Find x in order to maximize the volume of the box. Students can write a calculator or computer program or use the table function on their calculator to generate a table of values of x and the associated volume. The largest volume can be literally observed from the table. Alternatively, the function mo deling the problem can be graphed on a calculator or computer and the maximum point observed. Working with a numeric or graphical representation gives middle school students the power to solve this problem, rather than waiting until calculus provides th em the necessary machinery to use the traditional symbolic approach.
Technology can afford students increased opportunity to develop mathematical modeling skills.
For example, students can be challenged to write a computer or calculator program to simulate the selection of a five- card hand from a 52 card deck. The resul ts of many such simulations would allow students to estimate the probability of various types of card hands before they learned the counting principles necessary to compute the theoretical probabilities. In this exercise students must determine how to mo del a deck of 52 cards with the first 52 counting numbers. In addition to modeling skills, mathematical reasoning and communication skills are developed, as students must use precise language in order to communicate the appropriate tasks to the computer o r calculator. Precise language is essential when programming a calculat or or a computer to perform a desired task.