™
First Steps with TI-Nspire
First Steps
with
Technology for teaching and
learning mathematics
Seven Introductory Tutorials for the
Handheld
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First Steps with TI-Nspire
Contents
TI-Nspire Keypad Layout.................................................................................................. Page 5
Tutorial 1.......................................................................................................................... Page 6
TI-Nspire Documents: basic ideas
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Memory
Baꢂery Life
Documents, problems, pages, applicaꢀons and home screen
Use of / key and keyboard shortcuts
Home Screen
Scratchpad
Document Browser to navigate around documents and folders
Page Sorter to navigate inside documents
Different menus in different contexts
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The Document menu
Tutorial 2........................................................................................................................ Page 15
The Calculator applicaꢁon: arithmeꢁc and algebra
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Basic calculaꢀons
Standard layout of expressions
Recalling previous expressions and results
Approximate (decimals) and exact (fracꢀons) evaluaꢀons
Templates and menus
Document seꢁngs
Defining and using variables
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Working with Staꢀsꢀcal Distribuꢀons
Tutorial 3........................................................................................................................ Page 22
The Notes applicaꢁon
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Purposes of the applicaꢀon
Page layouts with split screens
Templates for the Notes menu
Using Interacꢀve Notes
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Creaꢀng Quesꢀons using the Teacher Soſtware
Tutorial 4........................................................................................................................ Page 27
Graphing
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The work area, entry line, funcꢀon history
Entering, ediꢀng, deleꢀng and hiding funcꢀons
Grabbing and dragging labels
Seꢁng the axes
Tracing along graphs
Marking and labelling points and coordinates
Using the Analyse Graph Tools
Transforming graphs and their funcꢀons manually
Using Sliders
Sequence Ploꢁng
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First Steps with TI-Nspire
Tutorial 5........................................................................................................................ Page 35
Geometry
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The Plane Geometry and Graphing views
Lines, segments and rays
Construcꢀon of parallel lines
Drawing and labelling points on objects
Construcꢀon of shapes
Selecꢀng and grabbing screen objects
Making measurements and storing as variables
Aꢂributes which change the appearance and lock screen objects
Tutorial 6........................................................................................................................ Page 41
Lists and Spreadsheet
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Entering and ediꢀng data and formulas
Lists and funcꢀons
Resizing cells
Ambiguous variable/cell names
Capturing data from the Graphs & Geometry applicaꢀon
Funcꢀon tables
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Frequency Chart
Tutorial 7........................................................................................................................ Page 46
One- and two-variable staꢁsꢁcs
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Creaꢀng one- and two-variable staꢀsꢀcal plots in the Data & Staꢀsꢀcs applicaꢀon
Using boxplots to compare data sets
Using categorical data for pie charts
Manually fiꢁng straight lines to data
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Automaꢀcally fiꢁng linear-regression lines to data
Appendix........................................................................................................................ Page 53
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Mulꢀple Representaꢀons – an example
Page 4
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First Steps with TI-Nspire
TI-Nspire CX Keypad Layout
Start by spending a few seconds looking at the layout of the keypad.
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First Steps with TI-Nspire
Tutorial 1: TI-Nspire documents
Tutorial 1
TI-Nspire Documents
This first tutorial introduces some of the key features of TI-Nspire™ learning technology, in parꢀcular the
structure of TI-Nspire documents, with different applicaꢀons operaꢀng on different pages. The various menus
are introduced, as well as creaꢀng and navigaꢀng around documents. The tutorial assumes that you are using
the TI-Nspire handheld device and the tutorial begins by drawing a comparison between this and other types
of technology.
Is it a calculator? Is it a computer? ….It’s a handheld device!
Pick up the TI-Nspire handheld device and, if you are used to using a calculator, parꢀcularly
a Texas Instruments TI-83 or TI-84 graphics calculator, you are likely to feel a certain reassuring familiarity:
there’s a screen and a keyboard laid out in a fairly familiar way. As with many calculators the on/off switch is in
the top right corner. So press c to switch on.
Nothing on the screen?
See Geꢂng Started with the TI-Nspire Handheld, Recharging the Handheld
Please don’t worry about what’s on the screen for the moment, but think about how to switch it off. The c
key has “off” wriꢂen in light blue above it so that’s the one to use aſter pressing the blue key marked /.
But just a minute, it was a key marked 2nd that you used on the calculators, and the change to the use of a ctrl
key is quite significant. The designers at TI have moved to making this device much more like a computer and
it has a ctrl key, /, and also a shiſt key g. Many of the main keys on the handheld have second funcꢀons
wriꢂen in blue above the key and these are acꢀvated using the ctrl key. Noꢀce for example q, p and h. The
ctrl key can be used in conjuncꢀon with the alphabeꢀc keys to create keyboard shortcuts just as you are used to
doing on a computer. For example, you can copy and paste using /C and /V. There’s also that most useful
keyboard shortcut for undoing a previous acꢀon, /Z, which can also be acꢀvated by pressing /d(ª).
(See Geꢁng Started guide, Using Keyboard Shortcuts for a full list).
Memory
Just like a computer, documents can be stored on the TI-Nspire CX handheld – The TI-Nspire™ CX handheld
comes equipped with 192 MB of memory Of the total memory, 128 MB is dedicated to document storage. As
documents are created and stored they take up space on the handheld’s memory so you may find that every
now and again you need to free space on memory aſter long-term use. If there isn’t enough memory on the
handheld, you can do one of the following:
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•
•
Back up documents and folders to a computer or another TI-Nspire CX
Delete documents and folders you no longer use
Reset the memory, which deletes all files and folders on the handheld
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First Steps with TI-Nspire
Tutorial 1: TI-Nspire documents
Baꢀery Life
The TI-Nspire™ CX handheld comes with a rechargeable baꢂery, which should be charged for at least six hours
before first use. The built-in rechargeable baꢂery does not need to be removed from the handheld in order to
recharge it. The handheld will sꢀll work and can be used while it is charging.
With use of 2 hours per day at the default brightness level the baꢂery should last for up to 10 days.
The handheld comes with the following cables:
•
•
Standard mini-A to mini-B USB cable for transferring files between handhelds
Standard A to mini-B USB cable for transferring files to and from a computer and for charging the baꢂery via
the USB port
Charging the handheld
To charge the baꢂery in the TI-Nspire™CX handheld:
•
Connect the handheld to a computer using a standard A to mini-B USB cable. If the driver is not found when
the handheld is connected to the computer download the soſtware that includes a driver from
hꢀp://educaꢁon.ꢁ.com/soſtware.
OR
•
Connect to a wall outlet using a TI wall adapter (sold separately).
OR
•
Place the handheld or mulꢀple handhelds in a TI-Nspire™ CX Docking Staꢀon.
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First Steps with TI-Nspire
Tutorial 1: TI-Nspire documents
The Home Screen
When you switched on a calculator you expected to see
what was called the Home Screen and you’d be able to
start carrying out calculaꢀons right away. But the TI-Nspire
handheld is different in this respect too. Press c, the
home buꢂon, a black key at the top right of the keypad. You
should see a screen similar to this. Navigate to the various
icons on the Home Screen using the large square Touchpad
on the keypad. This behaves as both a touchpad (like using a
laptop), and as a navigaꢀonal device as you can press on the
up, down, leſt and right arrows to move the selector around.
To click or select something you press the x square symbol in
the middle of the touchpad, or press the enter key. However
don’t select anything else yet!
Consider whether the TI-Nspire’s home screen is more reminiscent of a calculator or of a computer. When a
computer wakes up you first see the desktop and in many ways this TI-Nspire Home Screen is similar. With a
computer you have to choose an applicaꢀon to use -- a word-processor, spreadsheet or whatever. You then
must open a document within which you will be able to write text, do calculaꢀons, manipulate images etc.
Computer:
Desktop Choose Applicaꢀon Open Document
In many ways working with TI-Nspire is similar. You always have to work within a document and you can use
different applicaꢀons to calculate, draw graphs, , work with geometry, manipulate lists and spreadsheets, work
with data and staꢀsꢀcs, add notes and perform data logging.
The TI-Nspire applicaꢀons are:
• Calculator
• Graphs
• Geometry
• Lists & Spreadsheet
• Data & Staꢁsꢁcs
• Notes
• Vernier DataQuest™
Page 8
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First Steps with TI-Nspire
Tutorial 1: TI-Nspire documents
What is quite different from the computer is that within one document you can have mulꢀple pages or
problems that can make use of the different applicaꢀons. The spreadsheet on one page of a document can
interact seamlessly with calculaꢀons done on a calculator page and graphs drawn on another. You can also
have more than one different representaꢀon on one page.
This use of mulꢀple representaꢀons is one of the many things that make the TI-Nspire such a powerful tool.
So with TI-Nspire you first open a document, or start a new one, and then choose an applicaꢀon.
TI-Nspire:
Home screen New document Choose applicaꢀon
TIp: If you would like to return to the document you are working on without inserꢀng
a new page, from the Home screen select opꢀon 4: Current.
You can do this by pressing 4 on the keypad.
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First Steps with TI-Nspire
Tutorial 1: TI-Nspire documents
Scratchpad
Because there are some occasions when you really just
want to carry out a quick calculaꢀon or draw a quick graph
the TI-Nspire includes a feature called the Scratchpad.
The scratchpad is designed for those casual throw-away
calculaꢀons that need to be done from ꢀme to ꢀme, but
are not worth keeping in a full document. To access the
Scratchpad press ».
This opens a calculator page for performing quick calculaꢀons.
Pressing » again swaps between the calculator and a graph
scratchpad page. To close the Scratchpad simply press d.
Documents, problems and pages
In order to see what documents are pre-loaded on your
handheld you need to use opꢀon 2 on the Home screen:
My Documents…
Either use the touchpad to move the selector down to
the 2: My Docs… opꢀon then press x to select it.
Or use the touchpad to move the cursor over opꢀon 2 and
x Or just press 2 key to select opꢀon the 2nd opꢀon.
You should see a screen called the Document Browser and it
will be something like the one shown here. Documents are
organized into folders as they would be on a computer. A new
TI-Nspire handheld should have a folder called Examples:
Tip: You can use either x or · as
alternaꢀve key presses
Move the cursor to the folder enꢀtled Examples.
Then press x or · or ¢ on the touchpad to open the folder.
Inside the Examples Folder on your handheld you will
probably find a document enꢀtled ’Geꢁng Started 3_0’.
Use ¤ to locate and · to open the document.
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First Steps with TI-Nspire
Tutorial 1: TI-Nspire documents
If the handheld has been used previously you will see a dialog
box asking you if you want to save the document that is
currently open. Unless you want to save your previous work
press e or ¢ to move the highlight to No. To confirm this
choice press ·.
e is oſten used to move to and
highlight different parts of the screen
Navigaꢁng Documents
When the document opens you may see a screen similar
to the one shown on the leſt. For the moment, please do
not follow the instrucꢀons on the screen just yet! Conꢀnue
working through this tutorial, which will introduce you to
many of the key features of the TI-Nspire document model.
Among these key features are useful and easy ways to
navigate through documents. For example, pressing / ¢ will
take you to the next page in a document. Similarly, pressing
/¡ returns you to the previous page. Pressing /£ will
take you to the Page Sorter which enables you to move
quickly and easily through the pages of a document.
Noꢀce the informaꢀon typically provided on the Page Sorter:
Name of Document
e problem
Number or Name of the Problem
A TI-Nspire document can consist of mulꢀple problems and each problem can consist of mulꢀple pages.
For example, the document shown here consists of at least two problems, with 5 and 9 pages respecꢀvely.
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First Steps with TI-Nspire
Tutorial 1: TI-Nspire documents
Scroll downwards with the Touchpad and you will see all the problems in the document. If you move the
highlight onto Problem 2, say, and press ¡ the pages of that problem will close up. Pressing · or /¤ takes
you back to single page view on the page currently selected.
Each page of a document contains one (or more) of the TI-Nspire applicaꢀons.
As a reminder, these are the same applicaꢀons that can be accessed from the Home screen, i.e.:
• Calculator
• Graphs
• Geometry
• Lists & Spreadsheet
• Data & Staꢁsꢁcs
• Notes
• Vernier DataQuest™
The use of each of the applicaꢀons which you might want to
use for data logging is covered in the tutorials that follow. Any
page can be divided into as many as four work areas, allowing
up to four different applicaꢀons to be used per page. To do this,
See ‘Spliꢁng the Screen’ in Tutorial 3, page 23.
Shown here is a page that has been split into two with the
Lists & Spreadsheet applicaꢀon on the leſt, and the Notes
applicaꢀon beside it.
If the ‘Geꢁng Started 3_0’ document is present on your handheld, work through it now as far
as page 2.5. This will allow you to revise what has been covered so far in this tutorial
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First Steps with TI-Nspire
Tutorial 1: TI-Nspire documents
Contextual Menus
Return to the Home screen, and select 2: My Docs… to access
the document browser. Noꢀce that within the document
browser new folders may be created or folders renamed.
Items that are grey, rather than black in a menu cannot be
chosen in the current environment. For example, on the
screen on the leſt, opꢀon 3: Save As… is unavailable.
Pressing d will always close
down a menu or dialog box.
To save a document under a new name press ~.
This opens a menu providing access to document management features. By pressing 1 and then 5 the
document can be saved under another filename.
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First Steps with TI-Nspire
Tutorial 1: TI-Nspire documents
Then open a document in the browser and pressb again. It
is important to realise that b will always provide access to
the features of the current environment. For example, within
the Notes applicaꢀon, this menu offers only the available
opꢀons for that applicaꢀon (as shown to the right).
There are a number of tools that are available for managing
documents when you choose the use the Document menu
by pressing the ~buꢂon. Several opꢀons are marked by
the symbol ¢ and pressing ¢ on the Touchpad opens their
submenus.
Within any applicaꢀon, this Document menu retains the same features but any opꢀons that are currently
unavailable are greyed out.
The next tutorial describes creaꢀng a new document and using a first TI-Nspire applicaꢀon.
Check list of some key points in Tutorial 1:
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•
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•
•
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Understanding, the terms document, problem, page, applicaꢀon, and home screen
Use of the / key and keyboard shortcuts
The Home Screen
Scratchpad
Memory
Baꢂery Life
The Document Browser to navigate around documents and folders
The Page Sorter to navigate inside documents
The use of e and d
Why b produces different menus in different contexts
The Document menu
Page 14
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First Steps with TI-Nspire
Tutorial 2: The Calculator Applicaꢁon
Tutorial 2
The Calculator Applicaꢁon
At the heart of TI-Nspire is the Calculator applicaꢀon, the workspace for numeric and algebra operaꢀons.
This tutorial introduces some of the key features of the applicaꢀon, starꢀng with a new blank document.
This document will be saved, used again and added to in subsequent tutorials
Basic operaꢁons
First create a new blank document by pressing c and
choosing opꢀon 1: New Doc from the Home Screen.
To open a page which uses the calculator applicaꢀon:
press 1 or · or x.
Try keying in and entering expressions using the four basic arithmeꢀc operaꢀons, square roots, negaꢀves etc.
Look carefully at how the expressions as well as the results appear on the screen, in order to understand the
convenꢀons the handheld uses with its default seꢁngs.
NB mulꢀplicaꢀon
and division.
What do you expect the result
of this calculaꢀon to be?
Noꢀce that in many cases the layout of the expression changes when · is pressed—in parꢀcular watch how
the mulꢀplicaꢀon and division operaꢀons are handled.
Try typing a lengthy expression and, before pressing ·, see the effect of using . and then /..
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First Steps with TI-Nspire
Tutorial 2: The Calculator Applicaꢁon
A History Lesson
You will have noꢀced that, as new expressions are entered, previous ones scroll off the top of the screen. The
TI-Nspire handheld will remember a history of up to 99 expressions and these can be recalled using the up key
on the Touchpad. Press and hold £ and see the way the highlight flicks back through previous expressions and
results. Stop at some point in the history and press ·. You should see either the previous expression or the
result copied to the entry line ready to be used as all or part of a new expression.
Noꢀce that, aſter an expression has been evaluated, simply
pressing · again repeats the previous entry. What would
you expect to see if you repeatedly pressed · on this
screen? Try it by pressing
1·
lv1¢+1
···…
Noꢀce how entering an operaꢀon at the beginning of an
expression (the power operaꢀon in this example) causes the
automaꢀc entry of Ans, standing for the previous answer.
If you ever need to clear the history there is an opꢀon in the Acꢀons submenu: press b15. This is also a
way of producing an uncluꢂered screen for making screenshots such as the one above.
Approximate Calculaꢁons
If you repeat the key sequence above but replace the first ·
with /· you get the rather different results shown here.
Try it and conꢀnue pressing · unꢀl you get an (apparently)
unchanging approximaꢀon for the Golden Raꢀo.
The default mode for calculaꢀons is to give exact results
(using fracꢀons) rather than approximate results (using
decimals). It is possible to alter this using the system seꢁngs
as you will see later in this tutorial.
Another way of choosing a decimal result is to enter a decimal
in the expression that you type, e.g. try entering 1 / 7 and then 1.0 / 7.
Page 16
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First Steps with TI-Nspire
Tutorial 2: The Calculator Applicaꢁon
Templates
Many of the handheld’s keys provide templates to enable you to enter a range of mathemaꢀcal expressions. For
example, in this tutorial you have used the keys /q for square roots and l for powers. In both cases a small
box appears in the expression inviꢀng you to enter values. Some care is necessary when entering more complex
expressions using such templates.
For example, try entering √3+√5. In order to move out of the box aſter entering 3 you need to press either e
or ¢. This explains the use of ¢ in the key sequence in part b above.
More complex templates are available from the Maths
Templates Menu that can be opened by pressing t.
To make a selecꢀon from this menu you need to move the
highlight with the Touchpad and press ·.
A menu of maths templates
Those opꢀons which have a bold T superimposed are
not available on the numeric version of TI-Nspire as they
require a Computer Algebra System (which cannot be
used in most exams).
Try using a template to produce the sums of the first 20
square numbers. You will need to use an alphabeꢀc key
such as N to enter the variable name. Press e or use
the Touchpad to move from one small box to the next.
Now produce the sums of the first 20 cubic numbers. The
easiest key sequence to use is (probably!):
££·¡¡.3·
Other useful templates are the definite integral template,
and the differenꢀal at a point template.
These can also be accessed from the Calculus Menu b4.
Integral of x2+2x-3
between 1 and 5
Derivaꢀve of
x2+2x-3 at x=5
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First Steps with TI-Nspire
Tutorial 2: The Calculator Applicaꢁon
Geꢂng Set
The mode seꢁngs for a document can be changed using the
document seꢁngs dialog box: press
c521 or ~721 or
Click on the
icon then press 21
With dialog boxes it is important to remember
that you need to press e to move through
the various opꢀons.
Document seꢀngs dialog box
Noꢀce that here the first box is outlined bold, showing that
Display Digits is selected. Press ¤ to see the range of opꢀons
for fixed or floaꢀng decimal places. Change to the seꢁng
Fix 2, by highlighꢀng it and then moving to the next box
using e.
In the second box, change the angle seꢁng to Degree and in
the fiſth box choose Approximate.
Then press · again to apply the new seꢁngs to your
document.
You can check the angle seꢁng by hovering the cursor over
the
symbol.
Do some calculaꢀons to see the effect of these changes
before returning to the default seꢁngs, Float 6, Radian
and Auto.
In Approximate mode
all results are shown as
decimals rather than
fracꢀon
The effect of changed seꢀngs
Page 18
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First Steps with TI-Nspire
Tutorial 2: The Calculator Applicaꢁon
Some Algebra
The calculator applicaꢀon allows you to define variables as single numbers, funcꢀons, lists, matrices and even
strings.
There are three equivalent ways to store a variable.
You can use
/h
(store),
or
/t(Ï)
or
Define
Define can be typed leꢂer by leꢂer, followed by a space
or alternaꢀvely it can be entered from the Catalogue:
press kD to find it.
Noꢀce also you can:
•
•
display mulꢀple values in a list using curly brackets /);
use a colon for mulꢀple statements on the entry line º.
3 ways to define variables
In the last entry the value of r was changed to 5 but
noꢀce the difference between a and c(r): whereas
c is a defined funcꢀon of r, a had been given a
parꢀcular value.
What you type is not necessarily what
you get: above πr2 and 2πr were a
ctually typed as.
PIrRq
2PIrR
This screen illustrates the use of funcꢀon notaꢀon on the
calculator screen. Noꢀce that h(g(x)) can be evaluated
numerically but the TI-Nspire CAS would be able to
evaluate it algebraically.
You will see in Tutorial 4 that funcꢀons defined like this in the
Calculator applicaꢀon can then be used in the Graphs and
Geometry applicaꢀon. So please enter these definiꢀons of
g(x) and h(x) on your handheld now.
Use of funcꢁon notaꢁon
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First Steps with TI-Nspire
Tutorial 2: The Calculator Applicaꢁon
The Calculator Menu
Press b and look at the extensive system of menus and
submenus available in the Calculator applicaꢀon. If you used
the TI-83 or TI-84 graphical calculators you will be familiar
with many of these expressions.
More details can be found in the Geꢂng Started Guide.
This screen shows a simulaꢀon of 100 throws of two dice and
uses commands from the Probability and Staꢀsꢀcs
sub-menus.
To enter randInt you can either press
b542
Lists of random integers
to navigate through the menus or you can spell it out, leꢂer
by leꢂer.
You will find the mean command by pressing
b633.
Noꢀce that the expression d1+d2 produces a list of 100 sums of the corresponding
values from d1 and d2 i.e. 100 totals when 2 dice are thrown
Staꢁsꢁcal Distribuꢁon Tables
A useful feature of the TI-Nspire is the ability to work
with probability distribuꢀons such as the Binomial,
Poisson and Normal distribuꢀons. These can be found
by pressing b65.
These provide wizards which enable you to calculate
the probability for a given distribuꢀon instead of looking
up the value in a table.
Page 20
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First Steps with TI-Nspire
Tutorial 2: The Calculator Applicaꢁon
Variables Linked to Documents
Press h and you will see a floaꢀng menu showing all the
variables that you have defined while using the current
document.
When you load a different document these definiꢀons
will be replaced by those linked to that document. Make
sure your list includes the variables g, h, d1 and d2 and
then save the document, giving it the name FirstSteps.
The Save As.. opꢀon is in the Documents menu so press
~15, type the filename:
gFIRSTgSTEPS
List of defined variables
and press ·.
Check list of some key points in Tutorial 2:
•
•
•
•
•
•
•
The layout of expressions oſten changes when they are evaluated
Previous expressions and results can both be recalled for subsequent use
Evaluaꢀon can be either approximate (decimals) or exact (fracꢀons)
How to use templates and menus
Changing from default document seꢁngs
Using Staꢀsꢀcal Distribuꢀon funcꢀons
Defining and using variables and funcꢀons
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First Steps with TI-Nspire
Tutorial 3: The Notes applicaꢁon
Tutorial 3
The Notes page
This very short tutorial introduces this simple, innovaꢀve applicaꢀon and deals with the process of spliꢁng the
screen.
Why use Notes?
TI-Nspire documents may be readily shared with others, so
teachers can prepare and then distribute documents that are
a type of electronic worksheet. The Notes applicaꢀon allows
documents to include:
•
•
text instrucꢀons for the user
space for the user to document their own
mathemaꢀcal acꢀviꢀes
•
a means of teacher-student and student-student
interacꢀon.
Various text formaꢀng
Instrucꢁons
Recording results
Making Notes
Open a FirstSteps document that you created previously.
Open a new page for notes in that document by pressing c and then selecꢀng
.
Alternaꢀvely a Notes page can be added by pressing /~6 or by pressing (¿).
Enter some text using the alphanumeric keys. For upper case leꢂers use the shiſt key, g.
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First Steps with TI-Nspire
Tutorial 3: The Notes applicaꢁon
Press b to see the various opꢀons available when using the
Notes applicaꢀon.
Try to format some text.
To select a block of text for formaꢁng hold down the shiſt key,
g, while you move around the text using the Touchpad.
Spliꢂng the Screen
In any applicaꢀon you can split the screen into two or more
The Format sub-menu
parts using the page Layout opꢀon in the Document menu.
Press ~52 and you should see the various standard
opꢀons available. The icons on the leſt of the menu indicate
the way the screen will be split.
Choose any of the opꢀons to see your text appear on a split
screen.
Ways to split the screen
Important: to move from one
part of the screen to another
you need to press: /e
Add a Calculator applicaꢀon area to your page
and experiment with using Notes and Calculator
together.
You must press / e and then b
The opꢀon Custom Split enables you to change the width or height of secꢀons of the page. It can be used
either when the page is first being split, or subsequently to edit an exisꢀng split page.
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First Steps with TI-Nspire
Tutorial 3: The Notes applicaꢁon
More Opꢁons from the Notes Menu
Mathemaꢀcal expressions can be entered (and evaluated)
on a Notes page.
In addiꢀon the menus in the Notes applicaꢀon provide:
•
•
•
two templates for Q+A and Proofs
teacher and reviewer comments
small shapes such as ∆
Have a look at the examples of their use shown here. If you
want to explore them choose the relevant opꢀons aſter
pressing b.
An inserted comment
Use of Q+A template
Use of proof template and symbols
Interacꢁve Notes
A powerful feature of the Notes page is something called
Interacꢀve Notes. These enable you to create dynamic
calculaꢀons. Unlike the Calculator page, which when you
carry out a calculaꢀon gives an answer which will not
update, the MathsBox within the Notes page is dynamic.
Add a new Notes page by pressing:
/~6. For this simple example we will create a funcꢀon
calculator.
To do this simply add a MathsBox (b31 or /M) and
enter the calculaꢀon exactly as you would have done on the
Calculator page (i.e. the bold text in the image). Now try
ediꢀng either the funcꢀon or the input value, and see how
the output automaꢀcally updates.
The MathsBox aꢂributes (b51)
allows you to show just the input
or output if preferred
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First Steps with TI-Nspire
Tutorial 3: The Notes applicaꢁon
Asking Quesꢁons
If you also have access to TI-Nspire Teacher Soſtware, then you also have the ability to insert quesꢀons in to
your documents. To do this you use the Insert menu and choose Quesꢁon…
There are a number of different
quesꢀon types which can be used
In this example we’ve chosen the Custom Choice quesꢀon type, this is a mulꢀple choice template.
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First Steps with TI-Nspire
Tutorial 3: The Notes applicaꢁon
We then enter the quesꢀon in the top box and answers in the
fields below. To add mathemaꢀcal content insert a Maths
Box. To indicate the correct answer click on the Tick mark.
When viewed on the handheld the quesꢀon this will look like
this. If the correct answer has been set then the quesꢀon
can be either self-marked by pressing b2, or marked by
the teacher using TI Connect-to-Class or TI-Nspire Navigator
Teacher soſtware.
Check list of some key points in Tutorial 3:
•
•
•
•
•
•
Some possible uses for the Notes applicaꢀon
Creaꢀng and ediꢀng page layouts with split screens
Moving from one part of a split screen to another
Accessing templates from the Notes menu
Using Maths Boxes in Interacꢀve Notes
Creaꢀng quesꢀon using the TI-Nspire soſtware
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First Steps with TI-Nspire
Tutorial 4: Graphing
Tutorial 4
Graphing
The Graphs and Geometry applicaꢀons are probably the most visually exciꢀng of the TI-Nspire applicaꢀons.
This tutorial introduces the Graphs applicaꢀon and then concentrates on its use for graphing and exploring
funcꢀons. The applicaꢀon’s use for creaꢀng and exploring geometrical shapes is covered in Tutorial 5.
Graphs & Geometry: Two Views
Start by opening the document FirstSteps4 that you created in Tutorial 3. Press c then select
new page with the Graphs applicaꢀon. You should see the Graphing View, with the coordinate axes defined by
the default window seꢁngs and an entry line at the boꢂom of the screen.
to create a
A Graphing page can be turned into a Plane Geometry page by pressing b2 to open the View menu and 2
to choose the Plane Geometry View. This view has no entry line or axes and is ideal for drawing geometrical
shapes. Tutorial 5 will explore this aspect of the Graphs & Geometry applicaꢀon.
Return to the View menu and noꢀce that several opꢀons are now grey, indicaꢀng that they are not available in
this view. Choose b21 to return to the Graphing View.
Graphing Funcꢁons
Alongside f1(x)= enter 0.2x2–3
(0^2Xq-3) to see the screen shown here.
Noꢀce the label that appears alongside the funcꢀon’s graph
and the way the entry line has now disappeared.
In Tutorial 2 you defined the funcꢀon g(x):=x+4. Press e
to return the entry line and alongside f2(x)= enter g(x)
(G(X)) and draw the straight-line graph. Noꢀce that the
The Graphing View
entry line will again disappear.
Pressing e once again will return the graph entry line, pressing e repeatedly and the highlight moves to
different locaꢀons on the screen. Highlight the double arrow in the boꢂom right-hand corner and press ·.
This enables you to see all the funcꢀons entered so far––the funcꢀon history. Press d and you move to the
main work area with a cursor in the form of an arrow at the origin.
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First Steps with TI-Nspire
Tutorial 4: Graphing
Grab and Drag pracꢁce
Use the Touchpad to move the arrow around the work area, it behaves exactly like a trackpad on a laptop, so
you do not need to press down on the pad just let your finger lightly touch it.
As you move the cursor over the objects in the work area, three things may happen:
•
•
•
the cursor changes shape
the underlying object flashes
labels of the various objects appear, e.g. axes, graph etc.
In some posiꢀons two or more screen objects overlap and
you are prompted to press the e key to toggle through the
labels of various overlapping objects. Move the cursor to the
posiꢀon shown here.
Make certain that the open-hand (÷) icon is showing over the
highlighted label for f1(x) and grab the label by pressing and
holding x or by pressing /x.
The open-hand cursor
Noꢀce that the fingers of the hand close up ({) indicaꢀng that
you have successfully grabbed this label. Use the Touchpad
to drag the closed-hand icon and the funcꢀon label to a
new posiꢀon. Click again by pressing x or press d to stop
dragging. Being able to grab and drag items is one of the most
powerful features of the Graphs. However, some skill and
paꢀence is oſten needed to grab exactly the right item and,
without care, mistakes can easily be made.
If you do end up moving the wrong item,
remember that /Z or /d can be
used to undo the last change. As with a
computer / Y can be used to redo.
Changing the Axes
Get some more pracꢀce at grabbing objects as follows. Move
to a ꢀck mark on the x-axis such as the one shown here
represenꢀng x=6. Make certain that you can see the open-
hand icon – if you see an upward poinꢀng index finger (ø) you
are selecꢀng the axis itself, not just the ꢀck mark.
Grab the ꢀck mark and move gently to the leſt or right
watching the effect. Noꢀce that both the x- and y-axes are
rescaled.
Click again (x) or press d and /d to undo this and
return to the default set of axis.
Grabbed ꢁck mark on the axes
Now grab the ꢀck mark again and this ꢀme hold down the
shiſt key, g, while you move leſt or right. This ꢀme the
x-axis is scaled but the y-axis is unchanged.
Page 28
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First Steps with TI-Nspire
Tutorial 4: Graphing
You have just used a direct method for changing the axes, but
there are a number of other ways to do this. Press b4 and
you will see this Window sub-menu. Opꢀon 1 allows you to
enter numerical values to determine the extremes of the axes,
while the Zoom opꢀons, as on the TI-83 and TI-84, provide
automaꢀc rescaling.
The Zoom seꢀngs
It is worth menꢀoning one final very useful
way of changing the posiꢀon of the axes,
but without rescaling them. Move the arrow
cursor to an empty part of the screen and
grab the vacant space. An appropriate icon
appears (ù) indicaꢀng that you are grabbing
the whole working area. Now you can use the
Touchpad to reposiꢀon the axes as you wish.
The grabbed-sheet icon
Reset the axes using the (default) Zoom-Standard
opꢀon from the Window menu before conꢀnuing.
Ediꢁng, Deleꢁng or Hiding a Funcꢁon
Suppose you wish to make f2(x)=x+8. As well as changing g(x)
in the Calculator applicaꢀon on page 1.1, you can make the
change in two ways on this page.
•
In the work area, move the pointer to the label,
f2(x)=g(x) and, instead of grabbing it, double-click on
the label and an editable box opens up. Change the
definiꢀon and press · to update it.
•
Press ee· to highlight the funcꢀon history area
and scroll up to edit f2.
Funcꢀons may be deleted in similar ways, by simply deleꢀng
their definiꢀon and pressing ·.
Changing f2 in the funcꢁon history
To hide a funcꢀon’s graph click
on the Hide/Show buꢂon ú
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First Steps with TI-Nspire
Tutorial 4: Graphing
Tracing Graphs
Press b51 to choose the Graph Trace opꢀon.
Noꢀce the Trace icon in the top leſt
corner of the work area. This is typical of
many of the opꢀons from the menus.
Press ¡ and ¢ to trace along the graph and see the coordinates
of current points in the lower right corner. For intricate
funcꢀons progress can be slow along the curve but you
can change the Trace Seꢁngs to increase the Trace Step:
press b53 and try a step of 0.5 or 1. To start tracing at
an integer value of x, in Graph Trace mode simply type the
integer and press ·.
The current value of the trace is
displayed in the boꢂom corner
Press £ or ¤ to move to the other graph. To trace through all
the visible funcꢀons at once use Trace All b52. Noꢀce
that significant points such as maxima, minima and zeros are
automaꢀcally idenꢀfied.
To stop tracing you need to press d. Check to see that the
Trace icon is no longer showing in the top leſt corner.
points and coordinates
Here is the way to mark points of intersecꢀon of two lines.
•
•
•
Press b73 to choose the Intersecꢀon Point(s) opꢀon.
Noꢀce the icon has appeared in the top leſt corner.
Move the cursor to the graph of f1(x). With the graph
highlighted click x.
Move to the graph of f2(x). With the graph highlighted
click x.
Noꢀce that the Intersecꢀon Points icon is sꢀll visible so you
can go on to mark more intersecꢀons. For example you could
try marking where the two graphs cross the y-axis.
Points of intersecꢁon
Now press d.
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First Steps with TI-Nspire
Tutorial 4: Graphing
Noꢀce that all the intersecꢀons are added at once and that
their co-ordinates are automaꢀcally displayed.
We will now use the Text tool: b16. Try labelling one
of your fixed points by moving carefully to the point––make
quite certain that only the point is highlighted and not one
of the graphs or axes.
Points, lines and shapes can be drawn and manipulated on
the graphing work area and this will be explored in the next
tutorial. However, one more thing to try now is puꢁng a grid
on the work area. Press b26.
Coordinates and labelled points
It’s easy to change the number of decimal
places displayed: move the cursor over a
displayed value and press - or +.
Analyse Graph Menu
As well as tracing graphs and using the Points tool, important
points on graphs can also be idenꢀfied by using the Analyse
Graph tool. We will find the right-hand root of our quadraꢀc
funcꢀon by pressing b61 to acꢀvate the zero tool. Then
select the quadraꢀc graph by clicking on it with x, you will
then be prompted to select a lower bound my moving the
cursor somewhere to the leſt of the desired root and click
(x) and then to the right of the root and cl
Lower Bound
Upper Bound
There are number of features that can be idenꢀfied using
the Analyse Graph tool, spend some ꢀme exploring the other
opꢀons available by pressing b6.
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First Steps with TI-Nspire
Tutorial 4: Graphing
Manually Moving Graphs
You saw earlier that, when you change a funcꢀon’s equaꢀon the graph changes. An innovaꢀve feature of
TI-Nspire is that you can also do the reverse, i.e. manually manipulate the graph and see the funcꢀon’s
equaꢀon change. As the graph moves, all associated features such as points of intersecꢀon and their
coordinates also update.
First move the straight line graph, as follows.
Check that no icons are sꢀll showing in the top leſt corner of
the work area (press d if there is anything displayed) and
Alternaꢁve icons
then move the pointer to the graph of the funcꢀon f2(x)=x+2.
The line should be highlighted and you will see one of the
two icons shown here, depending on where exactly you
are on the screen. Move along the line and you will
discover the other icon.
Near the middle of the graph the icon suggesꢀng translaꢀon
appears, while the one suggesꢀng rotaꢀon appears towards
the ends of the graph. Decide which you would like to use and
grab the line by pressing and holding x.
Use the Touchpad to move the graph around. Noꢀce the way
that the funcꢀon’s equaꢀon updates too.
Transformed graph and equaꢁon
Press d and try the other transformaꢀon.
Try manipulaꢀng a quadraꢀc graph, and explore the
possible transformaꢀons available
Many of the techniques that have been introduced in this tutorial, in parꢀcular fixing points, grabbing and
labelling them, will be used again in Tutorial 5. In Tutorials 6 and 7 you will see how the Lists and Spreadsheets
applicaꢀon allows tables of values to be formed from funcꢀons defined in the Graphs applicaꢀon.
Using Sliders
Sliders are a powerful way of controlling the value of
constants in a graph or geometric construcꢀon. In this
example we will use a slider to explore the transformaꢀon
of a funcꢀon. To do this, start by creaꢀng a new Graphs
page by pressing c then selecꢀng
.
First enter the funcꢀon f3(x)=x2, then insert a slider by
pressing b1A. v1 will be highlighted. Change it to d
by pressing D· ·.
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First Steps with TI-Nspire
Tutorial 4: Graphing
Next add a second funcꢀon f4(x)=f3(x-d) by pressing
eF3(X-D)·, this funcꢀon is a transformaꢀon of
the original funcꢀon by d. Now grab the handle on the slider
and move it leſt and right and observe the effect on the graph.
Try changing the original funcꢀon, or moving the posiꢀon of d
in f4 to explore other transformaꢀons.
Sequence ploꢂng
We normally think of sequences as being lists of numbers,
but someꢀmes it is useful to look at them graphically. The
TI-Nspire makes this easy with the aid of its sequence ploꢁng
mode. To do this, create a new Graphs page by pressing c
then selecꢀng
.
Then press b351 to put the TI-Nspire in to sequence
mode. Enter the nth term of the sequence as u1(n)=2n-1 and
enter the Iniꢀal Terms as the first term in the sequence, 1,
and press·.
Adjust the window seꢁng by pressing b41 and change
the x-axis to go from -2 to 21 and the y-axis to go from -2
to 42. Now you can explore the sequence further by using
Graph Trace b51 or by displaying the sequence as a table
by pressing /T.
You can also use the sequence ploꢂer to explore recursive
sequences. For example you could instead define
u1(n)=u1(n-1)+u1(n-2) and set the Iniꢁal Terms set to 1,1
(1,1) which would give you a Fibonacci sequence.
Finally save the document as FirstSteps5 so that you can
refer to these graphs later.
© 2012 Texas Instruments Educaꢀon Technology
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First Steps with TI-Nspire
Tutorial 4: Graphing
Check list of some key points in Tutorial 4:
•
Items visible in the graphing view: the work area, the entry line, the funcꢀon history,
the warning icons in the top-leſt corner
•
•
•
•
•
•
•
Grabbing and dragging labels
Seꢁng the axes in three ways: by dragging, zooming and entering values
Tracing along graphs
Marking and labelling points and their coordinates
Using the Analyse Graph menu
Transforming graphs and their funcꢀons manually
Using Sliders
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First Steps with TI-Nspire
Tutorial 1: TI-Nspire documents
Tutorial 5
Geometry
This tutorial introduces interacꢀve geometry in TI-Nspire and builds upon the methods and features of
the Graphs and Geometry applicaꢀons that were covered in Tutorial 4. You are led step by step through a
geometrical construcꢀon which illustrates the simple concept that the areas of triangles with a fixed base and
constant height are equal. As you work through the construcꢀon you will meet many of the features that make
this one of the most powerful and aꢂracꢀve components of TI-Nspire.
A View for plane Geometry
If necessary open your FirstSteps5 document and use the
c key then select
to create a new Geometry page.
Much like with a Graphing page it is possible to convert the
Plane Geometry page in to a Graphing page by selecꢀng
b21. However for now leave the page in plane
Geometry View.
Two parallel Lines
We will start by drawing a line segment to represent the
base of a triangle and labelling it BC: press b7 to see the
opꢀons available for drawing Points & Lines. Segments have
two disꢀnct end points, lines are (in theory) infinite, while
rays have just one end. So choose opꢀon 5: Segment.
Move the cursor to a suitable posiꢀon for point B. Then click
(x) to fix the point and then gB to give it a label of B.
Move the cursor to where you want the other end of the
segment to be. Mark the point and label it C in the same way.
The icon in the top leſt corner is sꢀll showing you that you
could draw another segment if you wish. Press d to
remove the icon and leave that mode of operaꢀon.
Noꢀce that as usual the relevant icon
appears in the top leſt corner of the screen.
Drawing the base of the triangle
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First Steps with TI-Nspire
Tutorial 5: Geometry
The next step is to draw a line parallel to BC. This is a
construcꢀon so you need to press bA.
Choose opꢀon 2: parallel.
You must specify two things: the line to which it is to be
parallel, and a point the line must pass though (although
these can be chosen in either order). So move the cursor
to the segment BC––you will see its label when you are in
the right posiꢀon. Click (x) to select the segment, move
away, dragging a doꢂed parallel line and when happy with
its posiꢀon click again. Once again, don’t forget to press d,
if you do not want to add another parallel line.
Many opꢁons in the Construcꢁon menu
What’s grabbable?
At this point it is worth moving the cursor around the
screen to see which objects can be grabbed and dragged.
You should see the open hand cursor (÷) appear for point B,
for point C, for the segment BC, and for the point fixing the
parallel line. All of these are grabbable.
However, the parallel line itself cannot be grabbed and
dragged. It can however be selected for various purposes.
For example, you could delete it by clicking (x) to select it
and then pressing . to remove it.
Selectable, but not grabbable!
Construct the Triangle
First, a point A is needed on the parallel line. Later you will be
sliding this point along the line without moving the line itself,
so the point that you have already which defines the line is
not a good one to use. Therefore press b72 to select the
opꢀon: point On. Move the cursor to a new posiꢀon on the
line and then click (x) then press: gAd. The triangle
itself can be constructed using the Shapes menu (b92).
Check that the correct icon is showing in the top leſt corner,
and then carefully select, in any order, each of the points
A, B and C.
Point A is ready to be selected
Make certain you don’t click unꢀl its label and the poinꢀng-
finger icon appears as shown here.
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First Steps with TI-Nspire
Tutorial 5: Geometry
Making Measurements
With a triangle drawn on your screen, the next step is
to measure its area. Choose opꢀon 2: Area from the
Measurement menu (b8) and then move the cursor to
one of the sides of the triangle. The triangle label and the
poinꢀng-finger icon appear together with a calculated area
in the background. Click to confirm the choice of the triangle,
then move your cursor to where you want the measurement
displayed then click again to show the measurement and
finally press d to remove the icon from the top leſt corner.
Measur
The area is now displayed (to the number of significant figures
set in the Graphs & Geometry seꢂngs ~722).
Noꢀce the range of other
possible measurements available
from this menu.
Remember you can place the cursor over the calculated
value (you should see the open-hand icon) and press + or -
several ꢀmes. The effect is to reduce the number of displayed
decimal places. This feature can be applied to any numbers on
the screen in either the Graph or Geometry applicaꢀon.
Variables and Text
There are two ways to make it clear that the measurement at
the boꢂom of the screen represents an area. One method is to
simply add some text alongside the measurement. However,
a more powerful method is to allocate the measurement to a
variable and display the variable name alongside it. To do this:
•
•
•
move the cursor over the measurement (you will see the
open-hand icon;
press h and choose opꢀon 1: Store Var (Alternaꢀvely
press /h)
Storing the measurement as a variable
use the alphabeꢀc keys to give the variable the name
“area”. Press ·.
This variable may now be used on other pages of the
document. For example, if you move to a Calculator
page, type and enter area, the current value of the
area will be used.
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First Steps with TI-Nspire
Tutorial 5: Geometry
Now move to the top of the screen and enter some text, perhaps giving the user some explanaꢀon or
instrucꢀons. You will need to press:
•
•
•
b16 to select the Text opꢀon,
Then click to start a box where text can be entered.
Note you cannot do carriage returns in text boxes so do put in two lines you must use two text boxes!
Dynamic Changes
If you haven’t yet done so, try grabbing point A and sliding it
along its line. Make quite certain that you grab the point––
you must see its label. You may need to press e unꢀl the
point itself, rather than the triangle or label is selected. If you
do select the wrong item it is well worth remembering that
/d will undo any acꢀon if something happens that you
didn’t intend!
Noꢀce that as you move the point, two sides of the triangle
and the label A all move too. What does not change however,
is the area.
Ready to grab A and slide it
Now try grabbing and dragging point B or C, and then the
line segment BC and the line parallel to it. In each case noꢀce
which other items on the screen move, and which do not.
Thinking about how each item was originally defined should
explain whether it moves in relaꢀon to other items.
Tidying Up and Using Aꢀributes
Finally it’s well worth seeing how to improve the appearance
of the screen and prevenꢀng items from being grabbed
unintenꢀonally.
For this acꢀvity the scale in the top right corner may not be
needed. You can hide it with opꢀon 8 in the View menu.
The point that defines the parallel line may be rather
distracꢀng, so you could hide it using opꢀon 3 in the
Acꢀons menu.
Now from the Acꢀons menu choose opꢀon 4: Aꢀributes.
Move the cursor to one of the sides of the triangle and
click (x) to select it.
Changing the aꢂributes of the triangle
This allows you to change the thickness and style of the line.
Press · to confirm your choices.
To change the shading of the shape, you need to ‘right-click’
on the triangle by placing the cursor over one of the edges
and pressing /b.
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First Steps with TI-Nspire
Tutorial 5: Geometry
This brings up the contextual menu which gives the opꢀons
available for the opꢀon displayed. To change the shading
select Colour then Line Colour or Fill Colour which will open a
colour picker from which you can choose a colour.
Now move the cursor to point B and right click again (/b).
This gives you the contextual menu for the point, one opꢀon
here is to pin the point, which will prevent users from
grabbing and moving it. For example, there may be good
pedagogic reasons for only allowing point A to move in this
acꢀvity. For the moment pin points B and C.
To unpin an object just right-click on the object again and
select Unpin.
Conꢀnue to move the cursor around the screen and see
the opꢀons for changing the aꢂributes of the parallel line
and also the area measurement. When you look at the
aꢂributes for the area calculaꢀon you will see the opꢀon
of a padlock. Locking the measurement will fix the current
value constraining movement of other points accordingly.
Area is now locked
Locking some objects and unlocking others can have very interesꢀng effects and if you have ꢀme you may care
to invesꢀgate the following situaꢀons.
a) Locked/pinned:
The area measurement.
Unlocked/Unpinned: Points B and C and the parallel line through A.
Try Moving point B
b) Locked/pinned:
The area measurement and the parallel line through A.
Unlocked/Unpinned: Points B and C.
Try Moving point B
Once again save your document as FirstSteps6 before going any further.
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First Steps with TI-Nspire
Tutorial 5: Geometry
Check list of some key points in Tutorial 5:
•
•
•
•
•
•
•
•
Use of the Plane Geometry View rather than the Graphing View
Lines, segments and rays
Construcꢀng parallel lines
Drawing points on objects and labelling them
The construcꢀon of shapes
The difference between selecꢀng and grabbing screen objects
Making a measurement and storing as a variable
Aꢂributes which change the appearance and locking/pinning screen objects
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First Steps with TI-Nspire
Tutorial 6: Lists & Spreadsheet
Tutorial 6
Lists & Spreadsheet
The Lists & Spreadsheet applicaꢀon is a very powerful means of manipulaꢀng data lists and works seamlessly
with the other applicaꢀons to provide mulꢀple representaꢀons of data. This tutorial introduces the applicaꢀon,
showing how to use it as a simple spreadsheet. It also shows how the Lists & Spreadsheet applicaꢀon handles
lists and funcꢀons defined in the Calculator, and Graphs applicaꢀons.
In the next Tutorial you will see how Lists & Spreadsheet is used in conjuncꢀon with the Data & Staꢀsꢀcs
applicaꢀon to produce charts and staꢀsꢀcal summaries.
Entering Data as Lists
Open a document and press c then select
to add a
new page using the Lists & Spreadsheet applicaꢀon.
Enter some data similar to that shown here:
•
•
column A represents male shoe sizes,
column B has widths of hand spans in cm (paired data
with column A),
•
column C is female shoe sizes.
You will need 20 or 30 pairs of similar data in columns A and B
and at least 15 values in column C.
Differences from a spreadsheet?
Noꢀce the similariꢀes and differences between this screen
and a tradiꢀonal spreadsheet. In parꢀcular noꢀce the two
areas coloured white and grey at the top of each column.
•
•
The white area is for list names.
The grey area is for formulas that will apply to all items
in the list below.
Move to the white space beside A, type mshoe and
press ·.
Defining the list in column C
What you have just done is to define a new list. If you were
to move to a Calculator screen, pressing h would reveal
mshoe as one of the defined variables and lists,
and entering the name on that screen would produce the
result {11,8,7,12,9.5,…..}
Lists can also be defined in the
Calculator applicaꢀon
Define the data in columns B and C as lists mhand and fshoe.
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First Steps with TI-Nspire
Tutorial 6: Lists & Spreadsheet
Using Formulae
Suppose you wished to invesꢀgate the relaꢀonship between hand spans and shoe sizes. You might therefore
wish to divide every hand-span measurement by the corresponding shoe size. These raꢀos would best be
expressed in decimal rather than fracꢀonal format so change the Document Seꢁngs for Calculaꢀon Mode to
Approximate (~721).
There are 3 ways (at least!) of calculaꢀng the raꢀos on the TI-Nspire. Try one of the following now.
Either: in cell D1 type the expression =B1/A1. Select D1 and fill down the column by pressing b and
choosing the opꢀons 3: Data and 3: Fill Down.
Or:
Or:
in the grey formula area at the top of column D enter =mhand/mshoe.
in the grey formula area enter =b/a.
Conꢃict resoluꢁon
One way to enter a formula
Press b and noꢀce the various opꢀons
available in the Lists & Spreadsheet applicaꢀon.
TI-Nspire has most of the ediꢀng features that
you would expect from a spreadsheet including
selecꢀng, inserꢀng, moving and deleꢀng rows,
columns and cells.
Typical Spreadsheet Acꢁons
You can also create absolute cell references in the usual way using $ chosen from the symbols key menu (º)
and you can sort data in columns (b16). To sort mulꢀple columns at once by one column press £ unꢀl the
column is selected then hold down g and press ¡ or ¢ to select the columns you want before choosing Sort
from the Acꢁons menu.
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First Steps with TI-Nspire
Tutorial 6: Lists & Spreadsheet
Capturing Data
A powerful feature of TI-Nspire is its ability to capture data from a Graphs or Geometry page. Follow
through these steps to see an example of how this works, using the measurement of the area of a triangle
from Tutorial 5.
•
•
Create a new Lists & Spreadsheet page: (c then select
).
Choose the Manual Data Capture opꢀon from the menus
(b322).
You should see in the entry line: =capture(var,0).
Instead of typing ‘area’ you can also press
h, highlight area and then press ·.
•
•
•
•
Overtype var by typing the variable name area.
Resize the column (b121).
Move to cell A1 and capture the current value of area by pressing /^.
Move to the page where you constructed the triangle. If necessary unpin point B and unlock the area
variable, then grab B and move it. Noꢀce that this changes the area.
•
Return to page 1.6 and in cell A2 press /^.
In the formula the second parameter, 0, indicates manual
capture was selected. An interesꢀng variaꢀon involves using
automaꢀc capture (i.e. =capture(area,1)). Either edit the
formula in column A or enter it in column B (b321).
Then grab and move point B around again and see the huge
amount of data that are generated. (See the Appendix for
more ideas about using this feature).
If you have ꢀme you may care to measure the base and height
of the triangle on the Geometry page and capture these
values on the Spreadsheet page. How could such features be
used to develop an understanding of triangle area?
Capturing data by hand
Capturing data by hand
Funcꢁon Tables
It is quite possible to create from scratch a table of values for
funcꢀons that have been defined elsewhere in the current
document. For example, the screen shown here uses the
definiꢀons of f1 and f2 that were used previously. Don’t
worry if the values you see are different from these.
A hand-made funcꢁon table
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First Steps with TI-Nspire
Tutorial 6: Lists & Spreadsheet
Because funcꢀon tables are so useful, they can also be drawn
automaꢀcally. Follow through these steps.
•
Create another Lists & Spreadsheet page and press
b51 to switch to a funcꢀon table. Noꢀce the different
layout of the screen and a box with a list of the currently
defined funcꢀons.
•
•
Choose a funcꢀon and scroll up and down.
Press b5 again. These are the only opꢀons that are
available now: apart from the ability to resize columns.
•
•
Experiment with using opꢀon 5: Edit Table Seꢂngs.
A simple funcꢁon table
Now use opꢀon 4: Edit Expression. You
will see the values in the table change
and any associated funcꢀon will also
have changed.
Opꢁons for funcꢁon tables
Having a funcꢀon’s table on the same page as its graph can
clearly be a powerful learning tool and there is a very simple
way of arranging this on a split screen. On the relevant page
of your document choose opꢀon A in the View menu or
press /T.
The Funcꢀon Table view is an
alternaꢀve for any Lists & Spreadsheet
page. You can toggle between the two
views using /T.
With a split screen of this nature it is as well to remove
all unnecessary cluꢂer. Here the labels and unnecessary
funcꢀons have been deleted. Also the verꢀcal split between
graph and table was set using the opꢀon Custom Split from
the Documents/Page layout menu. (~51).
You can refine the split further by pressing the outer
edge of the touchpad to move the window separator
and then press ·.
Graph and table side by side
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First Steps with TI-Nspire
Tutorial 6: Lists & Spreadsheet
Frequency Charts
Oſten due to the quanꢀty of data it is more useful to work
with data in the form of a frequency chart, this can be for
either discrete or grouped data (using the midpoint). Let’s
look at some more shoe size data but this ꢀme as a frequency
chart. Create a new Lists & Spreadsheet page, then enter the
following data, with the headings gshoe (grouped shoe size)
and gfreq (grouped frequency). We’ll explore what we can do
with this data in the next secꢀon!
Once again save your document, now as FirstSteps7 before
going any further.
Check list of some key points in Tutorial 6:
•
•
•
•
•
•
Entering and ediꢀng data and formulas
Lists and funcꢀons defined in other secꢀons of the document
Resizing cells
Coping with ambiguous variable/cell names
Use of funcꢀon tables
Entering Frequency Tables
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First Steps with TI-Nspire
Tutorial 7: One- and two-variable staꢁsꢁcs
Tutorial 7
One and Two Variable Staꢁsꢁcs
One of the six core applicaꢀons of TI-Nspire is Data & Staꢀsꢀcs, the workspace for presenꢀng, interpreꢀng and
manipulaꢀng staꢀsꢀcal charts and graphs. This applicaꢀon works in combinaꢀon with the Lists & Spreadsheet
applicaꢀon and this tutorial uses the data that were entered as a spreadsheet at the beginning of Tutorial 6.
Shoe Sizes and Hand Spans
Start by locaꢀng in your Document the page that you created
in the first part of Tutorial 6. There should be 20 or 30 pairs of
(probably ficꢀꢀous) data in columns A and B and at least 15
values in column C.
•
•
List mshoe in column A represents male shoe sizes.
List mhand in column B has widths of hand spans in cm
(paired data with column A).
•
List fshoe in column C represents female shoe sizes.
Charts with One Variable
To create a new page for the charts press c then select
Data entered in Tutorial 6
.
Randomly distributed points: no variables
have yet been assigned.
Move the cursor to the boꢂom of the screen where it says:
Click to add variable. Press x.
A list of currently defined lists opens up, so use the Touchpad
Choosing a variable
to select mshoe and press · or x.
Iniꢀally you will see a dot plot.
Press b1 to see the Plot Type menu, which gives nine
types of plot. Because you have only defined a single
numerical variable so far, there are only three alternaꢀve
plots including a boxplot and a histogram.
Try these opꢀons now.
Three plots for numerical data
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Tutorial 7: One- and two-variable staꢁsꢁcs
Display the boxplot and then move the cursor over the chart.
You will be able to see the median, quarꢀles, maximum and
minimum values and, possibly, outlier values.
Upper quarꢁle displayed
Comparing Boxplots
This boxplot can be compared with a similar one represenꢀng
the female shoe sizes by displaying them, one above another.
To do this we add a second X Variable by pressing b24,
this will give you the choice of available lists.
This ꢀme select fshoe. The result is two side by side box plots
that can easily be compared.
This method can be used to add more box plots, up to five or
six can be easily compared on the same screen.
Comparing shoe sizes
Charts for Categorical Data
Create a new Data & Staꢀsꢀcs page and choose the variable
mshoe for the x axis.
This variable contains a list of numerical data but they could
also be thought of as categorical data, in which case it would
be appropriate to use a Pie Chart. By using the opꢀon Force
Categorical X in the Plot Properꢀes menu you can force the
handheld to treat the data in this way. Noꢀce the way in
which the labels on the axis change.
A Pie Chart displaying categorical data
Now you can use the Plot Type menu to choose Pie Chart.
It is also possible to enter non-numerical categorical data in
a Lists & Spreadsheet page, e.g., favourite pets, sandwich
fillings etc. Such data must be entered in quotaꢀon marks
by pressing /r(Ó).
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First Steps with TI-Nspire
Tutorial 7: One- and two-variable staꢁsꢁcs
Charts with Two Variables
Create a new Data & Staꢁsꢁcs page.
Noꢀce both axes are marked Click to add variable.
As before select mshoe for the horizontal axis.
Move the cursor to the leſt edge of the screen, click x and
select the variable mhand for the verꢀcal axis.
Ready to add a 2nd variable
This displays the scaꢂerplot.
It may be that there is a posiꢀve correlaꢀon and a relaꢀonship
between hand span and shoe size, so it may be appropriate
to model this relaꢀonship with a linear funcꢀon. The Analyze
menu provides a range of tools to use.
Fiꢂng a Line by Hand and Eye
First try adding a line of best fit by eye, using opꢀon
2: Add Movable Line. This displays a straight line together
with a funcꢀonal relaꢀonship between mshoe and mhand.
The line can be dragged into a best-fit posiꢀon using the two
cursors for rotate and translate, in exactly the same way as
a straight line can be moved manually in the Graphs and
Geometry applicaꢀons.
Powerful opꢁons in the Analyse menu
Move to the middle of the line to get the
translate cursor. Click and hold x to grab it.
Now move the line into posiꢀon. Click again
x to release the cursor.
Move towards one end of the line to show
the rotate cursor. Click and hold x to grab it.
Use the Touchpad to rotate the line.
Click again x to release the cursor.
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First Steps with TI-Nspire
Tutorial 7: One- and two-variable staꢁsꢁcs
Drawing the Regression Line
The line that was fiꢂed by hand and eye can be compared
with the calculated linear regression line using opꢀon 4 in the
Analyze menu. Pressing b461 will display a line with
equaꢀon of the form y=mx+b.
As usual, you can click and drag on the regression equaꢀon to
move it to a convenient place.
The calculated regression line
Geꢂng the Stats
There are two methods for displaying summary staꢀsꢀcs:
1. For a single staꢀsꢀc you can type its name and use
the h key to choose the variable, e.g. =median(fshoe).
=MEDIAN(h·
2. On a Lists & Spreadsheet page, you can enter a complete
set of staꢀsꢀcs into spreadsheet cells.
Open a new Lists & Spreadsheet page and press b41
to see the range of staꢀsꢀcal calculaꢀons. (Once again these
will be very familiar to users of the TI-83/4).
The Staꢁsꢁcs Calculaꢁons menu
Choose opꢀon 1: One-Variable Staꢁsꢁcs.
You have the opꢀon to display stats for more
than one list but for now choose 1 list and
then OK.
Choosing the data list can either be done
using the Touchpad, or you can type the
name.
Type the leꢂer of the column where you
want the results to appear.
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Tutorial 7: One- and two-variable staꢁsꢁcs
It is also possible to arrange side-by-side comparisons of
corresponding summary staꢀsꢀcs for two or more data sets
and this makes drawing inferences from the staꢀsꢀcs very
quick and very clear. The best way to do this is to select more
than one list above.
Dragging on the Charts
An interesꢀng feature is the ability to drag ploꢂed points
around charts, thus changing the original data. Go back to
the page on which you created the scaꢂerplot for male hand
spans and shoe sizes. You leſt the plot showing the y=mx+b
regression line and equaꢀon.
Sets of staꢁsꢁcs
Move the cursor to a point very near the line of best fit. The cursor changes to a hand with a finger poinꢀng
upwards when it is poinꢀng to a data point. Click and hold x.
Move the cursor to invesꢀgate the effect that moving this point has on the regression line. Below, the point has
been moved to the top of the screen for maximum effect.
The effect of moving a point from here …
… to here.
This shows the effect of changing a single hand-span value from 21cm to 32cm
Working with Frequency Data
In the previous tutorial we entered some grouped data for
shoe sizes. We will now explore some of the ways we can
work with that data using TI-Nspire. Start by returning to the
Lists & Spreadsheet page we created in the previous tutorial.
We can use the same process we used above to find summary
staꢀsꢀcs for this frequency data.
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First Steps with TI-Nspire
Tutorial 7: One- and two-variable staꢁsꢁcs
Press b411 to start the One-Variable Staꢁsꢁcs wizard,
again choose 1 list (remember mulꢀple lists are for when you
want to calculate staꢀsꢀcs for mulꢀple lists at the same ꢀme).
This ꢀme we set the X1 List to be ‘gshoe but change the
Frequency List from 1 to ‘gfreq, and set the Results Column
to be c (which is the first empty column).
This gives you the summary staꢀsꢀcs for this grouped data –
Noꢀce the mean comes out of to be just over 6, which
matches original data (as the shoe-sizes go from 4 to 8).
We can also graph this data. This can be achieved from either
the Lists & Spreadsheet page by pressing b35 to insert a
Summary plot, or from a Data and Staꢀsꢀcs page by pressing
b25 to insert an X Variable with Frequency. We will use
this second approach now, so create a new Data and Staꢀcs
page by pressing c then selecꢀng
.
Then press b25, this will give you the Frequency
Plot wizard.
This will give you the following graph. This can also be
displayed as a box plot by pressing b12.
If you are dealing with grouped data you may need to adjust
the Bin Seꢂngs by pressing b222.
Save your document as FirstStepsComplete, so you can return to this if you want at a
later date.
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First Steps with TI-Nspire
Tutorial 7: One- and two-variable staꢁsꢁcs
Check list of some key points in Tutorial 7
•
•
•
•
•
•
•
•
Creaꢀng one- and two-variable staꢀsꢀcal plots in the Data & Staꢀsꢀcs applicaꢀon
Ploꢁng categorical as opposed to numerical data
Using boxplots to compare data sets
Calculaꢀng and displaying summary staꢀsꢀcs
Manually fiꢁng straight lines to data
Automaꢀcally fiꢁng linear-regression lines to data
Dragging points on a scaꢂerplot
Working with Frequency Data
Page 52
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First Steps with TI-Nspire
Appendix: Mulꢁple Representaꢁons
Appendix
Mulꢁple Representaꢁons
The previous seven tutorials have introduced many of the key features of TI-Nspire learning technology, with
each of the applicaꢀons being discussed separately. However, one of the great strengths of TI-Nspire is that
it allows the applicaꢀons to be linked dynamically, encouraging different approaches to problem solving.
This appendix offers an example of what is meant by “mulꢀple representaꢀons”, showing how several of the
applicaꢀons can be used to invesꢀgate a mathemaꢀcal concept, in this case the relaꢀonship between a circle’s
diameter and circumference and between its radius and area.
By working through this appendix you will be able to revise many of the skills and techniques you met in the
tutorials. Here detailed instrucꢀons and key presses have been omiꢂed though you will find back references
if you need to remind yourself about parꢀcular techniques. However, try to concentrate on the big picture
of what is going on, asking yourself how each of the mulꢀple representaꢀons contributes to a deeper
understanding of the mathemaꢀcs.
Draw and Measure a Circle
•
•
•
Open a new document with a Geometry page.
Construct a large circle on the screen.
Construct a radius by drawing a segment from the
centre to the circumference.
•
To construct a diameter first construct a line (not a
segment) from the centre to the circumference. Then
construct the Intersecꢁon points of the line and the
circle: this generates the point on the opposite end
of the diameter.
•
•
Now measure the lengths of the radius, the diameter
and the circumference. Also measure the area. In each
case change the number of decimal points displayed.
Finally assign the measurements to variables. Click on
each measurement in turn. Press h. Type the leꢂer
appropriate for each measurement (r, d, C and A) and
press ·.
A measured circle
•
Check that the measurements all change when you
grab the edge of the circle and change its size.
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First Steps with TI-Nspire
Appendix: Mulꢁple Representaꢁons
A Spreadsheet for Data Capture
•
•
•
Open a new Lists & Spreadsheet page.
Type column headings for columns A to D.
Click in the funcꢀon entry line in column A (grey cell just
below the heading).
•
From the Data menu choose Automated Data Capture.
Type r and press ·. This will capture values of the
radius in column A.
•
•
Repeat for the other variables in columns B to D.
Beginning to capture data
Check that the data that appear are the same as the
current measurements on the previous page.
Two Scaꢀerplots
•
•
Open a Data & Staꢀsꢀcs page.
Choose the variable diameter for the horizontal axis and
circum for the verꢀcal axis.
•
So far there is only one data pair and one point for the
Scaꢂer Plot.
•
•
Open another Data & Staꢁsꢁcs page.
Choose the variable radius for the horizontal axis and area
for the verꢀcal axis.
Seꢀng up a scaꢂer plot
Collecꢁng Just a Liꢀle Data
•
•
Return to the Geometry page.
Click and drag on the circumference of the circle to move
it in and out just a liꢂle bit.
•
Review the amount of data you have collected in the
spreadsheet.
•
•
Review the relaꢀonships shown on the two scaꢂer plots.
You may need to update the window seꢁngs using
the opꢀon Zoom–Data from the Window/Zoom
menu -b52.
Data capture is under way
Page 54
© 2012 Texas Instruments Educaꢀon Technology
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™
First Steps with TI-Nspire
Appendix: Mulꢁple Representaꢁons
Go to Town with Data Collecꢁon
•
Return to the Geometry page and drag the
circumference in as far as you can.
•
•
Review the data in the spreadsheet.
Review the diameter/circumference scaꢂer plot,
using Zoom–Data to update the window seꢁngs.
A linear relaꢁonship
Fit a Straight Line
•
•
•
From the Analyze menu choose Add Movable Line.
Drag it into place to fit the ploꢂed points.
To ꢀdy the funcꢀon, choose Lock Intercept at Zero
from the Analyze menu.
Also review the radius/area scaꢂer plot. Using Zoom–
Data here will create a dramaꢀc change!
Moving a straight line by hand
Not a linear relaꢁonship!
© 2012 Texas Instruments Educaꢀon Technology
Page 55
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™
First Steps with TI-Nspire
Appendix: Mulꢁple Representaꢁons
The basic quadraꢁc ready for fiꢀng…
… and dragged into place
A Different Approach to Scaꢀerplots
•
•
Open a new Graphs page.
From the Graph Type menu choose Scaꢀer plot –
b34.
•
•
Set x to be radius and y to be area.
From the Window menu choose
Zoom–Data and hide the entry line to gain a good
view of the data points including the horizontal axis.
•
Now choose Funcꢁon from the Graph Type menu -
b31.
•
•
Enter f1(x)=x2.
Now you can click and drag the quadraꢀc curve
into place to fit the data, just as you did earlier
for the straight line.
Regression
Go back to the each of the scaꢂer plots on the Data &
Staꢁsꢁcs pages in turn. From the Analyze menu choose
Regression and place appropriate lines on the data.
What other mathemaꢁcal examples lend themselves to this sort of approach?
Page 56
© 2012 Texas Instruments Educaꢀon Technology
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