Order of Operations
Lesson 2 of 16
Objective: SWBAT use the order of operations.
The Do Now is a collection of topics that students have had difficulty with in the past. Students' approach for this Do Now will be different than normal, in that it will begin with a group discussion. Normally, students solve the problems independently and discuss their strategies and solutions with their group. Since I've observed misconceptions with these types of problems, students will first discuss the problem.
I will instruct students to, "Leave your pencils on your desks. Before you jump into solving the problems, discuss what you would do with your group. If you disagree with someone, discuss whether it's an incorrect strategy, or maybe just another strategy. Then you can work on finding the solution."
1. Use the GCF and distributive property to find the sum of 36 and 8.
2. What are the coordinates of (2,7) reflected over the y-axis?
3. What is the distance between (-5,2) and (-9,2)?
To create student' interest in the upcoming lesson, I will bring up the topic of pizza. I will call on a few students to share their thoughts with the class.
If you were to prepare a pizza at home, how would make it?
Most students will say that they first start with the pizza dough. Then, they add the tomato sauce. Then the cheese and any toppings.
So, there's a specific order to making your pizza? Would it be right if someone added the toppings before the sauce and cheese? Or if they just randomly mixed everything together in a bowl?
I will allow a few minutes for students to discuss and debate this.
I will make a comparison to the logical order of making pizza to the order of math operations.
Many years ago, mathematicians developed a correct order for performing math when you have more than one operation. Many of you are familiar with the acronym PEMDAS, but we to discuss common mistakes when using it.
I will present students with the PEMDAS diagram. This diagram helps students visual the order as separate steps, rather than a linear string of operations. I will reveal and discuss the diagram one step at a time.
P - Many students are familiar with parentheses. I will introduce them to other types of grouping symbols, like square/box brackets and curly brackets/braces.
E - Students have recently learned about exponents, but I will remind them of what exponents look like.
M/D - This step is a common mistake for students. It is important to emphasize for students that when they have multiplication and division, they are to perform these operations from left to right. They should understand that this means that sometimes they will multiply first and sometimes they will divide first, depending on the problem.
A/S - This step is another common mistake for students. It is important to emphasize for students that when they have addition and subtraction, they are to perform these operations from left to right. They should understand that this means that sometimes they will add first and sometimes they will subtract first, depending on the problem.
I will work through a couple of examples with students. One strategy that I will share with students is to perform only one step at a time. Each step that they perform should be underlined to show their work.
Example 1 - Simplify 18 - 3 x 3 + 6
See Example 1 Work
Example 2 - Simplify 27 / 3 x (5 - 2) + 15
See Example 2 Work
Example 3 - Simplify [6 + (2 x 8) + (42 - 9) 7] x 3
See Example 3 Work
Although students will be completing the Group Work problems in their own notebook, I will encourage them to talk through the steps with their group.
- Is the expression true? Yes or No. (4 + 3 x 2)+6 = 20
- Simplify 24 + 6 x (16 / 2)
- Simplify 2.4 [ 3.1 + (12 - 6.2) 4 ]
- Simplify [(2)(4)]2 - 3(5 + 3)
After 10 minutes, we will discuss the problems as a class. If time allows, I will call students forward to the board to show their steps.
I will remind students that if they are not arriving at the correct answer, it is easier to identify their mistake if they've underlined each step.
As a review of the lesson I will present students with the following question:
Why is it important to have an order of operations?
Students should realize that if they were to perform the operations in any order, then they may have different answers.