5. The Distributive Property, Multiplying Polynomials, Factoring, and Trinomials
The TI-83’s 8-line Home Screen and something called the Boolean Operator are perfect tools for developing a constructivist, guided discovery lessons.
The Boolean Operator
Those of you familiar with computer programming are no doubt familiar with the Boolean Operator. Its origins trace back to George Boole, an English mathematician who lived from 1815-1864. He is credited with developing the idea that a false statement resulted in a value of 0, while true statements resulted in 1’s. This amazingly simple concept was instrumental in the creation of modern day computers.
So, entering the statement 6 + 4 = 9 would return a value of 0. The statement 6 + 4 = 10 returns a value of 1. Now that we’ve looked at the Boolean Operator, let’s take a quick look at demonstrating the Distributive Property using the TI-83.
The Distributive Property
1. Discuss the Boolean Operator. Explain the responses of “0″ and “1″.
2. Ask students to complete a statement, such as 5(2 + 6) = _________.
3. Using an overhead calculator, enter student responses on the Home Screen, recording input equations and Boolean outputs.
To enter the equation using a TI-8X: 1) Enter the left-side of the equation. 2) Press TEST (2nd MATH) and select 1: =. 3) Enter the right-side of the equation.
(If using a TI-73, see 4. Comparing Unit Fractions for instructions on entering “=”.)
4. Repeat with other numeric equations until students show mastery.
5. Finally, repeat using equations involving variables, such as 5(x + 3) = 5 * x + 5 * 3.
Note: The calculator is not actually verifying an algebraic expression. The calculator is substituting its stored x-value for x. To see what this value is, press x and ENTER.
Multiplying Polynomials, Factoring, and Trig Identities
The Boolean Operator can also be used to help students to: “discover” difference of 2 squares and perfect square trinomial patterns, check binomial factors of trinomials, and “confirm” trig identities.
Whenever working with statements involving variables, remind students that the calculator is not performing algebraic skills. In fact, to avoid false positives, I would have students store an unusual value for x, such as their birthdates or boyfriend/girlfriend telephone numbers. (Let’s say a student enters x^2 + 9 = (x + 3)(x + 3). He/She will get a true statement if 0 is stored for x.)
To store a value for x, enter the number, press STO, press x, press ENTER. Changing x to such a number will make it highly unlikely for students to obtain false positives.
Parting Thoughts
If you give this Boolean Operator approach a try, please share your experiences — any modifications you found helpful and/or any other topics that leant themselves to a Boolean Operator approach.
