Stephen ARNOLD
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# Looking around the 84/83Plus

This introductory session will respond to varying skill levels of participants, beginning with an overview of the HomeScreen functions of the calculator (including MODE settings and using variables).

Generally, in the junior school, the MODE screen should look like the example shown (using degrees rather than radians).

If working with money, decimal places may be set from FLOAT to 2, 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 as P, 5/100 as R, 4 as N. Enter the compound interest formula.

Method 3: Press Y= and enter the formula P(1+R)^X (Note use X instead of the usual N). View each year using the table of values (2nd GRAPH).

Method 4: Choose APPS and select 1: FINANCE; choose 1: TVM Solver… Fill in the values as shown then move to FV (Future Value) and SOLVE by pressing ALPHA ENTER

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

When working in “ALGEBRA” mode, my students always begin with the Y=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 the STAT key, first entering their data, then either viewing it using STAT PLOT (2nd Y=) or perform calculations using STAT -> 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 into L1 and L2 .

Choose STAT PLOT (2nd Y=), select Plot 1 and set it up as shown.

Press ZOOM 9: ZoomStat and study the graph of this data.

Finally, press STAT -> CALC -> 5: QuadReg and, at the HomeScreen, type L1 (2nd 1), L2 (2nd 2), Y1 (VARS -> Y-VARS : 1: Y1).

When you return to the GRAPH screen, the regression line is drawn over the data.

Press TRACE, move UP to the quadratic function, then type 60 and the legal braking distance for 60 km/h will result.

EXAMPLE 3: An Experimental Probability Method for Finding PI

• 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) -> L1

Seq(-2+4rand, X, 0, 50, 1) -> L2

• Create a StatPlot using the plus sign as your Mark.

This can be done from the HOME screen by accessing the DRAW menu. 2nd/PRGM(DRAW)/#9 Circle. Enter Circle( 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 PLUS

In Algebra courses many of us have struggled with the decomposition method of factoring trinomials of the form ax2 + bx + c. This task becomes more challenging (and at times frustrating) when a isn't 1.

Consider the trinomial 6x2x – 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 6x2 + 8x – 9x - 12 , grouping the first two terms and the last two terms to yield: (2x - 3)(3x + 4).

Consider the following method on your calculator.

• In Y1 enter ac/x. In our example this becomes Y1 = -72/x.
• Let Y2 = X + Y1
These are shown in the first window to the right.
• Next enter 2nd/WINDOW(TBL SET)and adjust the TABLE SETUP to 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, Y1, Y2
• .
• Scan this table (up or down) until you find the value (-1 in our case) for the sum in Y2.
• The X and Y1 components are the desired combination.

Now write the trinomial as 6x2 + 8x – 9x - 72 and proceed as above.

Why does it work?

Repeat with 20x2 + 23x – 21.

Isn't technology great?!