## 4 Step Advanced Order of Operations Problems

#### Aligned To Common Core Standard:

**Grade 5 Operations** - 5.OA.1

What to expect with advanced order of operations problems - We are all familiar with 2-step and 3 step order of operations problems. The 2-step order of operation includes any two operations to solve. Similarly, the 3-step order of operations includes any three operations to solve. These problems are solved according to the PEMDAS rule.
Similar to 2-step and 3-step order of operation problems, we have a 4-step order of operation problems. 4-step order of operation has an addition of another operation to them. They are carried out in the same way as the 2-step and 3-step problems. The 4-step problem follows the same rule of PEMDAS; that is, parenthesis and exponents are given priority, and the rest four basic mathematical operations are solved afterward. Multiplication is given precedence over division, and addition and subtraction follow. For example, if you are given a problem,
(2^{3} + 3^{2}) x 49. You will start solving this problem by solving the parenthesis first. Within the parenthesis, you will resolve the problem for exponents first. After solving for exponents, you will move to solve addition. Once you are done with parenthesis, you will move to solve the multiplication problem outside the parenthesis.
These worksheets and lessons help students learn to tackle very advanced order of operations problems.

### Printable Worksheets And Lessons

Note: Please remember that when you are processing these higher level
operations, PEMDAS is not to be taking literally. Multiplication and
Division are at the same level. When confronted with either Multiplication
or Division at the same step, they should be processed left to right.

- Wacky Operations Step-by-Step Lesson- You will find that five operations exist in all the problems found in this section.
- Guided Lesson - The placement of parenthesis is what most throws kids with these problems.
- Guided Lesson Explanation - I created my own rendition of PEMDAS in this one.
- Practice Worksheet - I purposely did not use big numbers so that students could focus on the process rather than the math.
- Matching Worksheet - I can't believe that these little end results of the numbers in the problems resulted.
- Basics Lesson Worksheet- This is as simple as these problems gets.
- Word Problems Worksheet- Larger numbers are used in here to start to challenge kids a bit more.

#### Homework Sheets

This is where some students start to forget about the left-to-right rule. If you have two of the same operation, process them left-to-right.

- Homework 1 - We need to be reminded about the order in which attack a problem like this. The acronym PEMDAS indicates the order.
- Homework 2 -We process calculations in this order: Parentheses, Exponents, (Multiplication, Division), Addition, and Subtraction
- Homework 3 - Note the parentheses around multiplication and division. That is because those operations are at the same level.

#### Practice Worksheets

What works well here too is to outline the problem by simply labelling the order in which you are going to do the operations then proceed with it.

- Practice 1 - Find the final value of the following problem.
- Practice 2 - These questions are not much different from any of the other operations problems you have already mastered.
- Practice 3 - Once you handle the parenthesis, if you have the same operation in play, work the problem left to right.

#### Math Skill Quizzes

The scores on these might surprise you, if students haven't had some practice on the skill first.

- Quiz 1 - Division and multiplication is processed left to right.
- Quiz 2 - When deciding to divide or multiply on a step, we process the calculation to the left first.
- Quiz 3 - Just remember the order and work your way through.

### Why Does the PEMDAS Method Not Always Work?

When you start tackling very advanced order of operations problems you will run into situation where our good old PEMDAS rule does not apply. The first case where this holds true is been parenthesis are implied, but not visible. There was a problem floating around the social network circuit that was stumping even graduate students. It stemmed from the fact that multiplication and division hold the same level of priority in operations, so if you are confronted with an operation that contains both, you should process this in the order that they appear from the left to right. This same level of priority is found between addition and subtraction. When you find those in your path touching each other, go left to right as well. Your goal should be to recognize when this is true and process the operation left to right instead of focusing on the rule. The best approach to take is that when you identify an expression or statement that you need to complete, take a step back and see if any of these operations are touching one another. Once you have pondered the problem, process it as we just discussed.