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

Front

TI-15

A Guide for Teachers

TI.15:

A Guide for Teachers

Developed by

Texas Instruments Incorporated

Activities developed by

Jane Schielack

About the Author

Jane Schielack is an Associate Professor of Mathematics Education in the Department of Mathematics at

Texas A&M University. She developed the

Activities

section and assisted in evaluating the appropriateness of

the examples in the

How to Use the TI-15

section of this guide.

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Table of Contents 

CHAPTER PAGE

About the Teacher Guide

........................... v

About the TI-15

........................................... vi

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

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

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

Related Procedures..................................20

Constant operations

In the Range............................................... 24

Rounding

The Value of Place Value ..........................29

Place value

What’s the Problem?................................34

Number sentences, Problem solving

How to Use the TI.15 ....................... 38

1 Display, Scrolling, Order of

Operations, Parentheses..................39

2 Clearing and Correcting..................... 42

3 Mode Menus.........................................45

4 Basic Operations................................48

5 Constant Operations.........................55

6 Whole Numbers and Decimals..........63

7 Memory .................................................68

8 Fractions ............................................... 71

9 Percent................................................. 80

10 Pi.............................................................84

11 Powers and Square Roots ............... 88

CHAPTER PAGE

How to Use the TI-15 (continued)

12 Problem Solving: Auto Mode............ 94

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

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

Appendix A ................................................A-1

Quick Reference to Keys

Appendix B.................................................B-1

Display Indicators

Appendix C ............................................... C-1

Error Messages

Appendix D ...............................................D-1

Support, Service, and Warranty

About the Teacher Guide 

How the Teacher Guide is Organized

This guide consists of two sections:

Activities

and

How to Use the TI-15

. The

Activities

section is a collection of activities for

integrating the TI-15 into mathematics

instruction.

How To Use the TI-15

is designed

to help you teach students how to use the

calculator.

Activities

The activities are designed to be teacher-

directed. They are intended to help develop

mathematical concepts while incorporating

the TI-15 as a teaching tool. Each activity is

self-contained and includes the following:

• An overview of the mathematical purpose

of the activity.

• The mathematical concepts being

developed.

• The materials needed to perform the

activity.

• A student activity sheet.

How to Use the TI.15

This section contains examples on

transparency masters. Chapters are

numbered and include the following:

• An introductory page describing the

calculator keys presented in the examples,

the location of those keys on the TI-15, and

any pertinent notes about their functions.

• Transparency masters following the

introductory page provide examples of

practical applications of the key(s) being

discussed. The key(s) being discussed are

shown in black on an illustration of the

TI-15 keyboard.

Things to Keep in Mind

• While many of the examples on the

transparency masters may be used to

develop mathematical concepts, they

were not designed specifically for that

purpose.

• For maximum flexibility, each example and

activity is independent of the others.

Select the transparency master that

emphasizes the key your students need

to use to develop the mathematical

concepts you are teaching. Select an

appropriate activity for the

mathematical concept you are teaching.

• If an example does not seem

appropriate for your curriculum or

grade level, use it to teach the function

of a key (or keys), and then provide

relevant examples of your own.

• To ensure that everyone starts at the

same point, have students reset the

calculator by pressing − and ”

simultaneously or by pressing ‡,

selecting RESET, selecting Y (yes), and

then pressing <.

How to Order Additional Teacher Guides

To place an order or to request additional

information about Texas Instruments (TI)

calculators, call our toll-free number:

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

Or use our e-mail address:

ti-cares@ti.com

Or visit the TI calculator home page:

http://www.ti.com/calc

About the TI.15

Two-Line Display

The first line displays an entry of up to 11

characters. Entries begin on the top left. If

the entry will not fit on the first line, it will

wrap to the second line. When space permits,

both the entry and the result will appear on

the first line.

The second line displays up to 11 characters. If

the entry is too long to fit on the first line, it

will wrap to the second line. If both entry and

result will not fit on the first line, the result is

displayed right-justified on the second line.

Results longer than 10 digits are displayed in

scientific notation.

If an entry will not fit on two lines, it will

continue to wrap; you can view the beginning

of the entry by scrolling up. In this case, only

the result will appear when you press ®.

Display Indicators

Refer to Appendix B for a list of the display

indicators.

Error Messages

Refer to Appendix C for a listing of the error

messages.

Order of Operations

The TI-15 uses the Equation Operating

System (EOSé) to evaluate expressions. The

operation priorities are listed on the

transparency master in Chapter 1,

Display,

Scrolling, Order of Operations, and Parentheses

.

Because operations inside parentheses are

performed first, you can use X or Y to

change the order of operations and, therefore,

change the result.

Menus

Two keys on the TI-15 display menus: ‡

and ¢.

Press $ or # to move down or up through

the menu list. Press ! or " to move the

cursor and underline a menu item. To return

to the previous screen without selecting the

item, press ”. To select a menu item, press

® while the item is underlined.

Previous Entries # $

After an expression is evaluated, use #

and $ to scroll through previous entries

and results, which are stored in the TI-15

history.

Problem Solving (‹)

The Problem Solving tool has three features

that students can use to challenge

themselves with basic math operations or

place value.

Problem Solving (Auto Mode) provides a set

of electronic exercises to challenge the

student’s skills in addition, subtraction,

multiplication, and division. Students can

select mode, level of difficulty, and type of

operation.

Problem Solving (Manual Mode) lets

students compose their own problems,

which may include missing elements or

inequalities.

Problem Solving (Place Value) lets students

display the place value of a specific digit, or

display the number of ones, tens, hundreds,

thousands, tenths, hundredths, or

thousandths in a given number.

About the TI.15 (Continued)

Resetting the TI.15

Pressing − and ” simultaneously or

pressing ‡, selecting RESET, selecting Y

(yes), and then pressing ® resets the

calculator.

Resetting the calculator:

• Returns settings to their defaults:

Standard notation (floating decimal),

mixed numbers, manual simplification,

Problem Solving Auto mode, and Difficulty

Level 1 (addition) in Problem Solving.

• Clears pending operations, entries in

history, and constants (stored

operations).

Automatic Power DownTM (APDTM)

If the TI-15 remains inactive for about

5 minutes, Automatic Power Down (APD)

turns it off automatically. Press − after

APD. The display, pending operations,

settings, and memory are retained.

Patterns in Percent 2

Fraction Forms 6

Comparing Costs 11

Number Shorthand 15

Related Procedures 20

In the Range 24

The Value of Place Value 29

What’s the Problem? 34

Activities

Patterns in Percent Grades 4 - 6

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.)

Math Concepts

• multiplication

• equivalent

fractions,

decimals, and

percents

Materials

• TI-15

• pencil

• student

activity

(page 4)

Introduction

1. After students use manipulatives to develop the

meaning of percent (1% = 1 part out of 100 parts),

have them explore what happens when they

press ª on the calculator.

2. Present the following scenario to students:

Metropolis East (M.E.) and Metropolis West

(M.W.) are neighboring cities. The sales tax in

M.E. is 10%, but the sales tax in M.W. is only

5%. Collect data and display your results for

each percent in a table to compare the amounts

of money you would pay for tax on various

items in each city.

3. Have students make conjectures about percent

based on the patterns they observe. Students can

then use manipulatives to verify their

conjectures.

Examples:

• Students may observe that for every item, 10%

of its price is twice as much as 5% of its price.

• Students may observe that it is easy to

estimate 10% of a whole number by using

place value and looking at the digits to the

right of the ones place.

Collecting and Organizing Data

To guide students in organizing their data to bring

out patterns, ask questions such as:

•

How could you organize your data to compare

the 5% tax rate to the 10% tax rate?

•

Why would it be useful to keep 5% in the left-

hand column of one table all the way down and

just change the total quantity?

³When a student enters

a 6 ª, the TI-15

displays 6%. Then,

when the student

presses ®, the

display changes to

6%= 0.06 to show that

6% is another way to

write 0.06 or 6/100.

³You will need to show

students how to use

multiplication on the

TI-15 to express the

percent of a given

quantity. For example,

to show 10% of $20:

1. Enter 10.

2. Press ª V.

3. Enter 20; press ®.

Students can verify the

calculator display of 2

by using manipulatives

to show 10% of $20 =

$2.

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?

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: ____%

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?

__________________________________________________________________________

Fraction Forms Grades 4 - 6

Overview

Students will compare the results of using division

to create fractions under the different mode

settings for fraction display and make

generalizations from the patterns they observe.

Math Concepts

• division

• multiplication

• common

factors

• equivalent

fractions

Materials

• TI-15

• pencil

• student

activity

(page 9)

Introduction

1. Present students with a problem such as:

In a small cafe, there are 6 cups of sugar left in

the pantry to put into 4 sugar bowls. If you

want them all to contain the same amount of

sugar, how much sugar goes into each sugar

bowl?

2. Have students present their solutions to the

problem. Encourage them to find as many ways

to represent the solution as possible.

Examples:

• By thinking of using a ¼ cup scoop to fill the

bowls, each bowl would receive 6 scoops, or

6/4 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).

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.

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

d man 6

4

n

d auto 3

2

U n

d man 1 2

4

U n

d auto 1 1

2

Collecting and Organizing Data

To guide students in creating data that will exhibit

patterns in the fraction quotients, ask questions such as:

•

What denominator did you choose to explore

with? Why?

•

What denominators do you get with the settings

n

d

man

? With the settings U n

d

man

?

•

What denominators do you get with the settings

n

d

auto

? With the settings

U n

d

auto

?

•

What denominator are you going to choose to

explore with next?

Example:

After exploring with denominators of 2 and 3,

you might suggest exploring with a denominator

of 6 and comparing results.

•

How can you organize your results to look for

patterns?

Example:

Continuing to increase the numerators by 1 each

time.

Fraction Forms (Continued)

Analyzing Data and Drawing Conclusions

To focus students’ attention on the patterns in their

fractions and the relationship of these patterns to the

denominators, ask questions such as:

•

What patterns do you see in your results?

Example:

When a denominator of 4 is used in the n

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

need to be added, using the n

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

close enough, using the U n

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.

Fraction Forms Name ___________________________

Date ___________________________

Collecting and Organizing Data

1. Have each person in your group set his/her calculator to one of the

following combinations of modes for fraction display. (Each person

should choose a different setting.)

• improper/manual simp

• improper/auto simp

• mixed number/manual simp

• mixed number/auto simp

2. Select a denominator: __________________

3. Use this denominator with several numerators and record each

person’s results in the table below.

Numerator Denominator n

d Man n

d Auto U n

d Man U n

d Auto

0

1

2

3

4

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.

__________________________________________________________________________

Comparing Costs Grades 3 - 5

Overview

Students will solve a problem using division with an

integer quotient and remainder, division with the

quotient in fraction form, and division with the

quotient in decimal form and compare the results.

Math Concepts

• division

• multiplication

• fractions

• decimals

Materials

• TI-15

• pencil

• student

activity

(page 14)

Introduction

1. Introduce the following problem:

The maintenance department has determined

that it will cost $.40 per square yard to

maintain the district’s soccer field each year.

The soccer field is 80 yards wide and 110 yards

long. The six schools that play on the field have

decided to split the cost evenly. How much

should each school contribute to the soccer field

maintenance fund this year?

2. Have students use the calculator to solve this

problem in three ways:

• Finding an integer quotient and remainder.

• Finding the quotient in fraction form.

• Finding the quotient in decimal form.

Collecting and Organizing Data

Students should record their procedures and results

on the Student Activity page. To help them focus on

their thinking, ask questions such as:

•

What did you enter into the calculator to solve

the problem?

Example:

A student may have entered 80 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.

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.

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.

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?

Responses may vary. Some students may want to

use the decimal form, since it is the closest to the

representation of money. Some students may

want to use the integer quotient and remainder

form and suggest that the Central Office pay the

$4.00 remainder.

Although the fraction form of the quotient

describes the exact quantity that each school

should pay, most students will recognize, by

comparing it to the decimal form, that the

fraction form is not easily translated into money.

When you fix

586.666667 to 2

decimal places, and

then multiply by 6, the

calculator “remembers”

the original number and

uses it as the factor.

The product rounded to

the nearest hundredth,

using the original factor,

is 3520.00. When you

enter 586.67, the

calculator uses this

number for the factor,

showing the actual

product of 3520.02.

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.

Number Shorthand: Scientific Notation

Grades 5 - 6

Overview

Students will use patterns created on the

calculator with the constant operation (› or œ)

to develop an understanding of scientific notation.

Math Concepts

• multiplication

• powers of 10

• exponents

Materials

• TI-15

• pencil

• 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 left-

hand 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

110

The 1 represents using

x 10 one time.

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:

1 x 1011.

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 1011.

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.

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

1x10^11 represents the product 1 x 1011.

•

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

2x10^11 represents the product 2 x 1011.

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.

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

Display

0 (starting factor)

1

2

3

4

Number Shorthand:

Scientific Notation

Name ___________________________

Date ___________________________

Analyzing Data and Drawing Conclusions

1. What patterns do you see?

__________________________________________________________________________

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.

__________________________________________________________________________

Related Procedures Grades 2 - 6

Overview

Students will use the two constant operations (›

and œ) to compare the results of different

mathematical procedures and determine how they

are related.

Math Concepts

• whole numbers

• addition,

subtraction,

multiplication,

division

• fractions

(Grades 5-6)

• decimals

(Grades 5-6)

Materials

• TI-15

• pencil

• student

activity

(page 23)

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.

³To 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.

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 ›

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

›?

³To recognize the

equivalent procedures,

students may need to

use the Ÿ key to

change outputs from

decimal to fraction form

or vice versa.

Input Procedure Output

2P21

4P22

6P23

Input Procedure Output

1x22

2x24

3x26

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 ›

Table for œ

Input Procedure Output

1P2 0.5 = 5/10 = ½

2P21

3P2 1.5 = 15/10 = 1½

Input Procedure Output

1x½½

2x½1

3 x½ 1.5 = 1½

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 ›Table for œ

Input Procedure 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.

__________________________________________________________________________

In the Range Grades 3 - 6

Overview

Students will interpret the rounding involved in

measuring to identify the possible range of a given

measurement.

Math Concepts

• rounding whole

numbers

• rounding

decimals

• measurement

with metric

units (length,

mass, capacity)

Materials

• TI-15

• pencil

• meter sticks

or metric

measuring

tapes

• 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).

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.)

³To fix the display at 2

decimal places, press

Š ™ ®.

³Have students discuss

how the display of 1.36

matches their rounding

of the measurement to

136 cm.

1356.5 1357 1357.5

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.)

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.

³To round to the nearest

whole number, press

Š “ ®.

³To round to the nearest

tenth, press Š ˜ ®.

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.)

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? ______________________

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).

_______________________________________________________________________

The Value of Place Value Grades 2 - 6

Overview

Students will build their flexibility in using numbers

by exploring the connections between the number

symbols and their representations with base-ten

materials.

Math Concepts

Grades 2 - 4

• whole number

place value

(through

thousands)

• money

Grades 4 - 6

• decimal place

value (through

thousandths)

• metric units

(meters,

decimeters,

centimeters)

Materials

• TI-15

• pencil

•

Counting

on Frank

by Rod

Clement

• base-ten

materials

• student

activity

(pages 32

and 33)

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.)

³To 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.)

³To 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.)

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:

•

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.

³Students 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.

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.

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.

__________________________________________________________________________

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.

__________________________________________________________________________

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

• addition,

subtraction

• multiplication,

division (Grades

3 - 5)

• number sentences

(equations)

• inequalities

(Grades 3 - 5)

Materials

• TI-15

• counters

• pencil

• student

activity

(page 37)

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.

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).

³To 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.

To test your solution to

the equation, enter the

value of 10 and press

®. The calculator will

display YES.

³If 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.

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?

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.

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.

How to Use

the TI.15

Display, Scrolling, Order of

Operations, Parentheses 39

Clearing and Correcting 42

Mode Menus 45

Basic Operations 48

Constant Operations 55

Whole Numbers and Decimals 63

Memory 68

Fractions 7 1

Percent 80

Pi 84

Powers and Square Roots 88

Problem Solving: Auto Mode 94

Problem Solving: Manual Mode 100

Place Value 106

Display, Scrolling, Order of

Operations, and Parentheses 1

Keys

1. X opens a parenthetical expression.

You can have as many as 8

parentheses at one time.

2. Y closes a parenthetical expression.

3. ! and " move the cursor left and

right.

# and $ move the cursor up and

down through previous entries and

results.

Notes

• The examples on the transparency

masters assume all default

settings.

• The EOSTM transparency master

demonstrates the order in which

the TI-15 completes calculations.

• 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 right-

justified. If a whole problem will not

fit on the first line, the result will

display on the second line.

3

2

1

Equation Operating System

EOS

Priority Functions

1 (first) X Y

2¢

3¨ ¬

4M

5V W

6T U

7¦ 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.

Order of Operations

1 + 2 x 3 = Add

T

Press Display Multiply

1 T 2 V 3

®1Û2Ý3Ú 7 V

Parentheses

X Y

(1 + 2) x 3 =

Press Display

X 1 T 2 Y

V 3 ®Å1Û2ÆÝ3Ú 9

Clearing and Correcting 2

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.

3. ” clears the last entry, all pending

operations, and any error conditions.

You can then enter a new number

and continue your calculation.

Notes

• The examples on the transparency

masters assume all default

settings.

• 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.

1

2

3

Clearing entries

1. Enter 335 + 10.

2. Clear the entry and pending

operation.

3. Enter 335 N 9.

4. Complete the calculation.

Clear

”

Press Display

335 T 10 335Û10á

”

(clear the entry) á

335 U 9 335Ü9

®335Ü9Ú 326

Note: ” clears the screen, but not

the history.

Correcting entry errors using w

1. Enter 1569 + 3.

2. Change the 9 to an 8.

3. Add 3.

4. Complete the calculation.

Backspace

w

Press Display

1569 T 3 1569Û3á

w w w 8 1568á

T 3 1568Û3á

®1568Û3Ú 1571

Mode Menus 3

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) +1 ?

Clear Op 1 Op 2

RESET NY

2. ‹ ‡ displays the Problem

Solving Mode menu, from which you

can select the following options:

Setting Options

Mode Auto Man

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.

1

2

3

Mode Menus (Continued) 3

Calculator Mode Menu

Setting Option Explanation Example

Division (Þ).Displays division results as a decimal .75

n/d Displays division results as a fraction 3

4

Constant Operations

(OP)

+1 Shows the constant operation on the

display

1x5

15

? Hides the constant operation

15

Clear OP1 When selected, clears Op1

OP2 When selected, clears Op2

Reset N No; does not reset the calculator.

Y Yes; resets the calculator.

Problem Solving Mode Menu

Setting SubMenu Option Example

Auto Level of

difficulty 1 2 3

Operation + – x P ? (add, subtract, multiply,

divide, find the operation)

Manual 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 _ _

Mode Menus (Continued) 3

Fractions Menu

Setting Option Explanation Example

Display U n/d Displays results as mixed numbers 1 3

4

n/d Displays results as improper fractions 7

4

Simplify Man Allows manual simplification 6

8 =3

4

Auto Automatically simplifies to most

reduced form of fraction

3

4

Basic Operations 4

Keys

1. T adds.

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.

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.

Notes

• The examples on the transparency

masters assume all default

settings.

• 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.

7

6

5

4

3

2

1

Basic operations

2 + 54 N 6 =

Press Display

Add, Subtract

T U

Multiply, Divide

V W

2 T 54 U

6 ®2Û54Ü6Ú 50 Equals

®

3 x 4 P 2 =

Press Display

3 V 4 W 2

®3Ý4P2Ú 6

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.?

Negative

M

Press Display

M 3 T 12

®Ü3Û12Ú 9

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?

Integer Divide

£

Press Display

27 £ 6

®27Þ6Ú 4½3

Division with decimal result

Set the division display option to

decimal and divide 27 by 6.

Press Display

Divide

W

‡ ®Ù»Ä¸ /

ê

‡á

27 W 6 ®27Þ6 Ú 4Ù5

Division with fractional result

Set the division display option to

fraction and divide 27 by 6.

Press Display

Divide

W

‡" ®Ù»Ä¸ /

êêêê

‡n

d P

á

27 W 6 ®n

d P

5

10

¤® n

d P

5 1

10 2

4êê

4 êêê

27Þ6Ú 4 êê

ê

Calculating equivalent units of time

Sara ran 2 kilometers in 450

seconds. Convert her time to

minutes and seconds.

450 seconds = ? minutes

? seconds

Integer Divide

£

Press Display

450 £ 60

®450Þ60Ú 7½30

Constant Operations 5

Keys

1. › lets you define or execute

operation 1.

2. œ lets you define or execute

constant operation 2.

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 ¨.

• 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.

1

2

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

T

Press Display

› T 1 ›

(stores

operation)

Op1

Û1

4

(initialize using 4 )

Op1

4

›

(add 1 one at a

time)

Op1

4Û1

15

›Op1

5Û1

26

›Op1

6Û1

37

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.

Constant

Operations

›

Press Display

‡$"

(hide constant

operation)

+1 Ã

¼Á êê

‡á+

› T 5 ›

(store the

operation)

Op1

Û5

0

(initialize using 0 )

Continued

Op1

0á

Multiplication as “repeated addition”

Continued

Press Display

›Op1

1 5

›Op1

210

›Op1

315

›Op1

420

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

V

Press Display

› V 5 ›

(store the

operation)

Op1

Ý5

1

(initialize using 1 )

Op1

1á

›Op1

1Ý5

15

›Op1

5Ý5

225

›Op1

25Ý5

3 125

Using ¨ as a constant

Use this formula to find the volume

of each cube.

V = base3

Constant

Operations

›

Powers

¨

Press Display

› ¨3 ›Op1

É3

2 ›Op1

2É3

18

3 ›Op1

3É3

127

4 ›Op1

4É3

164

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?

Constant

Operations

›

œ

Press Display

› T 5 ›Op1

Û5

œ U 2

œ

Op1 Op2

Ü2

0Op1 Op2

0á

›Op1 Op2

0Û5

15

œOp1 Op2

5Ü2

13

›œ Op1 Op2

8Ü2

16

›œ Op1 Op2

11Ü2

19

Clearing constant operations

Before entering a new operation in

OP1 or OP2, you must clear the

current values.

Mode Menu

‡

Press Display

‡Ù ßÄ¸

êÞ

$ $¼ÁÏ ¼Á2

êêêê ç

®

(clears OP1) ¼ÁÏ ¼Á2

êêêê ç

" ®

(clears OP2) ¼ÁÏ ¼Á2

çêêêê

‡

(exits Mode menu) á

Note: Pressing ” does not clear

constant operations.

Whole Numbers and Decimals 6

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.

3. Š  rounds results to the

nearest thousand.

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.

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.

• 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.)

1

9

8

7

6

5

4

3

2

Whole Numbers and Decimals 6

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.

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.

Fix decimal

Š

Press Display

12 r 345

®12Ù345Ú

12Ù345

Š ™Fix

12Ù345Ú 12Ù35

Š ˜Fix

12Ù345Ú 12Ù3

Š šFix

12Ù345Ú

12Ù345

To cancel Fix:

Š r12Ù345Ú

12Ù345

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?

Fix decimal

Š

Press Display

Š ™ ®Fix

3 r 50 T

2 r 75 T

r 99 ®

Fix

3Ù50Û2Ù75

ÛÙ99Ú 7Ù24

Converting decimals to fractions

Convert the decimal .5 to a

fraction, and then view the decimal

again after the conversion.

Fix decimal

Š

Press Display

r 5 ®ÙÓÚ ØÙÓ

ŸN

D &n

d

ÙÓÚ Ó

ÏØ

Ÿ

(Return to

decimal) ØÙÓ

ííí

Memory 7

Keys

1. z functions as shown below:

z ®Stores displayed value

over value in memory.

z TAdds displayed value to

memory.

z USubtracts displayed

value from value in memory.

z V Multiplies displayed

value by value in memory.

z WDivides value in memory

by the displayed value.

z £Performs integer division

on value in memory using

the displayed value. Only

the quotient is stored

and displayed.

2. | recalls the contents of

memory to the display. When

pressed twice, it clears the

memory.

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.

2

1

Using memory to add products

Hamburgers 2 $1.19 =

Milk shakes 3 $1.25 =

Coupon for each

milk shake 3 $.20 =

Total cost =

Store to Memory

z

Memory Recall

Press Display

2 V 1 r 19

®2Ý1Ù19Ú 2Ù38

z ®M

2Ý1Ù19Ú 2Ù38

3 V 1 r 25

®

M

3Ý1Ù25Ú 3Ù75

z T

(Add milk shakes

to memory.)

M

3Ý1Ù25Ú 3Ù75

3 V r 20

®

M

3ÝÙ20Ú 0Ù6

z U

(Deduct coupon

from memory.)

M

3ÝÙ20Ú 0Ù6

|

(Recall the total

cost.)

M

5Ù53

|

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.

Store to Memory

z

Add

T

Press Display Memory Recall

96 T 85

®96Û85Ú 181 |

W 2 ®181Þ2Ú 90Ù5

z ®M

181Þ2Ú 90Ù5

87 T 98

®

M

87Û98Ú 185

W 2 ®M

185Þ2Ú 92Ù5

T |

®

M

92Ù5Û90Ù5Ú

183

W 2 ®M

183Þ2Ú 91Ù5

Fractions 8

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 whole-

number 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.

1

7

8

5

3

4

6

2

Fractions 8

Notes (continued)

• Dividing a fraction by a fraction

gives fractional results regardless of

the division setting (decimal or

fraction).

• The ¢ mode settings provide 4

possible display options for

computational results displayed in

fraction form. For example, for

6 ÷ 4, the displays would look like

this:

manual simp/improper (n/d): 6

4

auto simp/improper (n/d): 3

2

manual simp/mixed number: 12

4

(U n/d)

auto simp/mixed number: 11

2

(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.

• When you multiply or divide

fractions and decimals, the result

is displayed as a decimal. A

decimal cannot be converted to a

fraction if the result would overflow

the display.

• Clearing with w in fractions

occurs from right bottom to left

top. If you accidentally press ¥

(the denominator key) after

entering the numerator, without

entering a numeral for the

denominator first, using w will not

correct that error. You will need to

clear and begin the entry again.

• If the decimal place is set to 0, the

decimal equivalent for a fraction

will not be displayed.

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

8¦

2  3 

4 ¥ ® 3 3 1

84 8

¦57

8

ííí

íííííí

ííííí

4

74 2

Û

=

+

Mixed to Imprope

r

Conversion

Simplifying fractions

Method 1: The calculator chooses

a common factor

Simplify 18

24 .

Numerator Key



Denominator Key

Press Display ¥

18  24

(Enter the

fraction.)

18

24

Simplify

¤

(Prepare to simplify.) 18 S

24 Factorial

®

(Simplify the

fraction.)

N

D &n

d

18 9

24 12

§

(Optional: Check

factor. You must be

in Manual mode.)

2

§

(Return to the

fraction.)

N

D &n

d

9

12

¤ ®

(Continue

simplifying.)

9 3

12 4

ííííí

íííí

ííííí

íííí

ííí

íííí

à¾á

à¾

¤

§

Simplifying fractions

Method 2: You choose a common

factor

Simplify 18

24 .

Numerator Key



Denominator Key

Press Display ¥

18  24

(Enter the

fraction.)

18

24

Simplify

¤

(Prepare to

simply.)

18

24

6

(Enter a common

factor.)

18

24

®

(Simplify the

fraction.)

18 3

24 4

íííí á

íííí

ííííííí

à¾

à¾Ôá

à¾Ô

¤

Converting fractions to decimals

Convert the fraction 5

10 to a

decimal, and then view the original

fraction after the conversion.

Numerator Key



Denominator Key

Press Display ¥

5  10 ®N

D &n

d

55

10 10

Fraction to

Decimal

Ÿ

0Ù5

Ÿ

(Return to

fraction.)

N

D &n

d

5

10

Ÿ (Return

to decimal.) 0Ù5

íííí íííí

íííí

Ú

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 Display ¥

r 5 ®Ù5Ú 0Ù5 Fraction to

Decimal

ŸN

D &n

d

Ù5Ú 5

10

Ÿ

Ÿ (Return

to decimal.) 0Ù5

íííí

Converting between fractions and mixed numbers

Convert the improper fraction 6

4 to

a mixed number.

Numerator Key



Denominator Key

Press Display ¥

¢¿ »Ä¸ »Ä¸

êêêêêê Fraction Modes

$èæ

êêêê

¢ 6  4

®62

44

¤ ® 2 1

4 2

¦3

2

ííííííí

íííí

1

11

Ú

à¾

¢

ííí

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.

To compare the times as decimals:

Numerator Key



Denominator Key

¥

Press Display

5  3 

4 ®33

44

Ÿ

5Ù75

ŸN

D &n

d

75

100

Continue to compare as fractions:

5 r 72 ®5Ù72Ú 5Ù72

ŸN

D &n

d

72

100

ííí

íííííí

ííííí

55

5

=

ííí

Percent 9

Keys

1. y converts to a percent.

2. ª enters a percent.

Notes

• The examples on the transparency

masters assume all default

settings.

2

1

Converting with percent

Convert 25% to a decimal. Percent

Press Display ª

25 ª ®25ãÚ 0Ù25 Convert to

Percent

y

Convert 25

100 to a percent.

Press Display

25  100

¥ y ® 25

100

Convert 3 to a percent.

Press Display

3 y ®3àã 300ã

íííí àã 25ã

Converting with fractions, decimals, and percent

Convert 25% to a fraction, simplify

to lowest terms, and then convert

the fraction to a decimal.

Percent

ª

Press Display Fraction to

Decimal

25 ª ®25ãÚ 0Ù25 Ÿ

ŸN/D"n/d

25

100

¤ ®N/D"n/d

25 5

100 20

¤ ®N/D"n/d

5 1

20 4

Ÿ

0Ù25

y0Ù25àã 25ã

íííííí

íííííí à¾ íííí

ííí à ¾ ííí

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?

Percent

ª

Convert to

Percent

Press Display y

31.67 ®31Ù67Ú 31Ù67

Š ™Fix

31Ù67Ú 31Ù67

V 15 ª

®

Fix

31Ù67Ý15ãÚ

4Ù75

31.67 T

4.75 ®31Ù67Û4Ù75Ú

36Ù42

Pi 10

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.

1

Using pi to find circumference

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

Pi

©

Press Display

2 V ©2Ýß

V 3 ®2ÝßÝ3Ú Ôß

Ÿ

18Ù84955592

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

Pi

©

Press Display

12 ¨ 2 ßÝÏÐÉÐ

®ßÝÏÐÉÐÚS 144ß

Ÿ

452Ù3893421

12 m

Using pi to find volume

Use this formula to find how much

space a ball occupies.

V = 4pr3

3

Pi

©

Press Display

4 V © VÒÝßÝ

5 ¨ 3 ÒÝßÝÓÉÑ

W 3 ÒÝßÝÓÉÑÞÑ

®ÒÝßÝÓÉÑÞÑÚ

523Ù5987756

5 cm

Powers and Square Roots 11

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.

2. ¬ calculates the square root of

positive values, including fractions.

Notes

• The examples on the transparency

masters assume all default

settings.

1

2

Finding the area of a square

Use this formula to find the size of

the tarpaulin needed to cover the

entire baseball infield.

A = x2 = 902

Powers

¨

Press Display

90 ¨ 2

®×ØÉÐÚ 8100

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.

L = x = 36

Square Root

¬

Press Display

¬ 36 Y

®âÅ36ÆÚ 6

36 m2

of carpet

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?

Powers

¨

Press Display

2 ¨ 10 ®2ÉÏØÚ 1024

Calculating negative powers

Find the standard numerals for the

following powers:

2-3 =

-2-3 =

.2-3 =

(1/2)-3 =

Powers

¨

Negative

M

Press Display

2 ¨ M 3

®2ÉÜÑÚ ØÙÏÐÓ

M 2 ¨

M 3 ®Ü2ÉÜÑÚ ÜØÙÏÐÓ

r 2 ¨ M 3

®Ù2ÉÜÑÚ ÏÐÓ

1  2 ¨ M

3 ®1.

2

ê É ÜÑÚ Ö

Using powers of 10

1.3 x 103 = ? Powers

¨

Press Display

1 r 3 V

10 ¨ 3 ®1Ù3ÝÏØÉÑÚ

1300

1.3 x 10L3 = ?

1 r 3 V

10 ¨ M 3

®

1Ù3ÝÏØÉÜÑÚ

0Ù0013

Problem Solving: Auto Mode 12

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: Auto Man (Manual)

Level: 123

Type: +- x P ?

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

Select level of difficulty

Choose the level of difficulty. Problem Solving

‹

Mode

‡

Press Display

‹‡ ‹Auto

æè

êêêêê

$‹Auto

1 2 3

ê

êëì

" ®‹Auto

1 2 3

ê

‡

(to exit)

‹Auto

8ÛÃÚ808

êëì

Select type of operation

Choose the type of operation:

– addition

– subtraction

– multiplication

– division

– find the operator

Problem Solving

‹

Mode

‡

Press Display

‹‡ ‹Auto

æè

êêêêê

$‹Auto

1 2 3

ê

êëì

$‹Auto

Û Ü Ý Þ Ã ?

ê

" " ®‹Auto

Û Ü Ý Þ Ã ?

ê

‡

(to exit)

‹Auto

4Ý1Ú Ã

Test your skills

Enter solutions to the problems

that the calculator presents.

(Problems are random.)

Press Display

Problem Solving

‹

Mode

‡

‹ ‡‹Auto

æè

êêêêê

‡‹Auto

8Û3Ú Ã

11 ®‹Auto

8Û3Ú11

À¹¾ s

‹Auto

2ÛÃÚ7

4 ®‹Auto

2Û4Ú7

N»¼

‹Auto

2Û4Ç7

5 ®‹Auto

2Û5Ú7

À¹¾

View the Scoreboard

After every fifth problem, the

calculator displays a score board

that tallies your right and wrong

solutions.

You can also display the

scoreboard at any time by pressing

‡.

Problem Solving

‹

Mode

‡

Press Display

‡‹Auto

À¹¾ s »¼

50

Find the operator

Change the type of operation to

“find the operator” (?) and solve

the problems the calculator

presents.

Problem Solving

‹

Mode

‡

Press Display

‹ ‡‹Auto

æè

êêêêê

$ $‹Auto

Û Ü Ý Þ Ã ?

ê

" " " "

®

‹Auto

Û Ü Ý Þ Ã ?

ê

‡‹Auto

8Ã6Ú48

V ®‹Auto

8Ý6Ú48

À¹¾s

Problem Solving: Manual Mode 13

Keys

1. ‹ activates Problem Solving.

2. ‡ displays the menu for selecting

mode, level of difficulty, and type of

operation.

Mode: Auto Man (Manual)

Display: 11-. -1-.

In Manual mode, the student

composes his or her own problems.

3.  lets the student indicate a

missing element in Manual mode.

4.  lets the student test

inequalities.

Notes

• The examples on the transparency

masters assume all default settings.

• Teachers can check a student’s

progress at any time by pressing

‡ to display the Scoreboard.

You can also press # to review

previous problems.

• When you first press ‡, the

display shows the Scoreboard for a

moment before showing the menu.

• In Manual mode, for all operations

except inequalities, the calculator

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=?

(Answer is not an integer.)

• When a problem has no solution,

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 ‹.

2

1

4

3

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.

Problem Solving

‹

Mode

Press Display

‹ ‡‹Auto

æè

êêêêê Missing element

" ®‹Auto

æè

êêêê

‡‹

á

5 U 3 ®

 ®

‹

5Ü3ÚÃ

1 ¾¼º

2 ®‹

5Ü3Ú2

À¹¾

5 T  ®

9 ®

‹

5ÛÃÚ9

1 ¾¼º

3 ®‹

5Û3Ç9

»¼

4 ®‹

5Û4Ú9

À¹¾

‡



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.

Press Display

Problem Solving

‹

Mode

‡

Missing element



‹ ‡ "

®

‹Auto

æè

êêêê

‡‹

á

 T 

® 3 ®

‹

ÃÛÃÚ3

4 ¾¼º

2 ®‹

2ÛÃÚ3

1 ®‹

2ÛÏÚ3

À¹¾S

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 Display

‹‡ "

®

‹Auto

æè

êêêê

‡‹

á

1 U 2 ®

 ®

‹

1Ü2ÚØ

0 ¾¼º

”‹

á

Less than, greater than, equals

You can test inequalities and

equalities using Problem Solving.

Press Display

Problem Solving

‹

Mode

‡

‹‡ "

®

‹Auto

æè

êêêê

‡‹

á

2 T 1 ® 1

T 2 ®

5 T 4 10

®

‹

2Û1Ú1Û2

À¹¾

‹

5Û4Ç10

À¹¾S

r 5  

r 50 ®

‹

Ù5ÈÙ50

»¼

‹

Ù5ÚÙ50

À¹¾S

Equals

®

Greater Than,

Less Than



View Scoreboard

After every fifth problem, the

calculator displays a scoreboard

that tallies your right and wrong

solutions.

You can also display the scoreboard

at any time by pressing ‡.

Press Display

Problem Solving

‹

Mode

‡

‡‹

À¹¾ »¼

50

Place Value 14

Keys

1. ‹ activates Problem Solving.

2. ‡ lets you set the mode and

display option for Place Value.

Mode: Auto Man (Manual)

Display: 11- -1-

Example:

Enter 1 234.56

Press

Œ ’1 23_._ _ (using 11-)

_ _ 3_._ _ (using -1-)

3. Œ activates the place value

function in Manual mode. It also

works in conjunction with these

keys:

Key Displays

Number of thousands

‘Number of hundreds

’Number of tens

“Number of ones

˜Number of tenths

™Number of hundredths

šNumber of thousandths

Example:

Enter 1 2 3 .45 6

Press Œ 4 _ _ _ .4_ _

4 " .01

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

3

2

Place Value 14

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

the digit.

Page 108

How Many? Enter the number, press Œ, and press

“, ’, ‘, , ˜, ™, or š.

Page 110

• 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

“, ’, ‘, , ˜, ™, or š.

Page 111

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

Manual mode.

Determine place value

Enter 1234.567. Determine the

place value of 7 and 4.

Problem Solving

‹

Place Value

Œ

Press Display

‹‡ "‹

æè

êêêê

®‡ ‹

á

1234r567

Œ

‹ ƒ

1234Ù567

7‹ ƒ

1234Ù567

ííííÙíí7

‹ ƒ

1234Ù567

7ÜÈ0Ù001

4‹ ƒ

1234Ù567

ííí4Ùííí

‹ ƒ

1234Ù567

4ÜÈ1

Repeated digits

Enter 123.43. Determine the place

value of each 3.

Problem Solving

‹

Place Value

Œ

Press Display

‹ ‡ "‹

æè

êêêê

®‡ ‹

á

123 r43

Œ

‹ ƒ

123Ù43

3‹ ƒ

123Ù43

íííÙí3

‹ ƒ

123Ù43

3ÜÈ0Ù01

33 ‹ ƒ

123Ù43

íí3Ùíí

‹ ƒ

123Ù43

3ÜÈ1

How many?

How many hundreds are in

1234.567? How many hundredths?

Problem Solving

‹

Place Value

Œ

Press Display Hundreds

‹ ‡"

®

‹

æè

êêêê ‘

‡‹

áHundredths

™

1234r567

Œ

‹ ƒ

1234Ù567

‘‹ ƒ

1234Ù567

12ííÙííí

™‹ ƒ

1234Ù567

123456Ùí.-

What’s the digit?

What digit is in the hundreds place

in 1234.567?

Problem Solving

‹

Place Value

Press Display Œ

‹ ‡"

®

‹

æè

êêêê

$ " ®‹

11ÜÙ ÜÏÜÙ

êêêêê

‡‹

á

1234r567

Œ

‹ ƒ

1234Ù567

‘‹ ƒ

1234Ù567

í2ííÙííí

Quick Reference to Keys A

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.

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

‡

‡$

‡$$

‡$$$

Displays menu to select format of results of division: . n/d

Displays menu to show or hide (?) in Op1 or Op 2: +1 Op ?

Displays menu to clear Op1 or Op2: Op1 Clear Op2

Displays menu to reject or accept Reset: N Y

q h i j k l

m n o p

Enters the numerals 0 through 9.

TAdds.

USubtracts.

VMultiplies.

WDivides.

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

Problem Solving.

rInserts a decimal point.

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

X

Y

Opens a parenthetical expression.

Closes a parenthetical expression.

Quick Reference to Keys (Continued) A

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.

ŸConverts a fraction to a decimal, or converts a decimal to a fraction, if

possible. Converts p to a decimal value.

ªEnters a percentage.

Quick Reference to Keys (Continued) A

Key Function

yConverts a decimal or a fraction to a percent.

¬Calculates the square root of a number.

¨Raises a number to the power you specify.

(3.141592653590). In some cases, results display with symbolic p, and

in other cases as a numeric value.

zStores 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.

Quick Reference to Keys (Continued) A

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 Man

‹‡$ 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-. -1-.

(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 >.

ŒWhile 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.

Œ

d

Determines the place value of digit

d

of given number.

Œ 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.

Display Indicators B

Indicator Meaning

‹Calculator is in Problem Solving mode.

ŒCalculator is in place-value mode.

Fix The calculator is rounding to a specified number of places.

MIndicates that a value other than zero is in memory.

4MValue 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.

IInteger division function has been selected (appears only when cursor is

over division sign).

n/d PDivision 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.

Error Messages C

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.

Support, Service, and WarrantyD

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

Support, Service, and Warranty (Continued) D

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.

All Customers outside the U.S. and Canada

For information about the length and terms of the warranty, refer to

your package and/or to the warranty statement enclosed with this

product, or contact your local Texas Instruments retailer/distributor.

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

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