Top of Page

This introductory session will respond to varying skill levels of participants, beginning with an overview of theHomeScreenfunctions of the calculator (includingMODEsettings and using variables).Generally, in the junior school, the

MODEscreen should look like the example shown (using degrees rather than radians).If working with money, decimal places may be set from

FLOATto2, as in the following example.

EXAMPLE 1:If I invest $25 000 at 5% pa, how much will be in my account after 5 years?

Method 1:Enter the Principal, then press ENTER. Multiply by 1.05, press ENTER. Continue to press ENTER and the interest for each year is calculated automatically.

Method 2:Store 25000 asP, 5/100 asR, 4 asN. Enter the compound interest formula.

Method 3:PressY=and enter the formulaP(1+R)^X(Note useXinstead of the usualN).View each year using the table of values(2^{nd}GRAPH).

Method 4: ChooseAPPSand select1: FINANCE; choose1: TVM Solver…Fill in the values as shown then move toFV(Future Value)andSOLVEby pressingALPHA ENTER

Each of these methods illustrates a different functionality of the graphic calculator.

When working in “ALGEBRA” mode, my students always begin with theY=key. Here they enter the function or expression they wish to work with and view it using graph or table.

When working in “STATS” mode, they begin with theSTATkey, first entering their data, then either viewing it usingSTAT PLOT (2^{nd}Y=)or perform calculations usingSTAT -> CALC.

EXAMPLE 2:Driving your car towards some traffic lights, they turned red and you were forced to brake hard. A police officer saw what happened and accused you of speeding: she measured the skid marks from your car and found that they were 26 metres long. Were you driving legally in a 60 km/h zone? Your research before the court case revealed the following table which gives braking distances for a variety of speeds.

Speed in Km/h (

x)30

50

70

90

110

130

Braking distance in metres (

y)6

16

31

51

76

104

Choose

STAT -> 1: Edit…and enter the data above intoL1andL2.Choose

STAT PLOT (2, select^{nd}Y=)Plot 1and set it up as shown.Press

ZOOM 9: ZoomStatand study the graph of this data.Finally, press

STAT -> CALC -> 5: QuadRegand, at the HomeScreen, typeL1(2^{nd}1), L2 (2^{nd}2), Y1 (VARS -> Y-VARS : 1: Y1).When you return to the

GRAPHscreen, the regression line is drawn over the data.Press

TRACE,moveUPto the quadratic function, then type60and the legal braking distance for 60 km/h will result.

(Adapted from Nuffield Advanced Mathematics: Book 1, 1994, pp.16-17)

EXAMPLE 3:An Experimental Probability Method for Finding PIMichael McNally, Lower Canada College, Montreal, Canada, mmcnally@lcc.ca

- Create a [-3, 3] x [-2,2] WINDOW on your calculator.

- Scatter 50 random points in this window.

Seq(-3+6rand, X, 0, 50, 1) -> L_{1}

Seq(-2+4rand, X, 0, 50, 1) -> L_{2}- Create a StatPlot using the plus sign as your Mark.

This can be done from the

HOMEscreen by accessing theDRAWmenu. 2nd/PRGM(DRAW)/#9 Circle. EnterCircle( 0 , 0 , 1 )- How many points landed inside the circle (if a point lands on the circle, flip a coin to decide if it is in or out)?

Some questions:

What is the area of the WINDOW?What is the area of the circle?What is the theoretical probability of a point landing in the circle?What is the experimental probability?Assuming these probabilities are equal, solve for an approximate value of PI.Pool a series of results from different students and try to get a better estimate of PI.

EXAMPLE 4:A Factoring Method Using the Table Feature on the TI-83 PLUSMichael McNally, Lower Canada College, Montreal, Canada, mmcnally@lcc.ca

In Algebra courses many of us have struggled with the decomposition method of factoring trinomials of the form

ax^{2}+bx+c. This task becomes more challenging (and at times frustrating) whenaisn't 1.

Consider the trinomial

6x^{2}–x– 12.Traditionally we'd invoke the product-sum concept and have the students use trial and error, or a factor tree, etc. to come up with the correct combination; namely 8 and –9. At this point we would rewrite the trinomial as

6, grouping the first two terms and the last two terms to yield:x^{2}+ 8x– 9x- 12(2.x- 3)(3x+ 4)

Consider the following method on your calculator.

- In
Yenter_{1}. In our example this becomesac/xY_{1}=-72./x- Let
Y_{2}= X + Y_{1}These are shown in the first window to the right.- Next enter 2nd/WINDOW
(TBL SET)and adjust theTABLE SETUPto what looks like an appropriate starting point.More often than not Tbl Start will be 0 with Δ Tbl = 1, as shown in the second screen.- Now enter 2nd/GRAPH
.(TABLE)and view the third window with the three columns:X, Y_{1}, Y_{2}- Scan this table (up or down) until you find the value (
-1in our case) for the sum inY._{2}- The
XandYcomponents are the desired combination._{1}

Now write the trinomial as

6and proceed as above.x^{2}+ 8x– 9x- 72

Why does it work?Repeat with

20x^{2}+ 23x– 21.

Isn't technology great?!

For comments & suggestions, please e-mail Steve Arnold.