- 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)

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

This class will be taking a quiz today on solving equations. This will be an open note test, but may not share notes with their partners. I have told students that there is a quiz on Wednesday, as incentive, if they perform well and finish the quiz today, I will cancel the quiz on Wednesday. **At the end of the day (in your sub notes), please advise if you believe they have earned this reward…I trust your judgement.**

- Learning Target: Students will be able to communicate their understanding of solving one variable, multiple step equations and explain the reasoning of others who have solved this too!
- Success Criteria: I can solve a multiple step equation and can explain the reasoning of a problem solved wrong.

**Lesson Plan:**

- Entry Task (and attendance/admin stuff)
- Review Entry Task
- Practice Problems for Quiz (Pre-Quiz Practice Problems)
- Quiz

Quiz Guidelines

- Students may use all of their notes for this quiz.
- There are several different versions, so concentrate on your own version.
- Students may use a calculator (not their phone)
- Eyes on your own paper.
- No phones should be used on this assessment
- If a student refuses to follow instructions, talks during the quiz or is not following standard quiz guidelines. Please allow them to
**finish their quiz**and document the behaviors.

This class is small with no seating chart. Most students choose wisely but some groups talk a lot. 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. Use the links in the video description to jump to specific problems.

* Remind students they can always access this page of my website on mr.germanis.org if they want to view the video again! *Please encourage them to email me if they have any questions.

**Video Link: http://www.youtube.com/watch?v=o-jKdaZ7QnY**

**Lesson Plan:**

- Play video for entry task…allow students some time to work. Pause when it says pause.
- Resume video through the announcements and information about the quiz.
- Hand out worksheet…inform them of the update to the wording of question 4.
- “Compute the slope of the tangent line for the function at each point.”

**Write this on the board:***“Problems 3, 4, 5, & 6 are similar to your quiz. These exercises are classwork and homework. Go to http://mr.germanis.org/2018/11/19plans/ for video examples. Email rgermani@fwps.org if you have questions.”*- Allow students to work independently and with partners to complete these four problems.
- Please monitor for groups who are very off task…remind them that this is their opportunity to study for their quiz.

**Embedded Video Below**

EU 2.1 – The derivative of a function is defined as the limit of a difference quotient and can be determined using a variety of strategies.

- LO 2.1A – Identify the derivative of a function as the limit of a difference quotient.
- LO 2.1B – Estimate derivatives.
~~LO 2.1C – Calculate derivatives.~~~~LO 2.1D – Determine higher order derivatives.~~

We are really only assessing half of the standard right now and leaving the second half for later in the unit. You will need to be able to:

- Use the difference quotient (limit definition) of the derivative to compute the slope of a tangent line at a specific point
- Understand notation f'(a) and dy/dx as notations communicating a need for a derivative.
- Use a graph to estimate the derivative of a function based on the image provided (no equation provided for the function).
- Estimate (assuming a function is continuous) the derivative based on tables and graphs.

Here are some video resources from to support learning that may have been missed in class:

- Concept of a Derivative
- Secant Lines vs. Tangent Lines (Average Rate of Change –> Instantaneous Rate of Change)
- Derivative Notation (Practice Set)
- Derivative as Slope
- Limit Definition of Tangent Explained
- Estimating Limit from a Table of Values

P2 – 7:25 – 8:40 Algebra 1

Advisory – 8:45 – 9:20

P4 – 9:25 – 10:45 Calculus

P6 & Lunch 10:45 – 12:35

P8 – 12:40 – 1:55 Algebra 1

**NOTICE: Unit 2 Mid Unit Quiz will take place Next Monday & Wednesday before Thanksgiving break.**

Learning Target: I will learn to create multi-step equations in one variable.

Success Criteria: : I can create multi-step equations in one-variable.

LT: I will learn to solve multi-step equations.

SC: I can solve a multi-step equation.

SC: I can communicate the process of solving a multi-step equation.

- Intro to Two-Step Equations
- Intro to Two-Step EquationsTeachers Guide
- Multi-Step Tutorial (as needed)
- Multi-Step Homework
- Multi-Step Classwork (for students who finish quickly)

- Introduce yourself and announce that there will be a quiz on this material on Monday and Wednesday of next week before Thanksgiving Break
- Start lesson by distributing Two-Step Equations worksheet to class.
- Tell students they should be taking notes during the video on the worksheet as Mr. Germanis goes through these with them.
- Video Linked Here and Below
- Pause the video after problem 10 (instructions in the video) to allow students work time for problems 11-16
- Then, play the video again to have them check their answers.

- When students are done with the video, have them finish both sides of the worksheet.
- When students are done (or if they finish early), Have them work on the homework for the class which is additional practice problems which require simplifying before they can solve.
- Video Linked Here and Below

CCE Link (Students can use device to complete the survey or hard copies available) The QR Code links to the website.

This class is small with no seating chart. Most students choose wisely but some groups talk a lot. 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.

When appropriate, please pass out the class packets called **“POGIL – Derivatives 2”** students have used this worksheet before. There is a large binder at the front of the room under the table with the answers in there. It is identical to the students packet. It has lots of purple writing and can help guide you through the lesson if you want.

Finally, there is a segment at the end of the video AFTER students have had a lot of work time. Please play the last part of the video during the last 15 minutes of class. Students need to have attempted the problems before they see the last part of the video.

* remind students they can always access this page of my website on mr.germanis.org if they want to view the video again! *Please encourage them to email me if they have any questions.

- A.SSE.2 – Use structures of an expression to identify ways to rewrite it.
- A.SSE.3 – Factor to identify the roots or complete the square to solve for roots of a quadratic function.
- A.APR.6 – Divide Polynomials using the Tabular Method or Long Division.
- A.REI.4 – Solve quadratic equations in one variable.
- F.IF.7 – Graph functions expressed symbolically and identify key features

- A.SSE.1 – Interpret parts of an expression such as term, factor, and coefficient.
- A.SSE.2 – Use the structure of an expression to rewrite them into equivalent forms (factoring, dividing, multiplying polynomials).
- A.APR.1 – Add, Subtract & Multiply Polynomials
- A.APR.2 – Apply the Remainder Theorem (rewrite division problems as multiplication problems plus the remainder).

- Adding and Subtracting Polynomials
- Using Area to understand Distribution & Factoring
- Multiplying Polynomials Classwork
- Multiplying Polynomials HW
- Dividing Polynomials – Reverse Tabular (Lesson 3)
- Long Division w/ Polynomials (Lesson 4)
- Putting It All Together (Addition, Subtraction, Multiplication & Division) – Lesson 5
- Answers Guide Video (see description for specific question time stamps)
- Lesson 5 Teacher Guide

- Math Hospital (Polynomial Arithmetic)
- Explanation Video (see link for timestamps)