Introducing the CASIO ClassPad 300

Transcription

Introducing the CASIO ClassPad 300
A tool with a unique interface that among other things supports
mathematical thinking.
Version: 23 July 2005
WIP (Work in progress)
Prepared by Anthony Harradine
Director,
Noel Baker Centre for School Mathematics, Prince Alfred College.
Copyright Information.
The materials within, in their present form, can be used free of charge for the purpose of
facilitating the learning of children in such a way that no monetary profit is made.
The materials within, in their present form, can be reprinted free of charge if being used for
the purpose of facilitating the learning of children in such a way that no monetary profit is
made.
The materials or ideas cannot be reproduced in any other publications without the
express permission of the author.
© Anthony Harradine, 2005, all rights reserved (WIP)
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Index
Section
Page
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1.
Getting comfortable with the interface.
1.1
Introduction.
The CP 300 is a mini computer that is loaded with a number of CASIO made, pre-loaded
applications. The operating principles of the CP 300 are very similar to that of using MS
Windows.
Third party applications do exist and can be made by computer
programmers.
The CP 300 is menu driven with an extensive use of icons to assist in
smooth use. The applications/tasks that are represented by the icons
are launched by tapping on the touch sensitive screen at the position
occupied by the icon using the stylus. You can use any non-abrasive
pen like tool, even your finger.
On turning on your CP 300 for the first time and
following the setup procedure you will arrive at the
root menu (seen opposite).
Provided the Application Selector is set to All you
will be able to see all the applications that are
available to use. Standard applications are Main,
eActivity, Statisitcs, etc.
At the base of the screen you can see the Icon panel
(or master toolbar).
It is always present and is the way to (among other
things:
•
exits an application, by tapping
•
to stop a process that is in action, by tapping
and
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1.2
Application layout.
We will start by using the 3D Graph application to get a feel of how the applications are laid
out. All CASIO made applications are laid out in the same way.
Tap once on
to launch the application.
Each application has the sections seen opposite.
The most important thing to note is that there are
two windows. One window is active and one is
not. The active window is the window edged with
the bold edging (the top one in the picture
opposite).
To input something to the CP 300 we use an input box.
Tap anywhere in the working line where the input box you want to use is and the cursor will
flash just to the left of the input box. We can then enter an equation that represents a surface.
Enter 3x, using the
and the
from the hard
keypad. Then press
and tap, using the stylus,
(the ‘graph please’ icon) located in the toolbar. This enters the
equation z1=3x.
On doing this ‘something like the output’ see opposite should
result. Yours may differ a little for a variety of reasons we will
now look into.
Note that the bottom window is now active and the menu
options and the icons in the tool bar are different. Tap in the
top window – the icons change, tap in the bottom window, the
icons change. The menu items and the icons seen belong to the active window – see below.
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1.3
Preferences and the ‘doo-flicky’.
Maybe your graph had axes or a box on it. How come?
Each application, just MS Word or the like has a set of
preferences that can be changed. The preferences for
an application are found by tapping on the doo-flicky.
Then tap Settings, Setup and then 3D format. As seen
below you can select a number of different options.
Try each out, tapping
once the options are as
you wish.
Some of the outputs of the changes possible are seen below.
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1.4
The view-window.
To alter the view-window settings tap in the graph window so the graph windows icons are
present in the tool bar.
Tap
and you will be able to change the settings.
This icon is also available if the other window is active.
You can also access by tapping
and then Settings and
then View-window.
The ‘grid’ option determines the number of ‘lines of wire’
seen on the screen between the min and max values you
set.
Experiment with different view-window settings. You return to the
default setting using the ‘Initial’ option.
1.5
Editing an entry.
Say we want to change the equation entered to z1=3 x 2 . To do this, simply tap with the stylus
to the right of the x in the z1 line. Then use the carat (
and then press
) and the
from the keypad
.
Note that the CP 300 makes the entry ‘look nice’. The
CP 300 uses correct mathematical format and syntax,
even if you do not enter it that way.
Say we now wanted to make another change. You can now tap either in the base level or the
index of this equation and change at will.
To change it to z1=3 x 3 we could do to things.
1. Tap to the right of the 2 and then use
then enter
from the keyboard to delete the 2 and
OR
2. Drag across the 2 to highlight it and then simple over-type it with the
. Note
though not to highlight the whole index place holder, just the index value (as seen
below on the left) or the result below will occur.
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You should find the surface described by z1=3 x 3 looks as
seen opposite.
1.6
Inputting using correct mathematical format and syntax and the soft
keypads.
Suppose we want to define z2 to be e −0.65 x . The hard keypad is rather sparse and no ‘e’ is
present.
Press
on the hard keypad and the four soft
keypads of the CP 300 appear. Each of the four:
• mth (mathematics)
• abc (QWERTY)
• cat (catalogue)
• 2D – (equation editor)
can be made active by clicking the appropriate tab. Tap each
in turn.
Tap on the ‘mth’ tab. The ‘extra menus’ at the bottom
can be tapped and reveal extra functions. For
reveals trigonometric
example, tapping
functions. This menu can be closed using the ‘return
arrow’.
Tap on the 2D tab and then enter e −0.65 x for z2 and press
.
Note the radio button for z2 is checked and the one for z1 is not.
This means that z2 will be graphed and z1 will not.
Note the small down arrow at the bottom that will reveal more
input templates, as seen below.
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Graph z2 by tapping
and then tap
on the master toolbar.
Tapping the arrows in the window rotates the surface for you.
To make the surface rotate continually tap the diamond at the top right of the screen. There
are some hidden gems here. Then tap ‘Rotating’ and choose an option. To stop it rotating tap
.
Now tap
1.7
again and then tap
to make the graph window move to the bottom.
Copy and paste, drag and drop.
Now suppose we want to look at what the surface z = e −0.65 x sin(3x) .
1. Instead of re-entering the first part of this equation we carryout one of two shortcuts:
• select it by dragging the stylus across it
• tap Edit and then Copy
• tap in the z3 line so the cursor flashes in the input box
• tap Edit and then Paste
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2. Alternatively you can use the Apple Mac inspired ‘drag and drop’. Do the following:
•
•
select it by dragging the stylus across it and then take the stylus off the screen
then put the stylus back onto the highlighted expression and ‘drag’ it (stylus always
being in contact with the screen) into the working line of z3. The stylus does not need
to go into the input box of z3, when the stylus tip enter the working line of z3 the
cursor will flash just to left of the input box. Taking the stylus off when this occurs
and the result is the copy and paste being completed.
Once this is done you can now bring the soft keypads up, tap the mth tab and then TRIG and
enter sinx.
Note that you need to have the cursor flashing on the base level not the index level. The
operation of multiplication is assumed.
You will see that you can get the cursor at the correct level by tapping and putting it there, or
as in MS Equation Editor, use the right and left arrow keys on the
the possible positions.
to move through
Graph this surface.
Now tap the trace icon (
and up and down arrow
) and then use the left, right
keys (
) to trace over the surface. Note the CP 300
reports the x, y and z co-ordinates.
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Tap Edit and note the ‘Clear All’ option. It is not necessary to use this often unless you know
you will not require the material you have entered.
There is more to learn about the 3D application. Consult the Chapter 5 of the manual.
However, you have now learned the basics of working with the CP 300 interface.
1.8
Over to you.
1. Graph z = x 2 + y 2 . When entering y us the y on the hard keypad.
2. Graph z = cos( x) sin( y ) .
3. Use the drag and drop and editing facilities to define z = cos( x) + sin( y ) and then graph it.
Trace to one value where it cuts the x-axis.
4. Experiment for yourself.
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2.
Operating with symbols (and related knowledge).
2.1
Introduction.
The CP 300 allows the user to operate (in a computational way) with both numbers and
algebraic symbols.
It does this in a revolutionary manner, the simplicity of which is not matched by any other
interface being used on hand-held devices.
The application called Main is where such computation can
occur. Tap Menu on the master toolbar if necessary and then
. You should see a screen like that seen opposite.
tap
If you have any inputs on the screen use ‘Edit’ and ‘Clear All’
to produce a clear screen.
2.2
Variables – from the CP 300’s perspective.
The CP 300 uses the word variable to describe much more than what it means in a
mathematical sense.
The following are the main types of CP 300 variables:
• list
• matrix
• function
• memory (eg. a spreadsheet file)
• program
• geometry file
• expression
Each variable is given a name. This name can be basically anything (some restrictions apply,
eg. a list can only have 6 characters at most in its name).
2.3
Expression Variables and defining their value.
Expression variables are what we consider as mathematical variables. Two sorts of expression
variables exist:
• single expression variables (denoted by bold and italic single letters) and
• others (where a word or string of letters is used to name the variable).
The single variables should be reserved for function type use. The CP 300 understands that xy
means the product of x and y, but will interpret xy as a single variable called xy.
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These are defined as seen below using the little double arrow (
pad.
) from the ‘mth’ soft key
Note the way that the CP 300 interprets 2n3r when the bold and italic variables are not used
but instead n and r are entered from the QWERTY key pad.
2.4
List variables – from the CP 300’s perspective.
The screens below show one way to define a list and one way to display it.
In the Statistics application tap in the header of a list and then type the name you desire and
enter some data. It can be also displayed in Main application by just typing the name in an
input box.
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2.5
Function variables – from the CP 300’s perspective.
The screens below show how to define a function. Simply type the word ‘Define’ from the
QWERTY keyboard or input it from the catalogue.
Note the use of the dark italic variable (taken from the hard key pad or from the mth VAR soft
keypad. The second screen shows some uses.
Important note. If you do not have an input box then you will not be able to input anything.
To make one appear, simply press
2.6
.
Folders and files– from a CP 300 perspective
Being a mini computer, the CP 300 has an operating system and file structure. The system is
similar to MS Windows.
Return to the root menu and launch the Geometry application and the ‘Open’.
. Then tap on ‘File’
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Tapping on the arrow to the left of the folder names will
open them and reveal the files (variables) within.
Program files will not show up in the Geometry
application, but the files in the ‘wallies’ folder are
Geometry files and so they will be seen. Highlighting the
file and tapping Open with launch this file.
2.7
The variable manager – your best friend.
Given there are all manner of different types of variables, it would be good to have a simple
and easy way to handle them (delete them and so on). This is easily done in the variable
manager.
The variable manager can be accessed in any mode by tapping the icon that looks like this:
. Doing this in the Main mode we see something like the following.
The first bit on information given is the ‘Current’ folder. Whatever is current (and you can set
this here) is the folder that any expression variables will be saved into.
We see I have 24 variables at present, 23 in the ‘main’ folder and 1 in the ‘Geometry folder’.
Some of them being the ones we defined above. The second screen is gained by doubletapping on the ‘Geometry’ folder and the third by tapping Close and then double-tapping the
‘main’ folder.
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You can manage the variables here. For example I might delete all the variable definitions for
x and y as having then defined as a number will not be helpful if we need to be working with
symbolic algebra. This can be done as seen below.
Tip: A shortcut to this is to simply type ‘delvar x’ in the Main application and press EXE.
This will delete the definition. The x can be replaced by any variable name (for nay type of
variable. A space must be entered between delvar and the variable name.
2.8
More on files– from the CP 300’s perspective.
The screens below show how to save a new geometry file in a newly made folder called
Geometry.
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3.
CAS on the CP 300
3.1
Introduction.
Launch the Main application.
The CP 300 offers two ways to operate in a CAS manner:
• the old way, where you have to remember the correct syntax for each command –
using the Action Menu
• the CP 300 way, made easier due the presence of a stylus – using the Interactive
Menu.
In this section we will only illustrate the second (and far superior method).
Note the menus look identical. In fact they are, but the way you implement them is different.
3.2
Working less formally.
Launch the Main application. Suppose we wish to find
(
)
d −0.4 x
e
sin x .
dx
Do the following:
• enter e −0.4 x sin x in the first input box
• select the expression by dragging the stylus across it
• Tap
, then
and then
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You are asked to decide three things as seen opposite, with the
default options being the most likely required:
• Do you want the derivative function (Differentiation)
or the derivative at a point (Diff coefficient)
• What variable are you differentiating with respect to
(Variable)
• What order of derivative do you require (Order).
When these are set as seen above and OK is tapped the output, seen below should result.
Suppose we now wanted to solve the equation
•
•
•
(
)
d −0.4 x
e
sin x = 0 . Do the following:
dx
Tap
seen on the mth soft keypad and then enter the = 0.
Highlight the equation by dragging across it with the stylus
Tap
, then
and then
You are asked to decide two things,
• if you want a CAS solution (Solve) or a numerical
approximation (Num solve) and
• the variable you wish CP to solve for.
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The output is seen opposite. Tap the small arrow to see all of the
solution.
3.3
Working more formally.
Suppose we wish to find
d
(x + 2)2 (x − 1) . We could define a function f (x) and then work
dx
with it as follows.
Using the command Define we can define, using formal function notation f (x) . Simply type
‘define’ using the QWERTY keypad, then a SPACE then the rest as seen. Use the bold italic x
to be safe.
Alternatively you can retrieve Define from the
cat(alogue). Tapping
will see is entering into
the working line. Note that it is not case sensitive wrt the
D.
Now tap on the 2D tab of the soft keypad and use
to reveal more input options and enter
that seen below centre. Remember you can use the drag and drop feature. Then press/tap
EXE.
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Then do as seen below.
Of course the following is possible as well.
You can, of course, define many functions just about however
you like, for example see opposite.
If you would prefer to use the ‘old’ way then simple use the
Action menu. It allows you to enter the first part of the
command line, e.g. solve( , but then you have to manually enter
the rest, including the commas and all the required arguments.
3.4
Over to you.
Time for you to experiment for yourself.
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4.
Is there much else to see?
4.1
Introduction.
There is so much more to see that is very well worth seeing on the CP 300. The design of the
tool is so good, however, that by now you should be able to explore just about anywhere and
cope very well. You will find all the things you would totally expect to find are able to be
done on the CP 300. But then there are some amazing surprises.
4.2
Application integration – aiding desirable mathematical
learning/working?
The CP 300 is the only software tool to date that allows seamless integration between
applications that are bias to one way of thinking about a concept (graphically, algebraically,
numerically, geometrically). This allows students to develop a rich way to thinking and
working.
With the application Main running other applications can be launched by selecting them from
within the drop-down box seen below. Tapping the icon highlighted below launches the
Graph and Table application in a window. Remember the toolbar icons belong to the active
window. You can now select anything from the Main window and literally drag and drop it
into the graph window and if possible, it will be graphed.
Select and then drag g(x) into the lower window.
Try dragging other things from the Main window to the Graph and Table window.
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The power of this functionality will be illustrated using the following question taken from the
VCAA CAS-friendly examinations of 2004 – paper 2. It is Question 1.
Consider the function f :R → R, f ( x) = ( x − 1) 2 ( x − 2) + 1
a.
Find f ′(x)
1 mark
b.
The coordinates of the turning points of the graph of y = f (x) are (a, 1) and (b,
).
Find the values of a and b.
2 marks
c.
Find the real values of p for which the equation f (x) = p has exactly one solution.
2 marks
d.
For the following, k is a positive real number.
i. Describe a sequence of transformations which maps the graph of y = f (x) onto the graph of
.
ii.
Find the x-axis intercepts of the graph of
in terms of k.
iii. Find the area of the region bounded by the graph of
and the x-axis in terms of k.
2 + 2 + 2 = 6 marks
e.
Find the real values of h for which only one of the solutions of the equation f (x + h) = 1 is
positive.
2 marks
f.
The graph of y = ( x − 1) 2 ( x − a ) where a > 1 is shown below.
Find the exact value of a such that the local minimum at point A lies on the line with equation y = −4x.
3 marks
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A place for your own notes.
Page 23 of 24
4.3
A seamless link between Geometry and Algebra?
XX
4.4
eActivity
XX
4.5
Third party applications – Algy as an example
XX
4.6
Geometry – constraint based and the world of animation
XX
Show the AUI
4.7
Tools for demonstration
XX
4.8
Data logging
XX
4.9
Cables and data transfer
XX
Page 24 of 24

Introducing the CASIO ClassPad 300

Transcription

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