Introducing the CASIO ClassPad 300 · Introducing the CASIO ClassPad 300 A tool with a unique interface that among other things supports mathematical thinking. Version: 23 July 2005

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.

© Anthony Harradine, 2005, all rights reserved (WIP) Page 2 of 24

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.


Index Section Page


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 and

• to stop a process that is in action, by tapping


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.


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.


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 2x . To do this, simply tap with the stylus

to the right of the x in the z1 line. Then use the carat ( ) and the from the keypad

and then press . 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 3x we could do to things.

1. Tap to the right of the 2 and then use from the keyboard to delete the 2 and

then enter 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.


You should find the surface described by z1=3 3x 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 xe 65.0− . 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 example, tapping reveals trigonometric functions. This menu can be closed using the ‘return arrow’.

Tap on the 2D tab and then enter xe 65.0− 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.


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 again and then tap to make the graph window move to the bottom. 1.7 Copy and paste, drag and drop. Now suppose we want to look at what the surface )3sin(65.0 xez x−= . 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


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 to move through the possible positions. Graph this surface.

Now tap the trace icon ( ) and then use the left, right and up and down arrow

keys ( ) to trace over the surface. Note the CP 300 reports the x, y and z co-ordinates.


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 22 yxz += . When entering y us the y on the hard keypad. 2. Graph )sin()cos( yxz = . 3. Use the drag and drop and editing facilities to define )sin()cos( yxz += and then graph it.

Trace to one value where it cuts the x-axis. 4. Experiment for yourself.


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

tap . You should see a screen like that seen opposite. 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.


These are defined as seen below using the little double arrow ( ) from the ‘mth’ soft key pad.

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.


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 - . Then tap on ‘File’ and the ‘Open’.


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 double-tapping on the ‘Geometry’ folder and the third by tapping Close and then double-tapping the ‘main’ folder.


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.


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 ( )xe

dxd x sin4.0− .

Do the following: • enter xe x sin4.0− in the first input box • select the expression by dragging the stylus across it • Tap , then and then


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 ( ) 0sin4.0 =− xedxd x . Do the following:

• 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.


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 ( ) ( )12 2 −+ xx

dxd . We could define a function )(xf and then work

with it as follows. Using the command Define we can define, using formal function notation )(xf . 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.


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.


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.


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, 1)2()1()( 2 +−−= xxxf

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 )()1( 2 axxy −−= 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


A place for your own notes.


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

Documents

Introducing the CASIO ClassPad 300 · Introducing the CASIO ClassPad 300 A tool with a unique interface that among other things supports mathematical thinking. Version: 23 July 2005