3 Step Order of Operations Worksheets
This is the moment of truth to see if students truly grasped this concept. In most cases prior to getting to the third step students were able to use the PEMDAS approach literally and get the proper solution in greater than eighty percent of the time. Students will therefore have a false sense of comfort with these types of problems. Once we move to this level of problem you truly need to understand how this approach actually works. If you have some difficulty, check the bottom of this page. I will often get student teachers who are a semester from graduating college that never fully understood this as well. So it is not out of the realm of possibility that your elementary or middle school students will not be solid with it as well. These lessons and worksheets will help students understand how to tackle problems that require three steps to complete.
Aligned Standard: 5.OA.1
- PEMDAS Is The Name! Step-by-Step Lesson- Identifying the operations in each problem is most likely the hardest part.
- Guided Lesson - These might get a few blank stares from students at first.
- Guided Lesson Explanation - I also find that numbering the step you will take before doing the problem helps students.
- Practice Worksheet - Some of the end products in this one can get huge if you let them get away from you.
- Matching Worksheet - Find the outcomes of the problems in the list.
- Word Problems Worksheet- We use three-step skills in a sentence-based setting now.
- Answer Keys - These are for all the unlocked materials above.
Homework Sheets
You will find a completely worked through problem and a nice PEMDAS reminder for you here.
- Homework 1 - To solve all problems that have more than one operation, we use the acronym PEMDAS to tell us the order in which we complete each operation left to right.
- Homework 2 - Now apply this to our problem.
- Homework 3 - We start with the parenthesis first.
Practice Worksheets
Remember the steps as you progress through these. They should become second nature by the time you are completed.
- Practice 1 - Remember that exponents come before basic operations.
- Practice 2 - Restate the problem before you complete it.
- Practice 3 - These can help you put this stuff behind you.
Math Skill Quizzes
You will find a small scoring key at the bottom of these. The score is out of ten, so it's an easy calculation.
- Quiz 1 - What do you do when you come across the same operation?
- Quiz 2 - What if there are two terms of addition that are the same level of operations?
- Quiz 3 - Since there are no exponents in this work, you can remove the E and restate it as: PMDAS
What Are 3 Step Order of Operations Problems?
A 3 Step Order of Operations problem is similar to the one or two step problems. There is just another additional operator to contend with. For example, if in a two-step order of operations problem, the operations of addition and subtraction are used, there may be an inclusion of a multiplication operator in this version. For that matter it could be any of the four basic operations. You will often find that the third operator often differs from the other two that are present. Here is example where an additional operator is not present, instead you with find an exponent to deal with:
7 x 42 - 5 = 7 x 16 - 5 = 112 - 5 = 107
In the example solved above, it can be seen that the exponent is solved first. 42 becomes 16, and then 16 gets multiplied by 7, followed by the execution of subtraction. Here, it is quite evident that PEMDAS or BODMAS rule is applied, and exponents are solved before MDAS. Exponents also include values found under-roots since they are exponents in fractions.
How Should You Approach These Problems?
By this time, you already have had some experience with the concept of PEMDAS which dictates the order in which we apply operations that are found within the same equation or expression that we are simplifying. When we make the leap to adding a third step students begin to struggle a little more and this concept seems a bit more abstract, and this is often because students follow the PEMDAS strategy literally. The fact is that multiplication and division are ranked equally and the same is true about addition and subtraction seems to slip our student’s minds. What this means is that if you come across a problem that has you decide between multiplying or dividing, you would just process that in a left to right order. The same is true for addition and subtraction. I would encourage you to instead think of this acronym as:
P
E
MD
AS
Where operations that are equally ranked are stacked left to right.
The best way to approach these problems is to first label all the operators that must be considered. I encourage my students to label them with letters them first, then we go ahead and number the letters based on when they should be processed. Once you get in that habit, everything seems a great deal easier.