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The educational use of the graphic calculators TI-82, TI-83 and TI-84, published by Texas Instruments.
Graphic calculators | Main Graphs page

Some highlights

Sequences on a TI-83 | Growing dandelions on a TI-83
Statistical functions | Downloadable files
Review of TI-84 Plus Silver Edition
Review of TI-Smartview

ideas

Some starters

Investigate sequences. Key in a number, say 1 and press ENTER. Then enter + 2 ENTER. From now on, repeated presses of the ENTER key will produce the sequence of odd numbers, with a display like this:

Get the calculator to produce the even numbers, the three times table, or some of these:
1, 5, 9, 13,17...
50,48,46,44,42...
1, 2, 4, 8, 16, 32...
200, 100, 50, 25...

Sums

Here's a program that will present the user with a set of simple addition sums. At the end the score is given:

Program: SUMS :ClrHome :Input "QUESTIONS? ",Q :0->T :1->N :Lbl 0 :ClrHome :Output(1,1,"QUESTION") :Output(1,10,N) :Disp "" :randInt(1,12)->A :randInt(1,12)->B :Output(2,1,A) :Output(2,3,"+") :Output(2,5,B) :Disp "" Input C :If C=A+B:1+T->T :N+1->N :If N<Q+1:Goto 0 :Disp "" :Output(4,1,"CORRECT") :Output(4,10,T) :Stop

Gradient Functions

The TI 82/3 can display the "gradient function" of a curve. In other words, given the curve y=f(x), the curve dy/dx=f'(x) (where f'(x) is the derivative of f(x) with respect to x) can be displayed simultaneously.
To set up an investigation on this, go to the Y= screen. Against Y1=enter a simple curve, 3x²+1 for example. Against Y2=you should make the following selections:

MATH 8 VARS Y-VARS 1 1 then type in ,X,X)
The result should be that the Y= screen shows Y1=3x²+1 and Y2=nDerive(Y1,X,X). Going to the GRAPH screen, you will see the graphs of y=3x²+1 and the gradient function y=6x.

From now on, all you need to change is the curve Y1. Investigate the gradient functions of all kinds of curves...

using lists

The TI-83 (and 82) have many list-processing functions. For example, the instruction
{1,2,3,4,5}->L₁
will put the numbers 1,2,3,4 and 5 into List 1. But what is far more useful is to "attach a formula to a list name". This is described in the TI-83 manual but you could easily miss it. Once 1,2,3,4 and 5 are in List 1. Then you can enter
"L₁+3"->L₂
Note the quote marks. This only works on the TI-83. You will find 4,5,6,7 and 8 in List 2. The important thing is that if you now change the contents of List 1, then List 2 will update accordingly. The formula remains in the calculator memory. Thus you have the beginnings of a spreadsheet.

statistical functions

The binomial distribution

The TI-83 has a comprehensive collection of statistical functions. As an example, suppose you would like to fit a Binomial distribution to this set of data:

x	0	1	2	3	4
f	1	6	6	5	2

total frequency=20
mean=41/20=2.05

The Binomial distribution requires two parameters, n and p. Assume n=4. Either estimate p from the above data (p=mean/n=0.5125) or use an assumed value. In the calculator, select

binompdf(4,0.5125)

You will find this in the DISTR menu, option 0. The calculator will display in a sequence the probabilities of 0 to 4 successes:
{.0564804932 .2375077148 .3745313965 .2624920898 .0689883057}
You can scroll along the sequence using the arrow keys. Now enter:

x 20

and a sequence of the expected frequencies will be displayed (here shown rounded to 1 dp):
{1.1 4.8 7.5 5.2 1.4}
These can be compared with the observed frequencies in the above table (and tested if you like with the chi-squared test).

The Poisson distribution

Suppose, instead, that you would like to fit a Poisson distribution to the above set of data. The Poisson distribution requires one paramenter, lambda. Assume lambda=2.05. In the calculator, select

poissonpdf(2.05,{0,1,2,3,4})

You will find this in the DISTR menu, option B. Note the use of the two kinds of brackets () and {}. The calculator will display in a sequence the probabilities of 0 to 4 successes:
{.1287349036 .2639065524 .2705042162 .1848445477 .097328307}
These probabilities give the following expected frequencies:
{2.6 5.3 5.4 3.7 1.9}

The Normal distribution

You can also calculate Normal probabilities easily. The Normal distribution requires two paramenters, mean and standard deviation. Assume mean=2.05 and standard deviation=2. To find the probability of a randomly selected value being less than, say, 3, (ie., the probabality P(X<3)), select

normalcdf(-1E99,3,2.05,2)

You will find this in the DISTR menu, option 2. This is a litte cumbersome as you must enter -1E99 or -1 x 10⁹⁹ to indicate negative infinity. The calculator should display 0.68

If you wish to find probablities from the standard normal distribution, ie., N(0,1), then you can simply enter

normalcdf(-1E99,3)

to find the probability P(Z<3).

Here is a standard text book example on Normal probabilities:
IQ scores are assumed to be normally distributed with mean 100 and standard deviation 15. Find the perecentage of people expected to have an IQ between 80 and 120.

Answer
normalcdf(80,120,100,15)=0.8175... or 81.75%

Normal probabilities as areas

The above text book question could be answered using the ShadeNorm function instead (find this in the DISTR DRAW menu, option 1):

Answer

ShadeNorm(80,120,100,15)
which gives the display:
(Note that the required probability is displayed too):

Solving problems on the Normal distribution

Here is another standard text book problem:
An automatic filling machine is known to operate with a standard deviation of 1.5 g. To what "average filling" should the machine be set so that 95% of the packets are over 250g.

Answer
The question implies that P(Z < Z₀)=0.95, where Z₀=-(250 - x)/1.5

Use the invNorm function (in the DISTR menu, option 3) to calculate:

invNorm(0.95)=1.644853626

Hence 1.644853626=-(250 - x)/1.5, which gives x=252.46...

Displaying probability distributions

The TI-83 can be programmed to display a distribution. For example, taking n=7 and p=0.2, then this display can be obtained (and transfered to the PC using the TI-GRAPH LINK (83) available to download from Texas Instruments):

downloadable files

As a developing area of MathsNet, we are creating some files that you can download to your PC and then pass to the 82 or 83 via the TI GRAPH LINKsoftware.
For these MathsNet files, move to the Download... page.

- Omnigraph link

The Texas Instruments calculators TI-82 and TI-83 both have some graph and coordinate plotting functions that are similar to the software Omnigraph. In the last year or two, more and more students studying mathematics at A-Level or similar have purchased such graphic calculators, so that, whereas only a few might have Omnigraph at home, most will have the calculator. It therefore seems like a good idea to make some resources for investigating mathematics common to both media. With this in mind you will find by moving to the Download... page some files that can be loaded in your TI calculator.

User Group

This group is an independent organisation based in the Centre for Teaching Mathematics at the University of Plymouth. They publish a newsletter, graphiTi, three times a year, and can be emailed at jsharp@plymouth.ac.uk.

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