Grade 11 Applied Mathematics (30S) - Manitoba Education

3y ago
33 Views
2 Downloads
1.08 MB
56 Pages
Last View : 16d ago
Last Download : 2m ago
Upload by : Gideon Hoey
Transcription

Grade 11 AppliedMathematics (30S)A Course for Independent StudyField Validation Version

G r a d e 11 A p p l ie dMathemat ics (30S)A Course for Independent StudyField Validation Version2016M a ni t o b a E d u c a t i o n a n d Tr ainin g

Manitoba Education and Training Cataloguing in Publication DataGrade 11 applied mathematics (30S) : a course for independentstudy—Field validation versionThis resource is available in print and electronic formats.ISBN: 978-0-7711-7429-2 (print)ISBN: 978-0-7711-7430-8 (pdf)1. Mathematics—Study and teaching (Secondary).2. Mathematics—Study and teaching (Secondary)—Manitoba.3. Mathematics—Programmed instruction.4. Distance education—Manitoba.5. Correspondence schools and courses—Manitoba.I. Manitoba. Manitoba Education and Training.510Copyright 2016, the Government of Manitoba, represented by the Ministerof Education and Training.Manitoba Education and TrainingSchool Programs DivisionWinnipeg, Manitoba, CanadaEvery effort has been made to acknowledge original sources and to complywith copyright law. If cases are identified where this has not been done, pleasenotify Manitoba Education and Training. Errors or omissions will be correctedin a future edition. Sincere thanks to the authors, artists, and publishers whoallowed their original material to be used.All images found in this resource are copyright protected and should notbe extracted, accessed, or reproduced for any purpose other than for theirintended educational use in this resource.Any websites referenced in this resource are subject to change without notice.Disponible en français.Available in alternate formats upon request.

hat Will You Learn in This Course?3How Is This Course Organized?3What Resources Will You Need for This Course?4Who Can Help You with This Course?6How Will You Know How Well You Are Learning?7How Much Time Will You Need to Complete This Course?11When and How Will You Submit Completed Assignments?13What Are the Guide Graphics For?16Cover Sheets191Module 1: Quadratic FunctionsModule 1 Introduction3Module 1 Cover Assignment: Geometric Patterns5Lesson 1 Features of Quadratic Functions and Equations9Lesson 2: Roots, x-intercepts, and Zeros31Lesson 3: Using the Symmetry of a Quadratic Function55Lesson 4: Sketching a Quadratic Function65Lesson 5: Applying Quadratic Functions in the World81Module 1 Summary103Module 1 Learning Activity Answer KeysContentsiii

Module 2: Mathematics Research Project1Module 2 Introduction3Module 2 Cover Assignment: Historical Mathematical Problems7Lesson 1: Project Proposal: Topic and Question Selectionand Data Source Identification13Lesson 2: Collecting and Assessing the Data21Lesson 3: Interpreting the Data27Lesson 4: Presentation31Module 2 Summary35Module 3: Reasoning to Solve Problems1Module 3 Introduction3Module 3 Cover Assignment: Logic Puzzles5Lesson 1: Conjectures and Counter-examples13Lesson 2: Deductive Reasoning25Lesson 3: Invalid Reasoning47Lesson 4: Spatial Reasoning57Module 3 Summary73Module 3 Learning Activity Answer KeysModule 4: Geometry of Angles and TrianglesModule 4 Introduction3Module 4 Cover Assignment: Geometry in Tangrams5Lesson 1: Angles and Triangles11Lesson 2: Angle Properties of Polygons27Lesson 3: Exploring and Proving Properties of Parallel Linesand Transversals45Lesson 4: Applying Properties of Parallel Lines and Transversals57Module 4 Summary83Module 4 Learning Activity Answer Keysiv1Grade 11 Applied Mathematic s

1Module 5: TrigonometryModule 5 Introduction3Module 5 Cover Assignment: Geometric and Numerical Reasoning5Lesson 1: Right-Triangle Trigonometry15Lesson 2: The Sine Law for Acute Triangles27Lesson 3: The Cosine Law for Acute Triangles45Lesson 4: Solving Obtuse Triangles71Lesson 5: The Ambiguous Case93Module 5 Summary113Module 5 Learning Activity Answer Keys1Module 6: StatisticsModule 6 Introduction3Module 6 Cover Assignment: The Indigenous IdentityPopulation in Canada7Lesson 1: Measures of Central Tendency and Histograms13Lesson 2: Standard Deviation27Lesson 3: The Normal Distribution47Lesson 4: z-Scores71Lesson 5: z-Scores and the Normal Distribution83Lesson 6: Confidence Intervals107Module 6 Summary119Module 6 Learning Activity Answer KeysContentsv

Module 7: Mathematical Models1Module 7 Introduction3Module 7 Cover Assignment: Skyscraper Puzzles5Lesson 1: Rates in Your Life13Lesson 2: Drawing Graphs to Represent Rates21Lesson 3: Linear Functions41Lesson 4: Linear Inequalities51Lesson 5: Graphing Systems of Linear Inequalities69Lesson 6: Optimizing Solutions to Linear Inequalities95Module 7 Summary109Lesson 7 Learning Activity Answer KeysModule 8: Scale Factors for 2-D and 3-D Shapes1Module 8 Introduction3Module 8 Cover Assignment: Pattern Analysis7Lesson 1: Scale Diagrams of 2-D Shapes13Lesson 2: Scale Models of 3-D Objects29Lesson 3: Scale Factors and Area of 2-D Shapes51Lesson 4: The Relationship between Scale Factors andSurface Area of 3-D Shapes75Lesson 5: The Relationship between Scale Factors andVolume of 3-D Objects91Module 8 Summary117Lesson 8 Learning Activity Answer KeysTechnology AppendixviGrade 11 Applied Mathematic s1

AcknowledgementsManitoba Education and Training gratefully acknowledges the contributions of the followingindividuals in the development of Grade 11 Applied Mathematics (30S): A Course for IndependentStudy—Field Validation Version.Megan HudsonGoose Lake High SchoolMountain View School DivisionReviewerLinda IsaakIndependent ConsultantWinnipegManitoba Educationand TrainingCarole BilykCoordinatorDevelopment UnitInstruction, Curriculum and Assessment BranchLouise BoissonneaultCoordinatorDocument Production Services UnitEducational Resources BranchIan DonnellyProject LeaderDevelopment UnitInstruction, Curriculum and Assessment BranchLynn HarrisonDesktop PublisherDocument Production Services UnitEducational Resources BranchNathalie HouleConseiller pédagogique(from September 2015)Conseiller pédagogique—Mathématiques 9 à 12Division du Bureau de l’éducation française DivisionMyrna KlassenActing CoordinatorDistance Learning UnitInstruction, Curriculum and Assessment BranchGilles LandryProject ManagerDevelopment UnitInstruction, Curriculum and Assessment BranchPhilippe LeclercqConseiller pédagogique(until June 2015)Conseiller pédagogique—Mathématiques 9 à 12Division du Bureau de l’éducation française DivisionGrant MoorePublications EditorDocument Production Services UnitEducational Resources BranchWriterSchool Programs Division StaffAcknowledgementsvii

G r a d e 11 A p p l ie dMathemat ics (30S)Introduction

IntroductionOverviewWelcome to Grade 11 Applied Mathematics! This course is a continuation ofthe concepts you have studied in previous years, as well as an introductionto new topics. It builds upon the topics you were introduced to in Grade 10Introduction to Applied and Pre-Calculus Mathematics. You will put to usemany of the skills that you have already learned to solve problems, and learnnew skills along the way. This course helps you develop the skills, ideas, andconfidence you will need to continue studying math in the future.As a student enrolled in a distance learning course, you have taken on a dualrole—that of a student and a teacher. As a student, you are responsible formastering the lessons and completing the learning activities and assignments.As a teacher, you are responsible for checking your work carefully, notingareas in which you need to improve, and motivating yourself to succeed.What Will You Learn in This Course?In this course, problem solving, communication, reasoning, and mental mathare some of the themes you will discover in each module. You will engage ina variety of activities that promote the practical application of symbolic mathideas to the world around you.There are several areas that you will explore in this course, including linearand quadratic functions, logic and reasoning, geometry, trigonometry,statistics, and mathematical models.How Is This Course Organized?This course is divided into eight modules, organized as follows:QQModule 1: Quadratic FunctionsQQModule 2: Mathematics Research ProjectQQModule 3: Reasoning to Solve ProblemsQQModule 4: Geometry of Angles and TrianglesQQModule 5: TrigonometryQQModule 6: StatisticsQQModule 7: Mathematical ModelsQQModule 8: Scale Factors for 2-D and 3-D ShapesIntroduction3

The lessons in this course are organized as follows:nnnnnnnLesson Focus: The Lesson Focus at the beginning of each lesson identifiesone or more specific learning outcomes (SLOs) that are addressed inthe lesson. The SLOs identify the knowledge and skills you should haveachieved by the end of the lesson.Introduction: Each lesson begins by outlining what you will be learning inthat lesson.Lesson: The main body of the lesson consists of the content and processesthat you need to learn. It contains information, explanations, diagrams, andcompleted examples.Learning Activities: Each lesson has a learning activity that focuses on thelesson content. Your responses to the questions in the learning activities willhelp you to practise or review what you have just learned. Once you havecompleted a learning activity, check your responses with those providedin the Learning Activity Answer Key found at the end of the applicablemodule. Do not send your learning activities to your tutor/marker forassessment.Assignments: Assignments are found throughout each module within thiscourse. At the end of each module, you will mail or electronically submitall your completed assignments from that module to your tutor/marker forassessment. All assignments combined will be worth a total of 55 percent ofyour final mark in this course.Lesson Summary: Each lesson ends with a brief review of what you justlearned.Technology Appendix: The appendix provides basic information to helpyou learn how to use certain technology software and applications tocomplete this course.What Resources Will You Need for This Course?You will require access to an email account if you plan toQQcommunicate with your tutor/marker by emailQQuse Blackboard Learn to submit your completed assignmentsA valid email account is required for your Blackboard Learn profile. Thewebsite address for Blackboard Learn is https://bblearn.merlin.mb.ca/. Youwere issued a username and password when you registered for this course.Please note that you do not need a textbook to complete this course. All of thecontent is included with this package.4Grade 11 Applied Mathematic s

Required ResourcesTo complete this course, you will require a graphing calculator or access tocomputer software applications for graphing and statistical analysis. To writeyour examinations, you will need access to the same resources that you usedfor the modules.Contact your tutor/marker to make sure that the technology you are using isappropriate for the assignments and the examinations.Before you write your midterm examination, you will be asked to specifyone graphing app or graphing technology and, before you write your finalexamination, you will be asked to specify one graphing app or graphingtechnology and one statistics app or statistics technology. Make sure yourtutor/marker has approved your choices prior to writing the examinations.Optional ResourcesQQQQAccess to the Internet will be helpful in completing this course. There aremany online resources for this course and references are made to themin the lessons where they would be used. You can choose to use onlineresources to graph and solve linear and quadratic functions. Many statisticalmathematics operations can be completed with the help of online sites. Youcan search for resources online to complete your research project. You mayuse spreadsheets for scale factors, the research project, or other modules.Access to a photocopier would be helpful because it would let you makea copy of your assignments before you send them to your tutor/marker.That way, if you and your tutor/marker want to discuss an assignment, youwould each have a copy to reference, and you will have a copy to resubmit ifyour work goes missing.Resource SheetWhen you write your midterm and final examinations, you will be allowedto take a resource sheet with you into the examination. This sheet will be oneletter-sized page, 8½ ‘’ by 11”, and can be handwritten or typewritten. Bothsides of the page may be filled. It is to be submitted with your examination.The resource sheet is not worth any marks.Introduction5

Creating your own resource sheet is an excellent way to review. It alsoprovides you with a convenient reference and quick summary of theimportant facts of each module. Students are asked to complete a resourcesheet for each module to help with studying and reviewing.The lesson summaries are written for you to use as a guide, as are the modulesummaries at the end of each module. Refer to these when you create yourown resource sheet.After you complete each module resource sheet, summarize the sheets fromall the modules to prepare your resource sheet. When preparing yourMidterm Exam Resource Sheet, remember that the midterm examination isbased on Modules 1 to 4. When preparing your Final Exam Resource Sheet,remember that the final examination is based on Modules 5 to 8.Who Can Help You with This Course?Taking an independent study course is different from taking a course in aclassroom. Instead of relying on the teacher to tell you to complete a learningactivity or an assignment, you must tell yourself to be responsible for yourlearning and for meeting deadlines. There are, however, two people who canhelp you be successful in this course: your tutor/marker and your learningpartner.Your Tutor/MarkerTutor/markers are experienced educators who tutor Independent StudyOption (ISO) students and mark assignments and examinations. When youare having difficulty with something in this course, contact your tutor/marker, who is there to help you. Your tutor/marker’s name and contactinformation were sent to you with this course. You can also obtain thisinformation in the Who Is My Tutor/Marker? section of the distance learningwebsite at www.edu.gov.mb.ca/k12/dl/iso/assistance.html.Your Learning PartnerA learning partner is someone you choose who will help you learn. It may besomeone who knows something about mathematics, but it doesn’t have to be.A learning partner could be someone else who is taking this course, a teacher,a parent or guardian, a sibling, a friend, or anybody else who can help you.Most importantly, a learning partner should be someone with whom you feelcomfortable and who will support you as you work through this course.6Grade 11 Applied Mathematic s

Your learning partner can help you keep on schedule with your coursework,read the course with you, check your work, look at and respond to yourlearning activities, or help you make sense of assignments. You may evenstudy for your examinations with your learning partner. If you and yourlearning partner are taking the same course, however, your assignment workshould not be identical, and should be done independently.One of the best ways that your learning partner can help you is by reviewingyour midterm and final practice examinations with you. These examinationsand their answer keys can be found at www.edu.gov.mb.ca/k12/dl/downloads/index.html. Your learning partner can administer your practiceexamination, check your answers with you, and then help you learn thethings that you missed.How Will You Know How Well You Are Learning?You will know how well you are learning in this course by how well youcomplete the learning activities, assignments, and examinations.Learning ActivitiesThe learning activities in this course will help you to review and practisewhat you have learned in the lessons. You will not submit the completedlearning activities to your tutor/marker. Instead, you will complete thelearning activities and compare your responses to those provided in theLearning Activity Answer Key found at the end of each module.Each learning activity has two parts: Part A has BrainPower questions andPart B has questions related to the content in the lesson.Part A: BrainPowerThe BrainPower questions are provided as a warm-up activity for you beforetrying the other questions. Each question should be completed quickly andwithout using a calculator, and most should be completed without usingpencil and paper to write out the steps. Some of the questions will relatedirectly to content in the course. Some of the questions will review contentfrom previous courses—content that you need to be able to answer efficiently.Introduction7

Being able to do these questions in a few minutes will be helpful to you asyou continue with your studies in mathematics. If you are finding it is takingyou longer to do the questions, you can try one of the following:nnnwork with your learning partner to find more efficient strategies forcompleting the questionsask your tutor/marker for help with the questionssearch online for websites that help you practise the computations so youcan become more efficient at completing the questionsNone of the assignment questions or examination questions will require youto do the calculations quickly or without a calculator. However, it is for yourbenefit to complete the questions, as they will help you in the course. Also,being able to complete the BrainPower exercises successfully will help buildyour confidence in mathematics. BrainPower questions are like a warm-upyou would do before competing in a sporting event.Part B: Course Content QuestionsOne of the easiest and fastest ways to find out how much you have learned isto complete Part B of the learning activities. These have been designed to letyou assess yourself by comparing your answers with the answer keys at theend of each module. There is at least one learning activity in each lesson. Youwill need a notebook or loose-leaf pages to write your answers.Make sure you complete the learning activities. Doing so will not only helpyou to practise what you have learned, but will also prepare you to completeyour assignments and the examinations successfully. Many of the questionson the examinations will be similar to the questions in the learning activities.Remember that you will not submit learning activities to your tutor/marker.AssignmentsLesson assignments are located throughout the modules and includequestions similar to the questions in the learning activities of previouslessons. The assignments have space provided for you to write your answerson the question sheets. You need to show all your steps as you work outyour solutions, and make sure your answers are clear (include units, whereappropriate).8Grade 11 Applied Mathematic s

Once you have completed all the assignments in a module, you will submitthem to your tutor/marker for assessment. The assignments are worth a totalof 55 percent of your final course mark. You must complete each assignmentin order to receive a final mark in this course. You will mail or electronicallysubmit these assignments to the tutor/marker along with the appropriatecover page once you complete each module.The tutor/marker will mark your assignments and return them to you.Remember to keep all marked assignments until you have finished the courseso that you can use them to study for your examinations.Midterm and Final ExaminationsThis course contains a midterm examination and a final examination.QQQQThe midterm examination is based on Modules 1 to 4, and is worth20 percent of your final course mark. You will write the midtermexamination when you have completed Module 4. Due to the nature ofthe content of Module 2, it will not be assessed directly on the midtermexamination.The final examination is based on Modules 5 to 8 and is worth 25 percent ofyour final course mark. You will write the final examination when you havecompleted Module 8.In order to do well on the examinations, you should review all of the workthat you ha

confidence you will need to continue studying math in the future. As a student enrolled in a distance learning course, you have taken on a dual role—that of a student and a teacher. As a student, you are responsible for mastering the lessons and completing the learning activities and assignments.

Related Documents:

Teacher of Grade 7 Maths What do you know about a student in your class? . Grade 7 Maths. University Grade 12 Grade 11 Grade 10 Grade 9 Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Grade 1 Primary. University Grade 12 Grade 11 Grade 10 Grade 9 Grade 8 Grade 7 Grade 6 Grade 5 . Learning Skill

Grade 4 NJSLA-ELA were used to create the Grade 5 ELA Start Strong Assessment. Table 1 illustrates these alignments. Table 1: Grade and Content Alignment . Content Area Grade/Course in School Year 2021 – 2022 Content of the Assessment ELA Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade 10 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8

Math Course Progression 7th Grade Math 6th Grade Math 5th Grade Math 8th Grade Math Algebra I ELEMENTARY 6th Grade Year 7th Grade Year 8th Grade Year Algebra I 9 th Grade Year Honors 7th Grade Adv. Math 6th Grade Adv. Math 5th Grade Math 6th Grade Year 7th Grade Year 8th Grade Year th Grade Year ELEMENTARY Geome

3rd Grade 4th Grade 5th Grade Mathematics Reading Mathematics Reading Mathematics Reading Science 100.0% 95.5% 95.9% 98.6% 96.6% 96.6% 96.6% 6th Grade 7th Grade 8th Grade Mathematics Reading Mathematics Reading Mathematics Science 95.6% 100.0% 97.0% 98.5% 98.6% 97.2% 94.4% Grades 3-5 Grade

KAPA HiFi HotStart ReadyMix, 1μl5μMprimer,20μl captured library beads suspension. PCR amplification pro-gram was 98 C 2min; 98 C 30s; 65 C 30s; 72 C 30s, 13 cycles and a final step at 72 C for 4min. Purifications be-tween procedures were conducted using Agenco

o Grade 4: Reading and Mathematics. o Grade 5: Reading, Mathematics and Science. o Grade 6: Reading and Mathematics. o Grade 7: Reading and Mathematics. o Grade 8: Reading, Mathematics and Science. Grades 10-12 Ohio Graduation Tests Grade 10 March 12-25, 2012: Ohio Graduation Tests in reading, mathematics, wri

Grade K 27.01100 Grade 1 27.01200 Grade 2 27.01300 Grade 3 27.01400 Grade 4 27.01500 Grade 5 27.01600 Mathematics – Middle Grades (Grades 6 – 8) Secondary Pathway Options Accelerated Pathway Options Option 1 Option 2 Option 3 Option 4 Option 1 Option 2 Grade 6 Grade 6 27.02100 Grade 6 27.02100 Grade 6 27.02100 Grade 6 27.02100 Accelerated

Grade 1 Filipino Grade 2 English Grade 3 Mathematics Grade 4 Science Grade 5 Computer Grade 6 EPP/ TLE Grade 7 Araling Panlipunan (AP) Grade 8 Edukasyon sa Pagpapakatao (EsP) Grade 9 HISTORY/ HEKASI Grade 10 MAPEH Grade 11 Computer Hardware Servicing Grade 12 Con