Ms. Kivi S 2016/17 AP Calculus Syllabus
Ms. Kivi’s 2016/17 AP Calculus Syllabus
TeacherInformation:Ms.Kivi, WHS Room 103,
CourseResources:
●Cengage Learning Larson and Battaglia Calculus for AP
●Ebook: The class textbook is available also as an Ebook. Students will be given login access in class.
●YouTube:You will need to visit this address to “YouTube”, and save my channel as a favorite so you can have easier access for future videos. The videos are also saved on the WHS website, and can be accessed in the library during library hours. Videos may also be saved to a student provided flash drive (thumb drive) if given in a timely manner.
●Khan Academy: a great support resource if needed
●TI Calculator Lessons for Calculus: Lessons that teach you how to do certain concepts on your calculator
Course Objectives:
This course represents a multidimensional approach to calculus, with concepts, functions, and problems being expressed graphically, numerically, analytically, and verbally. Understanding the connection between these various forms is emphasized both verbally and in writing. Graphing calculators are used regularly to reinforce those connections. Students will learn the meaning of both derivatives and definite integrals and will sue the fundamental theorem of calculus to understand the relationship between them. It is expected (but not required) that students will seek college credit or placement at the conclusion of the course via Calculus AB advanced placement exam.
CourseDescription:
This course covers all topics included in the Calculus AB course outline as it appears in the AP Calculus Course Description. Instruction and practice on these topics help students develop a solid understanding of functions, graphs, limits, differentiation, and integration. Students solidify their understanding with examples demonstrating the relationship between calculus and the world around them through questions in context.
Throughout the course students are required to use multiple approaches to the understanding of calculus concepts. Students must be able to express solutions in numerical, graphical, analytical, and written forms. Students use the graphing calculator daily. Graphs are produced both with the calculator and by hand to facilitate the understanding of calculus concepts. Numerical solutions are completed with and without the graphing calculator. Checking solutions with multiple methods is required on a regular basis. Students are asked to explain problems and solutions in writing and verbally during discussions. Students will receive instruction on the TI-84 and TI-84 Plus.
Student will use the table function on their graphers to examine trends numerically. Calculators will also be used to find zeros and points of intersection, evaluate derivatives at a point, and evaluate definite integrals.
Throughout the course, students are given examples of AP Free Response in the form of in-class work, homework, quiz and exam questions. The AP Free Response questions provide excellent opportunities for the students to approach calculus from a graphical, analytical, numerical and verbal perspective. Students will be exposed to every nature of past AP Calculus Free Response questions. Students will work with functions given an equation, table, graph, or simply through a description of its properties. Students have AP Calculus for an entire calendar school year (2 semesters).
Expectations:
Toprovideeverystudentthebestopportunityforsuccessinthisclass,allstudentsareexpectedto bring these supplies each day:
●Paper, pencils,pens, highlighters.
●TextBook every day
●Some type of organizational device (3-ring binder, folder, spiral, expanding folder) to manage your course resources. It is expected that you will keep all notes and assignments until the AP Exam.
●ATI83orhighergraphingcalculator.IfyouchoosetopurchaseaCasiobrandcalculatoror a TI model higher than an 86, I will not be able to help you with the specific operationsofthecalculator.Calculatorfunctionsonstudentphonesarenotpermissiblecalculators during exams.
The Flipped Classroom:
Ms. Kivi offersa “flipped” classroom. Students, for homework, will watch a video at night on You Tube where a lesson is taught. Students will take thorough notes from the video’s content. At the beginning of class the next day, students will “turn in” their notes from the previous night’s video.Questions from the video will be answered, then a practice problem will be done before the classwork starts. Ms. Kiviwill then record a grade for the student’s video notes as the students start working together on the day’s classwork assignment. Students will spend the rest of class working on a collection of problems and collaborating on their work. I will provide assistance throughout the duration of the class period, and maintain an environment that is conducive for learning. The classwork will then be due at the end of class. Excuses for not being able to watch a video will be heard, but exceptions are rare. Students are encouraged to use all available resources to make sure that the videos are “watched”.
If a student does not have access to the internet at home, there are a couple of solutions:
1) I will copy the video onto a flash drive for the student.
2) All videos are on the WHS website, in Ms. Kivi’s class videos and are accessible in the library before school, during lunch, or after school.
Follow these rules and regulations:
●Demonstrate respect for each other, the instructor, and the property of WHS.
●Abidebyallschoolhandbookpolicies.Nohatsorhoodsaretobewornduringclass.AppropriatedressMUSTbeworn.Beforeenteringtheclassroom,allelectronicdevices(cell phones, Ipods, MP3 players, gaming devices, headphones, etc.) are to besilencedand stored off the student’sbody.
●All purses, lunch containers, and backpacks should be stored underneath your desk. Classroomsuppliesforthisparticularclassaretheonlyitemstobeatthe studentdesk.
Demonstrate responsibility for the learning opportunities by:
●Completing allassignments.
●Watch all assigned videos.
●Using any designated time in class to work on the given independentpractice.
●Seeking appropriate support for concepts not mastered. I am available for help before and after school.
●Knowing and adhering to the school attendance and tardypolicy.
●Being punctual and prepared with materials. Be seated with your book, notes, and calculator when the bellrings.
●Exhibiting student behaviors that contribute to the success of the class as awhole.
AssessmentPolicy:
●Tests and quizzes (Quests) must be completed within the class time allotted unless a studenthasanofficialplanonfilethatstatesthespecificdisabilityrequiringtestingaccommodation.Students with official plans have the responsibility ofdiscussing with the instructor their needs 2 class days prior to assessment so thatarrangements can be made to accommodate those needs. If prior arrangements arenotmade,theinstructorwillassumethatthestudenthasdecidedthattheaccommodationsare not necessary for that particularassessment.
●Sometestsmaynotallowtheuseofacalculator(anytype)forallorforaportionofthetest.
●On most assessments, work must be provided which sufficiently supports anyprocedural task and which explicitly supports an answer for any freeresponse task.Inordertobescoredforcredit,allsupportmustbelegible,organizedsothatathoughtprocessisclearlyandcompletelyindicated,andananswermustbeindicatedontheappropriate line or with ahighlighter.
●Assessment scores are calculated using a rawscore.
●Cell phones may not be used as a calculator on any assessment.
●All assessments are the property of the instructor and the math department, and thereforemaynotbetakenfromtheclassroom.Testswillbemaintainedinstudentfilesforthecourseduration.Thesefileswillbeavailabletostudentsforinclassroomreview by appointment. Assessments are destroyed at the end of the course followingfinals.
●Retestpolicy–you will be given one retest per quarter, available for one week after the assessment is scored. Use it wisely.
Recovering credit for assignments and tests in the event of a verified absence:
Itisthestudent’sresponsibilitytorecovercreditforallworkmissedwhileabsent.Iftheabsenceisverified,studentshaveonedayforeveryabsencetorecovercredit.Beprepared!Testsmissedduringaverifiedabsenceshouldbetakenwithinoneweekofreturningtoschool.Itisuptostudentstomakearrangements with parents, coaches, teachers, and employers and to plan accordingly. Students will be providedanamountoftimetocompletethetestequaltothatgiventheclassonthedayofthetest.Testsareexpectedtobecompletedwithinonesitting.Ifsportseligibilitydependsuponlatest grade or grades for missing assignments, students will need to plan accordingly. It isunrealistic to expect the test/work to be scored and the grade to be updated for sports participationthesamedayasworkissubmitted.Unverifiedabsences(includingtestdays)areby policy assigned zero points for anything done that day.
Latework:All work that is turned in late will be assessed a score of at most 50%. Quests (Tests and Quizzes), and FRQ’s may be made up for potentially full credit.
Maintaining credit in the event of a schoolapproved absence:
Foranyschoolapprovedabsence(sports,familytrips,bandevents,fieldtrip,etc),thestudentmustmakecertainofthenecessaryassignment(s)wellaheadoftime.Inordertomaintaincreditandthereforetoremaineligibletoparticipateinactivitiesofferingapprovedabsences,thework,evenifincomplete,isdueonthedaythestudentreturnsfromtheactivity.Studentsinvolvedintheseactivitiesmusttaketheinitiativetounderstandthelessonsmissedontheirownandattempttheassignmentsasbesttheycan. If you need assistance, you must seek me outside of regular class hours (before or after school)for help. The videos must be watched and the classwork attempted before any additional help will be given.Absencesfrommathclassarenotrecommendedastherewillalwaysbeadditionalinsights/instructionfromtheteacherthatyouwillmissbynotbeinginclass.Again,pleasedonotexpecttheinstructortobeabletoupdateyourgradetheverydayyousubmityourworkifyouarefacingineligibility.Be prepared!
CourseGrading:
Astudent’scoursegradeisbasedonhiscumulativeearnedpoints,whichareweightedbycategory.AsMrs. Bain provides numerouspointopportunitiesforstudents,therearenoadditionalassignmentsprovidedforextracredit.Occasionally,theremaybeabonusquestiononatest.Roundingofdecimalpercentsdoesnotoccuronanygradereportedtoparentsorcoachesorwhichistoberecordedonatranscript.Thefollowingprovidesthecategoriesandweights as well as the grade letter equivalents for percentage intervals for this course:
Quiz/FRQ…………………….…………………41%
Test/Quest……………………………………...41%100 90%...... A
Practice/Assignments………………………….18%89 80%...... B
79 70%...... C
69 60%...... DBelow59%...... F
Homework GradingInformation:
Toexpediteconceptfeedbackandtoplacetheresponsibilityoflearninginthehandsoftheactuallearner,Ms. Kiviusesthefollowingmethodofgradingandcollectionforhomework:
●Eachvideoassignmentistobecompletedtothebestofthestudent’sabilityPRIORtothebeginningofclass. Atthebeginning of class,thestudentistopresent their thorough notes.
●Classwork will be completed during class time. It will be turned in before the student leaves the class for the period.
For each student, Ms. Kivi will look at the assignment to determine the level ofcompleteness and assign a score. Completeness means that thorough notes from the video have been taken. ALLsupportingworkisshown. Eachassignmentisworth5points. Complete and thorough video notes and problems will receive 3 points, and the associated classwork will receive 2 points for a total of 5 points.
Writing Assignments:
Students will be expected to write technically throughout the course. as this is a significant component to the AP Calc Exam. Some of this writing will occur as part of the “Big Idea” writing assignments. Students will be given specific guidelines about the expectations of each assignment. There are a few overall guidelines:
1) When giving a written (verbal response), the given prompt must be restated at the beginning of the response. No pronouns may be used in any written component.
2) The assignment will be graded using the standards set forth by the AP College Board.
Students will be often asked to explain (justify), using complete sentences, calculus terminology, and relevant formulas for the solutions that have been attained. Students will be given an FRQ every other week, in which they will be required to solve and write about the “problem” meeting the
Support Outside ofClass:
Ms. Kivi is availablemost days before (6:45 – 7:30) and after school (2:45 – 3:45) to answer any questions, or to schedule makeup work.Mrs. Bain is notavailabletotutorortoteachentirelessonstoanindividualwhohasbeenabsent.Ifintensivesupportisneeded,considerformingastudygroupwithotherstrong students in the class, hiring a professional tutor, or securing a studenttutor from theNational Honor Society. Please seek support quickly. Do not get behind. Be pro-active about your educational needs.
Power School App and Email as Communication Tools Via the Computer:
Studentsuccessisimportanttome,andIrealizethatconvenientandconsistent opportunities for communication with all concerned parties are essential to that success. Ifyouhaveaconcernregardingyourstudent,pleasecontactme.Emailisthepreferredandmostefficientmethodformakingcontact.I am unavailable for phone conversations about students during the school instruction time. All phone contact will be made after instruction time has ended. Iattempttocheckandrespond toschoolemaildailybetweenthecontracthoursof7:30amand3pmondayswhenschoolisinsession.Pleasedonothesitatetocontactme viaemailduringthesetimes.
General Statement of Academic Integrity:
Integrityofscholarshipisessentialforanacademiccommunity. Winslow High SchoolexpectsthatstudentswillhonorthisprincipleandinsodoingprotectthevalidityofWinslow High School’s intellectualwork.Forstudents,thismeansthatallacademicworkwillbedonebytheindividualtowhom it is assigned, without unauthorized aid of any kind.
Student Evaluation:
WHS distribution of grades is 82% Test and Quizzes and 18% Practice and Assignments. Those items falling under tests and quizzes will be: Quests (quizzes and tests) (25 points), and Free Response (9 pts per Response). Practice will include homework (variable 5 points per assignment completion) and In-class Presentation of work (15 points for engaged participation). The students are required sometimes to complete homework or assessments with and without the use of calculators. The two quarter grades per semester are worth 90% of the final grade. The midterm or final exam completes the final 10% of the grade.
Students will be given a 5 question Quest approximately every other Wednesday. Three of the questions will be from the current material, and two of the questions will be from previous material. The alternate weeks, students will be completing FRQ assignments – some as individuals, and some as group work. Students will take a mid-term exam at approximately 9 weeks, and then a fall semester final. In the spring, students will take a mid-term exam and the AP Exam in May.
Mathematical Practices for AP® Calculus
Practices that will be developed in the AP® Calculus course are meant to train students to think like Mathematicians. However, these are also good habits to build for success in college and the work place. Therefore, every student will be growing not just in their math knowledge, but in areas of their life that involve, thinking, reasoning and communicating Information. These practices are not to be viewed as items to check off a list or received as an explicit grade. Throughout the course, I might weigh an assignment or project with the added emphasis on a specific practice. This will help to develop the skill and habits of a competent student of math. The eight practices are as follows with a brief description:
1)Reasoning with definitions and theorems: Use definitions and theorems to build arguments, justify conclusions and to prove results. Examples and counterexamples are important ways to help reason through an idea to see if it makes sense logically.
2)Connecting Concepts: Calculus is a united field of study: differentiation and Integration are two sides of the same coin of Limits. To be able to connect these concepts as well as how different representations of a function connect to one another shows perception and an ability to see the big picture.
3)Implementing Algebraic/computational Processes: Choosing an appropriate mathematical strategy is important to solving problems. There are often multiple ways of solving any given problem, and to be able to analyze a problem and choose the best method of solving quickly will greatly help reduce the amount of work a problem takes.
4)Connecting Multiple Representations: Depending on the problem, one representation may provide different information than any other. Being able to take a representation and construct another form will allow the student to show flexibility in presenting information. This will be valuable when asked to cite certain information about a function through a specific portrayal given a list of properties.
5)Building Notational Fluency: Mathematics is a language in and of itself. Developing notation and using a variety of math notation will help in communicating ideas and concepts without having to write out the process each time. Being able to interpret the notation in a written out form will help in effective delivery of results.
6)Communicating: Justifying ones conclusions ties back to the foundation of mathematics. Taking all the previous practices and presenting information will help in critical analysis, evaluation of one another’s work, and comparing the reasoning of multiple students to assess whether an idea has really been proved.
Course Outline Requirements with Examples by Topic.
The framework for this class is centered around 3 Big Ideas, that is, ideas which correspond to foundational concepts in Calculus.: Limits, Derivatives, Integrals and the Fundamental Theorem of Calculus. These ideas will be broken down by Enduring Understandings, Learning Objectives and Essential Knowledge. At the beginning of each Chapter, Students will receive a Standard Sheet with the Learning Objectives outlined. Students will have ample opportunities to demonstrate whether they have achieved the Learning Objective and their comfortability with each objective. Free Response Questions and Section Projects will seek to tie many Learning Objectives together in order to better connect concepts to the Big Idea. Additionally, there will be a writing prompt for each Big Idea with a final Paper that asks to unite all the Big Ideas into a single narrative.
Big Idea 1: Limits.
Chapter P: Preparation For Calculus (1.5 Weeks)
P.1 Graphs and Models
P.2 Linear Models and Rates of Change
P.3 Functions and Their Graphs
P.4 Fitting Models to Data
Chapter 1: Limits and Their Properties. (3.5 Weeks)
1.1 A preview of Calculus
1.2 Finding Limits Graphically and Numerically
1.3 Evaluating Limits Analytically
1.4 Continuity and One-Sided Limits
1.5 Infinite Limits.
8.7: Indeterminate Form and L’Hopital’s Rule
Sample Activities:
3 Methods of Discontinuity Using a Graphing Calculator: Students will use their graphing calculators to understand the nature of continuous and discontinuous functions, an activity provided through the Texas Instruments Website. For instance, students are asked to use the table feature on their calculator to examine the function f(x) = (sin x)/ x at x = 0.This will lead to the definitions of continuity of a function using limits.
Oil Spill Scenario Write Up: The student project for Big Idea 1 will focus on the theoretical definition of a limit at infinity and apply that to a situation of an oil spill. Students will reason with the definition of a limit as well as the Intermediate Value Theorem. They will be using the Deepwater Horizon Oil Spill as a model and use limits to evaluate the impact such an oil spill had on the surrounding environment. They will present their findings in a written form.
Big Idea 2: Derivatives.
Chapter 2: Differentiation (3.5 Weeks)
2.1 The Derivative and the Tangent Line Problem
2.2 Basic Differentiation Rules and Rates of Change
2.3 Product and Quotient Rules and Higher-Order Derivatives
2.4 The Chain Rule
2.5 Implicit Differentiation
2.6 Related Rates
Sample Activities
Discover the Product Rule: After learning the limit definition of a derivative, students will be given a series of functions from x to x^4. They must use the limit definition to find a generic derivative function of each Parent function. Analyzing the pattern ,students will then be asked to form a “rule” that can be used on any function of x^n and thereby derive the Power Rule.
Tootsie Pops: Students will use their knowledge of related rates to answer the well known question, “How many licks will it take to get to the center of a tootsie pop.” Upon arriving at their answer, they will collaborate their responses and give an argument for the reasonability of their responses. The world just may have an answer to this important question.