Using CASIO ClassPad in teaching mathematics Lilla Korenova Comenius University in Bratislava, Slovakia Jozef Hvorecky Vysoka skola manazmentu, Bratislava, Slovakia

A few considerations on teaching mathematics: Pure mathematics is about proving theorems: Time consuming Boring for not-gifted students Educational programs, graphics calculators etc.: Visible Experimental Applicable Our chance: Limitless experiments Creating hypotheses Verification

The aim of the workshop – practical examples Exercise 1: Find the values of the domain and the range of values of the function and state whether it is odd or even. Strategy of our solution: 1.Draw the function 2.Discuss the range of its values 3.Discuss its domain 4.Decide whether it is odd / even / none of those.

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 ?

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.

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 + Trace This is points X1, X2 aproximately We find values X1 and X2 exactly Tap MENU + Main + solve + equation/inequality....

Non-linear Models Two 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: $50 Variable cost per set: 2–0.1*x (x is the number of sets) 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: $50 Variable cost per set: 2–0.1*x (x is the number of sets)

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

Answer Exercises 5 It is seen that the minimum of the function is 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 Thank