**The Chain Rule**as a concept is essential to extending calculus to context based situations.**Implicit Differentiation**is an application of the Chain Rule that allows us to solve problems that would otherwise be impossible to solve.**Related Rates**help us understand how more than one quantity are intertwined with one another and we need to use both the chain rule and implicit differentiation to uncover new ideas.- (bonus) Also, organization of information and notation are more important than ever!

In an effort to support the learning that is happening in class, these three videos will provide the **conceptual understanding** behind these Calculus ideas and also provides several examples of how to use them in our course, this is **procedural** **fluency** which is just as important as concept understanding.

Work to understand how the notation of d/dx is similar to dy/dx. Along with an understanding of fractions, this is a key idea in Calculus.

Think about how the Chain Rule is being applied to each situation.

When solving these problems, they get easier the more you work to understand them. STAY ORGANIZED!

]]>Practice Derivative Skills Test (Answer key attached)

Please use this derivatives skills test to help practice these skills that will be assessed in class. Please feel free to ask questions as you have them, the only way to get better is through* productive struggle*.

Throughout this unit, students will be learning about functions that have linear relationships. This is one of the the most important concepts in Algebra 1 as a course. The following videos and resources will help you through this unit. It will require patience, attention and an effort to make connections to concepts that will support the learning in this class.

This video explains (almost in its entirety) how relations can be represented through words, mappings, ordered pairs, tables and graphical representations. You will learn what it means to be a function and be able to explain why something does not show a functional relationship.

This video discusses the relationship between slope, rate of change and starting point (just an introduction) between words, tables and graphs. This is a great starting place for students who are first learning or relearning about rates of change, slope and intercepts (starting point).

There are only a few tasks for today, mostly getting kiddos setup on computers or to the Library.

Students will be finishing up their iReady assessment, I have organized with the testing coordinator to have students finish class on laptops. Corrine Behme, the testing coordinator, will come over first thing in the morning to bring the computers and will help you get students logged in. She will come at the end of the period to help you coordinate putting away the computers (to avoid theft).

If needed, Corrine can reset students passwords. Somethings you and students should know:

- Students should work to finish the assessment TODAY.
- Scores will NOT hurt their grade, but if they do well enough, it can
**improve**their class grade. - Students may only use a calculator provided within the testing program
- Scratch paper is strongly encouraged, Mr. Germanis couldn’t do the problems without scratch paper, so students should use it too!

When students are done with their assessment, they need to begin working on their Practice Final (pink paper). **They will have an assessment on Friday, they will be able to use this practice test on their final exam.**

This class is working on a project, **you will need to get computers from the librarian, I have them reserved for this period.** You may send a student to get computers if needed, but all students should stay in the class, they are very responsible kids. If students ask, all information is on the website, please send them to the Calculus project website for more information: http://mr.germanis.org/2019/01/semester-1-calculus-project-2019/. If students have a more demanding question, they are encouraged to email me rgermani@fwps.org, I will be checking email throughout the day since I’m at a District training.

Today is a work day for them, they may use any textbook around the room and are encouraged to use the internet to do their research for the questions. **Remind students that the due date is Friday, Jan 25th @2:10 via email or paper copy.**

Students may use any resources in the blue closet at the front of the room (such as printer paper, colored paper, glue, colored pencils, etc.)

]]>- PS 2 – Find, describe, and compare limits and asymptotic/unbound behavior for functions analytically, graphically, numerically, and verbally including one-sided limits.
- PS 3 – Define continuity in terms of limits and graphs (including Intermediate Value Theorem and Extreme Value Theorem).
- PS 4 – Compute and determine the derivative of functions using the power rule, product rule, quotient rule, exponent rule analytically, numerically, and verbally and as rates of change and difference quotient.
- PS 5 – At a point, find the slope of a curve, the instantaneous rate of change, and average rate of change of the function analytically, graphically, numerically, and verbally. Write the equation of the tangent line.

Please select the link below to see the language of the project and the requirements for each standard assessed.

]]>- Students finish homework
- Show Video (linked here and embedded below)
- Quiz (approx. 30 min)
- students may use notes, a calculator and a rule
- Students may listen to music while working (respectfully)
- Cell Phones
**MUST**be away (please document those not following this rule)

These classes have great students, they will list and be respectful.

- Tell students to save the exponent POGIL packet given last class, we will work on it when Mr. Germanis returns.
- Read (or have student read) the “Project Instructions” PowerPoint
- Students may use the internet, textbooks or classwork to begin their project.
- A Link to the project page is here http://mr.germanis.org/2019/01/semester-1-calculus-project-2019/
- Distribute the dark orange project description.
- Encourage students to read the bottom of the paper first.

- If students have questions, please have them email Mr. Germanis at rgermani@fwps.org

- Simple Composition Functions
- Factoring
- Solving Equations (using the quadratic formula)
- Rates of Change
- Simplifying Rational Functions that include addition and subtraction.

In class we have (or have already) talked about derivatives and what they mean. I believe this video is a nice summary of the theory discussed in class. He speaks quickly but repeats ideas many times.

We have talked about “shortcuts” for doing derivatives in class, but these are more just techniques for doing the long derivatives. We have discussed a lot of the theory in class. If you want more theory, check out this video to understand visually the theory behind the derivative.

- Power Rule – https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-5/v/power-rule
- Constant, Sum, Difference and Constant Multiple Rule – https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-6a/v/derivative-properties-and-polynomial-derivatives
- Connected with Power Rule – https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-6b/v/differentiating-polynomials-example
- Product Rule – https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-8/v/applying-the-product-rule-for-derivatives
- Quotient Rule – https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-9/v/quotient-rule

P2 – 7:25 – 8:50 Algebra 1

P4 – 8:55 – 10:25 Calculus

P6 & Lunch 10:30 – 12:20 – Planning & Lunch

P8 – 12:25 – 1:55 Algebra 1

- Learning Target: Students will identify errors in others work and suggest solutions for solving those errors.
- Success Criteria: I can solve equations in one variable enough to finish the maze. I can analyze my work for errors in my thinking and edit my mistakes.

**Lesson Plan:**

- Explain problem 1 of the Error Analysis worksheet (Unit 2 – Lesson 4 – Homework)
- Provide 15 minutes for students to start this activity.
- Return Quiz to Students (answer Key’s attached)
- Provide 10 minutes for completing quiz corrections
- Distribute “Solving Multi-Step Equations (homework)” Worksheet
- Students should continue until the end of class
- Ask them to show you the “balance” representation for each
- For students who are done early, there is extra practice (or you can reward with a break).

This class is small with a new seating chart. This was shared last class…if they can’t remember, use your best judgement. Please use this YouTube Video that I curated to guide through the class. It will let you know when to pause the video and give students time to work. You should start the video after you take attendance.

I have provided you an answer key to help students through each of the problems…they should be able to get though Problem 12 by the end of class…otherwise it’s homework.

**Video Link: **

**Lesson Plan:**

- Entry Task: Students should discuss problem #6 from Derivatives 3 POGIL (extras provided).
- Please play the video linked below and pause when needed. There is an outline for students.
- You will pass back their quiz from last week. I have given you the key…students can take a picture, but there are explanations in the video.
*If students have questions, encourage them to Email rgermani@fwps.org if they have questions.*- Homework is #1 – 12 in the POGIL activity.

**Embedded Video Below:**

This PDF guide is meant to serve as a starting point to understanding what completing the square means visually and how to accomplish it for a simple case. More advanced cases will not be assessed but will help overall understanding and understanding in future courses.

**A GUIDE TO COMPLETING THE SQUARE (PDF)**

For additional resources see these links:

- Full Guide to Completing the Square (Math Is Fun, with visuals)
- Completing the Square (purple math, more technical)
- Khan Academy Guide (several videos and exercises)