Texas Instruments TI-15 Manuale utente

Front

TI-15

A Guide for Teachers

TI.15:

A Guide for Teachers

Developed by

Texas Instruments Incorporated

Activities developed by

Jane Schielack

About the Author

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

Texas A&M University. She developed the

Activities

section and assisted in evaluating the appropriateness of

the examples in the

How to Use the TI-15

section of this guide.

Important Notice Regarding Book Materials

Texas Instruments makes no warranty, either expressed or implied, including but not limited to any implied

warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials

and makes such materials available solely on an “as-is” basis. In no event shall Texas Instruments be liable to

anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the

purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the

form of action, shall not exceed the purchase price of this book. Moreover, Texas Instruments shall not be

liable for any claim of any kind whatsoever against the use of these materials by any other party.

Note: Using calculators other than the TIN15 may produce results different from those described in these

materials.

Permission to Reprint or Photocopy

Permission is hereby granted to teachers to reprint or photocopy in classroom, workshop, or seminar

quantities the pages or sheets in this book that carry a Texas Instruments copyright notice. These pages are

designed to be reproduced by teachers for use in classes, workshops, or seminars, provided each copy made

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Send inquiries to this address:

Texas Instruments Incorporated

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Attention: Manager, Business Services

If you request photocopies of all or portions of this book from others, you must include this page (with the

permission statement above) to the supplier of the photocopying services.

www.ti.com/calc

[email protected]

Except for the specific rights granted herein, all rights are reserved.

Printed in the United States of America.

Automatic Power Down, APD, and EOS are trademarks of Texas Instruments Incorporated.

Table of Contents 

CHAPTER PAGE

About the Teacher Guide

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

About the TI-15

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

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

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

The ªKey

Fraction Forms ........................................... 6

Auto and Manual Mode

Comparing Costs........................................ 11

Division with quotient/remainder,

fraction, or decimal result

Number Shorthand ...................................15

Scientific Notation

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

Constant operations

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

Rounding

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

Place value

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

Number sentences, Problem solving

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

1 Display, Scrolling, Order of

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

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

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

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

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

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

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

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

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

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

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

CHAPTER PAGE

How to Use the TI-15 (continued)

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

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

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

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

Quick Reference to Keys

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

Display Indicators

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

Error Messages

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

Support, Service, and Warranty

About the Teacher Guide 

How the Teacher Guide is Organized

This guide consists of two sections:

Activities

and

How to Use the TI-15

. The

Activities

section is a collection of activities for

integrating the TI-15 into mathematics

instruction.

How To Use the TI-15

is designed

to help you teach students how to use the

calculator.

Activities

The activities are designed to be teacher-

directed. They are intended to help develop

mathematical concepts while incorporating

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

self-contained and includes the following:

• An overview of the mathematical purpose

of the activity.

• The mathematical concepts being

developed.

• The materials needed to perform the

activity.

• A student activity sheet.

How to Use the TI.15

This section contains examples on

transparency masters. Chapters are

numbered and include the following:

• An introductory page describing the

calculator keys presented in the examples,

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

any pertinent notes about their functions.

• Transparency masters following the

introductory page provide examples of

practical applications of the key(s) being

discussed. The key(s) being discussed are

shown in black on an illustration of the

TI-15 keyboard.

Things to Keep in Mind

• While many of the examples on the

transparency masters may be used to

develop mathematical concepts, they

were not designed specifically for that

purpose.

• For maximum flexibility, each example and

activity is independent of the others.

Select the transparency master that

emphasizes the key your students need

to use to develop the mathematical

concepts you are teaching. Select an

appropriate activity for the

mathematical concept you are teaching.

• If an example does not seem

appropriate for your curriculum or

grade level, use it to teach the function

of a key (or keys), and then provide

relevant examples of your own.

• To ensure that everyone starts at the

same point, have students reset the

calculator by pressing −and ”

simultaneously or by pressing ‡,

selecting RESET, selecting Y(yes), and

then pressing <.

How to Order Additional Teacher Guides

To place an order or to request additional

information about Texas Instruments (TI)

calculators, call our toll-free number:

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

Or use our e-mail address:

[email protected]

Or visit the TI calculator home page:

http://www.ti.com/calc

About the TI.15

Two-Line Display

The first line displays an entry of up to 11

characters. Entries begin on the top left. If

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

wrap to the second line. When space permits,

both the entry and the result will appear on

the first line.

The second line displays up to 11 characters. If

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

will wrap to the second line. If both entry and

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

displayed right-justified on the second line.

Results longer than 10 digits are displayed in

scientific notation.

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

continue to wrap; you can view the beginning

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

the result will appear when you press ®.

Display Indicators

Refer to Appendix B for a list of the display

indicators.

Error Messages

Refer to Appendix C for a listing of the error

messages.

Order of Operations

The TI-15 uses the Equation Operating

System (EOSé) to evaluate expressions. The

operation priorities are listed on the

transparency master in Chapter 1,

Display,

Scrolling, Order of Operations, and Parentheses

Because operations inside parentheses are

performed first, you can use Xor Yto

change the order of operations and, therefore,

change the result.

Menus

Two keys on the TI-15 display menus: ‡

and ¢.

Press $or #to move down or up through

the menu list. Press !or "to move the

cursor and underline a menu item. To return

to the previous screen without selecting the

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

®while the item is underlined.

Previous Entries #$

After an expression is evaluated, use #

and $to scroll through previous entries

and results, which are stored in the TI-15

history.

Problem Solving (‹)

The Problem Solving tool has three features

that students can use to challenge

themselves with basic math operations or

place value.

Problem Solving (Auto Mode) provides a set

of electronic exercises to challenge the

student’s skills in addition, subtraction,

multiplication, and division. Students can

select mode, level of difficulty, and type of

operation.

Problem Solving (Manual Mode) lets

students compose their own problems,

which may include missing elements or

inequalities.

Problem Solving (Place Value) lets students

display the place value of a specific digit, or

display the number of ones, tens, hundreds,

thousands, tenths, hundredths, or

thousandths in a given number.

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 ªkey to collect data about

percentages of a given number. They will organize the

data and look for patterns in percents. (For

example, 10% of 20 is twice as much as 5% of 20.)

Math Concepts

• multiplication

• equivalent

fractions,

decimals, and

percents

Materials

• TI-15

• pencil

• student

activity

(page 4)

Introduction

1. After students use manipulatives to develop the

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

have them explore what happens when they

press ªon the calculator.

2. Present the following scenario to students:

Metropolis East (M.E.) and Metropolis West

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

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

5%. Collect data and display your results for

each percent in a table to compare the amounts

of money you would pay for tax on various

items in each city.

3. Have students make conjectures about percent

based on the patterns they observe. Students can

then use manipulatives to verify their

conjectures.

Examples:

• Students may observe that for every item, 10%

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

• Students may observe that it is easy to

estimate 10% of a whole number by using

place value and looking at the digits to the

right of the ones place.

Collecting and Organizing Data

To guide students in organizing their data to bring

out patterns, ask questions such as:

•

How could you organize your data to compare

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

•

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

hand column of one table all the way down and

just change the total quantity?

³When a student enters

a 6 ª, the TI-15

displays 6%. Then,

when the student

presses ®, the

display changes to

6%= 0.06 to show that

6% is another way to

write 0.06 or 6/100.

³You will need to show

students how to use

multiplication on the

TI-15 to express the

percent of a given

quantity. For example,

to show 10% of $20:

1. Enter 10.

2. Press ªV.

3. Enter 20; press ®.

Students can verify the

calculator display of 2

by using manipulatives

to show 10% of $20 =

$2.

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?

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