12th grade Math 4 (Calculus I) Syllabus

12th Grade Math (Math 4): 2018-2019 Course Syllabus:

PDF Version at: https://ajv.me/hth-2018-19/math-4/curriculum/Syllabus-2018-2019.pdf

Go down deep enough into anything and you will find mathematics.  Dean Schlicter

Pure mathematics is, in its way, the poetry of logical ideas.  Albert Einstein (1879 - 1955)

Instructor:                                                                                                  Office Hours:
Andrew J. Vernon (aka Dr. Drew)                                                             Mondays: 3:30-4:00
avernon@hightechhigh.org                                                                      Wednesdays: 11:45-12:15
Digital Portfolio: https://ajv.me/hth                                                             Fridays: 7:45-8:15 (by appointment)

Instructor:                                                                                                 Office Hours:
Ed Hanna                                                                                                 Mondays: 11:40 AM - 12:10 PM 
ehanna@hightechhigh.org                                                                     Thursdays: 3:30-4:00 PM
Digital Portfolio: https://edhannamath.webnode.com/

Course Overview:

Mathematics is the language of physics and many other disciplines, such as finance, economics, computer science and engineering (which has sometimes been referred to as applied physics). But mathematics is much more than that. For many mathematicians, mathematics is purely a human endeavor, similar to that of music for musicians and paintings and sculptures for artists: it is pursued for the joy of gaining insight and making new discoveries.

In this course, we will be exploring the world of mathematics from both perspectives. Much of what we will cover will be learning the language of mathematics and using those skills to solve problems, but we will also explore the more abstract nature of mathematics and (hopefully) develop an appreciation of its inherent elegance and how that elegance can manifest in abstract concepts. This exploration will be undertaken primarily using the resources from the CPM Education Program: Calculus Third Edition, which has a very strong emphasis on problem-based group work (collaboration and mathematical discourse). Other activities and short projects will also be used as a part of this exploration. For example, for each of the enduring understandings, there will be open-ended explorations that give you the opportunity to communicate the depth of your understanding.

In addition to exploring the world of mathematics, we will also focus on preparation for being successful with college-level mathematics. Students will be supported in learning essential skills: following lectures, note-taking, organization, using textbooks (both hardcover and e-book), calculator fluency, using office hours, using on-line resources, and so forth.

The work we do in math (and what we will present at Exhibition in December) will also be connected to the over-arching theme of the year (for all your senior classes): how you have changed over the years, particularly at High Tech High North County. You will be reflecting on your growth as a mathematician, your growth in understanding what mathematics is, and your growth in being prepared for college-level mathematics.

Essential Questions for Enduring Understanding:

  1. What are the skills and practices that help ensure success in math?
  2. How do we prepare for mathematics beyond high school?
  3. How can our understanding of math be applied to other disciplines?
  4. How can we utilize higher-level mathematics in a meaningful way?
  5. How can our mathematical ideas and discoveries be effectively communicated to others?

Course Objectives:

  1. Students will gain and apply the skills of mathematicians to various types of problem solving.
  2. Students will be able to communicate their ideas and understanding of mathematics.
  3. Students will continue to grow in their use of the Habits of a Mathematician to solve challenging problems and make relevant connections to their world.
  4. Students will develop confidence in their ability to be successful learning college-level mathematics.

Scope and Curriculum Standards

At High Tech High North County, the scope for Grade 12 Math is an extension of the Common Core State Standards for Mathematics that were covered in Grades 9-11 and includes a number of Big Ideas and Enduring Understandings (EU) from the CPM Calculus Third Edition:

  1. Big Idea: Limits
    • EU 1: The concept of a limit can be used to understand the behavior of functions.
    • EU 2: Continuity is a key property of functions that is defined using limits.
  2. Big Idea: Derivatives
    • EU 1: The derivative of a function is defined as the limit of a difference quotient and be determined using a variety of strategies.
    • EU 2: A function's derivative, which is itself a function, can be used to understand the behavior of a function.
    • EU 3: The derivative has multiple interpretations and applications including those that involve instantaneous rates of change.
    • EU 4: The Mean Value Theorem connects the behavior of a differentiable function over an interval to the behavior of the derivative of that function at a particular point in the interval.
  3. Big Idea: Integrals and the Fundamental Theorem of Calculus
    • EU 1: Antidifferentiation is the inverse process of differentiation.
    • EU 2: The definite integral of a function over an interval is the limit of a Riemann sum over that interval an can be calculated using a variety of strategies.
    • EU 3: The Fundamental Theorem of Calculus, which has two different formulations, connects differentiation and integration.
    • EU 4: The definite integral of a function over an interval is a mathematical tool with many interpretations and applications involving accumulation.

Class Grading

Assigning a "grade" to student work is an unfortunate consequence of the college admission process: your Math 4 grade must be factored into your GPA for consideration to be accepted. Ideally, your math work would not be graded on a numerical (100%, 90%, 80%, ...) or letter (A, B, C, ...) scale; rather, verbal or diagnostic written feedback on your progress in this course would be given on a recurring basis (from both your teacher and your peers).

To work around these constraints, the following over-arching rubric is used to assign your final semester-grade for the class:

If you come to (and stay in) class every day, and
If you do all the assignments and revisions, and
If you participate in sharing your work/ideas and discussing with the rest of us, and
If you post your work to your DP as required... you are guaranteed a B for the course.

If you come (and stay in) to class every day, and
If you do all the assignments with a clear effort at exploring and improving, and
If you participate in sharing your work/ideas and show real attention to the work/ideas of others and
If your DP exemplifies beautiful work... you are guaranteed an A for the course.

If you do all of the above, but with less effort or less reliability, you will receive a C, or a D, or ... F

To give you a sense of how you are doing with this rubric, approximately every two to three weeks a grade in PowerSchool will be entered that reflects your performance on this rubric. Remember: participation (individual, group and class) is key to getting an A: the extent to which you share your ideas and pay real attention to the ideas of others is critical (both during class discussions and during group work).

Grades for exams, tests, quizzes, homework, project benchmarks and other activities and assignments will use a 4-point scale, regardless of the "weight" of the assignment (in PowerSchool, weights will be used; for example, an exam grade will weighted higher than a quiz grade). This ensures that the grade is seen more as a reflection on that particular assignment and not so much its contribution to your final grade. Here is the 4-point scale:

Grade  Points Critique

A          4          Your work meets expectations and qualifies as "beautiful work". It is very likely your work                           could still be improved, and you are definitely encouraged to think about such                                           improvements for future assignments.

B          3          Your work exhibits authentic effort and mostly meets expectations. You are highly                                       encouraged to use the feedback given to revise your work and resubmit it for a higher                             grade.

C          2          Your work reflects a good effort and has the potential to be "beautiful work". You are                                 expected to make all the suggested revisions and do a check-in with me to ensure your                           work meets expectations.

D          1           While your effort to turn in work is appreciated, your work does not reflect your                                         potential. You are definitely expected to meet me to discuss how your work can be                                   transformed into work that meets most-if not all-of the expectations.

F          0           Your work is missing or lacks any originality.

Assignments and benchmarks will be graded multi-dimensionally; that is, you are not graded solely on your ability to solve a problem or "get the right answer", but you are also graded on your group work, collaboration, participation, sharing your mathematical reasoning (both written and verbal), willingness to give help, willingness to get help, your attitude and disposition, and so on.

Your actual final grade will be based on the rubric described above. Your PowerSchool grade will give you a sense of your progress: if your grades tend towards A's, you can expect an A; if most of your work is a B, you can expect a B, and so forth. The trends in your grades are important when a final grade is assigned: if you struggled at the beginning of the semester but persevered and improved your work, your final grade will reflect that growth. Likewise, if you start strong but then start to pay less attention to your work, your grade will reflect that reduction in your effort.

While PowerSchool does give a snapshot of your progress in the class, understanding of your growth and your challenges will come from three forms of feedback:

  1. the written and verbal feedback I provide,
  2. the feedback you receive from your peers, and
  3. the feedback you give yourself when you reflect on your work. If at any point in the school year you are unsure of your progress, you are definitely encouraged to come and talk to me.

All grades will appear online in PowerSchool and will be updated at least every two weeks, usually much more frequently.

Group participation is a crucial element of learning in this class (and in college and in the "real-world"); however, while students will often be working as a member of a group, group grades will not be given. Students will always be assessed on their individual effort and work.

Note: High Tech High policy is that a grade of a C- or higher is required in both semesters to pass the course. A D+ or lower in any one semester implies a mandatory summer school session.

Revising Work for More Credit

Critique and revising work are essential for producing beautiful work. In some cases, the critique and revision process are done formally, in a very structured way; in other cases, you are expected to self-critique or have friends and parents critique your work and do revisions. In some sense, a grade is form of critique from the teacher and it's possible that you may not be satisfied with the grade you received. You are always encouraged to ask if you may revise your work to receive additional credit.


There are many dimensions to learning mathematics and two important aspects are developing fluency with mathematical procedures and reviewing topics. There is a strong emphasis on rigor in this course, which includes covering topics in depth. To ensure this rigor and for students to develop fluency and review topics, it is necessary for students to do work beyond the classroom. Students should expect homework and structure their time to ensure its completion (this includes homework assigned in class and due the next day).

Challenge Options

With all assignments and projects, I expect the necessary components that show me you understand the concepts, but this is only the minimum. Every project and most assignments will be accompanied by a challenge option (or be structured as open-ended) allowing for a more in-depth exploration of course content and an enhanced development of skills-the opportunity to go beyond the minimum level of demonstrating that you understand the concepts. If your imagination and curiosity drive you beyond the benchmarks of a project, please act on it by accepting the challenge options. Or, if you have other ideas that go above and beyond, request that challenge: I want you to push yourself as far as you can go (and then a little bit further). Even if you pursue a challenge option and it doesn't quite turn out, it will reflect positively on your project and you will have gained invaluable experience.

Late Work and Absences

Work that is late cannot receive an A, unless you communicate with me before the deadline as to why you will not be able to submit the work on time (and I accept your excuse). Work can be submitted up to two days late and receive a 1-point deduction (A quality work becomes a B, B quality work becomes a C, and so on).


Pay close attention to assignment project due dates: Due dates and times for all project benchmarks will be established or communicated well in advance (normally at the beginning of the project). Remember: it is better to hand in unfinished work for partial credit (and potentially more credit for subsequent revision) than no work for zero credit.

Class Activities

While every attempt will be made to give students ample class time to finish class-based activities, please note that some activities will result in homework (or work for Academic Coaching) if the student did not finish in class, and homework assignments with deadlines will be given. Homework will not always be graded, but when it is, no late homework will be accepted (you will be graded on the amount completed).

Some assignments will require work to be handed in to the class inbox and/or an update to your Digital Portfolio (DP). These assignments will have deadlines, after which the work is late.


For a scheduled absence (including an early release from class), it is your responsibility to ensure that you leave prepared to complete all assignments that come due during your absence.

If you unexpectedly miss class time, it is your responsibility to stay caught up! Do whatever works best for you to find out what you missed and submit it on time:

  • Contact a friend (have contact info for at least two friends you can rely on!)
  • Follow the class on my DP
  • Contact me

Remember: Absences do not excuse missing work. If you miss an assignment or a project benchmark due date because you were absent, it is your responsibility to either complete the work during your absence and submit it when you return or come see me as soon as you return to discuss an alternative due date. Remember: it is your responsibility to follow-up after an absence.

Norms for a Supportive and Productive Learning Environment

During the first week of school, each class will establish its own particular set of classroom norms, particularly for doing group work. The following is a list the covers items I feel are particularly important for classroom discussion and group work (adapted from "Mathematical Mindsets", by Jo Boaler):

  • Everyone Can Learn Math to the Highest Levels: There is no such thing as a "math person"-everyone can reach the highest levels they want, with hard work.
  • Mistakes are Valuable: Mistakes make your brain grow. It is important to struggle and make mistakes.
  • Questions are Really Important: Always ask questions, always answer questions. Ask yourself: why does that make sense?
  • Math is about Creativity and Making Sense: Math is a very creative subject that is, at its core, about visualizing patterns and creating solution paths that others can see, discuss, and critique.
  • Math is about Connections and Communicating. Math is a connected subject, and a form of communication. Represent math in different forms-such as words, a picture, a graph, an equation-and link them.
  • Depth is Much More Important than Speed. The world's top mathematicians think slowly and deeply; you should too!
  • Math Class is about Learning, Not Performing: Math is a growth subject, and it takes time to learn. It's not about what you already know; it's all about effort to understand something new.

Student Support

Teacher-student communication is extremely important and encouraged in this class. I will have daily check-ins, but I encourage you to email me with additional questions/concerns. I am here to see you succeed, and I am willing to provide as much assistance as needed! If you should need additional academic support, there are two primary options:

  1. My office hours: Mondays 3:30 - 4:00 Wednesdays 11:45-12:15 and Fridays 7:45 - 8:15 (by advance appointment because i) sometimes this office hour will be preempted by meetings and ii) I will need to meet you to let you into the building).
  2. Academic Coaching (please inquire for details)

Student Digital Portfolios (DPs)

All students will be required to maintain and post selected work and projects to their Digital Portfolios. Posting work to a DP as an example of beautiful work is often a project benchmark.

Dr. Drew's Digital Portfolio (DP)

My Digital Portfolio is home to a lot of course information, including, the Daily Agendas, all assignments, this syllabus (in PDF form), class notes, project descriptions, and supplementary resources. Please become familiar with my DP and bookmark the URL (https://ajv.me/hth) so you can access it easily.

Materials and Supplies

The Constitution of the State of California requires that we provide a public education to you free of charge. Subject to certain exceptions, your right to a free public education means that we cannot require you or your family to purchase materials, supplies, equipment or uniforms for any school activity.

Many families have been asking what supplies their child may need during this school year. Below, I have a recommended list of supplies that your child may bring to school. Please note that if your child does not bring the recommended supplies, the school will provide the supplies for him/her. If you have any questions/comments about this, please contact me, or Shani Leader, the school director.

  • Pens, Pencils, Markers, Highlighters
  • Composition book for note-taking.
  • 3-ring binder (or equivalent for organizing handouts) + loose-leaf paper
  • Ruler
  • Calculator (no, you will not be able to use the calculator on your smart phone-see below)
  • Laptop


The nature of much of the work we will do in class requires the use of electronics, such as calculators and computers. As such, all students are encouraged to bring calculators and personal laptops to school, if possible. For students without their own calculators or personal computers, classroom calculators and computers are available. For some project work, students without home computers will have to make arrangements to use school computers outside of regular class time.

The following summarizes my "acceptable use" policy:

  • No messaging/texting or any form of social media during class. If there's an emergency I will need to know about it anyways, so ask before you reply to any urgent message. Texting without permission may result in your phone being confiscated for the remainder of the day. For repeat offenders, your phone will be handed to Ms. Aleida.
  • No making or receiving phone calls in class (if there is an urgency, let me know and we'll make arrangements for you).
  • No headphones (or earbuds, AirPods, ...) except during individual work time. If I must repeatedly remind you to remove headphones, you will lose the privilege of being able to use them in class.
  • No, you may not use your phone as a calculator. As part of the goals of college math readiness, you must be able to use your own or a classroom calculator.

Students bringing their own computers to class are required to follow an "acceptable use" policy:

  • The computer is being used solely for current classwork
  • No creation of personal hot-spots
  • No games of any type (this includes games on smart phones or other computing devices)
  • No use of external speakers

Misuse of personal computers can vary from temporary confiscation to a permanent revocation of the privilege to use them in the classroom.

Course Schedule

Due to the nature of Project-Based Learning, dates are subject to change. Be sure to check the official school calendar for important dates.

First Semester Course Schedule

Aug 27 - Aug 31 (5 days)

Introductory Unit: Introductions, Course Overview and Syllabus Review, Class Norms, Habits of Mathematicians, Digital Portfolios, Team Building, Topic Review, Mathematical Mindsets

Important Dates:

  • Sep 5 - Labor Day Holiday

Sep 3 - Sep 7 (4 days)

Algebra Review

Introduction to Piecewise Functions

Important Dates:

  • Sep 3 - Labor Day Holiday

Sep 10 - Sep 28 (20 days)

CPM Chapter 1: A Beginning Look at Calculus

Important Dates:

  • Sep 13 - Back to School Night

Oct 1 - Oct 19 (15 days)

CPM Chapter 2: Rates, Sums, Limits, and Continuity

Important Dates:

  • Oct 10 - 12th Grade College & Financial Aid Night
  • Oct 10-12 - SLCs

Oct 22 - Nov 23 (20 days)

CPM Chapter 3: Slope and Curve Analysis

Important Dates:

  • Oct 22 - All Staff Day-No School
  • Nov 11 - 12th Grade College Day
  • Nov 12 - Veteran's Day
  • Nov 19-23 - Thanksgiving Holiday

Nov 26 - Jan 11 (25 days)

CPM Chapter 4: The Fundamental Theorem of Calculus

Important Dates:

  • Dec 20 - Exhibition
  • Dec 21 - 1/2 Day (Senior Grades Due)
  • Dec 24 - Jan 4 - Winter Break
  • Jan 7 - Staff Day

Second Semester Course Schedule

Jan 14 - Feb 8: (20 days)

CPM Chapter 5: Derivative Tools and Applications

Important Dates:

  • Jan 15 - Grade 12 Internship Begins
  • Jan 21 - Martin Luther King Day
  • Jan 28 - Palomar Classes Start

Feb 11 - Apr 5: (20 days)

CPM Chapter 6: More Tools and Theorems

Important Dates:

  • Feb 19 - President's Day Holiday (Mon)
  • Mar 13-15 - Student-Led Conferences ("SLCs")
  • Mar 18-22 - Intersession
  • Mar 25 - Apr 5 - Spring Break

Apr 8 - May 10: (25 days)

CPM Chapter 7: Related Rates and Integration Tools

Important Dates:

  • Apr 8 - Staff Day
  • May 3 - Snow Day
  • May 9 - Grade 12 Internship Ends

May 13 - May 31: (15 days)

CPM Chapter 8: Volume

Important Dates:

  • May 27 - Memorial Day

Jun 3-7: Exam Week

Jun 10-14: Senior Week

2018-19 Grade 12 Math Syllabus


Students/Parents/Guardians, please review the following summary of the syllabus and ensure you understand each point. Please be sure to obtain any necessary clarifications before signing.

• Official grades will appear in PowerSchool and will be updated at least biweekly.

• Grading is on a 4-point scale: 4 (A), 3 (B), 2 (C), 1 (D) and 0 (F).

• A grade of a C or above is required to pass a semester (and avoid a summer school session).

• Absences are not an excuse for missing work. It is the student's responsibility to obtain assignments missed during an absence (or early release).

• Unexcused late work cannot receive full credit: late work will be accepted up to two days late (with a 1-point deduction).

• It is the student's responsibility to take advantage of my office hours, which are Mondays from 3:30 to 4:00 PM, Wednesdays from 11:45-12:15, and Fridays from 7:45 to 8:15 AM (by appointment).

• Course work will require the use of computers. Students without home computers must make arrangements to ensure adequate access to school computers.

• All electronics are subject to an "Acceptable Use" policy. Texting, messaging, and social media apps are not permitted in the classroom. Policy violations can result in confiscations and permanent bans.

• Headphones for audio can only be used during individual work time and not during group work, class discussions, or lectures. Policy violations can result in confiscations and permanent bans.

I, _______________________________ and ____________________________________,

Student Name (please print legibly) Parent/Guardian Name (please print legibly)

have read this 2018-19 Grade 12 Math syllabus, understand the course guidelines and policies, and agree to follow these guidelines and policies.

__________________________________________________ _______________________

Student Signature Date

__________________________________________________ _______________________

Parent/Guardian Signature Date

12th Grade Math (Math 4): 2018-2019 Honors Syllabus

PDF Version: https://ajv.me/hth-2018-19/math-4/curriculum/Syllabus-Honors-2018-2019.pdf

Instructor:                                                                                                  Office Hours:
Andrew J. Vernon (aka Dr. Drew)                                                             Mondays: 3:30-4:00
avernon@hightechhigh.org                                                                      Wednesdays: 11:45-12:15
Digital Portfolio: https://ajv.me/hth                                                             Fridays: 7:45-8:15 (by appointment)

Instructor:                                                                                                  Office Hours:
Ed Hanna                                                                                                  Mondays: 11:40 AM - 12:10 PM
ehanna@hightechhigh.org                                                                       Thursdays: 3:30-4:00 PM
Digital Portfolio: https://edhannamath.webnode.com/

Honors Overview:

High Tech High North County is committed to providing you with the experiences you need to be successful in life. An integral part of that success takes place in college which is why we are excited to offer an Honors Credit Option during your senior year.

Similar to your Grade 11 Honors options, the Grade 12 Math Honors is an opportunity for students to be guided through math concepts that are not covered in the regular class but also to dive deeper into topics that are covered and develop further the skills needed to be successful in college-level math. This includes:

Connections to AP Calculus:

The CPM Calculus Third Edition is aligned with the requirements for AP calculus. Honors students will become familiar with those requirements as the content is covered in the regular class. Occasionally, additional AP-based resources will be used to give students more practice with the AP requirements.

Critical Thinking and Collaboration:

Approximately every 2-3 weeks, I will give a mini-lesson on the trigonometry and calculus topics that are not covered in class. These will typically be held on Mondays at lunch, with the possibility of a repeat of the lesson on a Tuesday or Wednesday after school.


Each student will engage in peer assistance or an additional leadership role. You will be providing academic assistance to students in your class during lunch or office hours, or completing a review for students to utilize to prepare for quizzes and tests. Participation in additional peer tutoring during office hours and lunch may become required, at least 1 time a semester, but can happen more.


You will be responsible for additional, in class course work on a regular basis. For example you may be asked to answer more challenging questions, complete additional sections on exams, and so forth.

12th Grade Math 2018-2019 Honors Agreement:

The Honors program at High Tech High North County exists for students who desire an additional challenge. Students who wish to take the class for honors credit are committed to the regular class workload, plus additional project work, papers and exam questions. The additional workload requires a greater degree of mathematical knowledge and understanding, and perseverance to challenge yourself. I am highly recommending this course to students interested in the STEaM fields.

We recognize that one reason that students take honors courses is the weighted GPA that comes with this course, which helps during college admissions. Therefore, we allow students to take courses for honors credit for which UC will grant weighted GPA's, namely junior and senior core classes.

It will be the student's responsibility to prepare for the assignments and to seek assistance from the teacher whenever necessary. Honors coursework is graded and there is a zero tolerance policy for late honors-specific work. Work must be turned in on the specified due date. Students are aware of due-dates far in advance so they have plenty of time to work out computer/printer/life issues. The strict policy is not meant to put pressure on students but is a means for students to demonstrate high academic achievement and personal responsibility.

Students must commit to the honors program for the entire semester. Requests to take the Honors Credit Option must be submitted to Andrew Vernon no later than September 7th. Requests will be handled on a case-by-case basis, and will include an assessment of the Honors Summer Assignment.

I, ______________________________, am committed to taking 12th Grade Mathematics for Honors Credit. I understand that I am committed to the honors program for the entire semester regardless of what my grade is at any given point of the semester. I also understand that it is my responsibility to prepare for honors assignments and that I am required to seek assistance whenever necessary.

__________________________________________________ _______________________

Student Signature Date

__________________________________________________ _______________________

Parent/Guardian Signature Date

I will acknowledge acceptance for Honors Credit with my signature (after having a conversation with students about their preparedness for the challenge of this course, if necessary):

__________________________________________________ _______________________

Teacher Signature Date