Upload
sarthak-gupta
View
215
Download
0
Embed Size (px)
Citation preview
8/19/2019 B. GDC Tutorial Copy 2dwknnj
1/17
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
8/19/2019 B. GDC Tutorial Copy 2dwknnj
2/17
8/19/2019 B. GDC Tutorial Copy 2dwknnj
3/17
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
8/19/2019 B. GDC Tutorial Copy 2dwknnj
4/17
• 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
8/19/2019 B. GDC Tutorial Copy 2dwknnj
5/17
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 "#$.
8/19/2019 B. GDC Tutorial Copy 2dwknnj
6/17
' 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
8/19/2019 B. GDC Tutorial Copy 2dwknnj
7/17
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%
8/19/2019 B. GDC Tutorial Copy 2dwknnj
8/17
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
8/19/2019 B. GDC Tutorial Copy 2dwknnj
9/17
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
8/19/2019 B. GDC Tutorial Copy 2dwknnj
10/17
*. ?#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?
8/19/2019 B. GDC Tutorial Copy 2dwknnj
11/17
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
8/19/2019 B. GDC Tutorial Copy 2dwknnj
12/17
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
8/19/2019 B. GDC Tutorial Copy 2dwknnj
13/17
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
8/19/2019 B. GDC Tutorial Copy 2dwknnj
14/17
• 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&
$=ax,x3,4,&a=
=!=2d=2&=1R2=1
This is the e"uation o your curve ( ) , ' f s s s= + +
8/19/2019 B. GDC Tutorial Copy 2dwknnj
15/17
Aou need to e#lain what is !oin! on with the correlation coeicient (coeicient o determination), but
it introduces the idea o re!ression nicely beore it is met as #art o scatter dia!rams in the statisticscourse 9ll such eamination "uestions can be attem#ted on the GDC and then =co#ied> onto !ra#h
#a#er, much as in the way o the !ra#hin! "uestion shown earlier 4ther statistical techni"ues that have
to be em#hasised are the use o the summary statistics unctions and the limitations o these$ 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
(
8/19/2019 B. GDC Tutorial Copy 2dwknnj
16/17
*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
8/19/2019 B. GDC Tutorial Copy 2dwknnj
17/17
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