Texas Instruments TI-15 User manual

Front
TI-15
A Guide for Teachers

TI.15:
A Guide for Teachers
Developed by
Texas Instruments Incorporated
Activities developed by
Jane Schielack

About the Author
Jane Schielack is an Associate Professor of Mathematics Education in the Department of Mathematics at
Texas A&M University. She developed the
Activities section and assisted in evaluating the appropriateness of
the examples in the
How to Use the TI-15 section of this guide.
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Copyright © 2000 Texas Instruments Incorporated.
Except for the specific rights granted herein, all rights are reserved.
Printed in the United States of America.
Automatic Power Down, APD, and EOS are trademarks of Texas Instruments Incorporated.

© 2000 TEXAS INSTRUMENTS INCORPORATED TI-15:A Guide for Teachers iii
Table of Contents 
CHAPTER PAGE
About the Teacher Guide ........................... v
About the TI-15 ........................................... vi
Activities................................................ 1
Patterns in Percent ....................................2
The ªKey
Fraction Forms ........................................... 6
Auto and Manual Mode
Comparing Costs........................................ 11
Division with quotient/remainder,
fraction, or decimal result
Number Shorthand ...................................15
Scientific Notation
Related Procedures..................................20
Constant operations
In the Range............................................... 24
Rounding
The Value of Place Value ..........................29
Place value
What’s the Problem?................................34
Number sentences, Problem solving
How to Use the TI.15 ....................... 38
1 Display, Scrolling, Order of
Operations, Parentheses..................39
2 Clearing and Correcting..................... 42
3 Mode Menus.........................................45
4 Basic Operations................................48
5 Constant Operations.........................55
6 Whole Numbers and Decimals..........63
7 Memory .................................................68
8 Fractions ............................................... 71
9 Percent................................................. 80
10 Pi.............................................................84
11 Powers and Square Roots ............... 88
CHAPTER PAGE
How to Use the TI-15 (continued)
12 Problem Solving: Auto Mode............ 94
13 Problem Solving: Manual Mode ......100
14 Place Value..........................................106
Appendix A ................................................A-1
Quick Reference to Keys
Appendix B.................................................B-1
Display Indicators
Appendix C ............................................... C-1
Error Messages
Appendix D ...............................................D-1
Support, Service, and Warranty

© 2000 TEXAS INSTRUMENTS INCORPORATED TI-15: A Guide for Teachers iv
About the Teacher Guide 
How the Teacher Guide is Organized
This guide consists of two sections: Activities
and How to Use the TI-15 . The Activities
section is a collection of activities for
integrating the TI-15 into mathematics
instruction.
How To Use the TI-15 is designed
to help you teach students how to use the
calculator.
Activities
The activities are designed to be teacher-
directed. They are intended to help develop
mathematical concepts while incorporating
the TI-15 as a teaching tool. Each activity is
self-contained and includes the following:
• An overview of the mathematical purpose
of the activity.
• The mathematical concepts being
developed.
• The materials needed to perform the
activity.
• A student activity sheet.
How to Use the TI.15
This section contains examples on
transparency masters. Chapters are
numbered and include the following:
• An introductory page describing the
calculator keys presented in the examples,
the location of those keys on the TI-15, and
any pertinent notes about their functions.
• Transparency masters following the
introductory page provide examples of
practical applications of the key(s) being
discussed. The key(s) being discussed are
shown in black on an illustration of the
TI-15 keyboard.
Things to Keep in Mind
• While many of the examples on the
transparency masters may be used to
develop mathematical concepts, they
were not designed specifically for that
purpose.
• For maximum flexibility, each example and
activity is independent of the others.
Select the transparency master that
emphasizes the key your students need
to use to develop the mathematical
concepts you are teaching. Select an
appropriate activity for the
mathematical concept you are teaching.
• If an example does not seem
appropriate for your curriculum or
grade level, use it to teach the function
of a key (or keys), and then provide
relevant examples of your own.
• To ensure that everyone starts at the
same point, have students reset the
calculator by pressing −and ”
simultaneously or by pressing ‡,
selecting RESET, selecting Y(yes), and
then pressing <.
How to Order Additional Teacher Guides
To place an order or to request additional
information about Texas Instruments (TI)
calculators, call our toll-free number:
1-800-TI-CARES (1-800-842-2737)
Or use our e-mail address:
[email protected]
Or visit the TI calculator home page:
http://www.ti.com/calc

© 2000 TEXAS INSTRUMENTS INCORPORATED TI-15: A Guide for Teachers v
About the TI.15
Two-Line Display
The first line displays an entry of up to 11
characters. Entries begin on the top left. If
the entry will not fit on the first line, it will
wrap to the second line. When space permits,
both the entry and the result will appear on
the first line.
The second line displays up to 11 characters. If
the entry is too long to fit on the first line, it
will wrap to the second line. If both entry and
result will not fit on the first line, the result is
displayed right-justified on the second line.
Results longer than 10 digits are displayed in
scientific notation.
If an entry will not fit on two lines, it will
continue to wrap; you can view the beginning
of the entry by scrolling up. In this case, only
the result will appear when you press ®.
Display Indicators
Refer to Appendix B for a list of the display
indicators.
Error Messages
Refer to Appendix C for a listing of the error
messages.
Order of Operations
The TI-15 uses the Equation Operating
System (EOSé) to evaluate expressions. The
operation priorities are listed on the
transparency master in Chapter 1,
Display,
Scrolling, Order of Operations, and Parentheses
.
Because operations inside parentheses are
performed first, you can use Xor Yto
change the order of operations and, therefore,
change the result.
Menus
Two keys on the TI-15 display menus: ‡
and ¢.
Press $or #to move down or up through
the menu list. Press !or "to move the
cursor and underline a menu item. To return
to the previous screen without selecting the
item, press ”. To select a menu item, press
®while the item is underlined.
Previous Entries #$
After an expression is evaluated, use #
and $to scroll through previous entries
and results, which are stored in the TI-15
history.
Problem Solving (‹)
The Problem Solving tool has three features
that students can use to challenge
themselves with basic math operations or
place value.
Problem Solving (Auto Mode) provides a set
of electronic exercises to challenge the
student’s skills in addition, subtraction,
multiplication, and division. Students can
select mode, level of difficulty, and type of
operation.
Problem Solving (Manual Mode) lets
students compose their own problems,
which may include missing elements or
inequalities.
Problem Solving (Place Value) lets students
display the place value of a specific digit, or
display the number of ones, tens, hundreds,
thousands, tenths, hundredths, or
thousandths in a given number.

© 2000 TEXAS INSTRUMENTS INCORPORATED TI-15: A Guide for Teachers vi
About the TI.15 (Continued)
Resetting the TI.15
Pressing −and ”simultaneously or
pressing ‡, selecting RESET, selecting Y
(yes), and then pressing ®resets the
calculator.
Resetting the calculator:
• Returns settings to their defaults:
Standard notation (floating decimal),
mixed numbers, manual simplification,
Problem Solving Auto mode, and Difficulty
Level 1 (addition) in Problem Solving.
• Clears pending operations, entries in
history, and constants (stored
operations).
Automatic Power DownTM (APDTM)
If the TI-15 remains inactive for about
5 minutes, Automatic Power Down (APD)
turns it off automatically. Press −after
APD. The display, pending operations,
settings, and memory are retained.

© 2000 TEXAS INSTRUMENTS INCORPORATED TI-15: A Guide for Teachers 1
Patterns in Percent 2
Fraction Forms 6
Comparing Costs 11
Number Shorthand 15
Related Procedures 20
In the Range 24
The Value of Place Value 29
What’s the Problem? 34
Activities

© 2000 TEXAS INSTRUMENTS INCORPORATED TI-15: A Guide for Teachers 2
Patterns in Percent Grades 4 - 6
Overview
Students will use the ªkey to collect data about
percentages of a given number. They will organize the
data and look for patterns in percents. (For
example, 10% of 20 is twice as much as 5% of 20.)
Math Concepts
• multiplication
• equivalent
fractions,
decimals, and
percents
Materials
• TI-15
• pencil
• student
activity
(page 4)
Introduction
1. After students use manipulatives to develop the
meaning of percent (1% = 1 part out of 100 parts),
have them explore what happens when they
press ªon the calculator.
2. Present the following scenario to students:
Metropolis East (M.E.) and Metropolis West
(M.W.) are neighboring cities. The sales tax in
M.E. is 10%, but the sales tax in M.W. is only
5%. Collect data and display your results for
each percent in a table to compare the amounts
of money you would pay for tax on various
items in each city.
3. Have students make conjectures about percent
based on the patterns they observe. Students can
then use manipulatives to verify their
conjectures.
Examples:
• Students may observe that for every item, 10%
of its price is twice as much as 5% of its price.
• Students may observe that it is easy to
estimate 10% of a whole number by using
place value and looking at the digits to the
right of the ones place.
Collecting and Organizing Data
To guide students in organizing their data to bring
out patterns, ask questions such as:
•
How could you organize your data to compare
the 5% tax rate to the 10% tax rate?
•
Why would it be useful to keep 5% in the left-
hand column of one table all the way down and
just change the total quantity?
³When a student enters
a 6 ª, the TI-15
displays 6%. Then,
when the student
presses ®, the
display changes to
6%= 0.06 to show that
6% is another way to
write 0.06 or 6/100.
³You will need to show
students how to use
multiplication on the
TI-15 to express the
percent of a given
quantity. For example,
to show 10% of $20:
1. Enter 10.
2. Press ªV.
3. Enter 20; press ®.
Students can verify the
calculator display of 2
by using manipulatives
to show 10% of $20 =
$2.

© 2000 TEXAS INSTRUMENTS INCORPORATED TI-15: A Guide for Teachers 3
Patterns in Percent (Continued)
•
How can you make a similar table for 10% to
compare your data?
•
What do you think would happen if you order
the total quantity amounts from least to
greatest?
•
How else might you organize your data to
compare the two tax rates and find patterns in
the percents?
Analyzing Data and Drawing Conclusions
To focus students’ attention on looking for patterns
in their data, ask questions such as:
•
How are the percentages (amounts of tax) in
your 5% table like the amounts in the 10% table?
•
How does 5% of a $20 item compare to 5% of a
$10 item?
•
How does 10% of a $20 item compare to 10% of
a $10 item?
•
How does 10% of the cost of an item compare to
the total cost of the item?
•
What conjectures can you make about finding
10% of a number?
•
What conjectures can you make about finding
5% of a number?
•
How can you use manipulatives to test your
conjectures?
Continuing the Investigation
Students can create other percent scenarios to
investigate patterns in percents. For example, ask
students:
•
What happens if you increase the sales tax by
one percentage point each day?
•
How does the tax on a $20 item change each
day?
•
How does the tax on a $40 item change each
day?
•
How do the taxes on the 2 items compare?

© 2000 TEXAS INSTRUMENTS INCORPORATED TI-15: A Guide for Teachers 4
Patterns in Percent Name ___________________________
Date ___________________________
Collecting and Organizing Data
Use your calculator to collect data about percent, organize it in the
table below, and then look for patterns.
Cost of Item Amount of Tax in
Metropolis West
Tax Rate: ____%
Amount of Tax in
Metropolis East
Tax Rate: ____%

© 2000 TEXAS INSTRUMENTS INCORPORATED TI-15: A Guide for Teachers 5
Patterns in Percent Name ___________________________
Date ___________________________
Analyzing Data and Drawing Conclusions
1. What patterns do you see in your tables?
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
2. What conjectures can you make from these patterns?
__________________________________________________________________________
__________________________________________________________________________
3. Repeat the activity with a different percent in the left column and
compare your results.
__________________________________________________________________________
__________________________________________________________________________
4. Repeat the activity, changing the percents in the left column while
keeping the total quantity constant. Now what patterns do you see?
What conjectures can you make?
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________

© 2000 TEXAS INSTRUMENTS INCORPORATED TI-15: A Guide for Teachers 6
Fraction Forms Grades 4 - 6
Overview
Students will compare the results of using division
to create fractions under the different mode
settings for fraction display and make
generalizations from the patterns they observe.
Math Concepts
• division
• multiplication
• common
factors
• equivalent
fractions
Materials
• TI-15
• pencil
• student
activity
(page 9)
Introduction
1. Present students with a problem such as:
In a small cafe, there are 6 cups of sugar left in
the pantry to put into 4 sugar bowls. If you
want them all to contain the same amount of
sugar, how much sugar goes into each sugar
bowl?
2. Have students present their solutions to the
problem. Encourage them to find as many ways
to represent the solution as possible.
Examples:
• By thinking of using a ¼ cup scoop to fill the
bowls, each bowl would receive 6 scoops, or
6/4cups of sugar.
• By thinking of separating each cup into half
cups, there would be 12 half cups, and each
bowl would receive 3 half cups, or 3/2cups of
sugar.
• If a 1-cup measuring cup was used first, each
bowl would receive 1 cup of sugar, then the
last two cups could be divided into eight
fourths to give 1
2/4cups per bowl.
• The last two cups could be divided into 4
halves to give 11/2cups per bowl.
3. Have students identify the operation and record
the equation that they could use with the
calculator to represent the action in the situation
(6 cups ÷ 4 bowls = number of cups per bowl).
Refer to page 45 for
detailed information
about mode settings on
the TI-15.
Division can be
represented by 6 P4 or
6/4 (entered on the
calculator as 6 4 ¥).
In this activity, the
fraction representation
is used.

© 2000 TEXAS INSTRUMENTS INCORPORATED TI-15: A Guide for Teachers 7
Fraction Forms (Continued)
4. Have students enter the division to show the
quotients in fraction form, and record the
resulting displays.
5. Have students explore the quotient with the
different combinations of settings and discuss
the different displays that occur. If necessary,
have them use manipulatives to connect the
meanings of the four different fraction forms.
6. Have students, working in groups of four, choose
a denominator and record the different fraction
forms on the activity sheet provided.
7. Have students share their results, look for
patterns, and make generalizations.
For example, for 6 ÷ 4
as a fraction, enter
6 4 ¥. The displays
in the different modes
will look like the
following:
n
dman 6
4
n
dauto 3
2
U n
dman 1 2
4
U n
dauto 1 1
2
Collecting and Organizing Data
To guide students in creating data that will exhibit
patterns in the fraction quotients, ask questions such as:
•
What denominator did you choose to explore
with? Why?
•
What denominators do you get with the settings
n
d
man
? With the settings U n
d
man
?
•
What denominators do you get with the settings
n
d
auto
? With the settings
U n
d
auto
?
•
What denominator are you going to choose to
explore with next?
Example:
After exploring with denominators of 2 and 3,
you might suggest exploring with a denominator
of 6 and comparing results.
•
How can you organize your results to look for
patterns?
Example:
Continuing to increase the numerators by 1 each
time.

© 2000 TEXAS INSTRUMENTS INCORPORATED TI-15: A Guide for Teachers 8
Fraction Forms (Continued)
Analyzing Data and Drawing Conclusions
To focus students’ attention on the patterns in their
fractions and the relationship of these patterns to the
denominators, ask questions such as:
•
What patterns do you see in your results?
Example:
When a denominator of 4 is used in the n
dauto
column, every fourth number is a whole number.
•
How do the results of using a denominator of 2
compare with the results of using a
denominator of 4?
•
How does a denominator of 5 compare to a
denominator of 10?
•
Which other denominators seem to be related?
Example:
The pattern using a divisor of 6 is related to the
patterns for 2 and 3.)
•
What pattern do you see in the related
denominators?
Example:
They are related as factors and multiples.
Continuing the Investigation
Have students brainstorm situations in which they
would prefer to use each of the combinations of
settings of fraction forms.
Example:
• When working with probabilities that may
need to be added, using the n
dman settings
would keep the denominators of the
probabilities all the same and make mental
addition easier.
• In a situation where estimated results are
close enough, using the U n
dauto settings
would make it easier to see quickly the whole
number component of the result and whether
the additional fraction part was more or less
than ½.

© 2000 TEXAS INSTRUMENTS INCORPORATED TI-15: A Guide for Teachers 9
Fraction Forms Name ___________________________
Date ___________________________
Collecting and Organizing Data
1. Have each person in your group set his/her calculator to one of the
following combinations of modes for fraction display. (Each person
should choose a different setting.)
• improper/manual simp
• improper/auto simp
• mixed number/manual simp
• mixed number/auto simp
2. Select a denominator: __________________
3. Use this denominator with several numerators and record each
person’s results in the table below.
Numerator Denominator n
dMan n
dAuto U n dMan U n dAuto
0
1
2
3
4

© 2000 TEXAS INSTRUMENTS INCORPORATED TI-15: A Guide for Teachers 10
Fraction Forms (Continued)
Analyzing Data and Drawing Conclusions
1. What patterns do you see?
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
2. What generalizations can you make?
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
3. Try the activity again with a different denominator and compare your
results with the two denominators.
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________

© 2000 TEXAS INSTRUMENTS INCORPORATED TI-15: A Guide for Teachers 11
Comparing Costs Grades 3 - 5
Overview
Students will solve a problem using division with an
integer quotient and remainder, division with the
quotient in fraction form, and division with the
quotient in decimal form and compare the results.
Math Concepts
• division
• multiplication
• fractions
• decimals
Materials
• TI-15
• pencil
• student
activity
(page 14)
Introduction
1. Introduce the following problem:
The maintenance department has determined
that it will cost $.40 per square yard to
maintain the district’s soccer field each year.
The soccer field is 80 yards wide and 110 yards
long. The six schools that play on the field have
decided to split the cost evenly. How much
should each school contribute to the soccer field
maintenance fund this year?
2. Have students use the calculator to solve this
problem in three ways:
• Finding an integer quotient and remainder.
• Finding the quotient in fraction form.
• Finding the quotient in decimal form.
Collecting and Organizing Data
Students should record their procedures and results
on the Student Activity page. To help them focus on
their thinking, ask questions such as:
•
What did you enter into the calculator to solve
the problem?
Example:
A student may have entered 80 V110 ®to
determine the area of the soccer field, then
entered V0.40 ®to find the total maintenance
cost, then W6®to find the cost for each
school in fraction or decimal form.
To display an integer
quotient with a
remainder, use the £
key.
To display a quotient in
fraction form, press ‡
"®to select n/d,
then use the Wkey.
To display a quotient in
decimal form, press
‡!®to select .,
then use the Wkey.

© 2000 TEXAS INSTRUMENTS INCORPORATED TI-15: A Guide for Teachers 12
Comparing Costs (Continued)
•
Could you have solved the problem more
efficiently? How?
Example:
A student may see that 80 x 110 could be done
mentally, and the key presses could be simplified
to 8800 V.4 W6®.
•
How are your procedures alike for each type of
solution?
Examples:
They all involve finding how many square yards
in the soccer field; they all involve multiplication
and division.
•
How are they different?
You use different keys to tell the calculator in
what form you want the answer displayed.
Analyzing Data and Drawing Conclusions
To guide students in the analysis of their data, ask
questions such as:
•
How are your solutions in the three forms
alike?
They all have a whole number component of 586.
•
How are your three solutions different?
The remainder form just tells how many dollars
are left over. The fraction and decimal forms tell
how much more than $586 each school has to
pay.

© 2000 TEXAS INSTRUMENTS INCORPORATED TI-15: A Guide for Teachers 13
Comparing Costs (Continued)
•
What happens if you multiply each solution by
6 to check it?
For the remainder form, you have to multiply
586 x 6 and then add 4 to get the total cost of
$3520. You can multiply 5862/3x 6 in fraction
form to get $3520. If you enter 586.666667 x 6 and
press ®, you get 3520, but that doesn’t make
sense because 6 x 7 doesn’t end in a 0!
If you enter 586.66667, then fix the decimal
quotient to hundredths since it is money, and
then find 586.67 x 6, you still get 3520.00, which
still doesn’t make sense because 6 x 7 = 42. If you
clear the calculator and enter 586.67 x 6, and
press ®, then the display reads 3520.02, which
does make sense.
•
As a school, which form of the quotient would
you want to use?
Responses may vary. Some students may want to
use the decimal form, since it is the closest to the
representation of money. Some students may
want to use the integer quotient and remainder
form and suggest that the Central Office pay the
$4.00 remainder.
Although the fraction form of the quotient
describes the exact quantity that each school
should pay, most students will recognize, by
comparing it to the decimal form, that the
fraction form is not easily translated into money.
When you fix
586.666667 to 2
decimal places, and
then multiply by 6, the
calculator “remembers”
the original number and
uses it as the factor.
The product rounded to
the nearest hundredth,
using the original factor,
is 3520.00. When you
enter 586.67, the
calculator uses this
number for the factor,
showing the actual
product of 3520.02.