Transcript Some models of using ClassPad in teaching mathematics for

Using CASIO ClassPad in teaching
mathematics
Lilla Korenova
Comenius University in Bratislava, Slovakia
[email protected]
Jozef Hvorecky
Vysoka skola manazmentu, Bratislava, Slovakia
[email protected]
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
1
the range of values of the function y  2
( x  1)
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
x 1  0 ?
2
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:
1

2
 x   1
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)
C( x)  50  x(2  0.1x)  50  2x  0.01x2
• Why are we interested in the xcoordinate?
• What is the meaning of ycoordinate?
• 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)
C ( x)  50  x(2  0.1x)
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)
1
2

l ( x) 

, x  (0, )
sin(x) cos(x)
2
• 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 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!
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