3. The Order of Operations
Home Screen Overview
The power of an 8-line viewing screen is that students can see their input and the resulting output. Those of us old enough to remember the days of receiving monthly checking account statements in the mail will especially appreciate this feature. I remember laboriously entering all those credits and debits into my calculator and pressing =. Without fail, I would have unknowingly entered some number incorrectly and ended up with a different balance than the bank’s balance – with no recourse for checking the numbers I had entered.
The following Order of Operations Lesson is a great first lesson to use with students because only the 8-line home screen and hard keys are involved.
Order of Operations Lesson
A Word to the Wise: Before trying the following activity with your class, verify that your overhead calculator/hand-held device computes according to the order of operations!
For my Order of Operations lesson, I would:
1. Enter an expression, such as 3 + 6 * 3 – 2, in my overhead calculator and prompt students to predict the output before I pressed ENTER (the calculator’s = button). I quickly got a feel for who understood the basic PEMDAS order. (Note: Remember the calculator distinguishes between a subtraction sign and a negative sign.)
2. Enter an expression, such as 8 / 2 * 4 + 10 * 2, and ask for student predictions. This gave me a feel for students’ depth of understanding. Students responding with “21″ mistakenly thought that multiplication had to be done before division — not understanding that operations were to be performed left to right.
I found evaluating the second expression incorrectly to be a common mistake. Students who had previously heard of “PEMDAS” were often surprised that they missed this one. It helped to get students’ attention.
In addition, having the calculator give the correct answer was helpful. This topic often appears in one of the first lessons and, early in the year, students may still be feeling out the teacher and class dynamics. When the calculator screen displayed “36″, students were convinced that it had to be true.
3. Repeat with additional expressions that reinforce the left-to-right component until students showed mastery.
4. Repeat with more involved expressions that contain parentheses and/or exponents.
At this point, I write “GEMDAS” on the board — using a “G” to stand for grouping symbols. We discuss that parentheses are only one form of grouping symbols. Grouping symbols also include brackets, fraction bars, and absolute value symbols.
5. As appropriate based on prior learning, repeat with expressions involving fractions and absolute values.
6. Students practice simplfying expressions based on differentiation needs — complexity of expressions, individually or with a partner/small group. If student calculators are available, consider letting sudents check their answers with calculators.
Parting Thoughts: Have fun!
- If you give this a try, please let me know how it goes.
- Feel free to share other Order of Operations Lesson ideas.
