Using CASIO ClassPad in teaching Using CASIO ClassPad in teaching mathematicsmathematics

Using CASIO ClassPad in teaching Using CASIO ClassPad in teaching mathematicsmathematics

Lilla KorenovaLilla Korenova Comenius University in BratislavaComenius University in Bratislava, Slovakia, Slovakia

korenova@fmph.uniba.skJozef HvoreckyJozef Hvorecky

Vysoka skola manazmentu, Bratislava, SlovakiaVysoka skola manazmentu, Bratislava, Slovakiajhvorecky@vsm.sk

A few considerations on teaching mathematics:

Pure mathematics is about proving theorems: • Time consuming• Boring for not-gifted studentsEducational programs, graphics calculators etc.:• Visible• Experimental• ApplicableOur chance: • Limitless experiments• Creating hypotheses• Verification

The aim of the workshop – practical examples

Exercise 1:Find the values of the domain andthe range of values of the functionand state whether it is odd or even.

Strategy of our solution:1.Draw the function2.Discuss the range of its values3.Discuss its domain4.Decide whether it is odd / even / none of

those.

)1(

12

x

y

Function in the standard notation

1.Turn on your ClassPad.2.Select

3.If there are functions from a previous task, clear all using the drop down menu EDIT+ CLEAR ALL+ OK.

4.Store the function as y1. + 2D + +

Drawing the function

To draw the function ,tap

Configure in VIEW WINDOW parameters to unify our displays of ClassPads.

Tap ZOOM + QUICK STANDARD

• If the graph small, use ZOOM + ZOOM IN to enlarge it• If the graph is big, use ZOOM + BOX, to select the boundaries

To configure the View Window parameters:

Or use ZOOM IN.

Forming a hypothesis

To verify our hypothesis, let`s “walk” along the graph of the function and watch the axes.

Tap on ANALYSIS + TRACE

• Domain = Real numbers ?• Functional values = (O, 1) ?

Supporting our hypotheses

• Domain is R when the denominator must not equal to O for any x.

• Does there exist a solution to

?012 x

Tap MENU icon on +

Solve the quadratic equation

We generate a table of functional values

Menu – Graph... – Table

Specify a range of values for variable x Generate a number table

By solving inequality we can make sure that the maximum

value of the function is not bigger than 1.

Menu – Main - Action – Equation/Inequality – solve

We have proved that the maximum of the function is 1.

Whether the function is odd or even can be seen from the graph. Our hypothesis says the function is even because its graph is symmetric about the y-axis. We can prove it only if for all the variables x applies f(-x) = f(x).

To prove it let`s solve:

Thus our hypothesis is proved.

1

12x

Try to solve the Exercise 2 on your own.

You have got 5 minutes.(It’s an easy exercise.)

Solution - Exercise 2

Several Graphs (Exercise 3:)Tap MENU , then Graph Clear the previos function EDIT + CLEAR ALL + OK

Enter the functions “y1, y2, y3...”

To configure the View Window tap

Find intersection points with x-axis Tap MENU + Main + Action + equation/inequality +

solve

Solution - Exercise 3

Value of the range:Our hypotheses is – value of the range of this function

is interval (-,X1) U (X2, )Tap Analysis + TraceThis is points X1, X2 aproximatelyWe find values X1 and X2 exactlyTap MENU + Main + solve + equation/inequality ....

Non-linear ModelsTwo girls want to make money to buy

Christmas gifts for their relatives and friends. They see their opportunity in making and selling necklaces from glass beans. They realized that first they have to invest $50 to various tools. For each necklace they also need a set of beans. The supplier offers them for the basic price $2, but the price declines by 1 cent per set.

Revenue and Break-even point

Fixed cost: $50Variable cost per set: 2–0.1*x (x is the number of sets)

201.0250)1.02(50)( xxxxxC • Why are we interested in the x-

coordinate?• What is the meaning of y-

coordinate?• What if we would start selling

with discounts, too?

Why Should We Ever Mention the Word “Quadratic”?

Fixed cost: $50Variable cost per

set: 2–0.1*x (x is the number of sets)

)1.02(50)( xxxC

Exercises 5:• Carrying a ladder of 4meters and

holding it in a horizontal position in a corridor shown in Figure is it possible to turn round the corner? Is there enough room for the ladder? 

Answer Exercises 5• A ladder of maximum length which

"goes in" that corridor turn at that particular rotation (the angle of the rotation can be given by x)  is l(x)

• Using ClassPad plot the graph of the function and find the minimum   

)2,0(,

)cos(

2

)sin(

1)(

x

xxxl

Answer Exercises 5

•It is seen that the minimum of the function is 4.1619381 what means that the ladder of 4 meters can be turned round in the corridor turn.•The task can be solved geometrically, too.

The rest exercises are our homework!CP300 Manager free 30-day Trial

http://classpad.net/

Thank you! jhvorecky@vsm.sk korenova@ematik.sk