JBL 001 TI 15 Guide For Teachers (English) 15tg Book Eng

User Manual: JBL TI-15 Guide for Teachers (English) TI-15 Guide for Teachers

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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.

Important Notice Regarding Book Materials
Texas Instruments makes no warranty, either expressed 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 book. Moreover, Texas Instruments shall not be
liable for any claim of any kind whatsoever against the use of these materials by any other party.
Note: Using calculators other than the TIN15 may produce results different from those described in these
materials.

Permission to Reprint or Photocopy
Permission is hereby granted to teachers to reprint or photocopy in classroom, workshop, or seminar
quantities the pages or sheets in this book that carry a Texas Instruments copyright notice. These pages are
designed to be reproduced by teachers for use in classes, workshops, or seminars, provided each copy made
shows the copyright notice. Such copies may not be sold, and further distribution is expressly prohibited.
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federal copyright law.
Send inquiries to this address:
Texas Instruments Incorporated
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Attention: Manager, Business Services
If you request photocopies of all or portions of this book from others, you must include this page (with the
permission statement above) to the supplier of the photocopying services.

www.ti.com/calc
ti-cares@ti.com
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.

Table of Contents
CHAPTER

PAGE

About the Teacher Guide ........................... v
About the TI-15 ........................................... vi

CHAPTER

PAGE

How to Use the TI-15 (continued)
12 Problem Solving: Auto Mode............ 94

Activities................................................ 1

13 Problem Solving: Manual Mode ......100

Patterns in Percent ....................................2

14 Place Value ..........................................106

The ª Key

Fraction Forms ........................................... 6
Auto and Manual Mode

Comparing Costs........................................ 11
Division with quotient/remainder,
fraction, or decimal result

Number Shorthand ................................... 15
Scientific Notation

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

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

TI-15: A Guide for Teachers

iii

About the Teacher Guide
How the Teacher Guide is Organized

Things to Keep in Mind

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.

•

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 <.

Activities
The activities are designed to be teacherdirected. 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.

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:
ti-cares@ti.com
Or visit the TI calculator home page:
http://www.ti.com/calc

TI-15: A Guide for Teachers

About the TI.15
Two-Line Display

Menus

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.

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.

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.

Previous Entries # $

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 ®.

Problem Solving (‹)

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 X or Y to
change the order of operations and, therefore,
change the result.

After an expression is evaluated, use #
and $ to scroll through previous entries
and results, which are stored in the TI-15
history.

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.

TI-15: A Guide for Teachers

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).
TM

Automatic Power Down (APD )
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.

TI-15: A Guide for Teachers

Activities

Patterns in Percent

Fraction Forms

Comparing Costs

Number Shorthand

Related Procedures

In the Range

The Value of Place Value

What’s the Problem?

TI-15: A Guide for Teachers

Patterns in Percent

Grades 4 - 6
Math Concepts

Overview
Students will use the ª key 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.)

Materials

• multiplication

• TI-15

• equivalent
fractions,
decimals, and
percents

• 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 ª on the calculator.

When 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.

You 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:

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.

1. Enter 10.
2. Press ª V.
3. Enter 20; press ®.
Students can verify the
calculator display of 2
by using manipulatives
to show 10% of $20 =
$2.

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 lefthand column of one table all the way down and
just change the total quantity?

TI-15: A Guide for Teachers

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?

TI-15: A Guide for Teachers

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: ____%

TI-15: A Guide for Teachers

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?
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________

TI-15: A Guide for Teachers

Fraction Forms

Grades 4 - 6
Math Concepts

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.

Materials

• division

• TI-15

• multiplication

• pencil

• common
factors

• student
activity
(page 9)

• equivalent
fractions

Introduction
1. Present students with a problem such as:

Refer to page 45 for
detailed information
about mode settings on
the TI-15.

Division can be
represented by 6 P 4 or
6/4 (entered on the
calculator as 6 4 ¥).
In this activity, the
fraction representation
is used.

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
6/4 cups 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 3/2 cups 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 2/4 cups per bowl.

•

The last two cups could be divided into 4
halves to give 11/2 cups 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).

TI-15: A Guide for Teachers

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
man
d

6
4

n
auto
d

3
2

n
man
d

2
4

n
auto
d

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
n
? With the settings U d man?
d man

What denominators do you get with the settings

n
n
? With the settings U d auto?
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.

TI-15: A Guide for Teachers

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:
n

When a denominator of 4 is used in the d auto
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
n
need to be added, using the d man settings
would keep the denominators of the
probabilities all the same and make mental
addition easier.
•

In a situation where estimated results are
n
close enough, using the U d auto 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.

TI-15: A Guide for Teachers

Name ___________________________

Fraction Forms

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
d Man

n
d Auto

n
n
U d Man U d Auto

0
1
2
3
4

TI-15: A Guide for Teachers

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.
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________

TI-15: A Guide for Teachers

Comparing Costs

Grades 3 - 5
Math Concepts

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.

Materials

• division

• TI-15

• multiplication

• pencil

• fractions

• student
activity
(page 14)

• decimals

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:

•

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 W key.

To display a quotient in
decimal form, press
‡ ! ® to select ,
then use the W key.

What did you enter into the calculator to solve
the problem?
Example:
A student may have entered 80 V 110 ® to
determine the area of the soccer field, then
entered V 0.40 ® to find the total maintenance
cost, then W 6 ® to find the cost for each
school in fraction or decimal form.

TI-15: A Guide for Teachers

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 W 6 ®.

•

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.

TI-15: A Guide for Teachers

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 5862/3 x 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?

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.

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.

TI-15: A Guide for Teachers

Comparing Costs

Name ___________________________
Date

___________________________

Collecting and Organizing Data
The Maintenance department has determined that it will cost $4.00 per
square yard to maintain the district’s soccer field each year. The soccer field is
80 yards wide and 110 yards long. The 6 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?
1. Use division with an integer quotient and remainder:

2. Use division with a quotient in fraction form:

3. Use division with a quotient in decimal form:

Analyzing Data and Drawing Conclusions
Write a short paragraph comparing the three solutions.

TI-15: A Guide for Teachers

Number Shorthand: Scientific Notation
Grades 5 - 6
Math Concepts

Overview
Students will use patterns created on the
calculator with the constant operation (› or œ)
to develop an understanding of scientific notation.

Materials

• multiplication

• TI-15

• powers of 10

• pencil

• exponents

• student
activity
(page 18)

Introduction
1. Have students review the pattern created when
using 10 as a factor.
Example:
1 x 10 = 10
2 x 10 = 20
3 x 10 = 30
10 x 10 = 100
2. Ask students:
Based on this pattern, what do you think
happens when we multiply by 10 over and over
again?
3. After students share their conjectures, have them
use › to test their conjectures. As students
press ›, have them record the resulting
displays on the Student Activity page.
4. When students reach the point where the lefthand counter is no longer displayed, ask them
what they think has happened to the calculator.
(The product has become so large that there is
not room to display both the product and the
counter, so the counter has been dropped.)
Have students continue to record the counter
data, even though it no longer shows on the
calculator.
5. When the left-hand counter reappears, have
students describe what has happened to the
display of the product. (It has been replaced with
a right-hand display of scientific notation: for
example, 1x10^11.)

To multiply repeatedly
by 10, enter:
1. › V 10 ›
This “programs” the
constant operation.
2. Enter 1 as the
starting factor.
3. Press ›.
When you press › the
first time, the calculator
performs the operation
1 x 10 and the display
shows:
1x10
1

The 1 represents using
x 10 one time.

TI-15: A Guide for Teachers

Number Shorthand: Scientific Notation
(Continued)
6. Have students continue to press › and record
the results.
7. Have students analyze their data and make some
conclusions about the scientific notation display.
For example, 1x10^11 represents the product:
1 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10.

Explain to students that exponential or scientific
notation is a shorthand for repeated factors:
11
1 x 10 .
8. Have students continue to explore the use of
scientific notation to represent repeated
multiplication by 10 with other starting factors.
(For example, using 2 as the starting factor, the
display 2x10^11 represents multiplying 2 by 10
eleven times, or 2 x 10 11.

Collecting and Organizing Data
To focus students’ attention on the relevant changes
in the calculator’s display, ask questions such as:

•

What does the display 3 1000 mean?

•

When did the counter on the left disappear? Why
do you think that happened?

•

When did the counter on the left reappear? What
else has changed?
The product looks different. It changed from
1000000000 to 1x10^10.

•

What do the displays look like after this change
takes place?
The 1x10 stays the same, but the right-hand
number (the exponent) goes up one each time
› is pressed, and it matches the left-hand
counter.

TI-15: A Guide for Teachers

Number Shorthand: Scientific Notation
(Continued)

Analyzing Data and Drawing Conclusions
To focus students’ attention on the connection
between the repeated factors of 10 and the scientific
notation display, ask questions such as:

•

What patterns do you see in your products
before the counter disappears?
They all have a 1 followed by the same number of
zeroes as factors of 10 that were used in the
product.

•

If you continued this pattern, what would the
product be at the point where the display of the
product changed? How is the product related to
the new display?
For example, 1x10^11 is in the place where the
product should be 100,000,000,000. The display
11
1x10^11 represents the product 1 x 10 .

•

What happens if you use 2 as the starting factor
and multiply by 10 repeatedly?
The displays are the same, except the first
number in all the products is 2. The display
11
2x10^11 represents the product 2 x 10 .

Continuing the Investigation
Students can use other powers of 10 as the repeating
factor, record the results in the table, and look for
patterns. For example, using 100 as the repeating
factor causes the exponent part of the scientific
notation display to increase by 2 every time › is
pressed.
Students can use a starting factor of 10 or greater,
record the results in the table, and look for patterns.
For example, using 12 as the starting factor soon
results in a display like 12 1.2 x10^13 , where the
exponent part of the display is one more than the
number of times 10 has been used as a factor.

TI-15: A Guide for Teachers

Number Shorthand:
Scientific Notation

Name ___________________________
Date

___________________________

Collecting and Organizing Data
Program the constant operation feature on your calculator to multiply by
10. Record the results in the table below for each time you press ›.

Number of
Times
___
Used as a
Factor
0

Display

(starting factor)

1
2
3
4

TI-15: A Guide for Teachers

Number Shorthand:
Scientific Notation

Name ___________________________
Date

___________________________

2. What does it mean when the right-hand display changes?
(For example, 1x10^15.)
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________

3. Try the activity again with another multiple of 10 and compare your
results.
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________

TI-15: A Guide for Teachers

Related Procedures

Grades 2 - 6
Math Concepts

Overview
Students will use the two constant operations (›
and œ) to compare the results of different
mathematical procedures and determine how they
are related.

Materials

• whole numbers

• TI-15

• addition,
subtraction,
multiplication,
division
• fractions
(Grades 5-6)

• pencil
• student
activity
(page 23)

• decimals
(Grades 5-6)

Introduction
1. Have students program › with +2 and œ
with -2.
2. Have students enter 8 on their calculators, press
›, and read the output (1 10, which means
adding 2 once to 8 gives 10).
3. Have students press œ to apply the second
constant operation to the output of the first
constant operation, and then read the output
(1 8, which means subtracting 2 once from 10
gives 8).
4. Have students continue this process with various
numbers as their first input. Discuss their results.
(Pressing › and then œ always gets you back
to the first input number, which means › and
œ are inverse procedures.)
5. Challenge students to find more pairs of
procedures for › and œ that will follow the
same pattern and record their investigations
using the Related Procedures student activity
page.

To use › and œ:
1. Press › (or œ).
2. Enter the operation
and the number (for
example, T 2).
3. Press › (or œ).
4. Enter the number to
which you want to
apply the constant
operation.
5. Press › (or œ).
The display will have
a 1 on the left and the
result on the right. If
you press › (or œ)
again, the calculator
will apply the constant
operation to the
previous output and
display a 2 at the left,
indicating the
constant operation
has been applied
twice to the original
input.

TI-15: A Guide for Teachers

Related Procedures

(Continued)

Collecting and Organizing Data
As students use › and œ, have them record their
results in the appropriate tables on the Student
Activity page. For example, if a student is exploring
the relationship between x 2 and ÷ 2, the tables might
look something like this:
Table for ›
Input

Procedure

Output

Input

Procedure

Output

Table for œ

Analyzing Data and Drawing Conclusions
Ask students:

•

What patterns do you see in your data?

•

Are the procedures inverses of each other? How
do you know?

If the output number for › is used as the input
number for œ and gives an output number
equal to the original input number for ›, then
the procedures may be inverses of each other, as
in x 2 and ÷ 2.

•

Does the pattern work with special numbers like
1 and 0? With fractions and decimals? With
positive and negative integers?

•

What happens if you use œ first, and then
›?

To recognize the
equivalent procedures,
students may need to
use the Ÿ key to
change outputs from
decimal to fraction form
or vice versa.

TI-15: A Guide for Teachers

Related Procedures

(Continued)

Continuing the Investigation
Older students can investigate equivalent
procedures, such as dividing by a number and
multiplying by its reciprocal. For example, if a
student is exploring the relationship between x ½
and ÷ 2, the tables might look something like this:
Table for ›
Input

Procedure

Output

x½

1.5 = 1½

Input

Procedure

Output

0.5 = 5/10 = ½

1.5 = 15/10 = 1½

Table for œ

TI-15: A Guide for Teachers

Related Procedures

Name ___________________________
Date

___________________________

Collecting and Organizing Data
1. Choose a procedure for › (for example, x ½).
2. Choose a procedure for œ (for example, ÷ 2).
3. Select an input number to apply the procedure to and record both the
input and output numbers in the appropriate table.
4. Use the tables below to record and compare your results using ›
and œ.
Table for ›

Input

Procedure

Table for œ

Output

Input

Procedure

Output

Analyzing Data and Drawing Conclusions
5. How do the two procedures compare?
__________________________________________________________________________

6. What patterns do you see?
__________________________________________________________________________

7. Are the two procedures related? Explain.
__________________________________________________________________________

TI-15: A Guide for Teachers

In the Range

Grades 3 - 6
Math Concepts

Overview
Students will interpret the rounding involved in
measuring to identify the possible range of a given
measurement.

Materials

• rounding whole
numbers

• TI-15

• rounding
decimals

• meter sticks
or metric
measuring
tapes

• measurement
with metric
units (length,
mass, capacity)

• pencil

• student
activity (p.27)

Introduction
1. Have students measure the length of a table or
desk in the room and record the measurement to
the nearest millimeter, for example, 1357 mm.
Discuss how measurements in millimeters can be
recorded as 1357 mm or as thousandths of
meters, 1.357 m. Note that the measurement was
rounded to 1357 mm because it fell somewhere
between ½ of a millimeter less than 1357 mm
(1356.5 mm) and ½ of a millimeter more than
1357 mm (1357.5 mm).

1356.5

1357

1357.5

2. Have students then use rounding to record the
same measurement to the nearest centimeter
(136 cm or 1.36 m).
3. Enter the original measurement on the calculator
as 1.357 and fix the display at two decimal
places.
4. Have students fix the display at one decimal
place. Ask:
What does this number represent? (The
measurement rounded to the nearest tenth of a
meter, or the measurement rounded to 14
decimeters.)

To fix the display at 2
decimal places, press
Š ™ ®.

Have students discuss
how the display of 1.36
matches their rounding
of the measurement to
136 cm.

TI-15: A Guide for Teachers

In the Range

(Continued)

5. Have students fix the display to no decimal
places. press Š and then “ to display 1. Ask:
What does this number represent? (The
measurement rounded to the nearest meter.)

To round to the nearest
whole number, press
Š “ ®.

To round to the nearest
tenth, press Š ˜ ®.

6. Introduce the In the Range game by secretly
entering a number on the calculator with three
decimal places to represent a measurement in
millimeters; for example, 2.531. Then display the
number rounded to the nearest whole number
(3). Show this display to students.
7. Tell students that this number represents the
measurement of a length of board to the nearest
meter. Ask students:
What could its measurement be if it had been
measured to the nearest decimeter?
(2.5 m to 3.5 m)
8. Round the original number to the nearest tenth
(2.5). Ask students:
Does this lie within the range we identified?
9. Repeat for measuring to the nearest centimeter
(hundredths) and millimeter (thousandths). (The
range for centimeters would be 2.45 to 2.55, with
2.53 lying within that range; and the range for
millimeters would be 2.525 to 2.535, with 2.531
lying within that range.)
10. Have students work in pairs to play the game and
record their observations on their student
activity pages.

TI-15: A Guide for Teachers

In the Range

(Continued)

Collecting and Organizing Data
As students are playing the game, focus their
attention on the patterns that are developing by
asking questions such as:

•

When you record a measurement, why is
rounding always involved?

•

When you read a measurement, what interval
should that measurement always indicate to
you? (½ a unit less or ½ a unit more)

•

How would this interval look on a number line
(or meter stick)?

•

How is ½ represented in the metric system?

•

How are you deciding how to represent the
range of possible measurements? What patterns
are you using?

Analyzing Data and Drawing Conclusions
To guide students in the analysis of their data, ask
questions such as:

•

What range is indicated by every measurement?

•

What patterns did you use in identifying the
range of possible measurements?

•

How would you use these patterns to round
256.0295 to the nearest tenth?

Continuing the Investigation
Have students replace the units of length with units
of mass (grams, centigrams) or capacity (liters,
milliliters) to notice the same patterns.
Have students discuss why this decimal place-value
approach with the calculator does not work for
measurements in yards, feet, and inches. Have them
identify what range a measurement would lie in if it
was measured to the nearest yard, nearest foot, and
nearest inch. (For example, 2 yards would lie
between 1 yard and 18 inches and 2 yards and 18
inches.)

TI-15: A Guide for Teachers

In the Range

Name ___________________________
Date

___________________________

Collecting and Organizing Data
Have your partner secretly enter a measurement with three decimals places
into the calculator, and then fix the number to be rounded to the nearest whole
number. Now look at the display and answer the following questions:
1. What is the measurement to the nearest meter? _________________
a. What could be the range of the measurement if it had been
measured to the nearest tenth of a meter (decimeters)?
_______________________________________________________________________

b. Set Š to the nearest tenth (˜).
What is the measurement to the nearest tenth? _______________
Is that within the range you identified? ______________________
2. What is the measurement to the nearest tenth of a meter? ________
a. What could be the range of the measurement if it had been
measured to the nearest hundredth of a meter (centimeters)?
_______________________________________________________________________

b. Set Š to the nearest hundredth (™).
What is the measurement to the nearest hundredth? __________
Is that within the range you identified? ______________________
3. What is the measurement to the nearest hundredth of a meter? ___
a. What could be the range of the measurement if it had been
measured to the nearest thousandth of a meter (millimeters)?
_______________________________________________________________________

b. Set Š to the nearest thousandth (š).
What is the measurement to the nearest thousandth? _________
Is that within the range you identified? ______________________
© 2000 TEXAS INSTRUMENTS INCORPORATED

TI-15: A Guide for Teachers

In the Range

Name ___________________________
Date

___________________________

Analyzing Data and Drawing Conclusions
Identify three measurements to the nearest millimeter that would be:
a. 10 m when rounded to the nearest meter. ___________________
b. 9.0 m when rounded to the nearest tenth of a meter (decimeter).
_______________________________________________________________________

c. 9.05 m when rounded to the nearest hundredth of a meter
(centimeter).
_______________________________________________________________________

TI-15: A Guide for Teachers

The Value of Place Value

Grades 2 - 6
Math Concepts

Overview
Students will build their flexibility in using numbers
by exploring the connections between the number
symbols and their representations with base-ten
materials.

Grades 2 - 4

• whole number
place value
(through
thousands)
• money
Grades 4 - 6

• decimal place
value (through
thousandths)
• metric units
(meters,
decimeters,
centimeters)

Introduction

1. Read Counting On Frank by Rod Clement.
Discuss some other kinds of questions that a
person could ask about how many objects fit in
or on other objects.
2. Give each group of students a large pile of units
(over 300) from the base-ten materials, and tell
them that this is how many jelly beans fit into a
jar that you filled. Ask them to count the “jelly
beans,” and observe the techniques they use
(counting one at a time, making groups of 10,
etc.).
3. Tell students you have run out of unit pieces and
then ask:
How many rods (groups of 10) would I need to
use to make a pile of jelly beans the same size
as yours?
4. Have students explore the answer to this
problem with their units or apply their
knowledge of place value. Then show them how
to explore the answer using the calculator.
5. Have students compare their solutions with the
base-ten materials to the calculator display.
(They can make 31 tens rods from the 314 units,
with 4 units left over.)
© 2000 TEXAS INSTRUMENTS INCORPORATED

Materials
• TI-15
• pencil
• Counting
on Frank
by Rod
Clement
• base-ten
materials
• student
activity
(pages 32
and 33)

To use the Place Value
feature for this activity:

1. Press ‹ ‡.
2. Press " ® to select
MAN (Manual).
3. Press $ ® to set the
Place Value mode to
11–. This lets you find
out how many ones,
tens, hundreds, etc.,
are in a number. (The
mode – 1 – . is used to
find what digit is in the
ones, tens, hundreds,
etc., place.)
³

To explore answers to
this problem on the
calculator:

1. Press ‹.
2. Enter the number of
units (for example,
314).
3. Press Œ ’ to see the
display. (Using 314, the
display is 31í, meaning
there are 31 tens in
314.)

TI-15: A Guide for Teachers

The Value of Place Value

(Continued)

Collecting and Organizing Data
Have students use their base-ten materials and the
calculator to continue the exploration with other
numbers, identifying how many hundreds and
thousands (and 0.1s and 0.01s for older students).
Encourage exploration with questions such as:

•

How many hundreds are in 120? 2478? 3056?

•

How many tens are in 120? 2478? 3056?

•

How many units (ones) are in 120? 2478?
3056?

•

What numbers can you find that have 12 units?
12 tens? 12 hundreds?

•

What numbers can you find that have 60 units?
60 tens? 60 hundreds?

Analyzing Data and Drawing Conclusions
Have students use the table on The Value of Place
Value Student Activity page to record their findings
and identify the patterns they see. To help them
focus on the patterns, ask questions such as:

•

Students can use the
11 – . Place Value
mode to test their
conjectures. For
example, if they think
1602 has 160
hundreds, they enter
1602, press Œ ‘, and
see 16íí. They can
then use the base-ten
materials to see why
there are only 16
hundreds in 1602. (If
students use the – 1 – .
mode to find what digit
is in the hundreds
place, they will see í6íí
displayed to show that 6
is the digit in the
hundreds place.

How does the number of tens in 1314 compare
to the number 1314? How about 567? 2457?
4089, etc.?
If you cover the digit in the units place, you see
how many tens are in a number.

•

How does the number of hundreds in 1314
compare to the number 1314? How about 567?
in 2457? in 4089, etc.?
If you cover the digits to the right of the
hundreds place, you see how many hundreds are
in a number.

•

How does the display on the calculator compare
to what you can do with the base-ten materials?
If the calculator shows 31_, for 316, I should be
able to make 31 tens rods out of the 316 units I
have.

TI-15: A Guide for Teachers

The Value of Place Value

(Continued)

Continuing the Investigation
Connect the place-value patterns to money. For
example, ask students:

•

If each one of your “jelly beans” costs a penny,
how many pennies would you spend for 1,314
jelly beans?
1,314 pennies.

•

How many dimes (tens) would you spend?
131 dimes and 4 more pennies.

•

How many dollars (hundreds)?
13 dollars, plus 14 more pennies, or 1 dime and 4
pennies.

Older students can record the money (and enter it
into the calculator) in decimal form, 13.14. Then they
can use the calculator to connect dimes to one tenth
(0.1) of a dollar ($13.14 has 131 dimes or tenths) and
pennies to one hundredth (0.01) of a dollar ($13.14
has 1314 pennies or hundredths).
For older students, connect the place-value patterns
to conversions between metric units. For example, a
measurement of 324 centimeters can also be
recorded as 32.4 decimeters (or rounded to 32 dm)
because 1 dm = 10 cm, or it can be recorded as 3.25
meters (or rounded to 3 m), because 1 m = 100 cm.

TI-15: A Guide for Teachers

The Value of Place
Value, Part A

Name ___________________________
Date

___________________________

Collecting and Organizing Data
1. Use your base-ten materials and your calculator to explore how many
tens, hundreds, and thousands are in a number. Record your
observations in the table. What patterns do you see?

Number

Number of
Thousands

Number of
Hundreds

Number of
Tens

Analyzing Data and Drawing Conclusions: Patterns
2. Write 5 numbers that have 15 tens.
__________________________________________________________________________

3. Write 5 numbers that have 32 hundreds.
__________________________________________________________________________

4. Write 5 numbers that have 120 tens.
__________________________________________________________________________

TI-15: A Guide for Teachers

The Value of Place
Value, Part B

Name ___________________________
Date

___________________________

Collecting and Organizing Data
1. Use your base-ten materials and your calculator to explore how many
tenths, hundredths, and thousandths are in a number. Record your
observations in the table. What patterns do you see?

Number

Number of
Tenths

Number of
Hundredths

Number of
Thousandths

Analyzing Data and Drawing Conclusions: Patterns
2. Write 5 numbers that have 15 tenths.
__________________________________________________________________________

3. Write 5 numbers that have 32 hundredths.
__________________________________________________________________________

4. Write 5 numbers that have 120 tenths.
__________________________________________________________________________

TI-15: A Guide for Teachers

What’s the Problem?

Grades 2 - 5

Overview
Students will connect number sentences to problem
situations and use addition, subtraction,
multiplication, and division to solve the problems.

Math Concepts

Materials

• addition,
subtraction

• TI-15

• multiplication,
division (Grades
3 - 5)

• pencil

• number sentences
(equations)

• counters
• student
activity
(page 37)

• inequalities
(Grades 3 - 5)

Introduction
1. On a sentence strip or on the overhead, display a
number sentence such as “8 + 2 = ?” Have
students brainstorm situations and related
questions that this number sentence could be
representing. For example, “If I bought eight
postcards on my vacation and I had two
postcards already at home, how many postcards
do I have now?”

2. If necessary, have students act out the situation
with counters and determine that the value of “?”
is 10.

To test your solution to
the equation, enter the
value of 10 and press
®. The calculator will
display YES.

3. Demonstrate how to display this equation on the
calculator, and how to tell the calculator what
the value of ? is.
4. Now display an equation such as ? - 10 = 5. Have
students brainstorm situations and related
questions that this number sentence could be
representing. For example, “I had some money in
my pocket, and I spent 10 cents of it. I only have
5 cents left. How much money did I have in my
pocket to begin with?” Have students practice
the keystrokes necessary to display this equation
and test the value they determine for “?”.
5. Over a period of time, continue to introduce
students to different types of number sentences
to explore. For example, ? - 8 < 5 (which has 13
whole number solutions) and ? x ? = 24 (which
has 8 solutions of whole number factor pairs)
and ? x 4 = 2 (which has no whole number
solution).
© 2000 TEXAS INSTRUMENTS INCORPORATED

To display this equation
on the calculator, put
the calculator in
Problem Solving mode
by pressing the ‹ key.
Then enter the equation
8 + 2 = ? and press
®. The calculator
display (1 SOL) tells
how many whole
number solutions there
are to the equation.

If an incorrect value is
tested for ?, the
calculator will display
NO and provide a hint.
For example, if a
student tests 5 for the
equation ? - 10= 5, the
calculator displays NO,
then shows 5 - 10 < 5,
and then returns to the
original equation.

TI-15: A Guide for Teachers

What’s the Problem? (Continued)
Collecting and Organizing Data
As an ongoing activity, have students work in pairs
and use the What’s The Problem? Student Activity
sheet to create problem-solving cards. Have one
partner create an addition, subtraction,
multiplication, or division number sentence, using
the “?” and record it in the top box and on the
calculator. If possible, the other partner creates a
situation and question to go with the number
sentence and records it in the bottom box. The two
boxes can be glued or taped to opposite sides of an
index card.
Have students work together with the calculator to
explore how many whole number solutions the
equation has and test what the solutions are. Provide
ideas for exploration by asking questions such as:

•

What actions could be happening in your story
to go with addition (subtraction,
multiplication, or division)?

•

How could you use these counters to act out this
number sentence?

•

What could this number in the number sentence
represent in your story?

•

What could the question mark in the number
sentence represent in your story?

•

Can you make a story for a number sentence
that begins with a question mark?

Analyzing Data and Drawing Conclusions
To focus students’ thinking on the relationships
between their stories and the numbers and
operations in their number sentences, ask questions
such as:

•

How would using a different number here
change your story?

•

How would using a greater than or less than
symbol instead of an equal sign in the number
sentence change your story?

•

How would using a different operation in your
number sentence change your story?

TI-15: A Guide for Teachers

What’s the Problem? (Continued)
Continuing the Investigation
•

Have partners create stories and trade them.
Each partner can then write a number sentence
to go with the other partner’s story.

•

Have students sort the number sentences they
have made into categories: e.g., those with 0
whole number solutions, those with one whole
number solution, those with two whole number
solutions, those with infinite whole number
solutions.

•

Have students try to find an equation or
inequality with exactly 0 whole number
solutions, exactly 1 whole number solution,
exactly 2 whole number solutions, more than 5
whole number solutions, etc.

TI-15: A Guide for Teachers

What’s the Problem?

Name ___________________________
Date

___________________________

Write a number sentence using an operation and the “?”

Write a story that describes a situation and asks a question that can
be represented by the number sentence.

TI-15: A Guide for Teachers

How to Use
the TI.15
Display, Scrolling, Order of
Operations, Parentheses
Clearing and Correcting
Mode Menus
Basic Operations
Constant Operations
Whole Numbers and Decimals
Memory
Fractions
Percent
Pi
Powers and Square Roots
Problem Solving: Auto Mode
Problem Solving: Manual Mode
Place Value

TI-15: A Guide for Teachers

39
42
45
48
55
63
68
71
80
84
88
94
100
106

Display, Scrolling, Order of
Operations, and Parentheses

Keys
Notes
1. X opens a parenthetical expression. • The examples on the transparency
You can have as many as 8
masters assume all default
parentheses at one time.
settings.
2. Y closes a parenthetical expression. • The EOS TM transparency master
demonstrates the order in which
3. ! and " move the cursor left and
the TI-15 completes calculations.
right.
# and $ move the cursor up and
down through previous entries and
results.

•

When using parentheses, if you
press ® before pressing Y,
Syn Error is displayed.

•

Operations inside parentheses are
performed first. Use X or Y to
change the order of operations
and, therefore, change the result.
Example: 1 + 2 x 3 = 7
(1 + 2) x 3 = 9

•

The first and second lines display
entries up to 11 characters plus a
decimal point, a negative sign, and
a 2-digit positive or negative
exponent. Entries begin on the left
and scroll to the right. An entry will
always wrap at the operator.

•

Results are displayed rightjustified. If a whole problem will not
fit on the first line, the result will
display on the second line.

1
2

TI-15: A Guide for Teachers

Equation Operating System
EOS
Priority

Functions

1 (first)

X Y

¨¬

¦Ÿ

8 (last)

Because operations inside
parentheses are performed first,
you can use X Y to change the
order of operations and,
therefore, change the result.

TI-15: A Guide for Teachers

Order of Operations
Add

1+2x3=

T
Press

1 T 2 V 3
®

Multiply

Display
1Û2Ý3Ú

Parentheses

XY
(1 + 2) x 3 =
Press

X 1 T 2 Y
V 3 ®

Display
Å1Û2ÆÝ3Ú

TI-15: A Guide for Teachers

Clearing and Correcting
Keys
1. − turns the calculator on and off.
2. w clears the last digit you entered,
allowing you to correct an entry
without re-entering the entire
number.

Notes
• The examples on the transparency
masters assume all default
settings.
•

3. ” clears the last entry, all pending
operations, and any error conditions.
You can then enter a new number
and continue your calculation.

Pressing − and ” simultaneously
resets the calculator. Resetting
the calculator:
− Returns settings to their
defaults.
− Clears memory and constants.

•

Pressing ” does not affect the
mode settings, memory, or
constants.

TI-15: A Guide for Teachers

Clearing entries
1.
2.
3.
4.

Enter 335 + 10.
Clear the entry and pending
operation.
Enter 335 N 9.
Complete the calculation.

Press

335 T 10
”
( clear the entry)

335 U 9
®

Clear

”

Display
335Û10á

335Ü9

335Ü9Ú

326

Note: ” clears the screen, but not
the history.

TI-15: A Guide for Teachers

Correcting entry errors using w
1.
2.
3.
4.

Backspace

Enter 1569 + 3.
Change the 9 to an 8.
Add 3.
Complete the calculation.

Press

1569 T 3
w w w 8
T 3
®

Display
1569Û3á

1568á

1568Û3á

1568Û3Ú

1571

TI-15: A Guide for Teachers

Mode Menus
Keys
See the tables on the next two pages for details about
each mode setting option.

1. ‡ displays the Calculator Mode
menu, from which you can select the
following options:
Setting

Options

Division (P)

n/d

Constants (Op)

Clear

Op 1 Op 2

RESET

2. ‹ ‡ displays the Problem
Solving Mode menu, from which you
can select the following options:
Setting

Options

Mode

Auto

Level of difficulty

1 2 3

Operation

+ – x P ?

Display option

11-.

1-.

3. ¢ displays the Fractions menu,
from which you can select the
following options:
Setting

Options

Display

U n/d

n/d

Simplify

Man

Auto

Notes
• The examples on the transparency
masters assume all default
settings.
•

You must be in Problem Solving
(‹) to see its menu when you
press ‡. Otherwise, you will see
the Calculator Mode menu.

•

Press ‡ to display the
Calculator Mode menu, ‹ ‡ to
display the Problem Solving Mode
menu, or ¢ to display the
Fractions Mode menu. Press ®
after you make your selection, then
press ‡ or ¢ again to exit
the menu.

Man

TI-15: A Guide for Teachers

Mode Menus

(Continued)

Calculator Mode Menu
Setting

Option

Explanation

Division (Þ)

Displays division results as a decimal

.75

n/d

Displays division results as a fraction

3
4

Shows the constant operation on the
display

Constant Operations
(OP)

?
Clear

Reset

Example

1x5
1

Hides the constant operation

OP1

When selected, clears Op1

OP2

When selected, clears Op2

No; does not reset the calculator.

Yes; resets the calculator.

Problem Solving Mode Menu
Setting

SubMenu

Option

Auto

Level of
difficulty

1 2 3

Operation

+ – x P ? (add, subtract, multiply,
divide, find the operation)

Display option
(for Problem
Solving Place
Value only)

11-. (Displays the number of ones,
tens, hundreds, or thousands)

1234
For ‘:
12_ _

1-. (Displays the digit that is in the
ones, tens, hundreds, or thousands
place)

1234
For ‘:
_2__

Manual

Example

TI-15: A Guide for Teachers

Mode Menus

(Continued)

Fractions Menu
Setting

Option

Explanation

Display

U n/d

Displays results as mixed numbers

n/d

Displays results as improper fractions

Man

Allows manual simplification

Auto

Automatically simplifies to most
reduced form of fraction

Simplify

TI-15: A Guide for Teachers

Example
3

14
7
4

6 3
8 =4
3
4

Basic Operations
Keys
1. T adds.

Notes
• The examples on the transparency
masters assume all default
settings.

2. U subtracts.
3. V multiplies.
4. W divides. The result may be
displayed as a decimal or fraction
depending on the mode setting you
have selected.

•

The result of Integer Divide £
always appears as quotient and
remainder (__ r __).

•

The maximum number of digits for
quotient or remainder (r) is 5.
Quotient, remainder, and the r
character cannot total more than
10 characters.

•

If you use the result of integer
division in another calculation, only
the quotient is used. The remainder
is dropped.

•

All numbers used with £ must
be positive whole numbers.

•

If you attempt to divide by 0, an
error message is displayed.

•

T, U, V, W, ®, and £ work
with the built-in constants.

5. £ divides a whole number by a
whole number and displays the result
as a quotient and remainder.
6. ® completes the operation.
7. M lets you enter a negative number.

5
4
3
2
1
6
7
© 2000 TEXAS INSTRUMENTS INCORPORATED

TI-15: A Guide for Teachers

Basic operations
Add, Subtract

2 + 54 N 6 =

Multiply, Divide
Press

2 T 54 U
6 ®

Display
2Û54Ü6Ú

Equals

3x4P2=
Press

3 V 4 W 2
®

Display
3Ý4P2Ú

TI-15: A Guide for Teachers

Entering negative numbers
The temperature in Utah was N3° C
at 6:00 a.m. By 10:00 a.m., the
temperature had risen 12° C. What
was the temperature at 10:00 a.m.?

Press

M 3 T 12
®

Negative

Display
Ü3Û12Ú

TI-15: A Guide for Teachers

Division with remainders
Chris has 27 pieces of gum.
He wants to share the pieces evenly
among himself and 5 friends. How
many pieces will each person get?
How many pieces will be left over?
Press

27 £ 6
®

Integer Divide

Display
27Þ6Ú

4½3

TI-15: A Guide for Teachers

Division with decimal result
Set the division display option to
decimal and divide 27 by 6.
Press

‡ ®
‡
27 W 6 ®

Divide

Display

Ùê

»Ä¸ /

27Þ6Ú

4Ù5

TI-15: A Guide for Teachers

Division with fractional result
Set the division display option to
fraction and divide 27 by 6.

Press

‡" ®
‡
27 W 6 ®
¤®

Divide

Display

»êêêê
Ä¸ /
nP
d

á
nP
d

5
4 êêê
10

27Þ6Ú
nP
d

5
4 êêê
10

1
4 êê
2

TI-15: A Guide for Teachers

Calculating equivalent units of time
Integer Divide

Sara ran 2 kilometers in 450
seconds. Convert her time to
minutes and seconds.
450 seconds =

Press

450 £ 60
®

? minutes
? seconds

Display
450Þ60Ú

7½30

TI-15: A Guide for Teachers

Constant Operations
Keys
1. › lets you define or execute
operation 1.
2. œ lets you define or execute
constant operation 2.

•

The constant function works with
whole numbers, decimals, and
fractions.

•

When you use › or œ, a
counter appears at the left and
the total appears on the second
line at the right of the display. The
counter shows how many times the
constant has been repeated. If the
number at the right exceeds 6
digits, the counter will not be
shown. The counter returns to 0
after it reaches 99.

•

When you use £ with the
constant function, subsequent
calculations are performed with
the quotient portion of the result.
The remainder is dropped.

•

You can clear a stored constant
by resetting the calculator
(pressing − and ”
simultaneously) or by pressing
‡, pressing $ to scroll to the
CLEAR menu, selecting OP1 (or
OP2) and pressing ®. Pressing
− by itself does not clear the
constant function.

Notes
• The examples on the transparency
masters assume all default settings.
•

The constant memory is set in
conjunction with › and œ when
you perform a calculation that uses
T, U, V, W, £, and ¨.

1
2

TI-15: A Guide for Teachers

Addition as “counting on”
There are 4 frogs in a pond. If 3
more frogs jump into the pond 1 at
a time, how many frogs will be in the
pond?

Constant
Operations

›
Add

Press

› T 1 ›
(stores
operation)

4
( initialize u s i n g 4 )

›
(add 1 one at a
time)

›
›

Display
Op1

Û1
Op1

4
Op1

4Û1
1

5
Op1

5Û1
2

6
Op1

6Û1
3

7
TI-15: A Guide for Teachers

Multiplication as “repeated addition”
Maria put new tile in her kitchen.
She made 4 rows with 5 tiles in
each row. Use repeated addition to
find how many tiles she used.
Before you begin, set the calculator
to hide the constant operation.

Press

‡$"
(hide constant
operation)

‡

› T 5 ›
(store the
operation)

0
( initialize u s i n g 0 )

Constant
Operations

›

Display
+1
¼Á

Ã
êê

á+
Op1

Û5
Op1

0á

Continued
© 2000 TEXAS INSTRUMENTS INCORPORATED

TI-15: A Guide for Teachers

Multiplication as “repeated addition”
Continued

Press

Display

›

Op1

›

5
Op1

›

10
Op1

›

15
Op1

TI-15: A Guide for Teachers

Powers as “repeated multiplication”
Use this formula and repeated
multiplication to find the volume of
a cube with a base of 5 meters.
V = l x w x h = 5 x 5 x 5 = 53

Constant
Operations

›
Multiply

Press

› V 5 ›
(store the
operation)

1
( initialize u s i n g 1 )

›
›
›

Display
Op1

Ý5
Op1

1á
Op1

1Ý5
1

5
Op1

5Ý5
2

25
Op1

25Ý5
3

125

TI-15: A Guide for Teachers

Using ¨ as a constant
Use this formula to find the volume
of each cube.

Constant
Operations

›

V = base3

Powers

¨
Press

› ¨3 ›
2 ›
3 ›
4 ›

Display
Op1

É3
Op1

2É3
1

8
Op1

3É3
1

27
Op1

4É3
1

TI-15: A Guide for Teachers

Using OP 1 and OP 2 together
Ming received 5 stickers for each
household job she completed. She gave
her brother 2 stickers for helping with
each job. If they completed 3 jobs, how
many stickers does she have?
Press

› T 5 ›
œ U 2
œ
0
›
œ
›œ
›œ

Constant
Operations

›
œ

Display
Op1

Û5
Op1 Op2

Ü2
Op1 Op2

0á
Op1 Op2

0Û5
1

5
Op1 Op2

5Ü2
1

3
Op1 Op2

8Ü2
1

6
Op1 Op2

11Ü2
1

9
TI-15: A Guide for Teachers

Clearing constant operations
Before entering a new operation in
OP1 or OP2, you must clear the
current values.

Press

‡
$ $
®
(clears OP1)

" ®
(clears OP2)

‡
( exits Mode menu)

Mode Menu

‡

Display
Ù
ê
¼ÁÏ
êêêê
¼ÁÏ
êêêê

ßÄ¸
Þ
¼Á2
ç
¼Á2
ç

¼ÁÏ
ç

¼Á2
êêêê

Note: Pressing ” does not clear
constant operations.

TI-15: A Guide for Teachers

Whole Numbers and Decimals
Keys
1. r enters a decimal point.
2. Š sets the number of decimal
places in conjunction with the Place
Value keys (3 through 9 on the
illustration below). Only the
displayed result is rounded; the
internally stored value is not
rounded. The calculated value is
padded with trailing zeros if needed.

4. Š ‘ rounds results to the
nearest hundred.
5. Š ’ rounds results to the
nearest ten.
6. Š “ rounds results to the
nearest one.
7. Š ˜ rounds results to the
nearest tenth.
8. Š ™ rounds results to the
nearest hundredth.

3. Š rounds results to the
nearest thousand.

9. Š š rounds results to the
nearest thousandth.
Š r removes the fixed-decimal
setting.
You must press Š before a Place
Value key each time you want to
change the number of places for
rounding.
Notes
• The examples on the transparency
masters assume all default
settings.
•
2
3
4
5
6
7

The calculator automatically
rounds the result to the number of
decimal places selected. (Only the
displayed value is rounded. The
internally stored value is not
rounded.)

8
9

TI-15: A Guide for Teachers

Whole Numbers and Decimals

Notes (Continued)
• All results are displayed to the fixed
setting until you either clear the
setting by pressing Š r or reset
the calculator.
•

You can set 0 through 3 decimal
places.

•

If students are puzzled when they
round .555 to the nearest whole
number, for example, and the result
is 1, you may need to remind them of
the rules of rounding.

•

You can use r to enter decimal
numbers regardless of the fixed
decimal setting.

•

You must press ® before FIX
takes effect.

•

You can apply the FIX setting to an
individual value or to the result of an
operation.

TI-15: A Guide for Teachers

Setting the number of decimal places
Round 12.345 to the hundredth’s
place, the tenth’s place, the
thousandth’s place, and then
cancel the Fix setting.
Press

12 r 345
®
Š ™
Š ˜
Š š

Fix decimal

Display
12Ù345Ú
12Ù345
Fix

12Ù345Ú 12Ù35
Fix

12Ù345Ú

12Ù3

Fix

12Ù345Ú
12Ù345

To cancel Fix:

Š r

12Ù345Ú
12Ù345

TI-15: A Guide for Teachers

Addition with money
José bought ice cream for $3.50,
cookies for $2.75, and a large soda
for $.99. How much did he spend?
Press

Display

Š ™ ®
3 r 50 T
2 r 75 T
r 99 ®

Fix decimal

Fix

3Ù50Û2Ù75
ÛÙ99Ú
7Ù24

TI-15: A Guide for Teachers

Converting decimals to fractions
Convert the decimal .5 to a
fraction, and then view the decimal
again after the conversion.

Press

r 5 ®
Ÿ

Fix decimal

Display
ÙÓÚ

ØÙÓ
N n
&
D d

ÙÓÚ

Ó
ÏØ
ííí

Ÿ
(Return to
decimal)

ØÙÓ

TI-15: A Guide for Teachers

Memory
Keys
1. z functions as shown below:

z £ Performs integer division
on value in memory using
the displayed value. Only
the quotient is stored
and displayed.

z ® Stores displayed value
over value in memory.
Adds displayed value to
zT
memory.
Subtracts displayed
2. | recalls the contents of
zU
value from value in memory.
memory to the display. When
Multiplies displayed
pressed twice, it clears the
zV
value by value in memory.
memory.
Divides value in memory
zW
by the displayed value.
Notes
• The examples on the transparency
masters assume all default settings.
•

Results are stored to memory and
not displayed. The display remains
the same.

•

You can store integers, fractions,
and decimals in memory.

•

M is displayed anytime a value
other than 0 is in memory.

•

To clear the memory, press |
twice.

1
2

TI-15: A Guide for Teachers

Using memory to add products
Hamburgers
2 $1.19
Milk shakes
3 $1.25
Coupon for each
milk shake 3 $.20
Total cost
Press

2 V 1 r 19
®
z ®
3 V 1 r 25
®
z T
(Add milk shakes

=
=

Store to Memory

=
=

Memory Recall

Display
2Ý1Ù19Ú

2Ù38

2Ý1Ù19Ú

2Ù38

3Ý1Ù25Ú

3Ù75

3Ý1Ù25Ú

3Ù75

to memory.)

3 V r 20
®
z U
(Deduct coupon

3ÝÙ20Ú

0Ù6

3ÝÙ20Ú

0Ù6

from memory.)

|
(Recall the total

5Ù53

cost.)
© 2000 TEXAS INSTRUMENTS INCORPORATED

TI-15: A Guide for Teachers

Using memory to find averages
Dai has test scores of 96 and 85.
He has weekly scores of 87 and 98.
Find the average for each group of
scores and the average of his
averages together.
Press

96 T 85
®
W 2 ®
z ®
87 T 98
®
W 2 ®
T |
®
W 2 ®

Display

Store to Memory

z
Add

T
Memory Recall

96Û85Ú

181

181Þ2Ú

90Ù5

181Þ2Ú

90Ù5

87Û98Ú

185

185Þ2Ú

92Ù5

92Ù5Û90Ù5Ú
183
M

183Þ2Ú

91Ù5

TI-15: A Guide for Teachers

Fractions
Keys
1. ¢ displays a menu of mode
settings from which you can select
how the fraction results will be
displayed. You select 2 items.
U n/d (default) displays mixed
number results.
n/d displays fraction results.
Man (default) displays unsimplified
fraction results so you can simplify
them manually (step-by-step).
Auto displays fraction results
simplified to lowest terms.

2. lets you enter the wholenumber part of a mixed number.
3. lets you enter the numerator of
a fraction.
4. ¥ lets you enter the denominator
of a fraction.
5. ¦ changes a mixed number to
a fraction and vice versa.
6. ¤ simplifies a fraction using the
lowest common prime factor. If you
want to choose the factor (instead
of letting the calculator choose it),
press ¤, enter the factor (an
integer), and then press ®.
You must be in Manual mode to
use this function.
7. Ÿ changes a fraction to its
decimal equivalent and vice versa.

8. § displays the factor (divisor)
used to simplify the last fraction
result. You must be in Manual
mode to use this function.
Notes
•

The examples on the transparency
masters assume all default
settings.

TI-15: A Guide for Teachers

Fractions

Notes (continued)
• Dividing a fraction by a fraction
• When you multiply or divide
gives fractional results regardless of
fractions and decimals, the result
the division setting (decimal or
is displayed as a decimal. A
fraction).
decimal cannot be converted to a
fraction if the result would overflow
• The ¢ mode settings provide 4
the display.
possible display options for
• Clearing with w in fractions
computational results displayed in
occurs from right bottom to left
fraction form. For example, for
top. If you accidentally press ¥
6 ÷ 4, the displays would look like
(the denominator key) after
this:
entering the numerator, without
6
entering a numeral for the
manual simp/improper (n/d):
4
denominator first, using w will not
3
auto simp/improper (n/d):
2
correct that error. You will need to
2
clear and begin the entry again.
manual simp/mixed number:
14
• If the decimal place is set to 0, the
(U n/d)
decimal equivalent for a fraction
1
auto simp/mixed number:
12
will not be displayed.
(U n/d)
• You can enter the denominator or
numerator first.
• For operations, you can enter 1 to
1000 for the denominator. For
conversions to decimal, you can
enter 1 to 100,000,000 for the
denominator.

TI-15: A Guide for Teachers

Adding mixed numbers
A baby girl weighed 4 3/8 pounds at
birth. In the next 6 months, she
gains 2 3/4 pounds. How much does
she weigh?

Numerator Key

Denominator Key

¥
Unit Key

Press

Display

4 8 ¥
3 T

3 Û
4 ííí
8

2 3
4 ¥ ®

3 + 2ííí
3 =
4 ííí
8
4

Mixed to Improper
Conversion

¦
1
7 ííí
8
57
8

ííííí

TI-15: A Guide for Teachers

Simplifying fractions
Method 1: The calculator chooses
a common factor
18
Simplify 24 .
Press

18 24
(Enter the
fraction.)

¤
( Prepare to simplify.)

®
(Simplify the
fraction.)

Numerator Key

Denominator Key

Display

Simplify

18
24

ííííí

18 S
à¾á
24

ííííí

Factorial
N n
&
D d

18
à¾
24

9
12

íííí

ííííí

§
(Optional: Check
factor. You must be
in Manual mode.)

N n
&
D d

9
12

íííí

(Return to the
fraction.)

¤ ®
(Continue
simplifying.)

9
à¾
12

íííí

3
4

ííí

TI-15: A Guide for Teachers

Simplifying fractions
Method 2: You choose a common
factor
18
Simplify 24 .
Press

Denominator Key

Display

18 24
(Enter the
fraction.)

¤
(Prepare

Numerator Key

simply.)

6
(Enter a common
factor.)

®
(Simplify the
fraction.)

1íííí
8
á
24

Simplify

18 à¾
24

íííí

18
à¾Ôá
24

íííí

18
à¾Ô
24

íííí

3
4

ííí

TI-15: A Guide for Teachers

Converting fractions to decimals
5

Convert the fraction 10 to a
decimal, and then view the original
fraction after the conversion.

Numerator Key

Denominator Key

Press

5 10 ®

Display
N n
&
D d

5
Ú
10

5
10

íííí

Ÿ
0Ù5

Ÿ
(Return to
fraction.)

Fraction to
Decimal

N n
&
D d

5
10

íííí

(Return
to decimal.)

0Ù5

TI-15: A Guide for Teachers

Converting decimals to fractions
Convert the decimal .5 to a
fraction, and then view the decimal
again after the conversion.

Numerator Key

Denominator Key

Press

r 5 ®
Ÿ

Display
Ù5Ú

0Ù5
N n
&
D d

Ù5Ú

5
10

íííí

Fraction to
Decimal

(Return
to decimal.)

0Ù5

TI-15: A Guide for Teachers

Converting between fractions and mixed numbers
6

Convert the improper fraction 4 to
a mixed number.

Numerator Key

Denominator Key

Press

¢
$
¢ 6 4
®
¤ ®

Display
¿êêêêêê
»Ä¸

»Ä¸

è
êêêê

ííí

6 Ú
4

2
1 íííí
4

2
1 ííí
à¾
4

1
1 íííí
2

Fraction Modes

3
2

íííí

TI-15: A Guide for Teachers

Comparing fractions and decimals
Linda swims 20 laps in 5.72
minutes. Juan swims 20 laps in 5¾
minutes. Who swims faster?
Compare the time as decimals and
fractions.

Numerator Key

Denominator Key

To compare the times as decimals:
Press

5 3
4 ®

Display
3 =
5 ííí
4

3
4

ííí

Ÿ
5Ù75

N n
&
D d

75
100

íííííí

Continue to compare as fractions:

5 r 72 ®

5Ù72Ú

5Ù72
N n
&
D d

7ííííí
2
100

TI-15: A Guide for Teachers

Percent
Keys
1. y converts to a percent.
2. ª enters a percent.

Notes
• The examples on the transparency
masters assume all default
settings.

1
2

TI-15: A Guide for Teachers

Converting with percent
Percent

Convert 25% to a decimal.
Press

25 ª ®

Display
25ãÚ

0Ù25

Convert to
Percent

y
25
Convert 100 to a percent.
Press

Display

25 100
¥ y ®

2 5 àã
íííí
100

25ã

Convert 3 to a percent.
Press

3 y ®

Display
3àã

300ã

TI-15: A Guide for Teachers

Converting with fractions, decimals, and percent
Convert 25% to a fraction, simplify
to lowest terms, and then convert
the fraction to a decimal.
Press

25 ª ®

Display

25ãÚ

Percent

ª
Fraction to
Decimal

0Ù25

N/D"n/d

25
100

íííííí

¤ ®
¤ ®

N/D"n/d

25 à¾
100
íííííí

5
20

íííí

N/D"n/d

5 à
ííí
¾
20

1
4

ííí

Ÿ
0Ù25

0Ù25àã

25ã

TI-15: A Guide for Teachers

Calculating tips
The Chen family went to a
restaurant for dinner. Their bill was
$31.67. How much was the tip if
they left 15% of their bill? How much
was the total including the tip?
Press

31.67 ®
Š ™

ª
Convert to
Percent

Display
31Ù67Ú

Percent

31Ù67

Fix

31Ù67Ú

31Ù67

V 15 ª
®

31Ù67Ý15ãÚ
4Ù75

31.67 T
4.75 ®

31Ù67Û4Ù75Ú
36Ù42

Fix

TI-15: A Guide for Teachers

Pi
Keys
1. © enters p.

Notes
• The examples on the transparency
masters assume all default
settings.
•

Internally, pi is stored to 13 digits
(3.141592653590). Only 9 decimal
places are displayed.

•

To convert from p to a decimal
value, press Ÿ. Nine decimal
places are displayed.

TI-15: A Guide for Teachers

Using pi to find circumference
Pi

Use this formula to
find the amount of
border you need to
buy if you want to put
a circular border
around a tree at a
distance of 3 meters
from the tree.

C = 2pr = 2 x p x 3

Press

2 V ©
V 3 ®

Display
2Ýß

2ÝßÝ3Ú

Ôß

Ÿ
18Ù84955592

TI-15: A Guide for Teachers

Using pi to find area
Use this formula to find how much
of the lawn would be covered by a
sprinkler with a radius of 12 meters.

A = pr2 = p x 122

12 m

Press

Display
ßÝ

ßÝÏÐÉÐ

ßÝÏÐÉÐÚS 144ß

Ÿ
452Ù3893421

TI-15: A Guide for Teachers

Using pi to find volume
Use this formula to find how much
space a ball occupies.
V=

4pr3
3

5 cm

Press

4 V © V
5 ¨ 3
W 3
®

Display
ÒÝßÝ

ÒÝßÝÓÉÑ

ÒÝßÝÓÉÑÞÑ

ÒÝßÝÓÉÑÞÑÚ
523Ù5987756

TI-15: A Guide for Teachers

Powers and Square Roots
Keys
1. ¨ lets you specify a power for the
value entered. When you press ®,
the value is displayed if it is within
the range of the calculator.

Notes
• The examples on the transparency
masters assume all default
settings.

2. ¬ calculates the square root of
positive values, including fractions.

TI-15: A Guide for Teachers

Finding the area of a square
Use this formula to find the size of
the tarpaulin needed to cover the
entire baseball infield.

Powers

A = x2 = 902

Press

90 ¨ 2
®

Display
×ØÉÐÚ

8100

TI-15: A Guide for Teachers

Finding the square root
Use this formula to find the length
of the side of a square clubhouse if
36 square meters of carpet would
cover the floor.

Square Root

L = x = 36

36 m2
of carpet

Press

¬ 36 Y
®

Display
âÅ36ÆÚ

TI-15: A Guide for Teachers

Calculating powers
Fold a piece of paper in half, in half
again, and so on until it is not
possible to physically fold it in half
again. How many sections are there
after ten folds?

Press

2 ¨ 10 ®

Powers

Display
2ÉÏØÚ 1024

TI-15: A Guide for Teachers

Calculating negative powers
Find the standard numerals for the
following powers:
2-3 =
-2-3 =
.2-3 =
(1/2)-3 =

Press

¨
Negative

Display

2 ¨ M 3
®

2ÉÜÑÚ

M 2 ¨
M 3 ®

Ü2ÉÜÑÚ ÜØÙÏÐÓ

r 2 ¨ M 3
®

Ù2ÉÜÑÚ

1 2 ¨ M
3 ®

Powers

1ê É. Ü Ñ Ú
2

ØÙÏÐÓ

ÏÐÓ

TI-15: A Guide for Teachers

Using powers of 10
Powers

1.3 x 103 = ?

Press

Display

1 r 3 V
10 ¨ 3 ®

1Ù3ÝÏØÉÑÚ
1300

1.3 x 10L3 = ?

1 r 3 V
10 ¨ M 3
®

1Ù3ÝÏØÉÜÑÚ
0Ù0013

TI-15: A Guide for Teachers

Problem Solving: Auto Mode
Keys
1. ‹ activates the Problem Solving
tool.
In Auto mode, this function provides
a set of electronic exercises to
challenge the student’s skills in
addition, subtraction, multiplication,
and division.
2. ‹ ‡ displays the menu to select
mode, level of difficulty, and type of
operation.
Mode:
Level:
Type:

Auto
1
2
+
-

Man (Manual)
3
P
x
?

Auto, Level 1 , and Addition are the
default mode settings.
Notes
• The examples assume all default
settings.
•

In Auto mode (default), the TI-15
presents problems with one
element missing (for example
5+2=? or 5+?=7 or 5?2=7).

•

If the answer is not correct, the
TI-15 displays “no” and gives a hint
in the form of “<” or “>”.

•

After you enter three incorrect
answers, the TI-15 provides the
correct answer.

•

After every fifth problem, the TI-15
displays a Scoreboard that tallies
the student’s correct and
incorrect answers.

•

Teachers can check a student’s
progress at any time by pressing
‡ to display the Scoreboard.
You can also press # to review
previous problems.

•

In Problem Solving, you can view the
history, but you cannot edit.

•

To exit Problem Solving, press ‹
again. The Scoreboard is cleared
when you exit.

1
2

TI-15: A Guide for Teachers

Select level of difficulty
Problem Solving

Choose the level of difficulty.

‹
Mode

‡
Press

‹‡
$
" ®
‡
(to exit)

Display
‹

Auto

æ
êêêêê

‹

Auto

1ê

2
êëì

‹

3
Auto

2ê
3
êëì

‹

Auto

8ÛÃÚ808

TI-15: A Guide for Teachers

Select type of operation
Problem Solving

Choose the type of operation:

‹

– addition
– subtraction
– multiplication
– division
– find the operator

Press

‹‡
$
$
" " ®
‡
(to exit)

Mode

‡

Display
‹

Auto

æ
êêêêê
‹

Auto

1ê
‹

2
êëì

Auto

Ûê Ü Ý Þ Ã ?
‹

Auto

Û Ü êÝ Þ Ã ?
‹

Auto

4Ý1Ú Ã

TI-15: A Guide for Teachers

Test your skills
Enter solutions to the problems
that the calculator presents.
(Problems are random.)
Press

‹ ‡
‡
11 ®

Problem Solving

‹
Mode

Display

‡
‹

Auto

æ
êêêêê
‹

Auto

8Û3Ú Ã
‹

Auto

8Û3Ú11
À¹¾ s
‹

Auto

2ÛÃÚ7

4 ®

‹

Auto

2Û4Ú7
N»¼
‹

Auto

2Û4Ç7

5 ®

‹

Auto

2Û5Ú7
À¹¾

TI-15: A Guide for Teachers

View the Scoreboard
After every fifth problem, the
calculator displays a score board
that tallies your right and wrong
solutions.

Problem Solving

You can also display the
scoreboard at any time by pressing
‡.
Press

‡

‹
Mode

‡

Display
‹

Auto

À¹¾ s
5

»¼
0

TI-15: A Guide for Teachers

Find the operator
Change the type of operation to
“find the operator” (?) and solve
the problems the calculator
presents.

Problem Solving

‹
Mode

‡
Press

‹ ‡
$ $
" " " "
®
‡
V ®

Display
‹

Auto

æ
êêêêê
‹

Auto

Ûê Ü Ý Þ Ã ?
‹

Auto

Û Ü Ý Þ êÃ ?
‹

Auto

8Ã6Ú48
‹

Auto

8Ý6Ú48
À¹¾s

TI-15: A Guide for Teachers

Problem Solving: Manual Mode

Keys
1. ‹ activates Problem Solving.

Notes
• The examples on the transparency
masters assume all default settings.
2. ‡ displays the menu for selecting
mode, level of difficulty, and type of
• Teachers can check a student’s
progress at any time by pressing
operation.
‡ to display the Scoreboard.
Mode:
Auto
Man (Manual)
You can also press # to review
Display:
11-.
-1-.
previous problems.
In Manual mode, the student
• When you first press ‡, the
composes his or her own problems.
display shows the Scoreboard for a
3. lets the student indicate a
moment before showing the menu.
missing element in Manual mode.
• In Manual mode, for all operations
4. lets the student test
except inequalities, the calculator
inequalities.
accepts only integers.
• You can enter no more than 11
characters on the display.
• You can enter a problem that has
one solution, multiple solutions, or
no solution. For example:
1 solution: 2+5=?, 2+?=7, 2?5=7
Multiple solutions: ?+?=1, ?+?=6
0 solutions: 3P2=?
4
(Answer is not an integer.)
1
3
• When a problem has no solution,
2
the calculator will display “no” and
will continue to present the
problem until cleared manually.
• Problems with two missing
elements may have multiple
solutions. (?x?=24 has 8 solutions.)
They must be in the form of
?operator?=number.

•

In Problem Solving, you can view the
history, but you cannot edit.

•

To exit Problem Solving, press ‹.
TI-15: A Guide for Teachers

100

Problems with one solution
Problems with one solution are
equations with one missing element
(for example 7+2=? or 7+?=9).
Enter a problem and find a solution.
Press

Problem Solving

‹
Mode

Display

‹ ‡

‹

" ®

‹

‡

‹

5 U 3 ®
®
2 ®

‹

‡

Auto

æ
êêêêê

Missing element

Auto

è
êêêê

á
5Ü3ÚÃ
1 ¾¼º
‹

5Ü3Ú2
À¹¾

5 T ®
9 ®
3 ®
4 ®

‹

5ÛÃÚ9
1 ¾¼º
‹

5Û3Ç9
»¼
‹

5Û4Ú9
À¹¾

TI-15: A Guide for Teachers

101

Problems with more than one solution
Problems with two missing elements
may have more than one solution.
Enter a problem, find the number of
solutions, and then find a solution.

Problem Solving

‹
Mode

‡
Missing element
Press

‹ ‡ "
®
‡
T
® 3 ®
2 ®
1 ®

Display
‹

Auto

è
êêêê

‹

á
‹

ÃÛÃÚ3
4 ¾¼º
‹

2ÛÃÚ3
‹

2ÛÏÚ3
À¹¾S

TI-15: A Guide for Teachers

102

Problems with no solution
The TI-15 calculator is not designed
to handle certain types of problems.
These will result in a 0 SOL (no
solution) response from the
calculator.

Problem Solving

‹
Mode

‡
Missing element

Press

‹‡ "
®
‡
1 U 2 ®
®
”

Display
‹

Auto

è
êêêê

‹

á
‹

1Ü2ÚØ
0 ¾¼º
‹

TI-15: A Guide for Teachers

103

Less than, greater than, equals
You can test inequalities and
equalities using Problem Solving.

Problem Solving

‹
Mode

Press

‹‡ "
®
‡
2 T 1 ® 1
T 2 ®
5 T 4 10
®
r 5
r 50 ®

‡

Display
‹

Auto

è
êêêê

Equals

‹

Greater Than,
Less Than

‹

2Û1Ú1Û2
À¹¾

‹

5Û4Ç10
À¹¾S
‹

Ù5ÈÙ50
»¼
‹

Ù5ÚÙ50
À¹¾S

TI-15: A Guide for Teachers

104

View Scoreboard
After every fifth problem, the
calculator displays a scoreboard
that tallies your right and wrong
solutions.

Problem Solving

You can also display the scoreboard
at any time by pressing ‡.

Press

‡

‹
Mode

‡

Display
‹

À¹¾
5

»¼
0

TI-15: A Guide for Teachers

105

Place Value
Keys
1. ‹ activates Problem Solving.

3. Œ activates the place value
function in Manual mode. It also
works in conjunction with these
keys:

2. ‡ lets you set the mode and
display option for Place Value.
Mode: Auto Man (Manual)
Display: 11-1Example:
Enter
Press Œ ’

1 234.56
1 23_._ _ (using 11-)
_ _3_._ _ (using -1-)

Key

Displays

‘
’
“
˜
™
š

Number of thousands
Number of hundreds
Number of tens
Number of ones
Number of tenths
Number of hundredths
Number of thousandths

Example:
Enter
Press Œ 4

2
1

Notes
• The examples on the transparency
masters assume all default
settings.
•

The Place Value features work only
if you are in Problem Solving
Manual mode.

•

To exit Problem Solving completely,
press ‹.

1 2 3 .45 6
_ _ _ .4_ _
4 " .01

TI-15: A Guide for Teachers

106

Place Value

How to Use the Place Value Function
When you use the place value function, you can determine the place value of a
specific digit OR the number of ones, tens, hundreds, etc. in a given number.
•

The ‹ mode setting must be Manual and the display option 11-.
To determine:

Follow these steps:

Example:

Place Value

Enter the number, press Œ, and press Page 108
the digit.

How Many?

Enter the number, press Œ, and press Page 110
“, ’, ‘, , ˜, ™, or š.

•

When determining How Many?, be sure to explain to students that
12_ _ . _ _ _ (after you press ‘ on page 110) represents 12 hundreds in
the number 1234.567, or that 123456 . _ (after you press ™)
represents 123,456 hundredths in the number 1234.567.

•

When a number includes a repeated digit, the calculator first analyzes
its occurrence in the right-most position. To find the place value of other
instances, press the digit again. (See page 109 for an example.)

•

Once Œ is active, it is not necessary to press this key before each digit.
To enter a new number, however, you must press ”, enter the number,
and then press Œ again.

•

To exit Place Value, press ” and the TI-15 returns to Problem Solving,
Manual mode.

How to Use What’s the Digit Function
Another way to display place value is to show the digit that is in the ones
place, the tens place, etc.
•

•

The ‹ mode setting must be Manual and the display option -1-.
To determine:

Follow these steps:

Example:

What’s the Digit?

Enter the number, press Œ, and press Page 111
“, ’, ‘, , ˜, ™, or š.

To exit Place Value, press ” and the TI-15 returns to Problem Solving,
Manual mode.

TI-15: A Guide for Teachers

107

Determine place value
Enter 1234.567. Determine the
place value of 7 and 4.

Problem Solving

‹
Place Value

Œ
Press

‹‡ "
®‡

Display
‹

è
êêêê

‹

1234r567
Œ

‹ƒ

1234Ù567

1234Ù567
ííííÙ í í 7
‹ƒ

1234Ù567
7ÜÈ0Ù001

‹ƒ

1234Ù567
ííí4 Ù ííí
‹ƒ

TI-15: A Guide for Teachers

108

Repeated digits
Enter 123.43. Determine the place
value of each 3.

Problem Solving

‹
Place Value

Œ
Press

‹ ‡ "
®‡
123 r43
Œ
3

Display
‹

è
êêêê

‹

á
‹ƒ

123Ù43
‹ƒ

123Ù43
íííÙí3
‹ƒ

123Ù43
3ÜÈ0Ù01

‹ƒ

123Ù43
íí3Ùíí
‹ƒ

TI-15: A Guide for Teachers

109

How many?
How many hundreds are in
1234.567? How many hundredths?

Problem Solving

‹
Place Value

Œ
Press

‹ ‡"
®
‡
1234r567
Œ
‘
™

Display

Hundreds

‹

è
êêêê

‹

‘
Hundredths

™

‹ƒ

1234Ù567
‹ƒ

1234Ù567
12ííÙííí
‹ƒ

1234Ù567
123456Ùí.-

TI-15: A Guide for Teachers

110

What’s the digit?
What digit is in the hundreds place
in 1234.567?

Problem Solving

‹
Place Value

Press

‹ ‡"
®
$ " ®
‡
1234r567
Œ
‘

Display
‹

è
êêêê

‹

11ÜÙ

Üêêêêê
ÏÜÙ

‹

á
‹ƒ

1234Ù567
‹ƒ

1234Ù567
í2ííÙííí

TI-15: A Guide for Teachers

111

Quick Reference to Keys
Key

Function

−

Turns on the calculator. If already on, turns the calculator off.

”

Clears display and error condition.

−”

To reset the calculator, hold down − and ” simultaneously for a few
seconds and release. MEM CLEARED shows on the display. This will
completely clear the calculator, including all mode menu settings, all
previous entries in history, all values in memory, and the display. All
default settings will be restored.

Moves the cursor right and left, respectively, so you can scroll the entry
line or select a menu item.

Moves the cursor up and down, respectively, so you can see previous
entries or access menu lists.

Deletes the character to the left of the cursor before ® is pressed.

‡

Displays menu to select format of results of division:

‡$

Displays menu to show or hide (?) in Op1 or Op 2:

‡$$

Displays menu to clear Op1 or Op2:

‡$$$

Displays menu to reject or accept Reset:

qhijkl
mnop

Enters the numerals 0 through 9.

Adds.

Subtracts.

Multiplies.

Divides.

Completes operations. Enters the equal sign or tests a solution in
Problem Solving.

Inserts a decimal point.

Enters a negative sign. Does not act as an operator.

Opens a parenthetical expression.

Closes a parenthetical expression.

.
+1

Op1

TI-15: A Guide for Teachers

n/d

Clear

?
Op2

A-1

Quick Reference to Keys

(Continued)

Key

Function

When you divide a positive whole number by a positive whole number using
£, the result is displayed in the form Q r R, where Q is the quotient
and R is the remainder. If you use the result of integer division in a
subsequent calculation, only the quotient is used; the remainder is
dropped.

When pressed after entering a number, designates the numerator of a
fraction. The numerator must be an integer. To negate a fraction, press
M before entering numerator.

When pressed after entering a number, designates the denominator of a
fraction. The denominator of a fraction must be a positive integer in the
range 1 through 1000. If you perform a calculation with a fraction having
a denominator greater than 1000, or if the results of a calculation yield
a denominator greater than 1000, the TI-15 will convert and display the
results in decimal format.

Separates a whole number from the fraction in a mixed number.

Displays a menu of settings that determine how fraction results are
displayed.
• U n/d (default) displays mixed number results.
•

n/d displays results as a simple (improper) fraction.

If N/d"n/d is displayed after you convert a fraction to a mixed number,
you can further simplify the fractional portion of the mixed number.
¢$

Displays a menu to select the method of simplifying fractions:
• Man (default) allows you to simplify manually (step-by-step).
•

Auto automatically reduces fraction results to lowest terms.

Enables you to simplify a fraction.

Displays the factor that was used to simplify a fraction.

Converts a mixed number to an improper fraction or an improper fraction
to a mixed number.

Converts a fraction to a decimal, or converts a decimal to a fraction, if
possible. Converts p to a decimal value.

Enters a percentage.

TI-15: A Guide for Teachers

A-2

Quick Reference to Keys

(Continued)

Key

Function

Converts a decimal or a fraction to a percent.

Calculates the square root of a number.

Raises a number to the power you specify.

Enters the value of p. It is stored internally to 13 decimal places
(3.141592653590). In some cases, results display with symbolic p, and
in other cases as a numeric value.

Stores the displayed value for later use. If there is already a value in
memory, the new one will replace it. When memory contains a value other
than 0, M displays on the screen. (Will not work while a calculation is in
process.)

Recalls the memory value for use in a calculation when pressed once.
When pressed twice, clears memory.

›
œ

Each can store one or more operations with constant value(s), which
can be repeated by pressing only one key, as many times as desired. To
store an operation to Op1 or Op2 and recall it:
• Press › (or œ), enter the operator and the value, and press ›
(or œ) to save the operation.
•

Press › (or œ) to recall the stored operation.

To clear the contents of Op1 or Op2, press ‡$$, select Op1 or
Op2, and press ®. New operations can now be stored for repeated
use.
Š

Rounds off results to the nearest thousand.

Š‘

Rounds off results to the nearest hundred.

Š’

Rounds off results to the nearest ten.

Š“

Rounds off results to the nearest one.

Š˜

Rounds off results to the nearest tenth.

Š™

Rounds off results to the nearest hundredth.

Šš

Rounds off results to the nearest thousandth.

Šr

Removes fixed-decimal setting and returns to floating decimal.

TI-15: A Guide for Teachers

A-3

Quick Reference to Keys

(Continued)

Key

Function

‹

Provides a set of electronic flash cards to challenge your skills in
addition, subtraction, multiplication, and division.

‹‡

Displays menu list to select Auto or Manual operation: Auto

‹‡$

Displays menu list to select level of difficulty:

1 2 3

‹‡$$

Displays menu list to select type of problem:

+ - Q P ?

‹‡$

Displays menu to select display options for Place Value: 11-.
(This option available only if Man mode is selected.)

While in ‹ function, manual problem solving mode, lets you indicate a
missing element in an equation.

While in the ‹ function, manual problem solving mode, lets you test
inequalities. Press once to enter <. Press twice to enter >.

While in ‹ function, you can determine the place value of a particular
digit of given number or, in conjunction with place value keys, can
determine how many thousands, hundreds, etc., a number contains or
what digit is in a given place.

Œd

Determines the place value of digit d of given number.

Tells how many thousands a given number contains or what digit is in
the thousands place.

Œ‘

Tells how many hundreds a given number contains or what digit is in the
hundreds place.

Œ’

Tells how many tens a given number contains or what digit is in the tens
place.

Œ“

Tells how many ones a given number contains or what digit is in the ones
place.

Œ˜

Tells how many tenths a given number contains or what digit is in the
tenths place.

Œ™

Tells how many hundredths a given number contains or what digit is in
the hundredths place.

Œš

Tells how many thousandths a given number contains or what digit is in
the thousandths place.

TI-15: A Guide for Teachers

Man

-1-.

A-4

Display Indicators
Indicator

Meaning

‹

Calculator is in Problem Solving mode.

Calculator is in place-value mode.

Fix

The calculator is rounding to a specified number of places.

Indicates that a value other than zero is in memory.

Value is being stored to memory. You must press T, U, V, W, or ®
to complete the process.

Op1, Op2

An operator and operand is stored.

Auto

In calculator mode, Auto simplification of fractions to lowest terms is
selected. In ‹, Problem Solving function is in Auto mode.

Integer division function has been selected (appears only when cursor is
over division sign).

n/d P

Division results will be displayed as fractions.

N//d"n/d

The fraction result can be further simplified.

Previous entries are stored in history, or more menus are available.
Press # to access history. Press $ and # to access additional menu
lists.

$
!

You can press ! and " to scroll and select from a menu. You must
press ® to complete the selection process.

TI-15: A Guide for Teachers

B-1

Error Messages
Message

Meaning

Arith Error

Arithmetical error. You entered an invalid entry or an invalid parameter;
for example, L5 .

Syn Error

Syntax error. You entered an invalid or incorrect equation; for example,
5++2 or missing parenthesis.

P 0 Error

Divide by 0 error. You attempted to divide by 0.

Op Error

Error following steps for using Op1 or Op2.

Overflow Error

Overflow. The result is too large to fit within the boundaries of the
display.

Underflow Error

Underflow. Result is too small.

TI-15: A Guide for Teachers

C-1

Support, Service, and Warranty
Product
Support

Customers in the U.S., Canada, Puerto Rico, and the Virgin
Islands
For general questions, contact Texas Instruments Customer Support:
phone:

1-800-TI-CARES (1-800-842-2737)

e-mail:

ti-cares@ti.com

For technical questions, call the Programming Assistance Group of
Customer Support:
phone:

1-972-917-8324

Customers outside the U.S., Canada, Puerto Rico, and the
Virgin Islands
Contact TI by e-mail or visit the TI Calculator home page on the World
Wide Web.
e-mail:

ti-cares@ti.com

Internet: www.ti.com/calc

Product
Service

Customers in the U.S. and Canada Only
Always contact Texas Instruments Customer Support before returning
a product for service.

All Customers outside the U.S. and Canada
Refer to the leaflet enclosed with this product or contact your local
Texas Instruments retailer/distributor.

Other TI
Products
and
Services

Visit the TI calculator home page on the World Wide Web.
www.ti.com/calc

TI-15: A GUIDE FOR TEACHERS

D-1

Support, Service, and Warranty (Continued)
Warranty
Information

Customers in the U.S. and Canada Only
One-Year Limited Warranty for Commercial Electronic Product
This Texas Instruments electronic product warranty extends only to the
original purchaser and user of the product.
Warranty Duration. This Texas Instruments electronic product is
warranted to the original purchaser for a period of one (1) year from the
original purchase date.
Warranty Coverage. This Texas Instruments electronic product is
warranted against defective materials and construction. THIS
WARRANTY IS VOID IF THE PRODUCT HAS BEEN DAMAGED BY
ACCIDENT OR UNREASONABLE USE, NEGLECT, IMPROPER SERVICE,
OR OTHER CAUSES NOT ARISING OUT OF DEFECTS IN MATERIALS
OR CONSTRUCTION.
Warranty Disclaimers. ANY IMPLIED WARRANTIES ARISING OUT OF
THIS SALE, INCLUDING BUT NOT LIMITED TO THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
PARTICULAR PURPOSE, ARE LIMITED IN DURATION TO THE ABOVE
ONE-YEAR PERIOD. TEXAS INSTRUMENTS SHALL NOT BE LIABLE
FOR LOSS OF USE OF THE PRODUCT OR OTHER INCIDENTAL OR
CONSEQUENTIAL COSTS, EXPENSES, OR DAMAGES INCURRED BY
THE CONSUMER OR ANY OTHER USER.
Some states/provinces do not allow the exclusion or limitation of implied
warranties or consequential damages, so the above limitations or
exclusions may not apply to you.
Legal Remedies. This warranty gives you specific legal rights, and you
may also have other rights that vary from state to state or province to
province.
Warranty Performance. During the above one (1) year warranty period,
your defective product will be either repaired or replaced with a
reconditioned model of an equivalent quality (at TI’s option) when the
product is returned, postage prepaid, to Texas Instruments Service
Facility. The warranty of the repaired or replacement unit will continue
for the warranty of the original unit or six (6) months, whichever is
longer. Other than the postage requirement, no charge will be made for
such repair and/or replacement. TI strongly recommends that you insure
the product for value prior to mailing.
Software. Software is licensed, not sold. TI and its licensors do not
warrant that the software will be free from errors or meet your specific
requirements. All software is provided “AS IS.”
Copyright. The software and any documentation supplied with this
product are protected by copyright.

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TI-15: A Guide for Teachers

D-2

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JBL 001 TI 15 Guide For Teachers (English) 15tg Book Eng

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