# Public Activity Library

The attached activities are lesson plans, activities, or tasks that teachers have created as participants in this project. These focus on teaching and learning with the instructional technologies of either Geometer's Sketchpad dynamic geometry software or Fathom dynamic statistics software. Most of the activities are created mainly for high school Algebra 1 and Geometry courses, however a few are created for Algebra 2 courses. These activities are posted for public use.

**Algebra Activities using Fathom**

**Lesson Title:** Bouncing Ball & Rebound Heights

**Role Model Video** - Windlift and/or Transportation Roadways & Vertical Curves

**Synopsis** - This activity is designed to use the Go!Motion sensor to look at behavior of a bouncing ball, including rebound heights. Each bounce is represented by a quadratic function, and successive maximum rebound heights can be modeled by an exponential function.

**Materials** - Go!Motion sensor, Fathom, Logger Lite (if using VCL), balls that bounce well, two computers

**Notes** - Activity works best with groups of 3-4. Roles include: 1) student to hold the sensor, 2) student to drop the ball, 3) student to monitor experiment and manage data in Fathom/Logger Lite, and 4) a team leader to keep the group organized and on task by following actitvity displayed on their computer.

**Activity File: **

**Lesson Title: **More Is Less

**Submitted By: **Angel Rouson

**Role Model Video: **Windlift

**Tags:** Functions, Interpreting Data/Functions, Graphing Quadratic Functions, Rewriting Functions

**Common Core Alignment: **F.1F.1, F.1F.4-F.1F.9, F.BF.1, F.BF.3, F.BF.4, F.LE.3

**Synopsis:** This activity is designed to use Fathom software to record a controlled experiment involving bottle rockets. Each trial will use a different percentage of water capacity in the bottle to discover the amount of water that will give the rocket maximum height. It will help model quadratic functions and interpret the effects of controlled input values on each output value.

**Materials**: 16oz. bottles (standard 9/16" opening), water, cardboard, glue/tape, paint (decoration), link: http://www.grc.nasa.gov/WWW/k-12/bottlerocket/br2d_b.swf

**Notes: **This acitivity can be conducted in two ways: 1) The class can build their own bottle rockets and shoot them off in an open area or outdoors. 2) The class can use the website to simulate bottle rocket launches instead of building rockets from the materials.

Attached are the instructions as well as a Fathom file with sample data.

**Activity Files: **

**Lesson Title: **Launching Model Rockets and Using Piecewise Functions

**Submitted By: **Seth Risinger

**Role Model Video** - TechShop RDU Founder and UAV Pilot

**Tags** - Functions, Exponential, Piecewise, Analyzing & Interpreting Graphs

**Common Core Alignment** - F-IF.1 , F-IF.2, F-IF.4, F-IF.7

**Synopsis** - This activity is designed to compare a simplified model of a rocket launch to the actual data collected from an altimeter in a model rocket. Students will be modeling the quadratic pattern in the simplified version, and using a piecewise function from the actual launch

**Notes** - The Prelaunch calculations are complicated but do a good job teaching student's organization. The rocket launch isn't necessary, but is something the students enjoyed!

**Materials** - For the parabolic activity:Algebra 1 Fathom Book Activity, Student Experiment Handout and Questions

For the AFM Extension:-SkyTrax rocket data set and Fathom Workspace ,-Pre-Launch Calculations page,

-Launch Day Calculations page, -Post Launch Modeling Packet

For an actual launch:-Estes launch starter set that includes a payload rocket, -PerfectFlite Pnut Altimeter and USB data capture cord

**Activity Files: **

Quadratic Model Rocket Fathom Activity.docx

Modified PostLaunch With Fathom.docx

**Lesson Title: **Using Gym Memberships to Understand Systems

**Submitted By: **Felicia Persky

**Role Model Video** - Video Game Production Designer

**Tags** - System of Equations, Graphing Linear Equations, Application of Systems

**Common Core Alignment** - A.REI.6 Solve system of equations, A.REI.1.2 Represent and solve equations and inequalities graphically

**Synopsis** - This activity is designed to apply system of equations to the real-world situation of gym memberships. The students will conduct their own reasearch and use Fathom to analyze and interpret the graphs associated with purchasing a gym membership.

**Materials** -Fathom, two computers

**Notes** - Activity works best with groups of 3-4. Roles include: 1) two students to research gym rates 2) student to input the data into Fathom and create the tables and graphs, and 3) a team leader to keep the group organized and on task by following actitvity displayed on their computer.

**Activity Files: **

Systems of Equations Activity.docx

**Lesson Title: **Customer Satisfaction

**Submitted By: **Katie Mullins

**Role Model Video** - Customer Value Analyst - Jennifer Tripoli

**Tags** - Critical Thinking, Functions, Lines, Slopes, LSRL, Predictions

**Common Core Alignment** - S - ID.6a, S - ID.6c, S - ID.7, S - ID.8

**Synopsis** - This activity is designed to use Fathom to analyze real world customer satisfaction data to discover the relationships within the data and make predictions of furture customer satisfaction ratings.

**Materials** - Fathom, Food Data.csv, Airline Data.csv, Car Data.csv, Department Stores Data.csv, Hotel Data.csv

**Notes** - Activity is designed to work in pairs. Extension project is available within the lesson. Sample Student Food Data Fathom Lesson is attached.

**Activity Files: **

**Lesson Title: **Faster and Farther

**Submitted By: **Kevin McDaniel

**Role Model Video** - Systems Biologist - Cranos Williams - North Carolina State University

**Tags** - Functions, Linear, Quadratic, Motion Detector

**Materials** - Go!Motion sensor, Fathom, Logger Lite (if using VCL), five cars, two computers

**Description**: In this activity students, working in small groups, will conduct an experiment in which they formulate conjectures to determine which variables influence the velocity and total distance traveled of a car rolling down a ramp. They will test their conjectures by conducting a lab using Fathom and motion detectors and matchbox cars

**Activity Files: **

Faster and Farther Student.doc

Faster and Farther Template.docx

**Lesson Title: **Linear Equations and Real World Meanings of Slope

**Submitted By: **Brittany Bell

**Role Model Video Pairing: ** Transportation Roadways and Vertical Curves

**Keywords:** Linear Equations, Lines, Slopes, Variables, Critical Thinking

**Alignment to Common Core: **

**Students will interpret functions that arise in applications in terms of the context.**

**F-IF.4 **For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

**F-IF.5 **Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

**F-IF.6 **Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

**F-IF.9 **Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

**Students will build a function that models a relationship between two quantities.**

**F-BF.1 **Write a function that describes a relationship between two quantities.

**Synopsis:**

You are taking a nice drive in your beautiful car, when suddenly your brakes fail and your car is driving out of control. This activity will allow you to test several different surfaces to see which one would be ideal to safely stop your car.

You will simulate several “test drives” onto different available surfaces and determine which surface provides the best and safest stopping material for your “vehicle”.

**Materials:** One (1) toy car (bigger than a matchbox car works best), One (1) cardboard ramp approximately 6 inches, Go! Motion detector, Laptop with Fathom connection and Logger Lite, At least 3 different surfaces

**Activity Files: **

**Lesson Title: **Investigating Screen Brightness LCD Light and Holography

**Role Model Video** – LCD Light and Holography

**Tags** – Linear Functions, Modeling, Exponential Functions,

**Common Core Alignment** – F-IF 4-7

**Synopsis** - This activity is designed to use the Vernier Light Sensor to create a model to represent the change in brightness level for a computer display screen. Some models may represent a linear relationship; others may represent an exponential relationship.

**Materials** - computer screen(s) or cell phone(s) with brightness adjusting capabilities, fathom, logger lite, vcl, go!Link, Vernier Light Sensor

**Notes** - Activity works best with groups of 3. Roles include: 1) student to hold the sensor, 2) student change the brightness level, and 3) a student to monitor experiment and manage data in Fathom/Logger Lite.

**Activity Files: **

Investigating Screen Brightness.docx

Light Intensity of a Computer.ftm

**Lesson Title: **Gem of a Gym, Applying Systems of Equations

**Submitted By: **Candace Bailey

**Description: **The lesson plan attached is an application of systems of equations. Students will research gym memerships. Following their collection of data, they will compare the costs of different plans if a gym has more than one plan as well as compare memberships from gym to gym.

Students will find out which gym is the best to join for a certain amount of time. Students will be working in small groups (2 - 4) to research and create tables and graphs for the different options/gyms in Fathom.

Students will also be using Fathom to analyze and interpret the graphs created (and the least-squares line to find where graphs intersect).

**Common Core Alignment** - A.REI.6 Solve system of equations, A.REI.1.2 Represent and solve equations and inequalities graphically

**Notes** - Activity works best with groups of 2-4.

Roles include: 1) at least one student to research gym rates 2) student to input the data into Fathom and create the tables and graphs, and 3) a team leader to keep the group organized and on task by reading the activity displayed on their computer.

**Activity File:**

**Lesson Title: **Ball Bouncing The Quadratic and Exponential Relationships

**Submitted By: **Kevin McDaniel

**Description: **Attached you will find a Word document with Fathom Screen Shots that go through a lab that using Fathom and different types of balls. The student will be able to run a lab and find quadratic and exponential functions related to data collected. A major topic of discussion will be the a,h,k variables of a quadratic as well as the a,b variables of an exponential. A final discovery should be the idea of the "b" value of an exponential and it's relationship to loss of energy due to gravity.

**Activity File: **

Fathom Ball Bounce ExpQuad.docx

**Lesson Title: **Energy Consumption

**Description: **Exponential function activity to pair with role model video by systems engineer Joe DeCarolis.

**Activity Files:**

**Lesson Title: **Angry Birds: The Parabolic Version

**Role Model Video:** Video Game Production Designer- Shaun McCabe

**Keyword:** Quadratics

**Common Core Standards: **

A. SSSE. 3a,3b, 3c

A. CED. 1, 2, 3, 4

F.IF. 4, 5, 6, 7, 8, 9

**Synopsis:** The making of video games often involves a lot of math concepts. This lessons uses the idea of a very popular game today, Angry Birds! The birds are always bombing those pigs! The fight path of each bird just happens to be parabolic. In this lesson, the students will use Fathom to find the flight path.

**Notes:** Students should have worked with Fathom some and understand the basic working of the programs and its menus. You could extend this lesson by using the motion detector probes and collecting your down data by setting up your own game.

**Activity File:**

**Lesson Title: **Exploring Families of Graphs

**Submitted By: **Anna Head

**Role Model Video: **Biomedical Engineer - Greg Sawicki, NCSU

**Common Core Standards**: Math F-IF 1, 4, 6, 7, 8, 9; Math F-LE 1, 2, 3

**Synopsis:** This activity asks students to creates several functions using a motion detector. They will discover how time and distance traveled can be used to create linear, quadratic, and exponential graphs.

**Materials:** motion detector, Fathom software, computer, large flat surface (large piece of cardboard works great)

**Notes:** This activity can be used with beginners. The instructions are very basic and easy to follow.

**Activity Files: **

**Lesson Title: **Analyzing Quadratic Graphs

**Submitted By: **Anna Head

**Role Model Video: **Transportation Roadways and Vertical Curves

**Common Core Standards**: Math F-IF 4 7, 8; Math F-BF 1, 3

**Synopsis:** This activity asks students to create quadratic models using motion detectors and a bouncing ball, then asks them to find the equation of best fit for the data. They will explore the affects of the coefficients of the quadratic equation on the graph.

**Materials:** motion detector, ball, Fathom

**Activity File:**

**Note:** Students will need minimal experience with Fathom.

**Lesson Title: **Modeling Functions

**Submitted By:** Katie Mullins

**Role Model Videos: **IBM Worldwide Client Support, Vice President - Wendy Toh and Engineering Careers - Windlift,

**Common Core Standards:** Math F-IF 1, 4, 6, 7, 8, 9; Math F-LE 1, 2, 3

**Synopsis:** This activity has the students creating ten sepecific funcitons using the motion detector. By creating the graphs, the students will make conjectures about how time influences the distance that is traveled.

**Materials:** motion detector, Fathom software, computer, large piece of poster board or card board

**Notes:** This activity can be used with little to no Fathom experience.

**Activity File: **

**Lesson Title: **Modeling Quadratic Functions

**Submitted By: **Anna Head

**Role Model Videos: **Biomedical Engineer - Greg Sawicki, NCSU and Engineering Careers - Windlift

**Common Core Standards**: Math F-IF 4 7, 8; Math F-BF 1, 3

**Synopsis:** This activity has students creating a model of a quadratic function from a data set. They must use sliders to match their model as closely as possible to the data describing each transformation that happens when they manipulate the sliders. The students must also use their model (or graph) to make predictions and draw conclusions about the data in the context of the given situation.

**Materials:** Fathom

**Notes:** Students will need minimal experience with Fathom.

**Activity File: **

Modeling Quadratic Funtions.docx

**Lesson Title: **Modeling Exponential and Logarthmic Functions by Bouncing a Ball

**Submitted By: **Katie Mullins

**Role Model Video: **Any

**Common Core Standards**: Math F-IF 1, 3, 4, 5, 7, 8, 9; Math F-BF 1, 2, 3, 4, 5

**Synopsis:** The Fathom activity has students gathering data by bouncing a ball and transforming the data to represent the ball actually bouncing on the floor. Next, they are to gather the maximum values in a table and graph the values, showing an exponential model. From there, the students will create a model for the expoential data, then create an inverse for the data and the logarthmic model for the inversed data. The students will be required to make predictions and conjectures throughout the process.

**Materials:** bouncing ball, motion detector, Fathom

**Notes:** Students will need minimal experience with Fathom.

**Activity Files: **

Modeling Exponential and Logarithmic Functions.pdf

**Lesson Title: **Exponential Decay and Medication Dosage

**Role Model Video: **Oncology Nursing

**Description: **A fathom file, an activity worksheet and a lesson plan are attached. These are intended to be used in conjunction with the Oncology Nursing role model video and relate to how exponential decay impacts mecication dosage when a medication is to be administered at regular intervals over time.

**Activity Files: **

**Lesson Title:** Linearizing Data

**Submitted By: **Kevin McDaniel

**Description: **Attached you will find a Word Document and two Fathom documents. The word document and one of the fathom documents are for the students to have. The other fathom document is the Key. This is a great lab when teaching AFM and linearizing data. A student must have background knowledge of linearizing and fathom before attempting this lab.

**Activity Files:**

**Lesson Title: **Linear Equations and Line of Best Fit

**Submitted By: **Brittany Bell

**Role Model Video: **Fashion Designer

**Description: **In this lesson, students will find the correlation between arm span and height and relate this activity to the role model video of a fashion designer.

**Activity File: **

**Lesson Title: **Box Plots - Insurance

**Submitted By:** Heather Davis

**Role Model Video:** Analytics and Data Optimization

**Description: **In this activity, students will work in pairs to create and compare box plots then characterize the data as skewed left, skewed right, or symmetrical. Students will write up a report on their findings being sure to include graphs in their findings.

**Activity Files: **

Insurance Premiums Fathom Report.docx

**Lesson Title: **Meet in the Middel Systems of Equations

**Role Model Video** - Video Game Production Designer

**Tags** - System of Equations, Graphing Linear Equations, Application of Systems

**Common Core Alignment** - A.REI.6 Solve system of equations, A.REI.1.2 Represent and solve equations and inequalities graphically

**Synopsis** - This activity is designed to use systems of equations to solve a real-life problem with travel and intersection points. The students will have to create their own linear equations to represent each situation, then graph them to determine the solution. They will also be asked to analyze their graph and think about ways they could change/improve their outcome, using Fathom to test these ideas.

**Materials** -Fathom, Meet in the Middle Sheet

**Notes** - You could also use this with less "precise" data, and have the students determine a linear regression for each traveler first, then use that to predict a crossing point.

**Activity File: **

**Lesson Title: **Comparing City Temperatures

**Submitted By: **Anna Head

**Role Model Video: **Customer Value Analyst

**Key words:** mean, median, mode, 5 number summary, box plot, dot plots

**Common Core Standards:** S-ID 1-9, S-ID 1-6

**Materials:** Lesson handout, Student worksheet, Fathom document

**Description: **This activity uses Fathom to analyze city temperatures to compare mean, median, and mode. It can be paired with Customer Vaue Analyst video.

I found this activity online at http://jwilson.coe.uga.edu/EMAT6680Fa06/Parker/Fathom/Fathom-Mac.htm. It was created by Kelli Parker. It includes a lesson plan, student handout, and Fathom document with data. Students who are fairly new at Fathom should be able to complete this activity.

**Activity Files: **

Comparing City Temperatures.doc

Comparing City Temperatures Student Worksheet.doc

Comparing City Temperatures.ftm

**Lesson Title: **Systems of Equations - Big Business Project

**Submitted By: **Felicia Persky

**Role Model Video: **Systems Biologist

**Description: **Students will need to design their own business product and develop their financial business model.

**Activity File:**

Systems of Equations - Big Business Project

**Lesson Title: **Quadratic Exploration

**Submitted By: **Candace Bailey

**Description: **In this activity, students will plot a set of ordered pairs. They will explore the standard form of the quadratic equation as well as the vertex form of the equation through the use of sliders. With Fathom, the students will try to minimize the sums of the squares of the residuals between the expected value and the quadratic equation. There are several questions on the word document, meant to make the students think about how each of the values affect the graph of the quadratic equation. The students should be able to see what effect each of the values have on the graph of the parabola as well as how the values relate to the vertex, the roots/solutions/zeros.

It is suggested that after the students explore in small groups/pairs, that you come back and discuss the findings as a class.

This would be helpful before students get out of the unit on quadratics. There could be other questions that could be added in (about y-intercept, zeros/roots/solutions, etc.).

**Activity File: **

**Lesson Title: **NBA Top Thirty

**Submitted By: **Felicia Persky

**Role Model Video: **Analytics and Data Optimiztion

**Description: **Using the data from the National Basketball Association, let's draw some conclusions about these players.

**Activity File: **

**Lesson Title: **Runners Slope

**Submitted By: **Pamela Edwards

**Role Model Video: **Biomedical Engineer

**Algebra 1 with Fathom Activity**: Runners- Slope

**Synopsis:** Students will complete the Fathom activity to get a deeper understanding of slope, steepness of a line and being able to determine the slope directly from the graph based on observations of the graph of the line

**Activity File: **

**Lesson Title: **Model Rockets

**Submitted By:** Pamela Edwards

**Role Model Video:** Windlift, Robert Creighton

**Common Core Standards: **F.IF.7

**Synopsis:** This activity attached below is designed to use Fathom software to record a controlled experiment involving bottle rockets. Each trial will use a different percentage of water capacity in the bottle to discover the amount of water that will give the rocket maximum height. It will help model quadratic functions and interpret the effects of controlled input values on each output value.

**Activity File: **

**Lesson Title: **System of Equations, High Jump Records

**Submitted By: **Pamela Edwards

**Role Model Video: **Video Game Production Designer - Shaun McCabe

**Common Core Standard: **FI.F.7

**Description: ** This activity will be used to guide the students through solving system of equations in a real world problem.

**Activity File:**

**Lesson Title: **Polynomials and Polynomial Equations: Predicting the Future of Energy

**Submitted By: **Dwayne Jackson

**Role Model Video: **Systems Engineer - Joe DeCarolis, NCSU

**Keywords:** linear Programing, Rational Expressions, Polynomial Functions

**Common Core Standards: **N.Q.1, N.Q.2, N.Q.3, N.CN.9, A.APR.1, A.APR.2, A.APR.3, F.IF.1, F.IF.2, F.IF.3, F.IF.4, F.IF.7

**Synopsis:** The Student will need to analyze the behavior of Polynomial Functions. The video of System engineer deals with the use of practice patterns ( algebra Models ) of Energy being ran in order to forecast and predict the energy used based on variables. The student will need to use fantom to predict the behavior of function with the change of degrees and coefficients.

Notes: Students should have worked with Fathom some and understand the basic working of the programs and its menus.

Predicting the Future of energy Polynomial Functions**Goal:** To predict the future of the polynomial function by changing the degree, and coefficients.**Materials:** Paper with polynomial patterns, fantom, pencil**Directions:** 1. You are to graph the polynomials functions in fantom. 2. Analyze the graph with each change in degree and coefficient. 3. Note the beginning and the ending of each function with each change.

Polynomial Patterns!! ! ! ! Name:

Using Fathom, graph the functions below. In the table, record the requested information for each function.

**Activity File:**

Polynomials and Polynomial Equations: Predicting the Future of Energy

**Lesson Title: **Inverse Functions

**Submitted By: **Dwayne Jackson

**Keywords:** Inverse Functions, Radicals, and Roots

**Role model Video: **LCD Light and Holography - Michael Escuti

**Activity File:**

**Lesson Title: **What Price Should You Sell Your Nutrition Drink?

**Submitted By: **Seth Risinger

**Description: **Here is a lesson with an accompanying Fathom file that allows students to use both linear and quadratic models to determine the best price for their new nutrition drink.

**Activity Files:**

Nutrition Drink Quadratic Lesson

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