Texas Instruments TI-83 Plus Silver Edition Manual

Topics in Algebra 1
Software Application
for the
TI-83 Plus and theTI-73
Student andTeacher
Classroom Materials
Chapters 1 – 5
ti

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³TIp and ³Try-It! are trademarks of Texas Instruments Incorporated.

Table of Contents
Introduction to Topics in Algebra 1
Note to Teachers i
Organization of Topics in Algebra 1 ii
Classroom Materials iii
NCTM Principles and Standards for School Mathematics iv
Acknowledgements iv
Installing This Application v
Deleting an Application v
Navigating Topics in Algebra 1 vi
Chapter 1: Number Sense
Section 1: Integers
Student Worksheet 1-1
Teacher Notes 1-6
Section 2: Rational Numbers
Student Worksheet 1-11
Teacher Notes 1-18
Section 3: Real Numbers
Student Worksheet 1-23
Teacher Notes 1-30
Chapter 2: Linear Equations
Section 1: Using Graphs & Tables
Student Worksheet 2-1
Teacher Notes 2-6
Section 2: Using Algebra
Student Worksheet 2-10
Teacher Notes 2-16

Chapter 3: Linear Functions
Section 1: Slope with Grid
Student Worksheet 3-1
Teacher Notes 3-6
Section 2: Slope Using Coordinates
Student Worksheet 3-10
Teacher Notes 3-14
Section 3: Slope Rate of Change
Student Worksheet 3-18
Teacher Notes 3-24
Section 4: Slope-Intercept Form
Student Worksheet 3-28
Teacher Notes 3-33
Chapter 4: Linear Inequalities: 1-Variable
Section 1: Using Graphs & Tables
Student Worksheet 4-1
Teacher Notes 4-6
Section 2: Using Algebra
Student Worksheet 4-11
Teacher Notes 4-17
Chapter 5: Linear Systems
Section 1: Using Graphs & Tables
Student Worksheet 5-1
Teacher Notes 5-8
Section 2: Using Algebra
Student Worksheet 5-15
Teacher Notes 5-28
³TIpsé
³TIpé1: Resetting Your Calculator 1-1
³TIpé2: Adjusting Your Calculator Settings 2-1
³TIpé3: Graphing a Function in the Standard Window 3-1
³TIpé4: Creating a Table 4-1
³TIpé5: Adjusting the Viewing Window 5-1
³TIpé6: Using Lists 6-1
³TIpé7: Creating a Statistical Plot 7-1
³TIpé8: Finding the Best Line of Fit for a Set of Data 8-1
³TIpé9: Sending and Receiving Data between Calculators 9-1
³TIpé10: Managing Your Calculator’s Memory 10-1

Topics in Algebra 1 © 2001 Texas Instruments Introduction i
Introduction to Topics in Algebra 1
Note to Teachers
Welcome to the Topics in Algebra 1 software application for the TI-83 Plus and TI-73 graphing
calculators. The application and Classroom Materials were designed to help students review and
reinforce selected concepts taught at the Algebra 1 level. Topics in Algebra 1 is easy to use, even
for inexperienced calculator users, and it encourages students to explore concepts on their own.
Navigating Topics in Algebra 1 (pages vi–ix) explains how to move around the application. You
may wish to copy these pages for your students.
We hope Topics in Algebra 1 proves useful to you and your students. All of your comments and
suggestions are appreciated. You can contact TI:
•Phone 1-800-TI-CARES (1-800-842-2737)
•E-mail [email protected]
•TI website education.ti.com

Topics in Algebra 1 © 2001 Texas Instruments Introduction ii
Organization of Topics in Algebra 1
Topics in Algebra 1 is organized in textbook fashion with chapters and sections arranged in
table-of-contents form.
Chapters Sections
1: Number Sense 1: Integers
2: Rational Numbers
3: Real Numbers
2: Linear Equations 1: Using Graphs & Tables
2: Using Algebra
3: Linear Functions 1: Slope with Grid
2: Slope Using Coordinates
3: Slope Rate of Change
4: Slope-Intercept Form
4: Linear Inequalities: 1-Variable 1: Using Graphs & Tables
2: Using Algebra
Note: Chapters can be installed and deleted individually. This provides flexibility, allowing calculators to have only the applications
students currently need.
Each section in the application contains three subsections.
•The
Overview presents definitions and concepts for teachers to use in class discussions and
for students to use for study and review. They contain animation and real-world examples.
•The
Observations show concepts or examples, followed by Write An Observation screens.
Students are asked to write in the space provided on the Student Worksheet their
observations about the content presented. Screens entitled Did you know display additional
information and facts about the current concept.
•The
Activities include interactive activities that reinforce the concepts covered in the section.
Many of the activities are in the form of games. Students can practice calculating equations
with integers, rational numbers, and real numbers, or they can find the equation of a line. The
application checks answers, gives a score, and provides students with the correct answer if
they are unable to answer a question correctly. In the Linear Functions chapter, students can
play a game called Screen Cross where they link to each other’s calculators and race to see
who finishes first.

Topics in Algebra 1 © 2001 Texas Instruments Introduction iii
Classroom Materials
The Topics in Algebra 1 Classroom Materials include Student Worksheets, Teacher Notes (with
answers), and ³TIpsé.
•Student Worksheets provide explanations and instructions to students about using the
application to review the concepts in the section. Each worksheet is divided into four parts—
Overview, Observations, Activities (which correspond to the subsections of the application),
and ³Try-It!éon Your TI-83 Plus or TI-73.
³Try-It!éactivities let students investigate specific features on the calculator related to the
section concepts. This includes step-by-step instructions with the exact keys to press to
complete each step and corresponding screen pictures. The screens shown in the ³Try-It!
activities are for the TI-83 Plus. Usually, the TI-73 display varies only slightly, and the
students should have no problems following the instructions. However, in the cases where
the two calculators vary, the ³Try-It! activities contain two separate exercises, one for each
of the two calculators. Therefore, you only need to copy the section appropriate for the
calculator that you use in your classroom.
•Teacher Notes give a brief explanation of the concepts covered in the section, some of the
common student errors that might be encountered, and answers to the questions on the
Student Worksheets. There are Teacher Notes for each Student Worksheet.
•³TIpséprovide keystroke examples for some of the more common tasks that you and your
students need for Algebra 1 and beyond. The ³TIps are intended to help students learn how
to use the features of the calculator. The ³TIps topics are:
³TIp 1: Resetting Your Calculator
³TIp 2: Adjusting Your Calculator Settings
³TIp 3: Graphing a Function in the Standard Window
³TIp 4: Creating a Table
³TIp 5: Adjusting the Viewing Window
³TIp 6: Using Lists
³TIp 7: Creating a Statistical Plot
³TIp 8: Finding the Best Line of Fit for a Set of Data
³TIp 9: Sending and Receiving Data between Calculators
³TIp 10: Managing Your Calculator’s Memory
When students need to learn how to use the feature being covered, you can distribute the
³TIps to them to make sure they are prepared for the lesson.

Topics in Algebra 1 © 2001 Texas Instruments Introduction iv
NCTM Principles and Standards for School Mathematics
The Topics in Algebra 1 application and the Classroom Materials were written with the
guidelines of the NCTM Principles and Standards for School Mathematics in mind. Attention
was paid to the expectations laid out for the Algebra Content Standard for the Algebra 1 level
that crosses the 6–8 and 9–12 grade bands.
Some examples include:
NCTM Standards and Expectations On the Application
To understand patterns, relations, and
functions.
Students see how battery voltage values in a
series can be represented by a linear function.
To model and solve contextualized problems
using various representations, such as graphs,
tables, and equations.
Students experience how to work with tables of
values, graphs, and linear equations to see the
multiple approaches to problem solving.
To analyze the nature of changes in quantities
in linear relationships.
Students determine the constant rate of change of
a diving submarine along each segment of its dive.
In addition, scored, interactive activities at the end of each section help reinforce the concepts
reviewed in the Overview and Observations subsections.
You can find the complete expectations for the Algebra Content Standard and for the various
grade bands set out by the NCTM at:
http://standards.nctm.org/document/appendix/alg.htm
You can view the NCTM Principles and Standards for School Mathematics online at:
http://standards.nctm.org/
Acknowledgements
Texas Instruments would like to thank these individuals for their support, ideas, and suggestions.
Sharon Cichocki Hamburg High School Hamburg, NY
Michael Corrigan Assumption Catholic School Jacksonville, FL
Cathy Jahr Westview High School Martin, TN
John LaMaster Indiana University-Purdue University Fort Wayne Fort Wayne, IN
Brenda Levert Academy for Academics and Arts Huntsville, AL
Nicol Reiner Roosevelt High School Sioux Falls, SD
Melissa Rowe South Grand Prairie High School Grand Prairie, TX
Bill Stiggers Cleveland Public Schools Cleveland, OH
Bob Tower Roosevelt High School Sioux Falls, SD

Topics in Algebra 1 © 2001 Texas Instruments Introduction v
Installing This Application
Students may install all four chapters as a unit (ALG1PRT1) or one or more of the chapters
individually (ALG1CH1, ALG1CH2, ALG1CH3, ALG1CH4). This provides flexibility, allowing
calculators to have only the applications students currently need. When two or more chapters are
installed separately, they each must be accessed directly from the Œmenu.
Installing this application requires TI-GRAPH LINKésoftware and link cable. A link cable can be
purchased from the online store:
http://epsstore.ti.com
If an Archive Full error message appears while installing Algebra 1 or one of the chapters, the
calculator does not have sufficient memory for the application. Applications and/or archived
variables must be deleted to make room (see below).
Deleting an Application
Deleting an application completely removes the application from the calculator. The space then
becomes available for a different application. The deleted application may be reloaded at a later
date. Before deleting an application from the calculator, it can be backed up to a PC using the
Link > Receive Flash Application menu in TI-GRAPH LINK. You can reload it to the calculator
later using the Link > Send Flash Software menu in TI-GRAPH LINK.
To delete an application or archived variable:
1. Press yLto display the MEMORY menu.
2. Select 2:Mem Mgmt/Del (4:Delete… on the TI-73).
3. Select A:Apps... or B:AppVars... (8:Apps... or 9:AppVars... on the TI-73).
4. Press †until the 4indicator is next to the item you wish to delete.
5. Press {(Íon the TI-73).
6. Select 2:Yes when asked Are You Sure?
7. Press y5to return to the Home screen.

Topics in Algebra 1 © 2001 Texas Instruments Introduction vi
Navigating Topics in Algebra 1
Starting the Application
1. Press
9to display the APPLICATIONS menu.
2. Press
#until ALG1PRT1 (or a chapter such as ALG1CH1)is highlighted, and then press bto
select it. The application title page is displayed.
3. Press any key to start the application.
A Table of Contents page is displayed. It is the Table of Contents from which you last exited
Algebra 1. You may select one of the items on the menu or press áUPâas often as necessary to go
to the Table of Contents screen that you need.
Table of Contents Screens
There are three types of Table of Contents screens—chapters, sections, and subsections.
When you select a chapter, the Algebra Sections screen is displayed. The number of sections
listed varies according to chapter.
When you select a section, the Algebra Subsections screen is displayed. The items listed are always
the same—Overview, Observations, and Activities.
Note: When you exit and re-enter Topics in Algebra 1, you return to the Table of Contents screen from which you exited.
Topics in Algebra 1 title page
A
lgebra Chapters
A
lgebra Sections
A
lgebra Subsections
Note: If you have installed the
chapters individually, only the current
chapter is shown on this screen.
Press Íto select the chapter.

Topics in Algebra 1 © 2001 Texas Instruments Introduction vii
Navigating Topics in Algebra 1 (continued)
Selecting the Chapter, Section, and Subsection You Want
To select from a Table of Contents screen, press #if necessary to highlight the name of the
chapter, section, or subsection, and then press b.
When the Overview, Observations, or Activities opening screen appears, press ~to begin.
Returning to the Table of Contents
From most Overview, Observations, or Activities screens, you can press -las many times
as necessary to return to the Table of Contents. You may then select one of the items on the
menu or press áUPâto go to higher levels of the Table of Contents.
Note: If you see áCONTâon the current screen, you must first press any key to continue.
Leaving the Application
To leave the application, press -las many times as needed to return to a Table of
Contents screen, and then press áEXITâ. When you re-enter the application, you return to this
Table of Contents screen.

Topics in Algebra 1 © 2001 Texas Instruments Introduction viii
Navigating Topics in Algebra 1 (continued)
Navigation Star
The navigation star is located on the bottom right of most Overview and Observations screens.
When the right and left arrows of the navigation star are flashing, press |and ~on the
calculator to page back and forward between screens. When the up and down arrows are
flashing, }and †are used to navigate vertical menus (see below).
Horizontal Menus
A horizontal menu may be displayed at the bottom of the screen. The menu items help you move
between screens in the application. The menu items change from one screen to another. The
following are the most frequently displayed menu items.
Menu Item Press To Do This
áEXITâoExit the application.
áUPâqMove up a level in the menu structure.
áHELPâsDisplay the
HELP MENU.
áMAINâoReturn to the previous screen from the HELP MENU.
áBACKâpReturn to the HELP MENU from a HELP explanation screen.
áMENUâoReturn to the previous menu screen.
áQUITâoQuit an activity.
To select a menu item, press the calculator key that corresponds to the menu item on the screen.
&'()*
* In these materials, the items
in the horizontal menus are
shown in angle brackets; for
example áEXITâ, áUPâ, and
áHELPâ.
The menu items change
from one screen to another.
On some screens, different
menu items are mapped to
the calculator keys.
These menu items
map to
these calculator keys. *
Horizontal
menu
Navigation star
Press ~to display the
next screen.

Topics in Algebra 1 © 2001 Texas Instruments Introduction ix
Navigating Topics in Algebra 1 (continued)
Vertical Menus
When the up and down arrows of the navigation star are flashing, press †and }on the
calculator to highlight an item in a vertical menu.
Some vertical menus only provide information. Other vertical menus are used for navigation. If
Select or Select & Press [Enter] is displayed, you can press Íto select an item or to see more
information.
áCONTâ
When you see áCONTâ(continue), you can press any key to go to the next screen.
HELP
From a Table of Contents screen, press áHELPâto view information about features of the
application. To select an item, press #to highlight it, and then press Í.
Continue
V
ertical menu
First item is highlighted.
A
s you press †and }to move
through the menu, additional
information is displayed to the
right of the menu.
Press Íto select the
second item on the vertical
menu and display the first
in a sequence of screens
for this selection.
Press áMENUâ(&) to
return to the menu screen.

Chapter 1: Number Sense Name
Section 1: Integers Date
Topics in Algebra 1 © 2001 Texas Instruments Student Worksheet 1-1
Number Sense: Integers Student Worksheet
Overview
The Overview introduces the topics covered in Observations and Activities. Scroll through the
Overview using "(!to review, if necessary). Read each screen carefully. Look for new terms,
definitions, and concepts.
Observations
The Observations illustrate number sense concepts relating to the set of integers. Scroll through
the Observations using "(!to review, if necessary). Read each screen carefully. When you
come to a Write an Observation screen, stop and write the answers to the questions on your
worksheet.
Observation 1
How far apart are the bird and the fish? Should your answer be
positive or negative? Write an explanation for your answers here.
Observation 2
What is the sign of the answer to the problem L3 QL11?
In your own words, state the rules for multiplying and dividing
signed numbers (shown in the grids on the next screens).

Chapter 1: Number Sense Name
Section 1: Integers Date
Topics in Algebra 1 © 2001 Texas Instruments Student Worksheet 1-2
Activities
The Activities help you practice integer concepts. You can select from two different activities—
What Is My Sign? and Integer Smash. Follow these steps to play the activity and complete your
worksheet.
1. Make sure you are in the Activities for this section.
2. Highlight an activity using $or #, and press b.
Scoring:Every correct
response earns 2 points.
The game automatically
ends if you have
answered incorrectly four
times (shown in the top
right corner), or you press
áQUITâto stop.
What Is My Sign?
1. In your head, quickly solve the sliding expression to
determine if the result is positive, negative, or zero.
2. As soon as you know the sign of the result, press #and $to
move the expression into the proper category on the left
(+, 0, or M). Once the expression is in the correct row, you can
press !to slide it quickly to the left. If the answer is
incorrect, the correct answer is displayed; press any key to
resume play.
3. Follow your teacher’s instructions for how long to play the
activity.
4. What was your score?
5. How many incorrect answers did you have?
(Shown in top right corner of the screen.)

Chapter 1: Number Sense Name
Section 1: Integers Date
Topics in Algebra 1 © 2001 Texas Instruments Student Worksheet 1-3
Activities (continued)
Scoring: You get two
attempts to solve each
problem. You earn 2
points for a correct
answer on the first try, 1
point for a correct answer
on the second try.
You can earn up to 10
points.
Integer Smash
1. Highlight a level (bronze = least difficult; gold = most
difficult), and press bto select it.
2. For bronze or silver levels only, press á+â, áNâ, á¦â, or á÷âto
select the operation you want to practice.
3. Enter the missing number (press Ìfor negative numbers)
and press b. If the answer is incorrect on the second
attempt, the correct answer is displayed; press any key to
resume play. As you play the activity, write each number
sentence and solution. Show your work here.
4. What level and operation (bronze and silver only) did you
play?
5. What was your score?

Chapter 1: Number Sense Name
Section 1: Integers Date
Topics in Algebra 1 © 2001 Texas Instruments Student Worksheet 1-4
³Try-It!éon Your TI.83 Plus or TI.73
Learn to use the subtraction key (¹), the negation key (Ì), and the absolute value function
(abs().
Use the negation and the subtraction keys to calculate M5 NM4.
To Do This Press Display (TI.83 Plus shown)
1. Exit the Topics in Algebra 1
application and clear the Home
screen.
yl
áEXITâ:
2. Calculate
M5 NM4.
Note: The negation key (Ì) and the subtraction key
(¹) are different.
Ì5 ¹Ì4
Í
Enter M5 NM3 QM2, first without using parentheses and then using parentheses.
To Do This Press Display (TI.83 Plus shown)
1. Calculate
M5 NM3 QM2.
Note: On the TI-73, notice the difference between
the xvariable key (I) and the multiplication
key (M).
Ì5 ¹Ì3 MÌ2
Í
2. Calculate
M5 N(M3 QM2).
Ì5 ¹
DÌ3 MÌ2 E
Í
3. Calculate (M5 NM3) QM2.
DÌ5 ¹Ì3 E
MÌ2
Í
The calculator uses the Order of Operations rules, which say that multiplication and division are
performed from left to right, and then addition and subtraction are performed from left to right.
Notice that multiplication was calculated before subtraction in the expression M5 NM3 QM2. Notice
that the expression M5 N(M3 QM2) has the same answer.
The calculator performs operations inside the parentheses before operations outside the
parentheses. Notice that the expression (M5 NM3) QM2 has a different answer than the expressions
M5 NM3 QM2 and M5 N(M3 QM2).

Chapter 1: Number Sense Name
Section 1: Integers Date
Topics in Algebra 1 © 2001 Texas Instruments Student Worksheet 1-5
³Try-It!éon Your TI.83 Plus or TI.73 (continued)
Use the absolute value (abs() function on the calculator to find the absolute value of M12.
To Do This Press Display (TI.83 Plus shown)
1. Find the absolute value of M12, which
is written as |M12 |.
Note: The 1NUM menu varies slightly from the
TI-73 to the TI-83 Plus.
1"
2. Select the absolute value (abs()
function. It is copied to the Home
screen.
1:abs(
3. Calculate the result. a12 E
Í
Additional problems—Calculate the following problems by hand, then check your answers
using the calculator. Remember to use the Order of Operations rules.
1. M4 + M12 QM10 = 2. 4
QM8 −M10 Q2 =
3. M30 ÷M5 −6 = 4. |M12 +M28 |=
5. |M4 QM8 NM10 Q2 |= 6. M|M3 N14 NM10 |=

Chapter 1: Number Sense Section 1: Integers
Topics in Algebra 1 © 2001 Texas Instruments Teacher Notes 1-6
Number Sense: Integers Teacher Notes
Objectives
•To illustrate the set of integers in a Venn diagram.
•To give an overview of the following definitions: the sign of a number, numbers of opposite
sign, and absolute value.
•To give illustrations of the sets of positive and negative integers, and zero.
•To review ordering and the additive inverse property.
•To show examples of addition, subtraction, multiplication, and division of integers.
Math Highlights
This section begins with a Venn diagram and follows with an illustration of the use of integers on
the Fahrenheit and Celsius scales. The temperature equivalencies shown are integer values.
Students are reminded that the absolute value operation is defined as the distance of the number
from zero. Examples of addition, subtraction, multiplication, and division operations are given. A
number line model is used for addition and subtraction. Subtraction uses the add-the-opposite
rule.
Common Student Errors
Students may have trouble identifying rules, such as the add-the-opposite rule for subtraction.
Note: The number line model for addition and subtraction is shown on the calculator when the Topics in Algebra 1 application is
installed.
Following are some activities to help students construct the rules for multiplication and division.
These activities are not part of the Topics in Algebra 1 application.
Pattern Development for Multiplication and Division
Investigation 1: What is the product of a positive and negative
number?
Begin by writing the product of two positive numbers, for example,
3 Q3 = 9. Keep decreasing the second term by 1 to create the sequence
of multiplication values shown to the right. Notice the values on the
right side of the number sentences decrease by 3.
Observation: The product of a positive and negative number is
negative.
3
Q3 = 9
3
Q2 = 6
3
Q1 = 3
3
Q0 = 0
3
QM1 = M3
3
QM2 = M6
3
QM3 = M9
. . .