Ms. Kivi’s 2016/17 AP Calculus Syllabus

Teacher Information: Ms.Kivi, WHS Room 103, bkivi@wusd1.org

Course Resources:

● 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: https://www.youtube.com/channel/UCgrI_igLumMczqI8W03VBog 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.

Course Description:

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

1

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:

To provide every student the best opportunity for success in this class, all students are expected to 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.

● A TI83 or higher graphing calculator. If you choose to purchase a Casio brand calculator or a TI model higher than an 86, I will not be able to help you with the specific operations of the calculator. Calculator functions on student phones are not permissible calculators during exams.

The Flipped Classroom:

Ms. Kivi offers a “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. Kivi will 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.● Abide by all school handbook policies. No hats or hoods are to be worn during class. Appropriate

dress MUST be worn. Before entering the classroom, all electronic devices (cell phones, Ipods, MP3 players, gaming devices, headphones, etc.) are to be silenced and stored off the student’s body.

● All purses, lunch containers, and backpacks should be stored underneath your desk. Classroom supplies for this particular class are the only items to be at the student desk.

Demonstrate responsibility for the learning opportunities by:● Completing all assignments.● Watch all assigned videos.● Using any designated time in class to work on the given independent practice.● Seeking appropriate support for concepts not mastered. I am available for help before

and after school. ● Knowing and adhering to the school attendance and tardy policy.

2

● Being punctual and prepared with materials. Be seated with your book, notes, and calculator when the bell rings.

● Exhibiting student behaviors that contribute to the success of the class as a whole.

Assessment Policy:

● Tests and quizzes (Quests) must be completed within the class time allotted unless a student has an official plan on file that states the specific disability requiring testing accommodation. Students with official plans have the responsibility of discussing with the instructor their needs 2 class days prior to assessment so that arrangements can be made to accommodate those needs. If prior arrangements are not made, the instructor will assume that the student has decided that the accommodations are not necessary for that particular assessment.

● Some tests may not allow the use of a calculator (any type) for all or for a portion of the test.● On most assessments, work must be provided which sufficiently supports any procedural task and

which explicitly supports an answer for any freeresponse task. In order to be scored for credit, all support must be legible, organized so that a thought process is clearly and completely indicated, and an answer must be indicated on the appropriate line or with a highlighter.

● Assessment scores are calculated using a raw score.● 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 therefore may not

be taken from the classroom. Tests will be maintained in student files for the course duration. These files will be available to students for inclassroom review by appointment. Assessments are destroyed at the end of the course following finals.

● Retest policy – 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:

It is the student’s responsibility to recover credit for all work missed while absent. If the absence is verified, students have one day for every absence to recover credit. Be prepared! Tests missed during a verified absence should be taken within one week of returning to school. It is up to students to make arrangements with parents, coaches, teachers, and employers and to plan accordingly. Students will be provided an amount of time to complete the test equal to that given the class on the day of the test. Tests are expected to be completed within one sitting. If sports eligibility depends upon la test grade or grades for missing assignments, students will need to plan accordingly. It is unrealistic to expect the test/work to be scored and the grade to be updated for sports participation the same day as work is submitted. Unverified absences (including test days) are by policy assigned zero points for anything done that day.

Late work: 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:

For any schoolapproved absence (sports, family trips, band events, fieldtrip, etc), the student must make certain of the necessary assignment(s) well ahead of time. In order to maintain credit and therefore to remain eligible to participate in activities offering approved absences, the work, even if incomplete, is due

3

on the day the student returns from the activity. Students involved in these activities must take the initiative to understand the lessons missed on their own and attempt the assignments as best they can. 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. Absences from math class are not recommended as there will always be additional insights/ instruction from the teacher that you will miss by not being in class. Again, please do not expect the instructor to be able to update your grade the very day you submit your work if you are facing ineligibility. Be prepared!

Course Grading:

A student’s course grade is based on his cumulative earned points, which are weighted by category. As Mrs. Bain provides numerous point opportunities for students, there are no additional assignments provided for extra credit. Occasionally, there may be a bonus question on a test. Rounding of decimal percents does not occur on any grade reported to parents or coaches or which is to be recorded on a transcript. The following provides the categories and weights as well as the grade letter equivalents for percentage intervals for this course:

Quiz/FRQ…………………….…………………41%Test/Quest……………………………………...41% 100 90%.............APractice/Assignments………………………….18% 89 80%............B

79 70%............C69 60%............D Below

59%..........FHomework Grading Information:

To expedite concept feedback and to place the responsibility of learning in the hands of the actual learner, Ms. Kivi uses the following method of grading and collection for homework:

● Each video assignment is to be completed to the best of the student’s ability PRIOR to the beginning of class. At the beginning of class, the student is to present 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 of completeness and assign a score. Completeness means that thorough notes from the video have been taken. ALL supporting work is shown. Each assignment is worth 5 points. 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.

4

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 of Class:

Ms. Kivi is available most 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 not available to tutor or to teach entire lessons to an individual who has been absent. If intensive support is needed, consider forming a study group with other strong students in the class, hiring a professional tutor, or securing a studenttutor from the National 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:

Student success is important to me, and I realize that convenient and consistent opportunities for communication with all concerned parties are essential to that success. If you have a concern regarding your student, please contact me. Email is the preferred and most efficient method for making contact. I am unavailable for phone conversations about students during the school instruction time . All phone contact will be made after instruction time has ended. I attempt to check and respond to school email daily between the contract hours of 7:30am and 3pm on days when school is in session. Please do not hesitate to contact me via email during these times.

General Statement of Academic Integrity:

Integrity of scholarship is essential for an academic community. Winslow High School expects that students will honor this principle and in so doing protect the validity of Winslow High School’s intellectual work. For students, this means that all academic work will be done by the individual to whom 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.

5

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 ModelsP.2 Linear Models and Rates of ChangeP.3 Functions and Their GraphsP.4 Fitting Models to Data

6

Chapter 1: Limits and Their Properties. (3.5 Weeks) 1.1 A preview of Calculus1.2 Finding Limits Graphically and Numerically1.3 Evaluating Limits Analytically1.4 Continuity and One-Sided Limits1.5 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 Problem2.2 Basic Differentiation Rules and Rates of Change2.3 Product and Quotient Rules and Higher-Order Derivatives2.4 The Chain Rule2.5 Implicit Differentiation2.6 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.

Chapter 3: Applications of Differentiation (4 Weeks)3.1 Extrema on an Interval3.2 Rolle’s Theorem and the Mean Value Theorem3.3 Increasing and Decreasing Functions and the First Derivative Test3.4 Concavity and the Second Derivative Test3.5 Limits at Infinity3.6 A summary of Curve Sketching3.7 Optimization Problems

7

Sample Activities:

Mean Value Theorem Reasoning Exercise: Students are given an activity with various graphs on it. For each graph they must identify if the graph is continuous on a closed interval and differentiable on an open interval. From their, they must connect two points with a secant line, and determine whether there is somewhere else on the graph that a tangent line of the same slope can be found. Students will discover that if continuity or differentiability fails, it is not possible to find a tangent line between the points of a secant line. They are then given various scenarios in which they must reason whether the hypotheses and conclusions of the MVT apply to a given analytical problem.

Derivative Exploratory Calculator Exercise: As a beginning exploration exercise, students will use graphing calculators to graph various functions and their first derivatives. They will put them on the same viewing window and make conjectures about the relationships between the characteristics of f and f’.

Derivative Matching: Students receive a set of randomly shuffled cards which contain graphs, tables, and equations. Students must match in a given amount of time all of the equations with their parent graph, first derivative graph and second derivative graph. Students are called on to defend their matches and explain why the first and second derivatives match the graph of the parent function.

Rates Productions: At the end of the unit on Differentiation, students will have a Big Idea Project where they must create a word problem that involves related rates or an optimization problem. They will then make a video that captures the problem in real life and shows how to solve the problem using calculus and differentiation. Before the problem is solved, the video will be solved and student in class will try and solve the problem from the information in the video alone. After all have attempted an answer, the rest of the video will be shown to confirm their answers.

Big Idea 3a: Integrals and the Fundamental Theorem of Calculus.

Chapter 4: Integration (3.5 Weeks) 4.1 Antiderivatives and Indefinite Integration4.2 Area4.3 Riemann Sums and Defining the Definite Integrals4.4a The Fundamental Theorem of Calculus: The First Fundamental Theorem of Calculus4.4b The Fundamental Theorem of Calculus: The Second Fundamental Theorem of Calculus. 4.5 Integration by Substitution4.6 Numerical Integration

Sample Activities:

Riemann Sum Notation Telephone: Students will practice reading, writing and interpreting the limit of a Riemann Sum notation through a telephone type game. In groups of 4, each student will start off by writing a function and the limits of integration on that function. The paper will then go to the next person in the group, and they will have to put that function with it’s limits into Riemann Sum Notation. They will fold back the original equation and pass the paper forward. The next person has to decipher the Riemann Sum Notation and draw a representative graph of the function. They will fold behind the notation, and pass it forward. The Next will have to interpret the graph and write it again into integral notation. This can go around twice as necessary. Once they are done, they can open up the full sheet of paper and see if their equation matches the initial one. If not, they must locate where the misinterpretation was.

Fundamental Theorem of Calculus Comparison: Students are given a simple problem asking how far they would travel if they drive at 60mph for 2 hours. They are asked to create a velocity graph representing

8

the situation. Students will then analyze the graph using both definitions of the Fundamental Theorem of Calculus. Part one states if f is continuous on [a,b], then the functions g defined by g(x) = is an antiderivative of f. That is g’(x) = f(x)

for a < x < b. Part two states if f is continuous on [a,b], then = F where F(x) is any antiderivative of f(x). They will then be given an acceleration scenario and must use both definitions to arrive at how far they would travel accelerating. Students will write down their thoughts on why both definitions work and discussion will follow as to why both definitions make sense using the concept of a derivative.

FTC Calculator Exploration: Students complete the graphing calculator activity Fundamental Theorem of Calculus to explore the connection between an accumulation function, one defined by a definite integral, and the integrand. They also discover that the derivative of the accumulator is the integrand.

FTC Application Write-Up: Students will complete a write-pair-share activity which requires them to write a paragraph using complete sentences and proper grammar about what the Fundamental Theorem of Calculus means in the context of a given application problem. Students will calculate antiderivatives and definite integrals.

Driving Project: Students will use their knowledge of Riemann Sums and Definite Integrals to determine how far they traveled while driving. They will take data of their velocity in the car every 10 seconds. Once they have plotted the points, they will compute a sum on their data points to see how far they travelled. They will then check their answer with the odometer reading and confirm that Definite Integrals work and how they represent a sum of units over an independent variable

Review and End Semester I

Semester II: Big Idea 3b: Applications of Fundamental Theorem of Calculus

Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions (5.5 Weeks)5.1The Natural Logarithmic Function: Differentiation5.2The Natural Logarithmic Function: Integration5.3 Inverse Functions5.4 Exponential Functions: Differentiation and Integration5.5 Bases other than e and Applications5.6 Inverse Trigonometric Functions: Differentiation5.7 Inverse Trigonometric Functions: Integration

Sample Activities:

Present Inverse Trig Functions: Students will be given a trig function and will have to determine its inverse, the parameters of its inverse, and how each applies to its derivative. Students will work in groups and give a short presentation of each inverse, allowing time for other classmates to take notes and apply to a problem.

Chapter 6: Differential Equations (2 Weeks)6.1 Slope Fields 6.2 Differential Equations: Growth and Decay6.3 Separation of Variables

Sample Activities:

9

Slope Field Matching: Students receive a set of randomly shuffled Cards which contain slope field graphs, tables, differential equations, and solution equation. Students must match in a given amount of time all of the equations with their slope field graph. Then they are called on to defend their matches and explain why the slope field and solution equation matches a given differential equation.

Growth and Decay Research Project: Students will research a topic of interest that involves exponential growth or decay happening in physics, biology, or history. They will have to create a realistic problem involving the topic chosen using actual data related to that topic. Students will then have an opportunity to read the context of each problem, and solve the problem created by their classmates.

Chapter 7: Applications of Integration (3 weeks) 7.1 Area of Region Between Two Curves7.2 Volume: Disk Method7.3 Volume Shell Method8.1 Methods of Integration8.2 Integration by Parts

Sample Activities:

Modeling Volume I: Students will be given an equation to graph. They will then use a compass to take the radius of each point and make a circle of that radius. After making a circle for each point, they will cut out the circles and create a 3D model of a solid of rotation of the given equation using paper and wooden sticks. They will have to solve for the volume of their model and attach it on an info card. After they have each made a model, they will then present their model and how it reflects the graph of their function.

Modeling Volume II: After students make a model with a given equation. Students will then design their own 3D model for a volume of known cross section. Students will choose two different equations, and a known cross sectional area. They will then create a drawing of what they believe the 3D shape will look like when it is finished. After, they will cut out the appropriate size shapes and tape or glue them onto their model graph. They will then determine the area of their created shape and discuss whether it makes sense with their actual model.

Final Big Idea Narrative: Throughout the course, students will be asked to write up a summary paper of each Big Idea in Calculus using proper grammar and complete sentences. This will build on itself throughout the year as students will keep adding to the original paper new concepts or ways that each Big Idea relates to another in Calculus. For instance, students will first discuss the Big Idea of Limits and how Limits take us beyond precalculus and how they are used in Calculus. Once Derivatives are learned, students will have to write in well-written sentences how limits help define a derivative and how derivates are used in various contexts that would not have been solvable in a precalculus course. They will end the paper with Integrals and the first and second parts of the Fundamental Theorem of Calculus, explaining how limits and derivates are both necessary to the understanding of an integral and how the Fundamental Theorem unites all these previous ideas together. Students will share their narratives with the class before they turn in their completed paper.

Review for AP® Exam (4 Weeks)

Calculus Camp* (First Wednesday - Saturday in April)

Final Big Idea Narrative Due ( May 1, 2017)

AP® Calculus Exam (May 9, 2017)

10

Extra Topics and Final Video Project. Extra Topics may include Integration by Parts, Partial Fractions, or a fun look at polar and parametric calculus.

End Semester II.

*This trip will depend on availability and acquirement of funds

TEACHING STRATEGIES: The classes fall into two major categories:

Teacher led discussion – In these classes, I may present new material to them and have them work through problems using this concept; or we may expand on a known concept with me helping them along in the discovery of information.

Group work – Students break down into groups (usually 2 or 3) to work through a problem. I don’t interfere in these discussions although, in some cases, they confer with other groups. The problem is not solved until everyone in the group is able to explain the process. I find that some of the most intense discussions in class come from this type of work. Inherit to the flipped model, this practice will occur very often as students work through problems with guidance daily.

The only technology we have at our school is the graphing calculator (each student has one and we have an overhead graphing calculator in the classroom). Students have been using these calculators since Alg II and are trained to be comfortable with, but not dependent on, this technology.

Whenever we go through a new way to use the calculator, it is only used as a check of the analytical solution. From this point on, students are required to either solve algebraically and support graphically or solve graphically and confirm algebraically.

When we start discussing the concept of tangent to a curve, once they find the equation of the tangent, they use their calculator to confirm that this line really is tangent to the curve at the given point. Once the discussion turns to the idea of derivative, students practice finding the derivative from the graph by determining when the derivative is positive, negative, or zero; then they are allowed to check this by using the NDeriv option on their calculator.

Calc Camp:

Historically, FHS and CHS have taken many Calc students to AP Calc Camp in Prescott. I would like for WHS to take part in this tradition as well. Intensive time is spent reviewing for the course, learning tips and tricks from Exam writers and graders, and then fun “camp” activities such as a zip line, gaga ball, sand volleyball, cards, hiking, etc. More details and costs about this trip will be forth coming! In previous years the cost of camp has been about $200. Camp is tentatively scheduled for the beginning of April. We will revisit the costs, depending on the number of students attending. We believe this to be a highly productive time spent reviewing for the exam, and taking a practice exam on the final day. Camp typically runs Wednesday after school through Saturday afternoon.

11