Texas instruments TI-15 A Guide for Teachers
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
the examples in the
How to Use the TI-15
Activities
section of this guide.
section and assisted in evaluating the appropriateness of
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Copyright © 2000 Texas Instruments Incorporated.
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Table of Contents
CHAPTER PAGE
About the Teacher Guide
About the TI-15
........................................... vi
........................... v
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
CHAPTER PAGE
How to Use the TI-15
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
(continued)
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
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
iii
About the Teacher Guide
How the Teacher Guide is Organized
This guide consists of two sections:
and
How to Use the TI-15
section is a collection of activities for
integrating the TI-15 into mathematics
instruction.
to help you teach students how to use the
calculator.
How To Use the TI-15
. The
Activities
Activities
is designed
Activities
The activities are designed to be teacherdirected. They are intended to help develop
mathematical concepts while incorporating
the TI-15 as a teaching tool. Each activity is
self-contained and includes the following:
An overview of the mathematical purpose
•
of the activity.
The mathematical concepts being
•
developed.
The materials needed to perform the
•
activity.
A student activity sheet.
•
How to Use the TI.15
This section contains examples on
transparency masters. Chapters are
numbered and include the following:
An introductory page describing the
•
calculator keys presented in the examples,
the location of those keys on the TI-15, and
any pertinent notes about their functions.
Transparency masters following the
•
introductory page provide examples of
practical applications of the key(s) being
discussed. The key(s) being discussed are
shown in black on an illustration of the
TI-15 keyboard.
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
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
iv
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,
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.
Display,
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
®
Previous Entries
After an expression is evaluated, use
and $ to scroll through previous entries
and results, which are stored in the TI-15
history.
.
¢
while the item is underlined.
# $
Problem Solving (‹)
The Problem Solving tool has three features
that students can use to challenge
themselves with basic math operations or
place value.
Problem Solving (Auto Mode) provides a set
of electronic exercises to challenge the
student’s skills in addition, subtraction,
multiplication, and division. Students can
select mode, level of difficulty, and type of
operation.
Problem Solving (Manual Mode) lets
students compose their own problems,
which may include missing elements or
inequalities.
Problem Solving (Place Value) lets students
.
display the place value of a specific digit, or
display the number of ones, tens, hundreds,
thousands, tenths, hundredths, or
thousandths in a given number.
‡
#
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
v
About the TI.15
(Continued)
Resetting the TI.15
Pressing − and ” simultaneously or
pressing
(yes), and then pressing
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).
, selecting RESET, selecting
‡
resets the
®
Automatic Power DownTM (APDTM)
Y
If the TI-15 remains inactive for about
5 minutes, Automatic Power Down (APD)
turns it off automatically. Press − after
APD. The display, pending operations,
settings, and memory are retained.
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
vi
Activities
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
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
1
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.)
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.
Math Concepts
• multiplication
• equivalent
fractions,
decimals, and
percents
³
When a student enters
ª
6
a
, the TI-15
displays 6%. Then,
when the student
presses ®, the
display changes to
6%= 0.06
6% is another way to
write 0.06 or 6/100.
³
You will need to show
students how to use
multiplication on the
TI-15 to express the
percent of a given
quantity. For example,
to show 10% of $20:
1. Enter 10.
2. Press ª V.
3. Enter 20; press ®.
Students can verify the
calculator display of
by using manipulatives
to show 10% of $20 =
$2.
Materials
• TI-15
• pencil
• student
activity
(page 4)
to show that
2
Collecting and Organizing Data
To guide students in organizing their data to bring
out patterns, ask questions such as:
How could you organize your data to compare
•
the 5% tax rate to the 10% tax rate?
Why would it be useful to keep 5% in the left-
•
hand column of one table all the way down and
just change the total quantity?
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
2
Patterns in Percent
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?
(Continued)
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?
•
•
© 2000 T
How does the tax on a $40 item change each
day?
How do the taxes on the 2 items compare?
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
3
Name ___________________________
Patterns in Percent
Date ___________________________
Collecting and Organizing Data
Use your calculator to collect data about percent, organize it in the
table below, and then look for patterns.
Cost of Item Amount of Tax in
Metropolis West
Tax Rate: ____%
Amount of Tax in
Metropolis East
Tax Rate: ____%
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
4
Name ___________________________
Patterns in Percent
Date ___________________________
Analyzing Data and Drawing Conclusions
1. What patterns do you see in your tables?
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
2. What conjectures can you make from these patterns?
__________________________________________________________________________
__________________________________________________________________________
3. Repeat the activity with a different percent in the left column and
compare your results.
__________________________________________________________________________
__________________________________________________________________________
4. Repeat the activity, changing the percents in the left column while
keeping the total quantity constant. Now what patterns do you see?
What conjectures can you make?
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
5
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.
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.
Math Concepts
• division
• multiplication
• common
factors
• equivalent
fractions
Refer to page 45 for
detailed information
about mode settings on
the TI-15.
Materials
• TI-15
• pencil
• student
activity
(page 9)
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
2
fourths to give 1
•
The last two cups could be divided into 4
halves to give 1
/4 cups per bowl.
1
/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).
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.
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
6
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.
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?
For example, for 6 ÷ 4
as a fraction, enter
6 4 ¥. The displays
in the different modes
will look like the
following:
n
man
d
n
auto
d
n
U
man 1
d
n
U
auto 1
d
6
4
3
2
2
4
1
2
What denominators do you get with the settings
•
n
? With the settings
man
d
What denominators do you get with the settings
•
n
d
What denominator are you going to choose to
•
? With the settings
auto
U
U
n
d
n
d
man
auto
?
?
explore with next?
Example:
After exploring with denominators of 2 and 3,
you might suggest exploring with a denominator
of 6 and comparing results.
How can you organize your results to look for
•
patterns?
Example:
Continuing to increase the numerators by 1 each
time.
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
7
Fraction Forms
(Continued)
Analyzing Data and Drawing Conclusions
To focus students’ attention on the patterns in their
fractions and the relationship of these patterns to the
denominators, ask questions such as:
What patterns do you see in your results?
•
Example:
n
When a denominator of 4 is used in the
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:
auto
d
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
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
would make it easier to see quickly the whole
number component of the result and whether
the additional fraction part was more or less
½.
than
U
n
man
d
n
auto
d
settings
settings
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
8
Name ___________________________
Fraction Forms
Date ___________________________
Collecting and Organizing Data
1. Have each person in your group set his/her calculator to one of the
following combinations of modes for fraction display. (Each person
should choose a different setting.)
improper/manual simp
•
improper/auto simp
•
mixed number/manual simp
•
mixed number/auto simp
•
2. Select a denominator: __________________
3. Use this denominator with several numerators and record each
person’s results in the table below.
Numerator Denominator
n
Man
d
n
Auto U
d
n
Man U
d
n
d
Auto
0
2
3
4
1
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
9
Fraction Forms
(Continued)
Analyzing Data and Drawing Conclusions
1. What patterns do you see?
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
2. What generalizations can you make?
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
3. Try the activity again with a different denominator and compare your
results with the two denominators.
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
10
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.
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
:
Math Concepts
• division
• multiplication
• fractions
• decimals
To display an integer
quotient with a
remainder, use the
key.
To display a quotient in
fraction form, press
" ®
then use the W key.
To display a quotient in
decimal form, press
‡ ! ®
then use the W key.
to select
Materials
• TI-15
• pencil
• student
activity
(page 14)
£
‡
n/d,
to select
.
,
•
© 2000 T
What did you enter into the calculator to solve
the problem?
Example:
80
A student may have entered
determine the area of the soccer field, then
0.40
entered V
cost, then W
school in fraction or decimal form.
EXAS INSTRUMENTS INCORPORATED
®
to find the total maintenance
6
®
to find the cost for each
V
110
® to
TI-15: A Guide for Teachers
11
Comparing Costs
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
8800
to
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.
V .
4
W
6
®
.
(Continued)
Analyzing Data and Drawing Conclusions
To guide students in the analysis of their data, ask
questions such as:
How are your solutions in the three forms
•
alike?
They all have a whole number component of 586.
How are your three solutions different?
•
The remainder form just tells how many dollars
are left over. The fraction and decimal forms tell
how much more than $586 each school has to
pay.
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
12
Comparing Costs
What happens if you multiply each solution by
•
6 to check it?
(Continued)
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 586
form to get $3520. If you enter
press ®, you get
3520
2
/3 x 6 in fraction
586.666667 x 6
, 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
press ® , then the display reads
586.67 x 6
3520.02
, and
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.
and
, which
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.
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.
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
13
Name ___________________________
Comparing Costs
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.
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
14
Number Shorthand: Scientific Notation
Grades 5 - 6
Overview
Students will use patterns created on the
calculator with the constant operation (› or
to develop an understanding of scientific notation.
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?
œ
Math Concepts
• multiplication
)
• powers of 10
• exponents
Materials
• TI-15
• pencil
• student
activity
(page 18)
3. After students share their conjectures, have them
use › to test their conjectures. As students
press ›, have them record the resulting
displays on the Student Activity page.
4. When students reach the point where the lefthand counter is no longer displayed, ask them
what they think has happened to the calculator.
(The product has become so large that there is
not room to display both the product and the
counter, so the counter has been dropped.)
Have students continue to record the counter
data, even though it no longer shows on the
calculator.
5. When the left-hand counter reappears, have
students describe what has happened to the
display of the product. (It has been replaced with
a right-hand display of scientific notation: for
example,
1x10^11.
)
To multiply repeatedly
by 10, enter:
› V
1.
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.
10
›
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
15
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,
1 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10
Explain to students that exponential or scientific
notation is a shorthand for repeated factors:
11
1 x 10
8. Have students continue to explore the use of
scientific notation to represent repeated
multiplication by 10 with other starting factors.
(For example, using 2 as the starting factor, the
display
eleven times, or 2 x 10
.
1x10^11
2x10^11
represents the product:
represents multiplying 2 by 10
11
.
Collecting and Organizing Data
To focus students’ attention on the relevant changes
in the calculator’s display, ask questions such as:
What does the display
•
When did the counter on the left disappear? Why
•
do you think that happened?
3 1000
mean?
.
•
•
© 2000 T
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.
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
16
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,
product should be 100,000,000,000. The display
1x10^11
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
1x10^11
represents the product 1 x 1011.
represents the product 2 x 1011.
is in the place where the
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
exponent part of the display is one more than the
number of times 10 has been used as a factor.
12 1.2 x10^13
, where the
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
17
Number Shorthand:
Name ___________________________
Date ___________________________
Scientific Notation
Collecting and Organizing Data
Program the constant operation feature on your calculator to multiply by
10. Record the results in the table below for each time you press ›.
Number of
Times
___
Used as a
Factor
0 (starting factor)
1
Display
2
3
4
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
18
Number Shorthand:
Name ___________________________
Date ___________________________
Scientific Notation
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.
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
19
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.
Introduction
1. Have students program › with +2 and
with -2.
2. Have students enter
, and read the output (
›
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
are inverse procedures.)
œ
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
page.
8
on their calculators, press
1 10
, which means
student activity
œ
›
Math Concepts
• whole numbers
• addition,
subtraction,
multiplication,
division
• fractions
(Grades 5-6)
• decimals
(Grades 5-6)
³
To use › and œ:
1. Press › (or œ).
2. Enter the operation
and the number (for
example, T 2).
3. Press › (or œ).
4. Enter the number to
which you want to
apply the constant
operation.
5. Press › (or œ).
The display will have
1
a
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
indicating the
constant operation
has been applied
twice to the original
input.
Materials
• TI-15
• pencil
• student
activity
(page 23)
2
at the left,
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
20
Related Procedures
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
look something like this:
x 2
and
÷ 2
, the tables might
(Continued)
Table for
Table for
›
Input Procedure Output
1x22
2x24
3x26
œ
Input Procedure Output
2
4
6
P
21
P
22
P
23
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
.
³
To recognize the
equivalent procedures,
students may need to
use the Ÿ key to
change outputs from
decimal to fraction form
or vice versa.
•
•
© 2000 T
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
?
›
EXAS INSTRUMENTS INCORPORATED
first, and then
œ
TI-15: A Guide for Teachers
21
Related Procedures
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
÷ 2
and
, the tables might look something like this:
(Continued)
x ½
Table for
Table for
›
Input Procedure Output
1x½½
2x½1
3 x½ 1.5 = 1½
œ
Input Procedure Output
1
2
3
P
2 0.5 = 5/
P
21
P
2 1.5 = 15/
10 =
10 =
½
1½
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
22
Name ___________________________
Related Procedures
Date ___________________________
Collecting and Organizing Data
1. Choose a procedure for › (for example,
2. Choose a procedure for
(for example,
œ
3. Select an input number to apply the procedure to and record both the
input and output numbers in the appropriate table.
4. Use the tables below to record and compare your results using
and
.
œ
Table for
›
Input Procedure Output Input Procedure Output
).
x ½
).
÷ 2
Table for
›
œ
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.
__________________________________________________________________________
© 2000 T
EXAS INSTRUMENTS INCORPORATED
TI-15: A Guide for Teachers
23
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