƵƐĞĐůĞĂŶŝŶŐ͕ Θ ĨŝŶĂŶĐŝĂů ǁŽƌŬ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ƉĂŐĞƐ ƚŽ ďƵŝůĚ ĂŶĚ ƉůĂŶ ǇŽƵƌ ƌŽƵƚŝŶĞƐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx Ă ǀĂƌŝĞƚǇ ŽĨ ũŽƵƌŶĂůŝŶŐ ƉĂŐĞƐ ;ƐŽŵĞ ǁŝƚŚ ͞ŶŽƚĞďŽŽŬŝŶŐ ĨůĂŝƌ͟Ϳ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ŚŽŵĞƐĐŚŽŽů ƉůĂŶŶĞƌ ƉĂŐĞƐx ƌĞĐŝƉĞ ŶŽƚĞďŽŽŬ ƉĂŐĞƐΘ ŵƵĐŚ ŵŽƌĞ ƚŽ ĐŽŵĞ ʹ Ͳ ŶĞǁ ĐŽŶƚĞŶƚ ŝƐ ĂĚĚĞĚ ĞĂĐŚ ŵŽŶƚŚ͊ŚĞĐŬ ŝƚ ŽƵƚ ŽŶůŝŶĞ͗ŚƚƚƉ͗ͬͬŵŽŵƐƚŽŽůďĞůƚ͘ĐŽŵͬŵŽŵƐͲŚŽŵĞͲũŽƵƌŶĂůtĞ ŚŽƉĞ ǇŽƵ ĞŶũŽǇ ƚŚŝƐ ĨƌĞĞďŝĞ ĨƌŽŵ EŽƚĞďŽŽŬŝŶŐWĂŐĞƐ͘ĐŽŵ͊Ğ ƐƵƌĞ ƚŽ ĐŚĞĐŬ ŽƵƚ ŽƵƌ ǁĞďƐŝƚĞ ĨŽƌ Ă ĨƵůů ĂŶĚ ŐƌŽǁŝŶŐ ĐŽůůĞĐƚŝŽŶŽĨ ŶŽƚĞďŽŽŬŝŶŐ ƉĂŐĞƐ ĂŶĚ ŚŽŵĞƐĐŚŽŽůŝŶŐ ƌĞƐŽƵƌĐĞƐ ĂƐ ǁĞůů ĂƐŽƵƌ ŶĞǁ ŵĞŵďĞƌƐŚŝƉ ƉƌŽŐƌĂŵ͗dŚĞ EŽƚĞďŽŽŬŝŶŐ WĂŐĞƐ dƌĞĂƐƵƌǇ͘/Ĩ ǇŽƵ ĂƌĞ ůŽŽŬŝŶŐ ĨŽƌ Ă ĨĂŶƚĂƐƚŝĐ ǁĂǇ ƚŽ ŐĞƚ ŽƌŐĂŶŝǌĞĚ͕ ĐŽŶƐŝĚĞƌǀŝƐŝƚŝŶŐ ŽƵƌ ŶĞǁĞƐƚ ƐŝƚĞ͗ ŚƚƚƉ͗ͬͬŵŽŵƐƚŽŽůďĞůƚ͘ĐŽŵ ĂŶĚ ŽƵƌDŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ůů ^ĞĂƐŽŶƐ ;ĚĞƚĂŝůƐ ďĞůŽǁ͊Ϳ͘ůĞƐƐŝŶŐƐ͕ĞďƌĂ ZĞĞĚŚƚƚƉ͗ͬͬŶŽƚĞďŽŽŬŝŶŐƉĂŐĞƐ͘ĐŽŵŚƚƚƉ͗ͬͬŵŽŵƐƚŽŽůďĞůƚ͘ĐŽŵ
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- 117. Ğƚ ŽƌŐĂŶŝǌĞĚ ǁŝƚŚ DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ƐĞĂƐŽŶƐ͊DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ƐĞĂƐŽŶƐ ;ƉĚĨ ĨŝůĞ Θ ŵĞŵďĞƌƐŚŝƉ ƐŝƚĞͿ ŚĞůƉƐǇŽƵ ŐĞƚ Ă ŐƌŝƉ ŽŶ Ăůů ƚŚĞ ĂƌĞĂƐ ŽĨ ǇŽƵƌ ůŝĨĞ ďĞĨŽƌĞ ƚŚĞǇ ŐĞƚ Ă ŐƌŝƉ ŽŶ ǇŽƵ͊ĞĂƵƚŝĨƵů ĂƌƚǁŽƌŬ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶ ďƌĞĂƚŚĞƐ ŶĞǁ ůŝĨĞ ŝŶƚŽ ǇŽƵƌ ũŽƵƌŶĂů ;ŽƌũŽƵƌŶĂůƐͿ ĞǀĞƌǇ ƚŚƌĞĞ ŵŽŶƚŚƐ͘zŽƵƌ ƉƵƌĐŚĂƐĞ ŽĨ DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ƐĞĂƐŽŶƐ ĂůƐŽ ĐŽŵĞƐ ǁŝƚŚ ĂŽŶĞͲǇĞĂƌ ŵĞŵďĞƌƐŚŝƉ ƚŽ ŽƵƌ DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů DĞŵďĞƌƐŚŝƉ ^ŝƚĞ͘ ĂĐŚŵŽŶƚŚ͕ ƚŚŝƐ ƐŝƚĞ ŝƐ ƵƉĚĂƚĞĚ ǁŝƚŚ ŶĞǁ ĂŶĚ ƵƉĚĂƚĞĚ ĨŽƌŵƐ͕ ƚĞŵƉůĂƚĞƐ͕ƚŚĞŵĞƐ͕ ĞƚĐ͘^Ž ǁŚĂƚ͛Ɛ ŝŶĐůƵĚĞĚ ŝŶ ƚŚĞ ũŽƵƌŶĂů ͘ ͘ ͘ ƐŽ ĨĂƌ͍x ďĞĂƵƚŝĨƵů ĐŽǀĞƌ Θ ƐƉŝŶĞƐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ĞŵĞƌŐĞŶĐǇ Θ ĐŽŶƚĂĐƚ ŝŶĨŽ ƉĂŐĞƐx ǇĞĂƌ ĂƚͲĂͲŐůĂŶĐĞ͕ ǁĞĞŬͲĂƚͲĂͲŐůĂŶĐĞ͕ ĂŶĚ ŽƚŚĞƌ ͞ĂƚͲĂͲŐůĂŶĐĞ͟ ƉůĂŶŶŝŶŐ ƉĂŐĞƐx ĚŝǀŝĚĞƌ ƉĂŐĞƐ ;ĐŽƵůĚ ĂůƐŽ ďĞ ƵƐĞĚ ĂƐ ĐŽǀĞƌ ƉĂŐĞƐ ĨŽƌ ŝŶĚŝǀŝĚƵĂů ũŽƵƌŶĂůƐ ʹ ůŝŬĞ Ă ƌĞĐŝƉĞ ďŽŽŬͿ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ĐĂůĞŶĚĂƌƐ ĨŽƌ ϮϬϭϭ ;ĞŝŐŚƚ ƐƚǇůĞƐ ĨŽƌ ĞĂĐŚ ŵŽŶƚŚ͕ Ϯ ƉĂŐĞͲƐƉƌĞĂĚ͕ ĂŶĚ ŵŽƌĞ͊Ϳx ůŝƐƚƐ͗ ƐŚŽƉƉŝŶŐ͕ ŐŝĨƚ ƉůĂŶŶŝŶŐ͕ ŐŽĂů ƐĞƚƚŝŶŐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx Ă ǀĂƌŝĞƚǇ ŽĨ ƚŽͲĚŽ ůŝƐƚ ƉĂŐĞƐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ŚŽƵƐĞŚŽůĚ ĨŽƌŵƐ ĨŽƌ ŵĞŶƵ ƉůĂŶŶŝŶŐ͕ ŚŽƵƐĞĐůĞĂŶŝŶŐ͕ Θ ĨŝŶĂŶĐŝĂů ǁŽƌŬ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ƉĂŐĞƐ ƚŽ ďƵŝůĚ ĂŶĚ ƉůĂŶ ǇŽƵƌ ƌŽƵƚŝŶĞƐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx Ă ǀĂƌŝĞƚǇ ŽĨ ũŽƵƌŶĂůŝŶŐ ƉĂŐĞƐ ;ƐŽŵĞ ǁŝƚŚ ͞ŶŽƚĞďŽŽŬŝŶŐ ĨůĂŝƌ͟Ϳ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ŚŽŵĞƐĐŚŽŽů ƉůĂŶŶĞƌ ƉĂŐĞƐx ƌĞĐŝƉĞ ŶŽƚĞďŽŽŬ ƉĂŐĞƐΘ ŵƵĐŚ ŵŽƌĞ ƚŽ ĐŽŵĞ ʹ Ͳ ŶĞǁ ĐŽŶƚĞŶƚ ŝƐ ĂĚĚĞĚ ĞĂĐŚ ŵŽŶƚŚ͊ŚĞĐŬ ŝƚ ŽƵƚ ŽŶůŝŶĞ͗ŚƚƚƉ͗ͬͬŵŽŵƐƚŽŽůďĞůƚ͘ĐŽŵͬŵŽŵƐͲŚŽŵĞͲũŽƵƌŶĂůtĞ ŚŽƉĞ ǇŽƵ ĞŶũŽǇ ƚŚŝƐ ĨƌĞĞďŝĞ ĨƌŽŵ EŽƚĞďŽŽŬŝŶŐWĂŐĞƐ͘ĐŽŵ͊Ğ ƐƵƌĞ ƚŽ ĐŚĞĐŬ ŽƵƚ ŽƵƌ ǁĞďƐŝƚĞ ĨŽƌ Ă ĨƵůů ĂŶĚ ŐƌŽǁŝŶŐ ĐŽůůĞĐƚŝŽŶŽĨ ŶŽƚĞďŽŽŬŝŶŐ ƉĂŐĞƐ ĂŶĚ ŚŽŵĞƐĐŚŽŽůŝŶŐ ƌĞƐŽƵƌĐĞƐ ĂƐ ǁĞůů ĂƐŽƵƌ ŶĞǁ ŵĞŵďĞƌƐŚŝƉ ƉƌŽŐƌĂŵ͗dŚĞ EŽƚĞďŽŽŬŝŶŐ WĂŐĞƐ dƌĞĂƐƵƌǇ͘/Ĩ ǇŽƵ ĂƌĞ ůŽŽŬŝŶŐ ĨŽƌ Ă ĨĂŶƚĂƐƚŝĐ ǁĂǇ ƚŽ ŐĞƚ ŽƌŐĂŶŝǌĞĚ͕ ĐŽŶƐŝĚĞƌǀŝƐŝƚŝŶŐ ŽƵƌ ŶĞǁĞƐƚ ƐŝƚĞ͗ ŚƚƚƉ͗ͬͬŵŽŵƐƚŽŽůďĞůƚ͘ĐŽŵ ĂŶĚ ŽƵƌDŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ůů ^ĞĂƐŽŶƐ ;ĚĞƚĂŝůƐ ďĞůŽǁ͊Ϳ͘ůĞƐƐŝŶŐƐ͕ĞďƌĂ ZĞĞĚŚƚƚƉ͗ͬͬŶŽƚĞďŽŽŬŝŶŐƉĂŐĞƐ͘ĐŽŵŚƚƚƉ͗ͬͬŵŽŵƐƚŽŽůďĞůƚ͘ĐŽŵ
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- 125. Ğƚ ŽƌŐĂŶŝǌĞĚ ǁŝƚŚ DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ƐĞĂƐŽŶƐ͊DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ƐĞĂƐŽŶƐ ;ƉĚĨ ĨŝůĞ Θ ŵĞŵďĞƌƐŚŝƉ ƐŝƚĞͿ ŚĞůƉƐǇŽƵ ŐĞƚ Ă ŐƌŝƉ ŽŶ Ăůů ƚŚĞ ĂƌĞĂƐ ŽĨ ǇŽƵƌ ůŝĨĞ ďĞĨŽƌĞ ƚŚĞǇ ŐĞƚ Ă ŐƌŝƉ ŽŶ ǇŽƵ͊ĞĂƵƚŝĨƵů ĂƌƚǁŽƌŬ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶ ďƌĞĂƚŚĞƐ ŶĞǁ ůŝĨĞ ŝŶƚŽ ǇŽƵƌ ũŽƵƌŶĂů ;ŽƌũŽƵƌŶĂůƐͿ ĞǀĞƌǇ ƚŚƌĞĞ ŵŽŶƚŚƐ͘zŽƵƌ ƉƵƌĐŚĂƐĞ ŽĨ DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ƐĞĂƐŽŶƐ ĂůƐŽ ĐŽŵĞƐ ǁŝƚŚ ĂŽŶĞͲǇĞĂƌ ŵĞŵďĞƌƐŚŝƉ ƚŽ ŽƵƌ DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů DĞŵďĞƌƐŚŝƉ ^ŝƚĞ͘ ĂĐŚŵŽŶƚŚ͕ ƚŚŝƐ ƐŝƚĞ ŝƐ ƵƉĚĂƚĞĚ ǁŝƚŚ ŶĞǁ ĂŶĚ ƵƉĚĂƚĞĚ ĨŽƌŵƐ͕ ƚĞŵƉůĂƚĞƐ͕ƚŚĞŵĞƐ͕ ĞƚĐ͘^Ž ǁŚĂƚ͛Ɛ ŝŶĐůƵĚĞĚ ŝŶ ƚŚĞ ũŽƵƌŶĂů ͘ ͘ ͘ ƐŽ ĨĂƌ͍x ďĞĂƵƚŝĨƵů ĐŽǀĞƌ Θ ƐƉŝŶĞƐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ĞŵĞƌŐĞŶĐǇ Θ ĐŽŶƚĂĐƚ ŝŶĨŽ ƉĂŐĞƐx ǇĞĂƌ ĂƚͲĂͲŐůĂŶĐĞ͕ ǁĞĞŬͲĂƚͲĂͲŐůĂŶĐĞ͕ ĂŶĚ ŽƚŚĞƌ ͞ĂƚͲĂͲŐůĂŶĐĞ͟ ƉůĂŶŶŝŶŐ ƉĂŐĞƐx ĚŝǀŝĚĞƌ ƉĂŐĞƐ ;ĐŽƵůĚ ĂůƐŽ ďĞ ƵƐĞĚ ĂƐ ĐŽǀĞƌ ƉĂŐĞƐ ĨŽƌ ŝŶĚŝǀŝĚƵĂů ũŽƵƌŶĂůƐ ʹ ůŝŬĞ Ă ƌĞĐŝƉĞ ďŽŽŬͿ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ĐĂůĞŶĚĂƌƐ ĨŽƌ ϮϬϭϭ ;ĞŝŐŚƚ ƐƚǇůĞƐ ĨŽƌ ĞĂĐŚ ŵŽŶƚŚ͕ Ϯ ƉĂŐĞͲƐƉƌĞĂĚ͕ ĂŶĚ ŵŽƌĞ͊Ϳx ůŝƐƚƐ͗ ƐŚŽƉƉŝŶŐ͕ ŐŝĨƚ ƉůĂŶŶŝŶŐ͕ ŐŽĂů ƐĞƚƚŝŶŐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx Ă ǀĂƌŝĞƚǇ ŽĨ ƚŽͲĚŽ ůŝƐƚ ƉĂŐĞƐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ŚŽƵƐĞŚŽůĚ ĨŽƌŵƐ ĨŽƌ ŵĞŶƵ ƉůĂŶŶŝŶŐ͕ ŚŽƵƐĞĐůĞĂŶŝŶŐ͕ Θ ĨŝŶĂŶĐŝĂů ǁŽƌŬ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ƉĂŐĞƐ ƚŽ ďƵŝůĚ ĂŶĚ ƉůĂŶ ǇŽƵƌ ƌŽƵƚŝŶĞƐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx Ă ǀĂƌŝĞƚǇ ŽĨ ũŽƵƌŶĂůŝŶŐ ƉĂŐĞƐ ;ƐŽŵĞ ǁŝƚŚ ͞ŶŽƚĞďŽŽŬŝŶŐ ĨůĂŝƌ͟Ϳ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ŚŽŵĞƐĐŚŽŽů ƉůĂŶŶĞƌ ƉĂŐĞƐx ƌĞĐŝƉĞ ŶŽƚĞďŽŽŬ ƉĂŐĞƐΘ ŵƵĐŚ ŵŽƌĞ ƚŽ ĐŽŵĞ ʹ Ͳ ŶĞǁ ĐŽŶƚĞŶƚ ŝƐ ĂĚĚĞĚ ĞĂĐŚ ŵŽŶƚŚ͊ŚĞĐŬ ŝƚ ŽƵƚ ŽŶůŝŶĞ͗ŚƚƚƉ͗ͬͬŵŽŵƐƚŽŽůďĞůƚ͘ĐŽŵͬŵŽŵƐͲŚŽŵĞͲũŽƵƌŶĂůtĞ ŚŽƉĞ ǇŽƵ ĞŶũŽǇ ƚŚŝƐ ĨƌĞĞďŝĞ ĨƌŽŵ EŽƚĞďŽŽŬŝŶŐWĂŐĞƐ͘ĐŽŵ͊Ğ ƐƵƌĞ ƚŽ ĐŚĞĐŬ ŽƵƚ ŽƵƌ ǁĞďƐŝƚĞ ĨŽƌ Ă ĨƵůů ĂŶĚ ŐƌŽǁŝŶŐ ĐŽůůĞĐƚŝŽŶŽĨ ŶŽƚĞďŽŽŬŝŶŐ ƉĂŐĞƐ ĂŶĚ ŚŽŵĞƐĐŚŽŽůŝŶŐ ƌĞƐŽƵƌĐĞƐ ĂƐ ǁĞůů ĂƐŽƵƌ ŶĞǁ ŵĞŵďĞƌƐŚŝƉ ƉƌŽŐƌĂŵ͗dŚĞ EŽƚĞďŽŽŬŝŶŐ WĂŐĞƐ dƌĞĂƐƵƌǇ͘/Ĩ ǇŽƵ ĂƌĞ ůŽŽŬŝŶŐ ĨŽƌ Ă ĨĂŶƚĂƐƚŝĐ ǁĂǇ ƚŽ ŐĞƚ ŽƌŐĂŶŝǌĞĚ͕ ĐŽŶƐŝĚĞƌǀŝƐŝƚŝŶŐ ŽƵƌ ŶĞǁĞƐƚ ƐŝƚĞ͗ ŚƚƚƉ͗ͬͬŵŽŵƐƚŽŽůďĞůƚ͘ĐŽŵ ĂŶĚ ŽƵƌDŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ůů ^ĞĂƐŽŶƐ ;ĚĞƚĂŝůƐ ďĞůŽǁ͊Ϳ͘ůĞƐƐŝŶŐƐ͕ĞďƌĂ ZĞĞĚŚƚƚƉ͗ͬͬŶŽƚĞďŽŽŬŝŶŐƉĂŐĞƐ͘ĐŽŵŚƚƚƉ͗ͬͬŵŽŵƐƚŽŽůďĞůƚ͘ĐŽŵ
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- 140. Ğƚ ŽƌŐĂŶŝǌĞĚ ǁŝƚŚ DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ƐĞĂƐŽŶƐ͊DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ƐĞĂƐŽŶƐ ;ƉĚĨ ĨŝůĞ Θ ŵĞŵďĞƌƐŚŝƉ ƐŝƚĞͿ ŚĞůƉƐǇŽƵ ŐĞƚ Ă ŐƌŝƉ ŽŶ Ăůů ƚŚĞ ĂƌĞĂƐ ŽĨ ǇŽƵƌ ůŝĨĞ ďĞĨŽƌĞ ƚŚĞǇ ŐĞƚ Ă ŐƌŝƉ ŽŶ ǇŽƵ͊ĞĂƵƚŝĨƵů ĂƌƚǁŽƌŬ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶ ďƌĞĂƚŚĞƐ ŶĞǁ ůŝĨĞ ŝŶƚŽ ǇŽƵƌ ũŽƵƌŶĂů ;ŽƌũŽƵƌŶĂůƐͿ ĞǀĞƌǇ ƚŚƌĞĞ ŵŽŶƚŚƐ͘zŽƵƌ ƉƵƌĐŚĂƐĞ ŽĨ DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ƐĞĂƐŽŶƐ ĂůƐŽ ĐŽŵĞƐ ǁŝƚŚ ĂŽŶĞͲǇĞĂƌ ŵĞŵďĞƌƐŚŝƉ ƚŽ ŽƵƌ DŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů DĞŵďĞƌƐŚŝƉ ^ŝƚĞ͘ ĂĐŚŵŽŶƚŚ͕ ƚŚŝƐ ƐŝƚĞ ŝƐ ƵƉĚĂƚĞĚ ǁŝƚŚ ŶĞǁ ĂŶĚ ƵƉĚĂƚĞĚ ĨŽƌŵƐ͕ ƚĞŵƉůĂƚĞƐ͕ƚŚĞŵĞƐ͕ ĞƚĐ͘^Ž ǁŚĂƚ͛Ɛ ŝŶĐůƵĚĞĚ ŝŶ ƚŚĞ ũŽƵƌŶĂů ͘ ͘ ͘ ƐŽ ĨĂƌ͍x ďĞĂƵƚŝĨƵů ĐŽǀĞƌ Θ ƐƉŝŶĞƐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ĞŵĞƌŐĞŶĐǇ Θ ĐŽŶƚĂĐƚ ŝŶĨŽ ƉĂŐĞƐx ǇĞĂƌ ĂƚͲĂͲŐůĂŶĐĞ͕ ǁĞĞŬͲĂƚͲĂͲŐůĂŶĐĞ͕ ĂŶĚ ŽƚŚĞƌ ͞ĂƚͲĂͲŐůĂŶĐĞ͟ ƉůĂŶŶŝŶŐ ƉĂŐĞƐx ĚŝǀŝĚĞƌ ƉĂŐĞƐ ;ĐŽƵůĚ ĂůƐŽ ďĞ ƵƐĞĚ ĂƐ ĐŽǀĞƌ ƉĂŐĞƐ ĨŽƌ ŝŶĚŝǀŝĚƵĂů ũŽƵƌŶĂůƐ ʹ ůŝŬĞ Ă ƌĞĐŝƉĞ ďŽŽŬͿ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ĐĂůĞŶĚĂƌƐ ĨŽƌ ϮϬϭϭ ;ĞŝŐŚƚ ƐƚǇůĞƐ ĨŽƌ ĞĂĐŚ ŵŽŶƚŚ͕ Ϯ ƉĂŐĞͲƐƉƌĞĂĚ͕ ĂŶĚ ŵŽƌĞ͊Ϳx ůŝƐƚƐ͗ ƐŚŽƉƉŝŶŐ͕ ŐŝĨƚ ƉůĂŶŶŝŶŐ͕ ŐŽĂů ƐĞƚƚŝŶŐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx Ă ǀĂƌŝĞƚǇ ŽĨ ƚŽͲĚŽ ůŝƐƚ ƉĂŐĞƐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ŚŽƵƐĞŚŽůĚ ĨŽƌŵƐ ĨŽƌ ŵĞŶƵ ƉůĂŶŶŝŶŐ͕ ŚŽƵƐĞĐůĞĂŶŝŶŐ͕ Θ ĨŝŶĂŶĐŝĂů ǁŽƌŬ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ƉĂŐĞƐ ƚŽ ďƵŝůĚ ĂŶĚ ƉůĂŶ ǇŽƵƌ ƌŽƵƚŝŶĞƐ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx Ă ǀĂƌŝĞƚǇ ŽĨ ũŽƵƌŶĂůŝŶŐ ƉĂŐĞƐ ;ƐŽŵĞ ǁŝƚŚ ͞ŶŽƚĞďŽŽŬŝŶŐ ĨůĂŝƌ͟Ϳ ĨŽƌ ĞĂĐŚ ƐĞĂƐŽŶx ŚŽŵĞƐĐŚŽŽů ƉůĂŶŶĞƌ ƉĂŐĞƐx ƌĞĐŝƉĞ ŶŽƚĞďŽŽŬ ƉĂŐĞƐΘ ŵƵĐŚ ŵŽƌĞ ƚŽ ĐŽŵĞ ʹ Ͳ ŶĞǁ ĐŽŶƚĞŶƚ ŝƐ ĂĚĚĞĚ ĞĂĐŚ ŵŽŶƚŚ͊ŚĞĐŬ ŝƚ ŽƵƚ ŽŶůŝŶĞ͗ŚƚƚƉ͗ͬͬŵŽŵƐƚŽŽůďĞůƚ͘ĐŽŵͬŵŽŵƐͲŚŽŵĞͲũŽƵƌŶĂůtĞ ŚŽƉĞ ǇŽƵ ĞŶũŽǇ ƚŚŝƐ ĨƌĞĞďŝĞ ĨƌŽŵ EŽƚĞďŽŽŬŝŶŐWĂŐĞƐ͘ĐŽŵ͊Ğ ƐƵƌĞ ƚŽ ĐŚĞĐŬ ŽƵƚ ŽƵƌ ǁĞďƐŝƚĞ ĨŽƌ Ă ĨƵůů ĂŶĚ ŐƌŽǁŝŶŐ ĐŽůůĞĐƚŝŽŶŽĨ ŶŽƚĞďŽŽŬŝŶŐ ƉĂŐĞƐ ĂŶĚ ŚŽŵĞƐĐŚŽŽůŝŶŐ ƌĞƐŽƵƌĐĞƐ ĂƐ ǁĞůů ĂƐŽƵƌ ŶĞǁ ŵĞŵďĞƌƐŚŝƉ ƉƌŽŐƌĂŵ͗dŚĞ EŽƚĞďŽŽŬŝŶŐ WĂŐĞƐ dƌĞĂƐƵƌǇ͘/Ĩ ǇŽƵ ĂƌĞ ůŽŽŬŝŶŐ ĨŽƌ Ă ĨĂŶƚĂƐƚŝĐ ǁĂǇ ƚŽ ŐĞƚ ŽƌŐĂŶŝǌĞĚ͕ ĐŽŶƐŝĚĞƌǀŝƐŝƚŝŶŐ ŽƵƌ ŶĞǁĞƐƚ ƐŝƚĞ͗ ŚƚƚƉ͗ͬͬŵŽŵƐƚŽŽůďĞůƚ͘ĐŽŵ ĂŶĚ ŽƵƌDŽŵ͛Ɛ ,ŽŵĞ :ŽƵƌŶĂů ĨŽƌ ůů ^ĞĂƐŽŶƐ ;ĚĞƚĂŝůƐ ďĞůŽǁ͊Ϳ͘ůĞƐƐŝŶŐƐ͕ĞďƌĂ ZĞĞĚŚƚƚƉ͗ͬͬŶŽƚĞďŽŽŬŝŶŐƉĂŐĞƐ͘ĐŽŵŚƚƚƉ͗ͬͬŵŽŵƐƚŽŽůďĞůƚ͘ĐŽŵ
- 141. ©2012 Outstanding Guides, LLC 1Sample
- 142. ©2012 Outstanding Guides, LLC 2Outstanding MathGuide8/:vjItcfgUcorngRcemgvCnkipgfvqEqooqpEqtgEwttkewnwoWriƩen by:Rhonda Davis, Leslie Hilderbrand,Darby Jochum and Robert SheperdGraphic Design by:Sydney Hilderbrandwww.theoutstandingguides.com
- 143. ©2012 Outstanding Guides, LLC 3Sample DescriptionThe Outstanding Math Guide is a book series for 4th to 9th grade that offers reproduciblegraphic organizers that are aligned to Common Core. Each book contains twenty or so graphicorganizers that have steps, examples and vocabulary for every concept introduced in a year. Asstudents make the graphic organizers they glue them into a folded three prong folder withpockets that is transformed into their own Outstanding Math Guide (OMG). Students keep theOMG in the front of their notebook and use it as a reference for homework, spiraling material,and studying for test.This sample packet is designed to give teachers an idea of what grade specific books are like.Three sample graphic organizers are included in this packet:x 6th grade - Order of Operationsx 7th grade - Cross Sectionsx 8th grade - Scientific NotationThe introduction, overview, implementation and appendices information that follows areincluded in each book in the series to help teachers implement Outstanding Math Guides intheir classroom and or school. The front cover of this sample packet and the OMG pictures thatfollow are taken from the 8th grade OMG. If you are interested in the PDF version of the Out-standing Math Guide, they can be obtained at www.TeachersPayTeachers. If you would like theHard copy of the Outstanding Math Guide which includes a CD of folding videos you can visitwww.TheOutstandingGuides.com.Outstanding Math Guide
- 144. ©2012 Outstanding Guides, LLC 4IntroductionThe Outstanding Math Guide (OMG) is packed with creative folded graphic organizers whichcontain steps and examples for each key concept encountered throughout the year. These graph-ic organizers are kept in a folded, standard 3-prong pocket folder. The OMG serves as a visualreference that students keep in their notebooks and use in class or at home whencompleting homework, studying, or reviewing spiraling material. This book containsdifferentiated graphic organizer templates that can be reproduced for your students to create. Inaddition to key concepts aligned to Common Core Curriculum, the OMG includes a sectionwhere students can record vocabulary terms and examples as they are introduced in theclassroom.Materials NeededIncorporating OMGs in your math instruction requires limited out of pocket expenses.x Folders: Three prong folder with pockets for each student.x Paper: Lightweight and colorful.x Glue: Glue sticks only.x Scissors: Classroom set.x Heavy duty hole punch: To punch holes in folder.x File Box: To store extra copies of graphic organizer templates.x Disk (included): Can be used as an instructional guide when completing graphic organizerswith students. Disk also includes videos for initial folder set-up and folding instructions foreach graphic organizer.Outstanding Math Guide
- 145. ©2012 Outstanding Guides, LLC 5OverviewThese reproducible graphic organizers can be used by your students to make an OutstandingMath Guide (OMG). The OMG is a work in progress; graphic organizers are constructed as anintroduction or review of each topic. By the end of the year, your students will have an OMGthat can be easily referenced for years to come.Outstanding Math GuideA standard3 - prongpocket fold-er is foldedin half.Vocabulary sheetsallow terms and examples tobe recorded as they areintroduced in class.Holes are punchedso OMG will storein the front of anotebook.
- 146. ©2012 Outstanding Guides, LLC 6Outstanding Math GuidePockets in folder are cutdown each side so theywill open up.
- 147. ©2012 Outstanding Guides, LLC 7IMPLEMENTATIONTo implement a successful OMG program you will need flexible and supportive co-workers.At our school, we have been blessed with a supportive administration and a flexible math team;all students have their OMG in their math notebook at all times. Our principal has even beenknown to stop students in the hallway and ask to see their OMG.The following are the various components of the OMG implementation process:OMG: Every student in every grade creates an OMG. The OMG will only be as valuable asyou make it. The way to make it valuable and your students more independent is to requirethem to reference previously taught material as the need arises. We suggest that students haveOMG’s out during class time. You must get them in the habit of looking up questions in theirOMG. As students have increased ownership in the OMG, they will begin to see its valuebeyond a place to glue graphic organizers.Folder Set-up: For logistic purposes we recommend each grade level use a different colorfolder for their OMGs. To help minimize your costs, we suggest adding a specific color folderto your back-to-school supplies list, and some students will actually get their own folder (stressa 3 prong folder with pockets is needed). One of the first few days of school should be used toset up the OMG. See included disk for a video of folder set-up instructions.Graphic Organizers:Each graphic organizer can be used as unit introduction or review. Three types of graphicorganizer templates are offered in this book:x Completed notes and examples - targeting students with special needs.x Fill in the blank - targeting students on grade level.x Blank - targeting accelerated students or deviation from the provided material.Graphic Organizer Placement: Reference the layout placement guide to ensure that all thecreated graphic organizers fit inside the OMG.Vocabulary Sheets: Copies of the vocabulary sheets will be needed for each OMG. As asuggestion have the vocabulary template accessible on your website and request that studentsdownload copies for their OMG. See Appendix A for vocabulary template and Appendix B forvocabulary grading rubric.Outstanding Math Guide
- 148. ©2012 Outstanding Guides, LLC 8Absent Students: If a student is absent on the a day a graphic organizer is made, have anothertrusted student make one for them.New Students: To help new students create an OMG, delegate the responsibility to aclassmate. It is helpful to make additional graphic organizers as you go to provide new studentswith an up-to-date OMG.Lost OMG: Explain the consequences of losing your OMG. If the inevitable happens and astudent loses his OMG, give the student a time frame in which the graphic organizers should berecreated. You will be amazed when students realize they will have to remake the OMG ontheir own time they become much more protective of it!File Box: A file crate can be used to store extra copies of each graphic organizer template.Print labels have been provided in Appendix C.Parents: It is helpful for parents to be aware that the OMG is a reference tool. When studentshave questions on math homework, parents can suggest they use their OMG as a reference. Asample parent letter is provided in Appendix D.Outstanding Math Guide
- 149. ©2012OutstandingGuides,LLC9Vocabularyx exponent30QtfgtqhQrgtcvkqpu GzrtguukqpucpfGswcvkqpu6
- 150. ©2012 Outstanding Guides, LLC 101324Workfromlefttoright,whichevercomesfirst.AdditionSubtractionand4
- 151. ©2012OutstandingGuides,LLC11ParenthesesDo all calculations insideparenthesis first.OrderofOperations( ) x2x ÷ + -xponentsESimplifyallexponents.MultiplicationWorkfromlefttoright,whichevercomesfirst.Divisionand132
- 152. ©2012OutstandingGuides,LLC121324Work from left to right,whichever comes first.AdditionSubtractionand4_________________________________________________________________________
- 153. ©2012OutstandingGuides,LLC13ParenthesesDo all calculations insideparenthesis first.OrderofOperations( ) x2x ÷ + -xponentsESimplifyallexponents.MultiplicationWorkfromlefttoright,whichevercomesfirst.Divisionand132
- 154. ©2012 Outstanding Guides, LLC 14OrderofOperations()x2x÷+-
- 155. ©2012OutstandingGuides,LLC15Vocabularyx Basex cross sectionx parallelx perpendicular40EtquuUgevkqpuIgqogvt{Identifying the cross sections of solid figures7
- 156. ©2012 Outstanding Guides, LLC 16SectionsCross
- 157. ©2012OutstandingGuides,LLC17Slicedparallel tothe baseCross Section is aSlicedperpendicular tothe baseCross Section is aSliced at an cornerCross Section is aSliced parallel orperpendicular to thebaseCross Section is aSlicedparallel tothe baseCross Section is aSlicedperpendicular tothe baseCross Section is aSlicedperpendicular tothe baseCross Section is aSlicedparallel tothe baseCross Section is a

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