Order of Operations

The lesson below is still images taken from the fully animated PowerPoint I created that is available in my Teachers Pay Teachers store page. If the PowerPoint is not one of my freebies, you may also head over to my YouTube channel to see the slideshow fully animated and can pause as needed to be sure you grasp each concept before moving forward (each lesson will always be free there!).

This lesson will introduce how to determine the correct order to perform operations when looking at a problem. We go over why the order of operations is so crucial to getting the correct answer and walk through examples step-by-step to help clear up some of the most common errors students make.

So without further ado, read through the slides below to get a feel for how to correctly use the order of operations!

Order 1Order 2Order 3Order 4Order 5Order 6Order 7Order 8Order 9Order 10

Phew, that’s a lot to take in. Once you’ve gone over this and found some practice problems to cement the idea in your head what integers are, you may move on to the next lesson below!

Solving Equations by Adding and Subtracting

Just in case the slides aren’t your thing, here is a text outline of the main points of the lessons above!

  • Order of operations
  • Objectives
  • By the end of this lesson you should feel comfortable:
  • Recognizing different operations
  • Utilizing the order of operations to solve problems
  • Where to start?
  • Sometimes, we are presented with a problem that requires us to perform more than one calculation, or operation, in order to arrive at an answer.
  • For example, let’s say you your two friends are saving up for a trip by mowing lawns. Your dad also says he will give you double what you earn yourself (so you will have three times as much as what you make on your own).
  • Let’s say you make $15, one friend earns $20, and the other friend earns $10. How much did you make together?
  • How about a model?
  • Where to start?
  • So…what would we do first?
  • If we add everything up, we would have 15+20+10 = 45
  • Then multiply 45 by 3 to get 135. But is this correct?
  • Your dad is only tripling the amount YOU earn, not everyone.
  • So you’d have to multiply first.
  • 75 and 135 certainly aren’t equal.
  • Clearly the ORDER you perform the operations matters.
  • Operations
  • Before we can decide the correct order, however, first we should know all the different operations that are possible.
  • Operations are the different calculation techniques we can do to numbers.
  • Still fuzzy? How about a list of examples from the first things we learned.
  • All of these have a specific order we perform them in when combined together in a single problem.
  • pemdas
  • So what order do we follow?
  • Cool, so what does that mean?
  • It’s an acronym, which means each letter stands for an entire word.
  • In fact, you can remember this with a silly saying:
  • Please Excuse My Dear Aunt Sally”
  • Using Order of Operations
  • Alright, so let’s try putting PEMDAS to use and see what it really means:
  • Great, so lots of stuff going on. Let’s go down the line.
  • Do we see any parentheses? No.
  • Do we see any exponents? Yes. Let’s perform that operation first.
  • Next, we look for either multiplication or division. Whichever we see first reading from left to right, we perform first. Here we only have multiplication, so let’s do that next.
  • Using order of operations
  • Finally, we look for addition or subtraction. Again, we see which comes first reading from left to right. This time, subtraction appears first, so:
  • Then we have a simple addition problem left.
  • Ta da! You’ve solved your first multistep problem using order of operations!
  • Notice: In each step, we focus on one operation, then change only that answer in the next line and rewrite the rest of the problem exactly the same so that we can retrace our steps if we somehow make a mistake!
  • Using order of operations
  • One more problem so that we can introduce a final idea.
  • We use parentheses to designate that a specific operation should be done first.
  • In our example, we can see multiplication outside the parentheses, which normally would come before addition.
  • But remember our order!
  • Parentheses are the first thing we check for. Though they are not an operation, they designate which operation, or set of operations, are to be performed first.
  • Using order of operations
  • With that in mind, let’s do what’s in the parentheses!
  • Notice that now we have 5 x 4. This is because a number outside of a set of parentheses is math notation for multiplication.
  • Now we can follow along with our order!
  • Are there any exponents? No.
  • Do we see multiplication or division? Yes, so let’s go left to right.
  • And the last step is to simply multiply our final problem.
  • Ta da! Another problem finished successfully!
  • conclusion
  • Operations include:
  • Addition
  • Subtraction
  • Multiplication
  • Division
  • Exponents
  • The order of operations follows PEMDAS, which can be remembered by “Please Excuse My Dear Aunt Sally.”
  • Multiplication and Division are performed left to right, whichever appears first.
  • Addition and Subtraction are then also performed left to right.
  • Though parentheses are not an operation, they set aside a part of the problem to be done first no matter the operation(s) inside.