Getting Started

TI InterActive!

Microsoft, Windows, Windows NT, Abode, Acrobat, and Reader are trademarks of their respective owners. TI InterActive! contains Formula One from Visual Components. Copyright 1994-1997. All rights reserved. Exercise 5 data provided by Michael J. Shepston & Associates, www.scottsdalelaw.com
Copyright 2000, 2001, 2003 Texas Instruments Incorporated.
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Important

Texas Instruments makes no warranty, either express or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an as-is basis. In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this product. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.
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Table of Contents

Use the hands-on exercises in this book to familiarize yourself with the basic features of the TI InterActive! software.
Introduction... 4 Installing TI InterActive!... 5 Exercise 1: Performing Calculations in a Document. 10 Exercise 2: Storing Values as Variables.. 18 Exercise 3: Creating a Function-Graphing Assignment. 27 Exercise 4: Creating a Report... 33 Exercise 5: Analyzing Data from a Web Site.. 40 Exercise 6: Reviewing Miscellaneous Functions.. 46 Essential Skills for Using TI InterActive!.. 50 Where Do I Go from Here?... 58 Texas Instruments (TI) Support and Service Information. 59 Texas Instruments (TI) End-User License Agreement. 60 Index.... 62
Getting Started with TI InterActive!
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Introduction

TI InterActive! is a document-creation program with the math features of a powerful TI graphing handheld. It lets you build documents that contain not only text and pictures but also dynamically connected graphing and calculation objects.
What makes a TI InterActive! document different?
The interactive math objects in a TI InterActive! document set it apart from the documents that you create with other Windows applications. Your documents can use data from the Internet, TI data-collection tools, and supported TI graphing handhelds TI-83, TI-83 Plus, TI-83 Plus Silver Edition, TI-89, TI-92, TI-92 Plus, Voyage 200.

Internet data

Math calculations
Graphing Handheld Data-collection devices
What can I do with TI InterActive!?

Teachers can create:

Compelling classroom activities You can create activities that encourage learning by discovery. Captivating lessons You can design attractive lessons that cover necessary information while allowing exploration. Homework that encourages learning You can build printed, conventional assignments or live assignments in the form of TI InterActive! files that students can complete and return.

Students can create:

Informative reports You or your teacher can create preformatted labs and other types of reports. Attractive, clear homework papers You can create homework that shows the flow of your work with your results.
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Installing TI InterActive!
TI InterActive! can be installed from a TI InterActive! CD-ROM or from a file downloaded from the Web. Check the system requirements below, and follow the steps for the installation method that applies to you.

System requirements

The PC that you use to run TI InterActive! must have: Microsoft Windows 98, Windows 2000, Windows ME, Windows NT, or Windows XP. Microsoft Internet Explorer 5.5 or later. Available RAM: 16 MB for Windows 98 (20 MB RAM recommended), 32 MB for Windows ME or Windows NT, 64 MB for Windows 2000, or 128 MB for Windows XP. A hard disk with available storage space: 19 MB for TI InterActive! and 45111 MB for Internet Explorer (depending on installation type). A CD-ROM drive (if installing from a CD). A video monitor with VGA or better resolution. A mouse or mouse-compatible pointing device.

i (imaginary number)

Let variable x = value y Store value y to variable x

x := y yx or y =: x

Appearance of items in a Math Box
Using the TI Math Palette, you can change the appearance properties of the entry and the result independently. You can even hide the entry or its result. Some of the properties you can control include:
The font, size, and color used for the entry or result. Whether the result is displayed on the next line or the same line as the entry. Whether the entry or result is displayed in text format, such as (x^2)/(4y), or in math format, such as 4y.
Whether the entry or result is shown or hidden. You cannot hide both.
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Changing the appearance of a Math Box
In this example, you can change the appearance of items in a Math Box. Suppose you want to hide the expression or the result. next to the default option in the 1. Click the down arrow Input box. Click Hide Input.
TIP: Once you evaluate the expression, the Input and Output settings return to the default settings.
2. To hide the result, click the down arrow next to the default option in the Output box. Click Hide Output.
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3. Click (or on the Math Palette menu, click Edit 4 Properties) to modify properties such as scaling factors, font type, size, and color.
Saving a TI InterActive! document
TI InterActive! uses a.tii extension to identify its documents. 1. On the TI InterActive! toolbar, click the Save button Because you have not yet saved this document, TI InterActive! displays the Save As dialog box.
2. If necessary, navigate to the folder where you want to store the document. 3. In the File name box, type a name (such as first report) for the document. 4. Click Save. Note: You can also export a document to other formats. Choose Export from the File menu. The options are Html Web Page, Word Compatible, Rich Text Format, and Plain Text.
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Exercise 2: Storing Values as Variables
You can store a value as a named variable and then use the name to refer to that value in subsequent Math Boxes and graphs. When TI InterActive! evaluates an expression containing the name, it substitutes the value stored under that name.
Define a variable and assign a value to it. Display a variables value in a document. Remove a variable. Perform symbolic calculations. Reposition TI InterActive! objects in a document. Reset all variables.

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Creating a title for the assignment
1. At the left side of the formatting toolbar, click the down arrow next to the font name, and click Arial as the font for the assignment title. next to the text size and click 24 as 2. Click the down arrow the text size for the title. 3. Type the three title lines shown at the top of the sample on the previous page. Press the Enter key on the computer keyboard after each line. 4. Press Enter again to leave a blank line after the title.
Inserting and defining a graph
1. Click the down arrow next to the text size and click 10 as the size for the documents normal text. 2. Type Heres a graph of the function y=sin(x): and press Enter on the computer keyboard.
TIP: The Graph buttons toolbar image reflects the most recently used graph type. To create a new graph of that type, just click the button instead of the down arrow.
3. On the TI InterActive! toolbar, locate the Graph button next to it. A group of buttons is and click the down arrow displayed, representing the available graph types.
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4. Click the Y= button. The Functions editor is displayed along with the Graph window.
TIP: You can define many functions and choose to graph selected ones. Clear the checkmark for those that you dont want to graph.
5. In the uppermost text box of the Y= tab, type sin(x), and then press Enter on the computer keyboard. TI InterActive! graphs the function. 6. in the Graph Click the Save To Document button window to insert the graph into the document.

Resizing the graph

1. Click the graph in the document. A selection box appears around the graph to show that it is selected.
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NOTE: See page 51-54 for more details on formatting and using objects.

Enter statistical data using the List Editor. View plotted data. Calculate a regression and display the results. Graph a regression and analyze the data.
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Entering the data

You have recorded the following rates of sink after making several timed descents at different gliding speeds. You decide to enter the airspeeds into list L1 and the sink rates into L2.
Airspeeds (L1) Sink Rates (L2)
30 mph 40 mph 50 mph 60 mph 70 mph
600 ft./min. 550 ft./min. 700 ft./min. 875 ft./min. 1050 ft./min.
1. On the TI InterActive! toolbar, click the List button. The List Editor is displayed, with the empty cell at the top of list L1 selected and ready for an entry.
TIP: The tabs at the bottom of the editor let you switch quickly among list editing, matrix editing, and spreadsheet operations.
2. Type the first airspeed, 30, and then press the down arrow key on the computer keyboard to move to the next cell. 3. Type the next airspeed, press the down arrow key, and continue until you have entered all the airspeeds into L1. 4. Click the empty cell at the top of list L2. 5. Type the sink rates in the second column in a similar manner, with the number in each cell corresponding to the number in the first column as shown in the table above.
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6. Click the List Editors Close button into the document. LL875 1050

. The list is inserted

Plotting the glide performance
1. With the cursor positioned at the end of the list, press Enter to create a new line. 2. On the TI InterActive! toolbar, locate the Graph button next to it. A group of buttons is click the down arrow displayed, representing the available graph types. and
. The Functions editor is 3. Click the Scatter Plot button displayed along with a Graph window. 4. Make sure that the Stat Plots tab is selected. 5. In the uppermost text box, type L1 to specify it as the list containing the x coordinates. 6. Press the Tab key to move to the second text box, and type L2 to specify it as the list containing the y coordinates.
7. If it is not already checked, click the check box at the left to select this plot. TI InterActive! plots the data points in the Graph window. The points are not visible because they are outside the default viewing boundaries of the Graph window.

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Viewing the plotted data

1. In the Graph window, click the Zoom Statistics button. The viewing boundaries are adjusted automatically to show all the plotted data. 2. Click the Save To Document button to close the Graph window and insert the graph in the document.
Calculating a regression on the data
TI InterActive! lets you calculate several types of regressions on data stored in lists. In this exercise, you calculate a quartic regression on the plotted pairs of airspeeds (L1) and sink rates (L2). 1. Position the cursor between the list and the graph and press Enter on the computer keyboard. 2. Click the Stat Calculation Tool button on the TI InterActive! toolbar. The Statistics Calculation tool is displayed. 3. Click the down arrow next to Calculation Type, scroll down through the list, and click Quartic Regression.
After calculating a regression equation, you can graph it by entering this name in the graph.
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4. In the text box labeled X List, type L1. 5. In the text box labeled Y List, type L2.
TIP: Before saving results to the document, click the check boxes next to the results you want displayed.
6. Click Calculate to calculate the regression equation and its variables. 7. Click the Save Results button. TI InterActive! stores the results in variables, closes the Statistics Calculation tool, and displays the selected results in your document.
Graphing the regression equation
1. With the cursor positioned at the end of the regression results, press Enter on the computer keyboard to move the cursor to the next line. Type the heading Graphed regression equation:, and then press Enter again. 2. Double-click the graph that you inserted earlier. 3. Click the f(x) tab. 4. In the uppermost text box of the f(x) tab, type regEQ(x) and then press Enter on the computer keyboard. 5. Click the Zoom Fit button the viewing boundaries. in the Graph window to adjust
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6. In the text box for Ymin at the bottom of the graph, change the value to 450 and press Enter. This makes it easy to see the bottom of the regression curve.

Ymin text box

7. Click the Save To Document button to insert the graph into the document.

in the Graph window

Finding the planes minimum sink glide speed

TI InterActive! can find the minimum value of a function between specified starting and ending x values. For our data, the lowest point on the function marks the speed that produces the planes slowest rate of sink. 1. Double-click the graph you just created to activate the Graph window. 2. In the Graph window, click Calculate 8 Minimum. The Calculate Minimum window is displayed.
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3. You can enter starting and ending x values in the limit entry boxes or you can click and drag the limit lines on the graph.
Note: This is the glide speed that will keep the plane aloft for the longest period of time. However, it is not the speed that produces the greatest horizontal glide distance.
4. Click Calculate to find the minimum x and y values.
5. Type the following sentence to complete your report. The planes minimum-sink glide speed should be around 36 mph at 531 ft./min.
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Exercise 5: Analyzing Data from a Web Site
You can extract data directly from a Web page into a TI InterActive! document. This exercise is similar to the previous one, except that in this case you extract automobile braking distance data from a Web page and analyze it.
Data provided by Michael J. Shepston & Associates, http://www.scottsdalelaw.com/ shepston/braking.html
Select and extract data from a Web page. Plot the extracted data and calculate a regression. Display the plotted data and the regression equation together for visual comparison.
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Opening the sample Web page
You dont need a working Internet connection to perform this exercise. The sample Web page was copied to your hard disk during installation of TI InterActive!. 1. On the TI InterActive! toolbar, click the New button TI InterActive! displays a new, blank document.
2. Type the title Effect of Speed on Braking Distance at the top of the page, and press Enter on the computer keyboard. 3. Type the heading Data extracted from braking.htm:, and press Enter on the computer keyboard. 4. Click the Web Browser button browser opens. The TI InterActive!
5. On the browsers menu, click File 8 Open. 6. If necessary, navigate to the folder in which you installed TI InterActive!. 7. Click the filename braking.htm, and click Open. The browser displays a page with a table of braking distance data.

Picture Object

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Saving objects

Objects can be saved to the document to preserve their characteristics at any time. In this way, the saved information may be modified and updated to facilitate mathematical exploration. Some objects, such as the Math Box, are automatically saved to the document upon entering information. Other objects, such as the graph and list editors, require you to specifically save the information to the document. Look for the Save To Document item under the File menu in each component. A corresponding icon is also available. The icon is usually positioned in the leftmost position of the toolbar for the various object editors. is the Save To For example, Document icon for the List Editor. You might want to open an object so you can view or change the contents of the object. There are three ways to open an object that has been saved to a document.

Opening objects

Using the mouse, simply point to the object and then double click. Using the mouse, point to the object and single click. Then go to the menu and select Edit 8 Object 8 Open/Activate. Using the mouse, point to the object and then right click. A menu appears as shown below. Click on Open/Activate.
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Resizing objects

There are two ways to resize an object.
To resize an object that has been saved to the document, select the object with a right mouse click, select Format from the right-click menu, and change the resize settings as desired. Select the object and drag the resize handles to an appropriate size. Resize handles are the small squares located on the selection outline. In the example below, the diagonal arrow cursor next to the 6 indicates that the list object can be resized by dragging the mouse.
TIP: This method is especially useful for resizing list and spreadsheet objects.

Resize handle

Resize cursor

Moving objects

TIP: Use View 8 Nonprinting Characters, which displays line breaks as , to view the lines in a document.
To move an object, point to the object with your mouse and drag it to the new location. If the object does not drop at the location you want, it may be because there isnt an empty space or sufficient room. Since objects are inserted into the document as characters, there must be an empty space with sufficient room in which to place the object. Empty spaces are found next to existing objects or text and on empty lines. Sometimes it may appear that there is an empty line at the end of the document when there is not. There are two ways to delete objects that have been inserted in a TI InterActive! document.

Deleting objects

Point to the object using the mouse and single click. Then press the Delete key on the computer keyboard. For objects that have been inserted as inline-with-text objects (see next page), position the cursor to the right of the object and press the Backspace key on the computer keyboard.
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Using floating objects

TIP: The Edit 8 Object menu is also available via a right-mouse-click on the object.
The default for TI InterActive! is to create objects as inline-with-text objects. To place objects precisely in the document, convert them to floating objects. To convert objects to floating objects, select the object and then select one of the Edit 8 Object menu items.
Inline with text Causes the object to float in line with the text. Floating with text around Causes the object to float on the page with text or other inline objects flowing around it. Floating with text top & bottom Causes the object to float on the page with text or another inline object above and below it.

Inline with text

Floating with text around
Floating with text top & bottom
To move a floating object, drag the object with the mouse to the desired location. For additional control, select the object and use the arrow keys on the computer keyboard to position the object on the page. If two or more objects are floating objects, they can be placed adjacent to each other or overlapping. Once an object is changed to floating and placed in the document, it does not change its position unless you move it.
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Math updates

The TI InterActive! math system is dynamic and performs updates of all variables whenever a new object is defined, modified, or moved. This feature enables new ways in which to illustrate ideas and concepts. It may also require some experience in order to know what to expect. Each object has an evaluation point that determines when its information is available for evaluation by the math system. Evaluations occur in a specific order.

Objects whose evaluation point appears above or to the left of other objects evaluation points are evaluated first. Subsequent objects are evaluated in this spatial order until all objects in the document are evaluated.
This evaluation occurs many times during the course of creating or editing a document. The example below illustrates the importance of the math evaluation order.

Document 1 Document 2

In Document 1, a is defined as 20 and 30 in consecutive Math Boxes on the same line. In Document 2, the definition order is reversed, and a is defined as 30 and 20, again in consecutive Math Boxes on the same line. The position of the second Math Box is significant to the evaluation of the third Math Box, which contains the expression factor(a). In the first document, a is equal to 30 when the third Math Box is evaluated. In the second document, a is equal to 20 when the third Math Box is evaluated.
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An additional aspect of math updates is the location of the evaluation points for each object. For all objects (except the Math Box, graph, and matrix), the evaluation point is located at the topleft corner of the object. For the Math Box, graph, and matrix, the evaluation point is located at the bottom-right corner. To view the evaluation points in a document, select the View 8 Nonprinting Characters menu option. A small dot displayed on the object indicates its evaluation point.
It is important to review the default preferences when you first install TI InterActive! This will help you understand the results that you see. Go to the Edit 8 Preferences menu to select preferences for the following items.
Document Math Box Graph List Editor Table Web Browser Screen Capture
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Using the catalog

The Catalog, found in the Math Palette, includes information and examples for every TI InterActive! math command. , or select To open it, select the Catalog icon Tools 8 Command Catalog on the Math Palette. Click the Details button to see examples for the selected command.
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Where Do I Go from Here?

Now that you have the skills for building TI InterActive! documents, you might want to explore more features. The builtin documentation, which is accessible through the Help menu and various Help buttons, can help you master the TI InterActive! software.

To find out more about:

Look here in online Help:
Using the math, algebra, and statistics functions not covered in this book Graphing parametric and polar equations

Functions & Instructions
Graphing: Creating a graph: Defining functions for graphing Matrices Spreadsheets Linking to a Graphing Handheld, CBL, CBL 2, or CBR
Creating and manipulating matrices Performing spreadsheet operations Capturing a handhelds screen or transferring data between TI InterActive! and a connected device Collecting samples from a connected CBL, CBL 2, or CBR data-collection tool Extracting data from a Web page
Linking to a Graphing Handheld, CBL, CBL 2, or CBR; Collecting and plotting Quick Data lists Web Browser: Extracting data from a web page Web Browser: Inserting a hyperlink in a document
Inserting a link to a Web page into a TI InterActive! document
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Texas Instruments (TI) Support and Service Information

For general information

Home Page: KnowledgeBase and E-mail Inquiries: Phone:

education.ti.com

education.ti.com/support
(800) TI-CARES (800) 842-2737 For U.S., Canada, Mexico, Puerto Rico, and Virgin Islands only education.ti.com/support (Click the International Information link.)
International Information:

For technical support

KnowledgeBase and Support by E-mail: Phone (not toll-free):
education.ti.com/support (972) 917-8324
For product (hardware) service
Customers in the US, Canada, Mexico, Puerto Rico, and Virgin Islands: Always contact TI Customer Support before returning a product for service. All other customers: Refer to the leaflet enclosed with this product (hardware) or contact your local TI retailer/distributor.
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Texas Instruments (TI) End-User License Agreement
END-USER LICENSE AGREEMENT
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If you paid a license fee for a Single User License, Licensor grants to you a personal, non-exclusive, nontransferable license to install and use the Program on a single computer. You may make one copy of the software for backup and archival purposes. You agree to reproduce all copyright and proprietary notices shown in the software and on the media. Unless otherwise expressly stated in the documentation, you may not duplicate such documentation. If you paid a license fee for an Educational Multiple User License, Licensor grants you a non-exclusive, non-transferable license to install and use the Program on the number of computers specified for the license fee you paid. You may make one copy of the software for backup and archival purposes. You agree to reproduce all copyright and proprietary notices shown in the software and on the media. Except as expressly stated herein or in the documentation, you may not duplicate such documentation. In cases where TI supplies the related documentation electronically you may print the same number of copies of the documentation as the number of computers specified for the license fee you paid. All the computers on which the Program is used must be located at a single Site. Each member of the institution faculty may also use a copy of the Program on an additional computer for the sole purpose of preparing course materials. If you paid a license fee for an Educational Site License, Licensor grants you a non-exclusive, nontransferable license to install and use the Program on all institution owned, leased or rented computers located at the Site for which the Program is licensed. You may make one copy of the software for backup and archival purposes. You agree to reproduce all copyright and proprietary notices shown in the software and on the media. Except as expressly stated herein or in the documentation, you may not duplicate such documentation. In cases where TI supplies the related documentation electronically you may print one copy of such documentation for each computer on which the Program is installed. Each member of the institution faculty may also use a copy of the Program on an additional computer for the sole purpose of preparing course materials.

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This Agreement will immediately terminate if you fail to comply with its terms. Upon termination of this Agreement, you agree to return or destroy the original package and all whole or partial copies of the Program in your possession and so certify in writing to TI. The export and re-export of United States original software and documentation is subject to the Export Administration Act of 1969 as amended. Compliance with such regulations is your responsibility. You agree that you do not intend to nor will you, directly or indirectly, export, re-export or transmit the Program or technical data to any country to which such export, re-export or transmission is restricted by any applicable United States regulation or statute, without the proper written consent or license, if required of the Bureau of Export Administration of the United States Department of Commerce, or such other governmental entity as may have jurisdiction over such export, re-export or transmission. If the Program is provided to the U.S. Government pursuant to a solicitation issued on or after December 1, 1995, the Program is provided with the commercial license rights and restrictions described elsewhere herein. If the Program is provided to the U.S. Government pursuant to a solicitation issued prior to December 1, 1995, the Program is provided with "Restricted Rights" as provided for in FAR, 48 CFR 52.227-14 (JUNE 1987) or DFAR, 48 CFR 252.227-7013 (OCT 1988), as applicable. Manufacturer is Texas Instruments Incorporated, 7800 Banner Drive, M/S 3962, Dallas, Texas 75251.

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Acrobat, 5 Browser, 8, 41, 49, 58 CBL, 5, 58 CBR, 5, 58 Character string, 21 command catalog, 57 Computation Mode, 12, 13 data-collection, 4, 58 deleting objects, 53 Edit, 17, 29, 33, 34, 35, 42, 48, 49 e-mail, 7, 8, 9 entering an expression, 14 entering and formatting text, 11 evaluating a math expression, 11 floating objects, 54 inline with text, 54 with text around, 54 with text top and bottom, 54 Font, 11, 15, 17, 28, 49 Function, 7, 10, 13, 15, 21, 23, 24, 27, 28, 29, 35, 38, 42, 45, 46, 58 Graph, 4, 10, 18, 21, 27, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 42, 43, 44, 45, 58 inserting objects, 47, 51 installing TI InterActive!, 6 Internet, 4, 5, 8, 9, 41 Internet Explorer, 5 landscape, 49 List, 7, 15, 21, 22, 23, 33, 34, 35, 36, 37, 42, 43, 58 List Editor, 49, 50, 52, 56 Math Box, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 24, 49 changing the appearance of, 16 math object, 4, 21, 22 Math Palette, 10, 11, 12, 14, 15, 19, 25 math updates, 55 Matrix, 21 Microsoft, 5 Minimum, 38 Mode Settings, 12, 13 mouse, 5, 14, 30, 32 moving objects, 53 Object Format, 48 objects
TII_GettingStarted.doc Getting Started with TI InterActive! Karen Davis Revised: 8/22/03 12:20 PM Printed: 8/25/03 8:04 AM Page 62 of 64
deleting, 53 floating, 54 inserting, 47, 51 moving, 53 opening, 52 resizing, 53 saving, 52 opening objects, 52 Parametric equations, 58 Polar equations, 58 portrait, 49 power regression, 36 printing documents, 49 regression, 7, 33, 36, 37, 40, 42, 43, 44, 45 resizing objects, 47, 53 Save, 10, 17, 29, 31, 36, 37, 38, 42, 43, 44, 45 saving objects, 52
Stat Plots, 35, 43, 44 Statistics, 33, 58 support and service, 59 supported file types, 47 system requirements, 5 Table, 3, 49 Text-wrapping, 46, 48 TI Connect, 5 TI Connectivity Cable, 5 toolbar, 7, 8, 11, 12, 17, 19, 28, 30, 31, 32, 34, 35, 36, 41, 42, 43, 44, 47, 48, 49 USB, 5 Variable, 7, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 37, 44 Web, 5, 7, 8, 40, 41, 42, 49, 58 Windows, 1, 4, 8 Windows 2000, 5 Windows 98, 5 Windows ME, 5
Scatter Plot, 35, 42 Windows NT, 5 Screen Capture, 49 Windows XP, 5 setting preferences, 49, 56 zeros, 27 Stat Calculation, 37, 43 Zoom, 27, 30, 31, 36, 37, 43
TII_GettingStarted.doc Getting Started with TI InterActive! Karen Davis Revised: 8/22/03 12:20 PM Printed: 8/25/03 8:04 AM Page 63 of 64

About the Authors

CHRIS BRUENINGSEN is Head of Upper School at Nichols School in Buffalo, New York. In 1996, he received the Presidential Award for Excellence in Mathematics Teaching and was a Member of the NCTM Task Force on Integrated Mathematics. He has taught math and science to all levels of middle and high school students and has co-authored several Texas Instruments technology workbooks. He has also written a number of articles for math and science journals and speaks frequently at educational conferences. BILL BOWER is a teacher and Chairman of the Mathematics Department at The Kiski School in Saltsburg, Pennsylvania. Throughout his 19-year career he has taught all levels of high school math. In recent years, graphing calculator technology has become an integral part of his teaching. He is a co-author of Math and Science in Motion: Activities for Middle School. RON ARMONTROUT is a teacher and chair of the mathematics department at The Peddie School in Hightstown, New Jersey. In 1986, he was a Woodrow Wilson fellow at Princeton University and was a site leader in the NSF funded Boston College Discrete Mathematics for Secondary School Teachers project. He co-authored the How Should Algebra Be Taught? section of the ALGEBRA for the 21st CENTURY report published by NCTM. He has taught math to all levels of middle and high school students and speaks frequently at mathematics conferences. LIZ SUMNER is an Academic Technology Specialist at Nichols School in Buffalo, New York. She works closely with teachers, helping them prepare lesson plans with strong integration of technology. She also creates materials for and conducts inservice workshops on a variety of software products, such as Microsoft Office 2000. She is the schools webmaster and has authored numerous web sites.

Getting Started

About TI InterActive!
TI InterActive! is a user-friendly, interactive computer software program that enables high school and college teachers and students to easily investigate ideas in mathematics and science. Teachers can enhance students learning through interactive lessons that encourage exploration, visualization, data analysis, and writing. TI InterActive! can help students master math and science concepts and improve problem-solving skills.

Features

Word processor with integrated math system TI graphing calculator functionality Symbolic Computer Algebra System Integrated Web browser Data editor with spreadsheet Calculator connectivity

Things to Know

Math Box
The Math Box enables you to perform mathematical calculations and integrate those with other features of TI InterActive!, such as lists and graphs. The Math Box must be positioned above the list or graph you are working with in the TI InterActive! document. To see how changes in a Math Box affect a graph, position the Math Box above the graph, make your changes, then examine how those changes instantly update the graph.

Collecting the Data

Place the motion detector on a table or desk and stand at least 50 cm from it. Aim the motion detector at the walker as shown in the illustration below.

Motion detector

When you are ready to start collecting data, click Run in the Quick Data dialog box and start walking away from the motion detector at a slow, steady pace. You will have 10 seconds to collect the data. When data collection is done, click the Zoom Statistics button. The viewing boundaries adjust automatically to show all the plotted data. You should also see the Functions dialog box as shown below.
The plot of straight-line distance versus time should be linear. If you are not satisfied with your data, click Run in the Quick Data dialog box to perform another trial. If you are satisfied with your plot, move to the box below the graph and enter a 0, then press Enter. This will change the minimum value of y to 0 and allow you to see the x-axis. You can make a sketch of your time versus distance data plot on one of the blank grids in the Appendix. Label the horizontal and vertical axes on your sketch. Click the Save to Document button document. to save the graph in your TI InterActive!
The slope-intercept form of a linear equation is: Y = MX + B where M is the slope or steepness of the line and B is the y-intercept or the starting value. In this activity, the control variable, X, represents time, and Y represents distance. Press and use the right and left arrow keys in the Trace Value dialog box or use your keyboard to move the cursor along your distance versus time plot. Identify the starting value (the Y-value when X = 0) and record this below as the intercept, B. B=
Since you have a value for B to find the equation of the line that fits your data, you will use a guess-and-check method to determine the value of M. With your mouse, highlight the B value in the Trace window and press Ctrl+C to copy it. Close the Trace dialog box, and click the f(x) tab in the upper left corner of the Functions dialog box. Start with an initial guess of M = 1. Type f(x):= 1*x + B (your value of B) in the uppermost text box of the f(x) tab. Press Ctrl+V to paste your B value. Record your guess for M in the box below. For example, f(x):= 1*x +.599289. Press Enter to superimpose the graph on the plotted data. It is unlikely that your first guess for the value of M produced a model that matched the data closely. Click in the text box of the f(x) tab again and edit the linear function, replacing the old value, M = 1, with your new guess for M. Press Enter to update the graph. Repeat the guess-and-check procedure until you find an M-value that models the data well and record your guesses in the spaces below:

Guess #1 Guess #2 Guess #3 Guess #4 Final M-value
Using this value of M and the B-value determined in questions 1 and 2, complete the slope-intercept form of the equation and record it below.
Another way to get a linear function model for the data is to press again. Move along the plot with the arrow keys and identify two points (x1, y1) and (x2, y2) and record them below. Try to pick the points that are not too close together.

x1 y1 x2 y2

When the coordinates of two points on the same line are known, the slope of the line can be computed by finding the difference in y-values divided by the difference in x-values: slope = y2 y1 x2 x1
Use this formula to compute the slope of the linear plot and record the result below.

slope =

How does this value compare with the value of M you found experimentally in question 2?
TI InterActive! lets you check the values of M and B you just found by calculating the line of best fit. Close the Graph window to return to the Data Editor. Click Statistical Regressions. Click the down arrow next to Calculation Type, scroll down, and click on Linear Regression (ax + b). In the text box labeled X List, type TIME; in the box labeled Y List, type DISTANCE. Click Calculate to find the regression equation, y = ax + b and its variables. Record the regression equation values of a and b in the table below.

y = ax + b a= b=

Click the Save To Document button. TI InterActive! stores the results in variables, closes the Statistical Regressions tool, and displays the selected results in your document. How does the value of a in the linear regression equation compare with the M-value you found by guess-and-check?
How does the value of b compare with the y-intercept value, B, you identified earlier? Explain.
Double-click on the graph in the TI InterActive! document to refresh the Graph window. In the second text box of the f(x) tab, type f(x):= regEQ(x) and press Enter. TI InterActive! graphs the equation that was created as the Stat Regression result. Which equation seems to fit the data better? Which equation is a better linear function model? Why?
Remember, slope is defined as change in y-values divided by change in x-values. Complete the following statement about slope for the linear data set you collected. In this activity, slope represents a change in ______________________________ divided by a change in ______________________________. Based on this statement, what are the units of measurement for the slope in this activity?
As mentioned earlier, the intercept value, B, can be interpreted as the starting position or the starting distance from the motion detector. What does the value of M represent physically? (Hint: Think about the units of measurement for the slope you described in question 6). Save and print your TI InterActive! document.
Change your rate of walking speed and redo the activity with this new data. Describe any differences in the linear models. Start about 3.5 meters away from the motion detector and walk towards it. Describe any differences in the linear models. Stand in front of the motion detector and do not move. Describe any differences in the linear models.

In science class, you have probably used the equation: distance = rate time. This is really the same as the equation y = kx, because the y-values represent total distance traveled and the x-values represent total elapsed time. For this activity, what is the real-world meaning of the k value you computed earlier using the guess-and-check method? What are the units of measure for the k value?
You probably noticed that increasing and decreasing the constant of variation, k, changes the steepness of the line you are graphing. For this reason, the constant k in the linear equation y = kx is called the slope of the line. Using guess-and-check, you determined an overall slope for the train data. You also determined that this number approximates the average speed of the train over all of its ten stops.
We know, however, that the train was not traveling that exact speed between every city. You may be able to get a pretty good idea of when the train was moving fastest just by looking at the graph and finding the steepest sections. You can use another feature of TI InterActive! to figure out where the train was going fastest and slowest. Mathematically, slope is defined as the change in y-values divided by the change in x-values, y/x. Click the Graph close box Save to Document button. Choose Yes when asked if you want save changes. Click the to save the graph in your TI InterActive! document.
To find the slope of the segment between each pair of points (the speed of the train between each of its stops), double-click on the gray box that reads L4. In the dialog box that appears, click in the Formula box and type deltaList(L3)/deltaList(L2), and click OK. The numbers that appear in list L4 represent the average speeds for the train between stops. Between which two cities was the train moving slowest? What was the average speed between these cities?
TI InterActive! lets you check the value of k you found by calculating the line of best fit.

a. b. c. d. e.

Click the Graph close box Click Statistical Regressions Click the down arrow
to return to the Data Editor.
next to Calculation Type, scroll down the list and click on
Linear Regression (ax + b).
In the text box labeled X List, type L2; the the box labeled Y List, type L3. Click Calculate to find the regression equation, y = ax + b, and its variables. Record the regression equation values of a and b below:
Click Save Results. TI InterActive! stores the results in variables, closes the Statistical Regressions tool, and displays the selected results in your document. How does the value of a in the linear regression equation compare with the k-value you found by guess-and-check?

In theory, what should the b-value from the regression equation be? Explain.
Do you think that the linear modeling equation you developed in this activity could be used to accurately predict when the train will arrive in New Orleans? (Hint: What happens to the train in Memphis?) What factors would you have to take into account if you wanted to use your equation to predict arrival times? Save and print your TI InterActive! document.
Edmund and Ted are going skiing for the weekend. After work, they pack the car and set off for their trip. Leaving town, they drive on a small road for 30 minutes at a constant speed of 40 mph. When they reach the highway, they speed up to 65 mph and drive for two hours. What is the average speed (total distance divided by total time)? Why isnt the answer the same as the average of the speeds: 52 mph? (Hint: Think about how long they were traveling at each speed). Suppose that, in the previous question, Edmund and Ted had to drive an additional 30 minutes at 30 mph on a windy road from the highway to the ski mountain. What is the average speed for the entire trip now? Tonya is going to Barbaras house for a slumber party, but has to stop and pick up Mary first. Tonya walks mile to Marys house in 5 minutes, but has to wait there while she packs her sleeping bag. Marys dad offers to drive them, but only if they sit down and try some of his experimental grapefruit and marshmallow cookies. By the time they explain to Marys dad that they would prefer a good walk to a stomach ache, 15 minutes have passed. They leave the house, and walk mile to Barbaras house in 10 minutes. What is the total distance for the trip? What is the total time (including the time they were at Marys house)? What is the average speed for the whole trip? What is the average speed for just the walking portion of the trip? Mr. Bryan is taking his dog Tater for a walk. They leave home and walk two blocks down Amherst Street in 3.6 minutes, then stop for 1 minute while Tater watches a neighbors cat. Next, they walk four blocks on Parkside Avenue in 7.5 minutes, three blocks on Tillinghast Place in 5.1 minutes, stop for 45 seconds so Tater can sniff a tree, and finally walk five blocks back home in 8.5 minutes. Assume that a block is 1/10 of a mile. What is the total distance for the trip? What is the total time (including the time when Tater was busy)? What is the average speed for the whole trip? What is the average speed for just the walking part of the trip?

TI InterActive! lets you check the value of k you just found by calculating the line of best fit.
Click the Save to Document Click Statistical Regressions Click the down arrow
button and return to the Data Editor.
next to Calculation Type, scroll down the list and click on Linear Regression (ax + b). In the text box labeled X List, type L1; in the box labeled Y List, type L2. Click Calculate to find the regression equation, y = ax + b, and its variables. Record the regression equation values of a and b below:
Click Save Results. TI InterActive! stores the results in variables, closes the Statistical Regressions tool, and displays the selected results in your document. Close the Data Editor.
How does the value of a in the linear regression equation compare with the k-value you found by guess-and-check?
What should the b-value from the regression equation be? Explain.
Drag the graph to position it below the Statistical Regressions result if necessary, and then double-click on the graph in the TI InterActive! document to refresh the Graph window. In the second text box of the f(x) tab, type f(x):= regeq(x) and press Enter. TI InterActive! graphs the equation that was created as the Statistical Regressions result. Which equation seems to fit the data better? Which equation is a better direct variation model? Why?
Use the direct variation modeling equation you found in this activity to predict the voltage reading corresponding to a 5 cm long graphite segment. Record this value in the table below as the predicted voltage reading.
Voltage Readings Predicted Actual
Test your prediction by positioning the red CBL voltage lead at the 5 cm mark on the graphite segment you used in this experiment. Be sure the CBL is in multimeter mode (or, if you are using the CBL 2, be sure that you have executed the DATAMATE program). Record this value in the table above as the actual voltage reading. How do these results compare?
Save and print your TI InterActive! document.
Repeat the experiment, but this time start with an 8 cm segment instead of a 12 cm segment of shaded with graphite paper. Take voltage readings every 2 cm. Note the value of the constant of variation, k, between voltage and segment length. Repeat for a 20 cm segment of graphite paper (take readings every 5 cm). Record the k-value. Does there appear to be a relationship between the total length of the shaded segment and the voltage of the battery?

solve(y=m*x+b, b)

The only variable in the equation should be b. The b at the end of the solve command tells the computer to solve the equation for b. Press Enter to execute the command. How does the b-value found by the computer compare to the value you found using basic algebra techniques?
Double-click on the graph in the TI InterActive! document to refresh the Graph window. Click the f(x) tab in the upper left corner of the Functions window. Type f(x):= m*x + b in the uppermost text box of the f(x) tab, using the numerical value for m and b from above. Press Enter to superimpose the graph on the plotted data. How well does the linear model you found fit the data set?
TI InterActive! lets you check the value of m and b you found by calculating the line of best fit.
Click the Graph close box Click Statistical Regressions

Click the down arrow

Linear Regression (ax + b). In the text box labeled X List, type L1. In the box
labeled Y List, type L2. Click Calculate to find the regression equation, y = ax + b, and its variables. Record the regression equation values of a and b below:
Click Save Results. TI InterActive! stores the results in variables, closes the Statistical Regressions tool, and displays the selected results in your document. How does the value of a in the linear regression equation compare with the m-value and b-value you found using algebraic techniques?
Double-click on the graph in the TI InterActive! document to refresh the Graph window. In the second text box of the f(x) tab, type f(x):= regeq(x) and then press Enter. TI InterActive! graphs the equation that was created as the Statistical Regressions Result together with the linear model you entered earlier. Which equation seems to fit the data better?
You can use the equations you found in this activity to predict a Fahrenheit temperature for any given Celsius temperature. Click in the upper-right
. Set corner of the Graph window to display the table screen. Click Table Setup the Independent Mode to Ask and the Dependent Mode to Auto, as shown below, then click OK.
An empty table is displayed. As you enter values for the independent variable (x), values for the dependent variable (y), will be generated using the equations in the function editor.
To start, type the number 100 (corresponding to 100 degrees Celsius, the boiling point for water) into the first x-cell, then click on the corresponding y-cell to display corresponding Fahrenheit temperature. Repeat for x = 22 (corresponding to 22 degrees Celsius, room temperature), and record your values in the second column of the table below.
Celsius temperature Fahrenheit temperature (model) Fahrenheit temperature (regression)
How do the results compare with known Fahrenheit temperatures for boiling water and room temperature?

Use the data you collected together with the TI InterActive! tools used in this activity to build a mathematical model that converts Fahrenheit temperatures to Celsius temperatures. Find a physical science or physics textbook that gives a conversion formula from Celsius temperatures to Fahrenheit temperatures. How does this conversion formula compare to the linear model you found in this activity?
Teacher Notes Activity 5: Two Hot, Two Cold
Internet Data Collection Tables Linear Function
Start by asking students to describe the differences between Celsius and Fahrenheit temperatures. Can they predict what a graph of Fahrenheit versus Celsius would look like? If you do not have access to the Internet, you can use temperature listings in USA TODAY for data.
City Celsius Temperature Dallas, Texas (high) Dallas, Texas (low) Anchorage, Alaska (high) Anchorage, Alaska (low) New York, New York (high) New York, New York (low) Paris, France (high) Paris, France (low) -13 --1 Fahrenheit Temperature 8 -30

1. 2. 3. 4. 5. 6. 7.

m = 1.83. x = 22, y = 72; 72=1.83(72) + b; b = 31.76. b = 31.76. They have the same value. The line fits the data reasonably well. a = 1.845, b = 32.232. They match closely. The regression equation seems to fit the data slightly better. For C = 100, F(model) = 214.76 and F(regression) = 216.76. For C = 22, F(model) = 72.02 and F (regression) = 72.83. These values agree with the actual Fahrenheit values for boiling water (212 degrees F) and room temperature (about 70 degrees F).

Activity 6

Its a Small World
The populations of the United States and the world have grown rapidly during recent history. Many different factors can affect the rate at which a population changes, including the climate, technology, and the economy. It is important in a number of areas to be able to predict future populations. Different mathematical models are appropriate over different lengths of time.
In this activity, you will collect population data for the world on ten different days. You will then find a model for this data set assuming that over a short period of time the data can be considered to be linear. Finally, the model will be evaluated over a much longer period to determine the validity of the linear model.
Computer TI InterActive! software A working Internet connection Adobe Acrobat Reader software
Start TI InterActive! The software opens to a new, blank document. Title your document Small World, and add your name and the date. Click the Save button to save and name your document. to open the TI InterActive! browser. Click on the Data
Sites button. Under the Activity Book Links category, click on TI InterActive! Data Collection and Analysis. Choose Activity 6: Its a Small World.
Once the page has been loaded in the browser, click Population Clocks. On the POPClocks page you should see the current estimated population of the United States and of the world.

Record the date, day number, and population of the world in the table below. Use the number of days since the year 2000 began in column two, allowing January 1, 2000 to be day one. You will need ten different days on which to collect this data. Although taking readings at the same time each day might be the best technique, differences of a few hours either way will not have a significant effect on the model.
Date Day Number Population of the World
Click the List button , then click the empty cell at the top of list L1. Type the initial value and then press the down arrow key on the keyboard to move to the next cell. Continue entering the number of days since January 1, 2000 until you have entered all of the day values into L1. Click the empty cell at the top of list L2. Enter the corresponding population values for each day that you recorded in L1. You may need to resize L2 so you can read the data. To do this, click and drag the bar on the right side of the cell labeled L2. Click the Scatter Plot button and then click the Stat Plots tab. In the uppermost text box, type L1 to specify it as the list containing the x coordinates. Press the Tab key and move to the second text box. Type L2 to specify the list containing the y coordinates.
The plot of number of days versus the population of the world should appear to be linear in nature. Click on the Save to Document button TI InterActive! document. to copy this plot into your
Click on and move along the plot of your data using the arrow keys. Choose two points that would appear to lie on a line of best fit and make a note of the day numbers of these points below. Day # Day #
Record the day # and population for the two days you chose above as ordered pairs in the space below. Refer to the table or Data Editor for the exact values of the coordinates.
Click on Save to Document Math Box m=
to return to your TI InterActive! document. Click on
and use the two points you selected above and the slope formula
y2 y1 to find the slope of the line of best fit. Record your answer below. x2 x1
A simple way to describe slope is change in y over change in x. What is the real-world interpretation of the slope that you found in the question above?
To find the y-intercept of your linear model, you will need to solve the equation
y = mx + b for b. To do this, click on Math Box and enter solve(y=mx+b,b) substituting the value of the slope you found in step 3 for m and either of the points you selected in step 2 for x and y. Press Enter to solve for b, and record the solution below.
A simple way to describe the y-intercept is to say it is the point where the graph crosses the y-axis. In this model, what is the real-world meaning of the y-intercept?

Once the page has been loaded in the browser, scroll down to the And/Or section and check the box for the Ford Mustang. Scroll down to the bottom of the page and click on the CONTINUE button. You will use the Mustang convertible for your first investigation, so check the box for the convertible. (Just the plain convertible, nothing fancy.) Scroll down and click on the GO SEARCH button. You should find lots of data for the values of Mustang convertibles. When the page of Mustang data appears, scroll down to the data and drag the cursor over it to select. Click spreadsheet. to import the data into your TI InterActive!
Before you proceed, clean up the data in the spreadsheet.
Click on Edit, Replace. In the Find What text box, type Convertible and in the Replace With box, type a space. Click Replace All. This removes the word convertible from all the cells in your spreadsheet. With the Replace dialog box still open, type $ in the Find What text box. (Leave the space in the Replace With box.) Click Replace All. Click Close. Click on the B at the top of the second column. Press and hold the shift key, then click on columns C and D. Click on Edit, Delete. (In the Delete dialog box, Entire Column will be selected.) Click OK. Columns F and G become the new columns C and D. Using the directions in steps g and h, delete these new columns C and D.

e. f. g.

Click on the Save to Document button

Investigating the Data

Look through the data. You may need to drag the bottom handle of the spreadsheet frame to display all of the data. In your TI InterActive! document, record any observations you may have about the values of Mustang convertibles with respect to the year they were produced. In looking at the data, is it clear that the value of the Mustang convertible is a function of its age? In other words, its current value is dependent upon how old the car is. Many people consider old Mustangs to be classic cars. What do you think it means to be a classic car? Look at the data. At what time does the car change from being a classic car to being just another used car? Explain your answer in your TI InterActive! document.

Sites button. Under the Activity Book Links category, click on TI InterActive! Data Collection and Analysis. Choose Activity 10: Coffee Break.
Once the page has been loaded in the browser, scroll down to the heading The Company and click News. Then click Company Overview. Finally, click Timeline. Scroll through the Starbucks timeline narrative and note the total number of coffee shop locations each year, starting with 1987 and ending with 1997. Record this data in the table provided.

Year 1996 1997

Years since 11
Total Number of Starbucks Locations 1 17
Click the List button , and then click the empty cell at the top of list L1. Type the starting time value, 0, and then press the down arrow key to move to the next cell. Continue entering the number of years since 1986 until you have entered all of the time values into L1. Click the empty cell at the top of list L2. Type the total number of Starbucks locations for each corresponding time value in L1. Click the Scatter Plot button then click the Stat Plots tab. In the uppermost text box, type L1 to specify it as the list containing the x coordinates. Press the Tab key to move to the second text box, and type L2 to specify the list containing the y-coordinates.
The plot of number of coffee shops versus the number of years since 1986 should be curved upward.
If you are not satisfied with your results, check your data against the Web site again. If you are satisfied with your data, you can make a sketch of the coffee shops versus the number of years since 1986 data that you collected on a blank grid in the Appendix. Label the horizontal and vertical axes on your sketch.
When the relationship can be expressed in the form y = A B x, with B > 1, y is said to grow exponentially with x. The constant B is called the base. Notice that when x = 0, the y value is equal to A. Use your data table to determine the value of A and record it below: A=
In order to find an exponential model for data you collected, you will need to find an appropriate value for B using the guess-and-check method. Click the f(x) tab in the upper left corner of the Functions dialog box. For exponential growth, the model demands that B > 1, so start with an initial guess of B = 2. Type f(x):= A*2^x in the uppermost text box of the f(x) tab, using the numerical value of A from above. Press Enter to superimpose the graph on the plotted data. It is unlikely that your first guess for the value of B produced a model that matched the data closely. Click in the text box of the f(x) tab again and edit the exponential equation, replacing the old value, B = 2, with your new guess for B. Press Enter to update the graph. Repeat the guess-and-check procedure until you find a B-value that models the data well and record it in the space below (give your answer to two decimal places): B=

If the scatter plot looks confusing, click the Stat Plots tab of the Functions dialog box, then click the box to the right of the check box. This will bring up the Stat Plot Styles shown above. Change the Plot Type to XY line and click OK.
Your plot should appear to be a number of parabolas opening upward and rising from left to right. If you are satisfied with your data, click on Save to Document to save the graph in your TI InterActive! document. If you are not satisfied, close the Graph window and return to step 3 to collect a new data set.
The plot you recorded is a distance versus time graph. Convert the recorded distances to heights by subtracting each value from the distance to the floor. The distance to the floor will be the maximum distance point that you collected. Double-click on listname L1, type time in the Formula box, and click OK. Double-click on listname L2, type max(distance)-distance in the Formula box, and click OK. This will convert your distance readings to heights. Click the Graph button , and then click the Stat Plots tab of the Functions dialog box. In the uppermost text box, type L1 to specify it as the list containing the x coordinates. Press the Tab key and move to the second text box. Type L2 to specify the list containing the y coordinates. Press Enter, then click the Zoom Statistics button automatically to show all the plotted data. The viewing boundaries adjust
For this activity, you will analyze only one bounce of the ball. To choose a particular bounce, press and move to the first point on the left side of any bounce. Record the coordinates of this point in the table below. Continue to trace to the last point on the right side of the bounce and record its coordinates in the table below.
Click the Save to Document button Editor.
to close the graph and bring up the Data
Scroll downward, observing the values in L1 until you find the x-value of the first point you entered in the table above. Place the cursor in this cell. Click and drag down and over so that all the values in lists L1 and L2 are highlighted from the first value in the table above to the last value in the table above. Press Ctrl+C to copy the selected values from L1 and L2. Move the cursor to the first cell in L3 and press Ctrl+V to paste the selected values into L3 and L4. , and then click the Stat Plots tab. In the uppermost text box, type L3 to specify it as the list containing the x coordinates. Press the Tab key and move to the second text box. Type L4 to specify the list containing the y-coordinates.

10. Click the Graph button
11. Press Enter to turn the plot on. Click the Zoom Statistics button

. The viewing

boundaries adjust automatically to show all the plotted data.
12. Click the Save to Document button
to save this graph in your TI InterActive!

document.

13. Close the Data Editor.
In this activity, the ball bounced straight up and down beneath the detector. The original plot, however, seemed to depict a ball moving sideways, rising, and upside down. Explain why this is so.
Click on the graph of the single parabola in your TI InterActive! document and press to move along the plot of your parabola. Estimate the x- and y-coordinates of the vertex, round these values to the nearest hundredth, and record them in the table below.
x-coordinate y-coordinate
The theoretical model for an object in free fall is quadratic. We will attempt to fit the data with the vertex form of a quadratic equation y = a(x-h) 2+k. In this model the coordinates (h, k) represent the coordinates of the vertex and a is a constant. Substitute the values for h and k from the table above in this equation and record it below. y=
Close the Trace Value dialog box and click on the f(x) tab of the Functions dialog box. Enter the equation above, but substitute a -1 for a. Click Enter to graph the function. How well does it fit the data?
To obtain a good fit of the data you will need to adjust the value of a. Return to the Functions dialog box and try different values of a until you achieve a good model for the data. When you are satisfied with the fit, record your final values and equation below. a= h= k= y=
Describe how changing the value of a effects the shape of the parabola.
TI InterActive! can find its own model for the data by calculating the quadratic curve of best fit.
to close the Graph window.
Click on Stat Calculations Tool Click the down arrow Quadratic Regression.
In the text box labeled X List, type L3; in the box labeled Y List, type L4. Click Calculate to find the regression equation y = ax 2 + bx + c and its variables. Record the regression equation values of a, b, and c below: