Algorithms: An Introduction to Programming

With increasing technology in today's society, computer navigation is an essential skill. The ability to write computer programs provides multiple opportunities for students beyond high school. Utilizing the TI-83 graphing technology in the mathematics classroom introduces students to formalizing and communicating algorithms. Algorithmic thinking is a problem solving skill.

What is an algorithm?

We use algorithms everyday. Specifically, it is a procedure for solving a mathematics problem. Examples include using the order of operations to evaluate an expression, completing the square, and using prime factorization to find the GCF or LCM. Calculators are already programmed with the order of operations algorithm, but what about algorithms the calculator does not interpret. The TI-83 does not know how to factor, but a series of commands can direct the calculator to follow the same process repeatedly. Learning to speak in programming language is parallel with asking yourself "What is the next step to solving this problem?" If the next step is known, translate it into code and the calculator will do it for you. Repetition of the algorithm can provide understanding; but if you can teach the calculator to do it, then you have achieved total comprehension.

Programs for the TI-83

The following are algorithms for solving problems required in high school mathematics. How many times have I used the quadratic formula? Now using the same process, the calculator can be told to do it. Almost all programs require some sort of input to complete the process. For example to find the area of a triangle, you must substitute the base and height into the formula (1/2)*b*h. The programs increase in complexity farther down the list.

Area of a Triangle (suitable for middle school and up)

Standard Form to Slope-Intercept form (Algebra 1 and up)

Quadratic Formula (using "IF") (Algebra 1 and up)

Factoring ax^2 + bx + c into (mx+n)(ux+v) (Algebra 1 and up)

Sierpinski's Triangle (Geometry and up)

Solve a System with Cramer's Rule (Algebra 2 and up)

Synthetic Division (Algebra 2 and up)

General Command Information

References