4. Comparing Rational Numbers with the TI-73
The TI-73’s 8-line Home Screen and something called the Boolean Operator are perfect tools for developing a constructivist, guided discovery lesson on comparing fractions/decimals/percents. Let’s start by talking about this Boolean Operator thing.
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 entering fractions and <, >, and = symbols using the TI-73.
Entering Fractions and Comparison Symbols
Let’s look at the key strokes needed to enter the statement 1/3 < 1/4. Fortunately, fractions will be stacked when they appear on the TI-73 screen.
(NOTE: This can also be done using a TI-8X, although the fractions will not be stacked. For instructions on entering comparison symbols with a TI-8X, please see 5. Distributive Property, Factoring, and Trig Identities.)
- To enter a fraction, press the numerator’s number, the b/c key, and the denominator’s number. After entering the first fraction, press the right directional arrow to move the cursor to the right of the fraction.
- To enter a <, >, or = symbol, press TEXT (2nd MATH). You should see a game-like keypad. You will use the directional arrows to move to the desired symbol. Once the box surrounds the desired symbol, press ENTER. Then press DONE to return to the Home Screen. The selected symbol will be pasted on the Home Screen.
- Enter the second fraction.
- Press ENTER to see if the statement is false (0) or true (1).
Comparing Unit Fractions
- Explain how the Boolean Operator works. Use an overhead calculator to demonstrate the results returned when entering 6 + 4 = 9 and 6 + 4 = 10.
- Ask students to consider the fractions 1/3 and 1/4. Have them predict the pair’s relationship, and then check their predictions by entering their statements and pressing ENTER.
- Repeat with other fraction pairs, such as 1/4 and 1/5, 1/8 and 1/9, 1/12 and 1/13.
- Once students see the relationship, they reverse the order of the fractions in each pair and enter new comparison statements.
- Students generalize their conclusions — orally and in writing.
- Finally, students complete written comparison statements involving both < and > symbols, using the calculator to check answers as needed. Depending on differentiation needs, students can work independently, with a partner, or with a small group.
More Boolean Operator Rational Number Lesson Ideas
- Comparing fractions with like and unlike numerators and denominators
- Comparing any pair of fractions/decimals/percents
- Determining if fractions are equivalent
- Determining if an improper fraction and a mixed number are equivalent
Parting Thoughts
If you give this a try, write and let me know how it goes… including any tweaks that worked well for you and your students.
And, please share any other ways you find to use the Boolean Operator in your classes.
