B. GDC Tutorial Copy 2dwknnj

8/19/2019 B. GDC Tutorial Copy 2dwknnj

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How Do I Use themkedmkmedkde GDC?

The only GDC that I have used is the TI 83(+) and thus the comments below are restricted to this

How Do I Teach With thdmekdee GDC?

Classroom Resources

First, to detail the resources we have available (these vary rom room to room, accordin! to when the

e"ui#ment was #urchased)$ and the minimum re"uirements needed, in the classroom to ully utilise the

GDC%

de&mede&d' loc& mounted #oster o the GDC * sim#le, but eective, or #ointin! out the buttons on the

calculator Teas #rovides the #oster with their viewscreen GDCs

The viewscreen GDC * this can be used to #ro-ect the calculator.s ima!e onto a whiteboard3 TI converter lin&ed to T/ screen

0 TI converter lin&ed to 1CD #ro-ector and screen

This may seem rather basic to many #ractitioners o the GDC, but I thin& it is best to have a means o

dis#lay that can be written on Thus, I would say that o#tion 0 above is the least eective means o

dis#lay * unless you can #ro-ect directly onto the whiteboard (This is the line we will !o down romnow on, the T/ 2which I deli!demde&medmd&me&ht in writin! on bein! suited to small classrooms

only) 4#tions and 3 have the advanta!e over ' in that they can be lin&ed to a 5C (i you have onein the classroom) to show internet or sotware ima!es to the class, in addition to #ro-ectin! the screen

ima!e

Thus ar we have not !one down the route o usin! interactive whiteboards because we are unsure

where these would enhance our teachin! beyond the e"ui#ment we have$ eedbac& would be mostwelcome on this issue 6either have we used the data lin&a!e devices to the GDC that would allow

immediate data collection$ and thus #ro#er modellin! * that, I eel, should be the route orward

In short, the mathematics classroom is becomin! more o a s#ecialist teachin! venue, rather than the

!eneral teachin! room o days !one by This has im#lications or mana!ement in terms o timetablin!

mathematics classrooms and resourcin! the sub-ect #ro#erly The days o mathematics as a 7chea#7sub-ect are ar behind us

GDC Resources Required for the Mathematical Studies Standard e!el

#eciic areas o the #ro!ramme in which the GDC should be utilised can be identiied 9 su!!ested

startin! #oint is !iven below


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Gra"hin# Techniques on the GDC

' Introduction to !ra#hin! on the GDC

• the #rocess to be observed when !ra#hin! a unction• use o the C91C button• drawin! a tan!ent to a !ra#h (and then !ra#hin! it)

Calculus on the GDC

• drawin! the !radient unction• use o the second dierential (:) ; could be done or 1


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• settin! out an eamination "uestion

Teachin# the MSS Course & the Initial Weeks

The GDC is a com#letely new tool to our students, and we eel it unli&ely that our avera!e his GDC o, we be!in the course with areas

o the syllabus that are !reatly enhanced by the use o the GDC

These are%

' 9 review o unctions asic tatistics

ut, #recedin! these, we review o ty#ical !ra#hin! "uestions rom the IGC? course 9n eam#le is

shown below$ in it we ta&e a ty#ical eamination "uestion with which they are all amiliar, we !etthem to com#lete it by hand and then re#eat the #rocess on the GDC Followin! this, an eercise with

similar "uestions is set 9n eam#le is included below

Throu!h this we ho#e to review the ideas o scalin! !ra#hs, drawin! them accurately, solvin!

e"uations !ra#hically and drawin! tan!ents$ all valid techni"ues re"uired by


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6ote that the curve is a "uadratic, with its e#ected U sha#e and a nice line o symmetry and a

symmetrical table o values

Find ( )'(C f

3 olve the e"uation ( ) D f x = by loo&in! at your !ra#h

0 olve the e"uation ( ) 3 f x = − by drawin! the line 3 y = − on your !ra#h(I do not want an al!ebraic solution)

Draw the tan!ent to the !ra#h at the #oint ,(C x = and, rom the tan!ent, estimate the !radient o

the curve at this #oint

E Find the coordinates o the minimum #oint on the curve

Brite down the ran!e o the unction or the !iven domain

We will now re"eat this question on the GDC

To draw the !ra#h o the unction ( ) , 3 C f x x x= − − or the domain x− ≤ ≤

5ress% Y=

Ty#e in% ϒ ;3 −5

This enters the equation of the curve into the calculator.

The screen should a##ear thus%

5ress% 2nd TABLE

This gives you the values of the function (the range) for the required domain, C

x− ≤ ≤

. However, therequired domain may not be shown on the screen; to alter this use the “nintendo !eys on the "#$.


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' Brite down the maimum value o the unction on the domain x− ≤ ≤ Brite down the minimum value o the unction on the domain , C x− ≤ ≤

These values will be used to set the si%e of the window on your calculator.&'rom the screen shots above

these are seen to be and * res+ectively.

5ress% WINDOW

Ty#e in% Xmin = -2Xmax = 5X!" = 1

Ymin a number smaller than the minimum aboveYmax = a number !reater than the maimum valueY!" = 2

This +rocess ensures that the gra+h will fit on the screen

5ress% GRAPH

'inally, you should have your function drawn on the screen.

6ow we will use the GDC to answer the "uestions that were #osed above This is done mainly by

usin! the #AL# menu ound by #ressin! the yellow 2nd button ollowed by the blue TRA#E button Doin! this should !ive you the screen%

' Find ( )'(C f

5ress% 2nd #AL# ENTER


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6ow enter the x coordinate o the #oint that you re"uire

olve the e"uation ( ) D f x = by loo&in! at your !ra#h

5ress% 2nd #AL# 2 ENTER

Aou !et the =starred> cursor at this #oint Aou have to move it via the 6intendo &eys to the let

o the =Hero> (where the curve crosses the y ais, the line x -) then #ress ENTER This is thenre#eated on the ri!ht hand side o the Hero ENTER is then #ressed a third time to !et the GDCstarted

3 olve the e"uation ( ) 3 f x = − by irst drawin! the line 3 y = − on your !ra#h

5ress% Y2 = -3

5ress% GRAPH5ress% 2nd #AL# 5 ENTER ENTER ENTER

The series o screen shots below should be what you !et on your screen%

Givin! inally%


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the coordinates o the #oint o intersection

0 Draw the tan!ent to the !ra#h at the #oint x = and, rom the tan!ent, estimate the !radiento the curve at this #oint

5ress% 2nd DRAW 5 ENTER

6ow enter the x coordinate o the #oint that you re"uire

The dia!rams are shown below (I have deleted the line y irst to ma&e the dia!rams

clearer)

The tan!ent has been drawn and its e"uation !iven This allows you to read o the !radient asyou re"uire

Find the coordinates o the minimum #oint on the curve

5ress% 2nd #AL# 3 ENTER

Aou may have to use =common sense> to determine the eact coordinates o the #oint re"uired

* i you reco!nise it * otherwise, a##roimate to 3 si!niicant i!ures as re"uired

by the


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Be ind that such an a##roach, reinorcin!, as it does, wor& which the students ou!ht to &now (but

have, in all li&elihood, or!otten) and yet addressin! it in a dierent way, motivates the students towant to use the GDC rom the outset It is a low level o entry to the machine but one which !ives

rather s#ectacular results It also allows and teaches the students to veriy their own wor&

The Re!iew of *unctions

Be teach this usin! a #iece o sotware, thou!h it could as easily be done on the GDC, since we use

sotware in our teachin! * and in the students. #ro-ects to a considerable etent This is the irst #ieceo wor& we as& the students to do as #art o the


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*. ?#lain what chan!in! the value o m does to the !ra#h o the line

.ow/ lea!e m = 2 and chan#e the !alue of c- What ha""ens to the line on the screen?

?ercise3. Draw a s&etch o the line when m / and c 3/. 4n the same dia!ram, draw a s&etch o the line when m / and c

. 4n the same dia!ram, draw a s&etch o the line when m / and c 3

4. 4n the same dia!ram, draw a s&etch o the line when m / and c *. ?#lain what chan!in! the value o c does to the !ra#h o the line

To be honest, you should already &now about m (the !radient) and c the interce#t o a strai!ht line

The uadratic Function y ax bx c= + +

In omni!ra#h irst ty#e in% a = 1 b = 0 and c = 0

Then ty#e in% y ax bx c= + +

This is the basis or all "uadratic !ra#hs The curve y x=

ea!e b = 0 and c = 0 and chan#e the !alue of a- What ha""ens to the cur!e on the screen?

Tr$ 0oth "ositi!e and ne#ati!e num0ers-

?ercise

3. Draw a s&etch o the curve when a / and c -/. 4n the same dia!ram, draw a s&etch o the curve when a

. 4n the same dia!ram, draw a s&etch o the curve when a /

4. 4n the same dia!ram, draw a s&etch o the curve when a

*. ?#lain what chan!in! the value o a does to the !ra#h o the curve

.ow/ lea!e a = 1, b = 0 and chan#e the !alue of c- What ha""ens to the cur!e on the screen?

?ercise3. Draw a s&etch o the line when a 3 and c 3/. 4n the same dia!ram, draw a s&etch o the curve when c

. 4n the same dia!ram, draw a s&etch o the curve when c 3

4. 4n the same dia!ram, draw a s&etch o the curve when c

*. ?#lain what chan!in! the value o c does to the !ra#h o the curve

.ow/ lea!e a = 1, c = 0 and chan#e the !alue of 0- 1n$ ideas?


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3 The ine Function sin( ) y 1 0x=

?nter the values or 0 and 1 and then enter the curve Aou will need to chan!e the aes to tri# a,esrom the 2oom dro# down menu

ea!e B = 1 and chan#e the !alue of A- What ha""ens to the cur!e on the screen? Draw

dia#rams to illustrate the effect $ou see- Remem0er to use ne#ati!e !alues of B as well-

.ow/ lea!e A = 1 and chan#e the !alue of B- What ha""ens to the cur!e on the screen? Draw

dia#rams to illustrate the effect $ou see- 1#ain/ remem0er to use ne#ati!e !alues of B as well-

0 The Cosine Function cos( ) y 1 0x=

Je#eat 3 or the sine unction

*irst/ lea!e B = 1 and chan#e the !alue of A- Then/ lea!e A = 1 and chan#e the !alue of B-

1#ain/ draw dia#rams to illustrate what ha""ens to the cur!e-

The ?#onential Function x y 0 b= ×

?nter the values or 0 and 1 and then enter the curve Aou will need to chan!e the aes bac& romtri# a,es rom the 2oom dro# down menu

ea!e b = 2 and chan#e the !alue of A- What ha""ens to the cur!e on the screen? Where does

the cur!e cross the y a,is? Draw dia#rams to illustrate the effect $ou see-

.ow/ lea!e A = 1 and chan#e the !alue of b- What ha""ens to the cur!e on the screen? Draw

dia#rams to illustrate the effect $ou see-

Did $ou remem0er to tr$ ne#ati!e !alues of A and b?

E The Cubic Function3

y ax bx cx d = + + +

Draw the !ra#h o3 y x d = + and e#lain the relevance o d by chan!in! its numerical value

Draw the !ra#h o3 y ax= and e#lain the relevance o a


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Draw the !ra#h o3 3 ' y x x= − + or interest This is the ty#e o sha#e you will see with most

cubics Aou will need to remember this sha#e

The inal #art is included to !ive the students some idea o cubic curves beore they meet them in theiro#tion to#ic For those not studyin! that o#tion, it can be omitted

Calculus on the GDC

The calculus o#tion itsel lends itsel beautiully to a !ra#hic a##roach$ the initial dierentiation result

can be =discovered> by the students, the modellin! side o the sub-ect can be resolved nicely in a!ra#hic manner, with the tedious (and #erha#s ina##ro#riate) al!ebra let until the end o the course

rather than havin! it #laced at the outset The calculus also lends itsel nicely to


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The above is a very inefficient method of answering this question. #iscuss with your teacher 5 or

another member of the class 5 other +ossible methods.

2our +ro6ect should involve a number of these methods; you need to com+are these and evaluate which

is the best (most efficient, most accurate, easiest to use777) 'inally, you should see! to answer the

question +osed above 5 does the design of can used minimise the use of materials.

Statistical Techniques on the GDC

It is #ossible to lin& the !ra#hical ideas enunciated above with the statistical unctions on the GDC by=curve ittin!> eercises This can then be etended to methods o dierences or "uadratic ma##in!s,and these can be utilised in


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• First, the data must be #ut into two lists on the TI 83 * one or the s data (the side o the s"uare)and one or the ( ) f s data (the number o dots)

5ress STAT then EDIT to !ive the list dis#lay

5ut the s data into list L1 then #ut the ( ) f s data into list L2

• 6ow we need to #lot the data on a !ra#h (actually we can miss this out but it is useul )

5ress 2nd STATPLOT ENTER

Aou will have a menu to !o throu!h or PLOT 1

Aou want T$%& second icon out o the si shownX Li'( L1Y Li'( L2)a*+( ,

• 6ow you need to set the aes so that the #oints a##ear on the !ra#h ; you will always need to dothis

5ress WINDOW to access the menu

Xmin = Xmax = 5X!" = 1

Ymin Ymax = Y!" = 5

6ow #ress GRAPH ; you should !et the !ra#h o your data

• 6ow, this is the clever bit Aou can ind the e"uation o your curve in the ollowin! way

5ress STAT #AL# 2this is /0a*'R& ENTER

The ollowin! shows on your screen /0a*'i!R&

$=ax,x3,4,&a=

=!=2d=2&=1R2=1

This is the e"uation o your curve ( ) , ' f s s s= + +


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Aou need to e#lain what is !oin! on with the correlation coeicient (coeicient o determination), but

it introduces the idea o re!ression nicely beore it is met as #art o scatter dia!rams in the statisticscourse 9ll such eamination "uestions can be attem#ted on the GDC and then =co#ied> onto !ra#h

#a#er, much as in the way o the !ra#hin! "uestion shown earlier 4ther statistical techni"ues that have

to be em#hasised are the use o the summary statistics unctions and the limitations o these$ oream#le, with a !rou#ed re"uency table the calculator !ives the wron! estimate o the median and the

"uartiles * linear inter#olation bein! needed This can be done on the GDC, thou!h whether it is a

useul techni"ue is moot It is included below #rawing a $' #iagram on the "#$

?am#le

7 ?nter the class boundaries into L12these are , ', , LL,

8 ?nter the re"uencies (and Hero) into L2

(


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*indin# the median ; this can be done only by loo&in! at the !ra#h and Hoomin! in

The total re"uency is ' so the median occurs when the y (cumulative re"uency) value is

a##roimately '12

2

≈

Be use 8OO)BOX rom the 8OO) menu to ind out where this re!ion is on the !ra#h

Draw a bo at around y 0 ; 5ress ENTER to 8OO) in

Aou should have a line and a cross (the cursor) on the screen


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The x coordinate is the median (3M in this case)

Find the "uartiles in the same wayIt is ho#ed that some o the above techni"ues mi!ht #rove useul to teachers o the

B. GDC Tutorial Copy 2dwknnj

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