What is a logarithm? The answer is more simple than meets the eye. Essentially, a logarithm is the “backwards” version of an exponent and we will explore it that way. For many reasons we’ll discuss on class, there is a variety of connections between logarithms and exponential functions. Find some helpful videos below to build meaning around what a logarithm is, the properties it holds and how to use them to solve exponent problems.
F.BF.B.4  Find the inverse functions. 
F.BF.B.5  Understand the inverse relationship between exponents and logarithms and use this relationship to solve problem involving logarithms and exponents. 
F.IF.C.7.e  Graph exponential and logarithmic functions, showing intercepts and end behavior. 
F.LE.A.4  For exponential models, express as a logarithm the solution to abct= d where a,c, and d are numbers and the base b is 2, 10 or e; evaluate the logarithm using technology. 
F.BF.B.3  Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd function from their graphs and algebraic expressions for them. 
You will be demonstrating your understanding of applying calculus to real world problems and showing your knowledge of implicit differentiation when solving related rates problems.
Standard  Description  1
Never Present 
2
Sometimes Present 
3
Regularly Present 
4
Always present 
PS 7 – Solve problems using the derivative analytically, graphically, numerically, and verbally for a variety of problems (including optimization, related rates, and rectilinear motion).
Overall Score:
_____________ 
Student presents a well written question and interprets the problem for the reader.  
Student uses implicit differentiation to solve the problem.


Picture provided aids any reader in better understanding the question being asked. Values and variables are labeled in the picture.


Student interprets the answer for the reader and puts numbers into usable meanings.


PS9 – Solve problems including those that model area, volume and surface area.
Overall Score:
_____________ 
Students have 2 of the 4 required types of related rates problems.  
Student demonstrates understanding of formulas needed to solve the problem.


Student demonstrates understanding of variables used.


Student correctly answers the question showing all work leading to the answer.

Problem Description:

Picture:


Question your problem will answer:


Formula’s used in your problem (area, volume, etc.):


Variables & Constants:
Problem Workspace:


The answer to the question being asked above (in context):


Summary paragraph of the problem and answer in context:


Attach a selfevaluated rubric for BOTH of your problems (meaning you will have one rubric for the two problems you submit. You should edit your project if it does not meet all of the criteria. 
Please talk with Michelle Pierce in the main office for Advisory lesson plans.
Play the video below and follow the directions in the video. Ryan is a student who has been asked to help support the pacing of this lesson since there will be MANY STOPS AND STARTS. Please support the pacing that is natural for students who are consistently working. Students WILL get stuck, but they need to struggle before they watch the video…they’ll have greater buy in. There are obvious places to PAUSE the video.
Please talk with Michelle Pierce in the main office if there are any additional needs.
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This unit will be focusing on exponential functions. We will start by reviewing exponent rules, looking at rational exponents (exponents that have fraction exponents), then we will use function notation to make data tables and graph those. There are MANY applications to exponents, many used in everyday life. We will explore how to create exponential expressions based on contexts to answer real world questions.
F.IF.A.2  Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 
A.SSE.B.3.c  Use the properties of exponents to transform expressions for exponential functions.

F.IF.C.8.b  Use the properties of exponents to interpret expressions for exponential functions. 
F.BF.A.1  Write a function that describes a relationship between two quantities. 
Day 1: Exponent Laws Discovery Activity
Day 2: Drug Filtering Worksheet
Day 3/4: Bees Gone Crazy Task – Exponential Functions
Day 4: Who is right, who is wrong (answers)
]]>Here is an outline of the tasks that need to be completed during today’s lesson. I am at a training in the building so students may see me. I will be in the Library.
Students were provided class time and homework for the following problems: 710, 712, 713, 714 and 716
Students will work on classwork (720, 721 and 722) and be assigned the following homework problems (724, 725, 728).
Have students complete the survey https://www.surveymonkey.com/r/HHJBBB6
Here is an outline of the tasks that need to be completed during today’s lesson.
Students are learning about the characteristics around what exponential graphs look like…this will require students to use Desmos to access the learning.
When done with the QUIZ (Exit Ticket):
When I return, I will also recheck understanding of the core problems in this lesson.
Students in this class will be taking a Scantron test of the derivative rules. Please leave about 20 minutes at the end of class to allow them time to finish. If they do not finish by the end of class, their scores will be entered as is and they can retake the assessment next week if they are unhappy with their scores. They may write in this workbook.
Entry Task: POGIL #28
Whiteboard Task:
Derivatives Skills Test:
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).