Secondary Lesson Plan: Scatter Plots and Exponents

Made by Karly Sachs March 11 and 12 2015

Name of class: Algebra II

Length of class: 90 Minute Block

LEARNING GOALS to be addressed in this lesson (What standards or umbrella learning goals will I address?): Construct and compare linear, quadratic, and exponential models and solve problems.

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). (F-LE.2.)

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. (F-LE.3.)

LEARNING OBJECTIVES (in ABCD format using verbs from Blooms Taxonomy): Students will graph an exponential function and determine the equation of an exponential function given two points on a graph. Students will Identify an exponential function from the table it generates and use the table to create a closed form or recursive definition of the function. Students will extend the laws of exponents to include all real number exponents and express the laws as function equations. Students will evaluate the inverse of the function y=b^x either exactly or approximately. Students will define the term correlation. Students will determine the line of best fit of a data set by using the TI Inspire. Students will predict different situational outcomes by using a line of best fit. Student Friendly Statements: I can graph an exponential function and determine the equation of an exponential function given two points on a graph.

I can Identify an exponential function from the table it generates and use the table to create a closed form or recursive definition of the function. I can extend the laws of exponents to include all real number exponents and express the laws as function equations. I can evaluate the inverse of the function y=b^x either exactly or approximately. I can define the term correlation. I can determine the line of best fit of a data set by using the TI Inspire. I can predict different situational outcomes by using a line of best fit. CONTENT (What specific concepts, facts, or vocabulary words will I be teaching in this lesson?): Vocabulary:

Exponential Function Growth Decay Constant Ratio Correlation

SKILLS: (What skills will students acquire or practice?) Students will reason by continuity to extend the definition of exponents to include all real numbers. Students will visualize exponential growth by examining graphs and tables of exponential functions. Students will draw logical conclusions from the laws of exponents and properties of exponential functions to solve problems and prove conjectures.

RESOURCES/MATERIALS NEEDED (What materials and resources will I need?): Handouts for the Students: Calculator Steps handout Guided Discovery Activity packet

Handouts for the Elmo: Goals handout Practice Data handout Answer Packet handout Correlation Notes notes page

Other Materials: TI Inspire Pencil Colored Pencils Composition Notebook

LEARNING PLAN (How will you organize student learning in this lesson?

ACTIVATE (How will I pre-assess my students understanding, activate their prior knowledge, or get them excited about my lesson?) Think, Pair, Share: Think, pair, share to the question Describe a data set that would follow the general trend of exponential growth. Describe a data set that would follow the general trend of exponential decay. First think to yourself and jot down some notes on the yellow sticky note in front of you. After three minutes or so, pair with your shoulder partner and discuss. Write down what you talked about on the pink post it in front of you. After three minutes, face forward and be ready to share your answers with the class. ACQUIRE & APPLY (What instructional strategies will I choose to help my students acquire and apply the knowledge, skills, attitudes, and behaviors outlined above? Correlations Lesson:

Explain what a correlation is Generally explain how it can be(show what it looks like)

o Positive o Negative o Neither

Generally explain how it can be(show what it looks like) o Strong (r = 0.7 or greater) o Weak (r= 0.3 or less) o Medium (0.3-0.7)

But how do you know if the data has a relationship? This is where technology comes into play

o It gives students something to visualize. Now the numbers in the table are not just numbers, but a part of something bigger

Take out your calculator and o Press New Document and click add lists and spreadsheets. This should

be choice 4 o Now type in the data for the data set 1

Make sure to title each column (you can just type in xxx and yyy if you want to shorten it)

o Now we want a new page so click control I to insert a new page o Now click choice 5 which is called add data and statistics o You will see a bunch of points all in a mess. To get them straightened out

either Use your curser to click the x and y axis or just press tab to get to

where you want to go Click the corresponding titles

o Now a graph will appeardo you see a correlation? o Now lets find a line of best fit

To do so click menu, analyze, regression Choose the type of regression you think best fits the data

o Data 1 will be linear A line of best fit will appear!!

o Now lets find out how strong our correlation is Insert a new page (Control I) Click option 1 (calculator page) Press menu, statistics, stat calculations

Pick the same regression type you did earlier Rewrite the corresponding titles with the list rows and then tab

your way down to ok A list of information will appear What does r equal? This shows how strong your correlation is

o We can also find out information for points that are not clearly exhibited in the data set

o To do so Define your function

Press menu, actions, define o You can also just type in the word define

Now write your function exactly how it is shown in the page prior. Make sure to put f (x)=###### and then click enter

Now you can solve for x and y by either typing o f (#) o Or solve (# = f (x),x)

How easy was that! Now do the in class activity Now explain why this lesson with technology is beneficial

o This is the Close of the lesson o We will discuss the overall understandings of the activity as well as

discuss how technology was beneficial for the lesson to occur.

ASSESSMENT (How will asses student understanding?): Informal Assessment: 1. Homework Check 2. Thumbs up, Thumbs down: Ask the students if this is what they got? Do they understand the material so far? And so forth. 3. Walk around the room and see if the students are understanding the material 4. Students will turn in the Activitythis will allow me to see if students are understanding the general concepts of the lesson 5. Close: 321 (talking version): 3: With your shoulder partner talk about the 3 types of correlations we discussed today. 2: With you vertical partner discuss 2 reasons why analyzing exponential data is important in every day life. 1. On the sticky note in front of you write down 1 concept you are still confused about. (Place this sticky on the door when you leave the room) Homework: None! Have a fabulous Spring Break!

LESSON PLAN SEQUENCE & PACING (How will I organize this lesson? How much time will each part of the lesson take?) 1. Homework Check 2. Go over Homework? 3. Think, Pair, ShareActivation 4. Correlation Lesson 5. Correlation Example Problem

6. Correlation Activity 7. 321Close

Goals for the Day: I can graph an exponential function and determine the equation of an exponential function given two (or more) points on a graph. I can identify an exponential function from the table it generates and use the table to create a closed form or recursive definition of the function. I can define the term correlation. I can determine the line of best fit of a data set by using the TI Inspire. I can predict different situation outcomes by using a line of best fit.

Think, Pair, Share (Launch)

Think: Describe a real life situation that would a) Have a data set that would follow the general trend of exponential growth. b) Have a data set that would follow the general trend of exponential decay. Jot down some notes on the yellow sticky note in front of you. Pair: Pair up with your shoulder partner and discuss. Jot down some notes on the pink sticky note in front of you Share: Face forward and be ready to share your responses with the class.

Detailed Calculator steps

Take out your calculator and o Press New Document and click add lists and spreadsheets. This

should be choice 4 o Now type in the data for the data set 1

Make sure to title each column (you can just type in xxx and yyy if you want to shorten it)

o Now we want a new page so click control I to insert a new page o Now click choice 5 which is called add data and statistics o You will see a bunch of points all in a mess. To get them straightened

out either Use your curser to click the x and y axis or just press tab to get to

where you want them to go Click the corresponding titles

o Now a graph will appeardo you see a correlation? o Now lets find a line of best fit

To do so click menu, analyze, regression Choose the type of regression you think best fits the data

Data 1 will be linear A line of best fit will appear!!

o Now lets find out how strong our correlation is Insert a new page (Control I) Click option 1 (calculator page) Press menu, statistics, stat calculations

Pick the same regression type you did earlier Rewrite the corresponding titles with the list rows and then tab

your way down to ok A list of information will appear What does r equal? This shows how strong your correlation

is o We can also find out information for points that are not clearly

exhibited in the data set o To do so

Define your function Press menu, actions, define

o You can also just type in the word define Now write your function exactly how it is shown in the

page prior. Make sure to put f (x)=__________ and then click enter

Now you can solve for x and y by either typing o f(#) o Or solve (# = f (x), x)

How easy was that!

Name: ___________________________

Block: ____________________________

Correlations Discovery Activity:

Directions: Solve the following problems using the detailed calculator steps as well as your TI Inspire. Please work in groups of 2 or 3. The Data: The data below shows the cooling temperatures of a freshly brewed cup of coffee after it is poured from the brewing pot into a serving cup. The brewing pot temperature is approximately 180 F.

The Task: 1. Type the data into your Calculator 2. Make a scatter plot of the data. Sketch it below.

3. Determine an exponential regression model equation to represent this data. Equation: _________________________________________________________ 4. Is this equation a good fit for the data? Why or why not? __________________________________________________________________

__________________________________________________________________

__________________________________________________________________

5. Based upon the exponential regression model, what was the initial temperature of the coffee? How did you figure this out? Initial Temperature of the Coffee: __________________________________ I found this by

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

6. When is the coffee at a temperature of 106 degrees? Write down the steps you took to find this answer.

Answer: ___________________________

7. What is the predicted temperature of the coffee after 1 hour? Write down the steps you took to find this answer.

Answer:___________________________

8. Real Life: In 1992, a woman sued McDonald's for serving coffee at a temperature of 180 that caused her to be severely burned when the coffee spilled. An expert witness at the trial testified that liquids at 180 would cause a full thickness burn to human skin in two to seven seconds. It was stated that had the coffee been served at 155, the liquid would have cooled and avoided the serious burns. The woman was awarded over 2.7 million dollars. As a result of this famous case, many restaurants now serve coffee at a temperature around 155. How long should restaurants wait (after pouring the coffee from the pot) before serving coffee, to ensure that the coffee is no hotter than 155? Show your work in the space provided. If you need more room, work on the back of this page.

Wait Time: _____________________________

In Class Example for the Elmo:

Years Number of cell phone users 1986

498

1987

872

1988

1527

1989

2672

1990

4677

1991

8186

1992

14325

1993

25069

1994

43871

321 3: With your shoulder partner talk about the 3 types of correlations we discussed today. 2: With you vertical partner discuss 2 reasons why analyzing exponential data is important in every day life. 1. On the sticky note in front of you write down 1 concept you are still confused about. (Place this sticky on the door when you leave the room)