Standards, Big Ideas & Essential Questions

I will be teaching a unit on the order of operations. PEMDAS is an acronym for parenthesis, exponents, multiply, divide, add and subtract. Students will be taught if they have an equation with multiple operations which to do first.

Oregon Common Core Standard
6.3.1 Use order of operations to simplify expressions that may include exponents and grouping
symbols.

Big Ideas: Simplification of Expressions

Essential Questions:
Topical: What are the steps to simplifying expressions? When do you simplify?

Overarching: How is this applicable to the real world/outside class and why are we learning this topic? Why is it important to simplify?

Big Ideas: Order of Operations

Essential Questions:
Topical: What is the certain order that operations are used?

Overarching: How will the answer change if the order is used versus not used?  What is the essential background information needed to understand the lesson?

STANDARD: 6.3.1 Use order of operations to simplify expressions that may include exponents and grouping symbols.

SUBJECT: The unit I am covering during my practicum is the order of operations and using PEMDAS (parenthesis, exponents, multiply, divide, adding and subtracting) to simplify expressions. The order of operations uses the acronym PEMDAS to help students remember which operation goes in what order. Parenthesis are first, exponents second, multiplication or division third and addition or subtraction last. PEMDAS is imperative in understanding mathematical concepts. There are times in mathematics when there are more than one operation involved in a mathematical problem.  It must be solved by using the correct order of operations. It allows students to understand which part of an equation to do first. The standard that supports the teaching of PEMDAS is: 6.3.1 Use order of operations to simplify expressions that may include exponents and grouping symbols.

STUDENT: It is beneficial for the students to demonstrate proficiency understanding the order of operations.  PEMDAS is useful for students because it will promote accuracy when doing computation work. Additionally, if they are not using the order of operations then their whole answer will be off. The Order of Operations provides students with a fixed approach to solving mathematical expressions, and without them, it would be impossible for all students to get the same results because all students would solve mathematical problems in whatever way they would like and students would end up with multiple answers. With the Order of Operations, everyone who solves a given problem will arrive at the same solution(s).

SOCIETY: Students will eventually integrate themselves into society.  Therefore, they need to understand that there is a certain order and process for life tasks which includes work and daily life. Learning the Order of Operations is a specific process for math, but being able to carefully follow certain steps and the order is applicable to the real world. Doing the order of operations will help teach students that there is a specific way to do certain things. In the real world, there are many things you have to do in order; it is not limited to mathematics. For example, students have an order of how they attend classes in a day. Math may be first period, science second and so forth.  If they randomly decide to go to their classes in whatever order they please, they will probably not be covering material that is relevant to them.  The order of things is very important in life and not just in mathematics. The order of operations is relevant to society to help teach order on a larger scale.
 

Pre-Requisite Skills:

Things students must know are...

1. How to add, subtract, multiply or divide in one step equations (ex: 3 + 4 = 7).

2. Multi step equations with one type of operation (ex: 3 + 4 + 7 = 14).

3. What a parenthesis is and looks like.

4. How to follow a given order.

5. How to work in groups.

6. Basic mathematical terminology (ex: add, subtract, multiply, divide, equation).

Common Core Standard: 6.3.1- Use order of operations to simplify expressions that may include exponents and grouping symbols.

I am teaching a 6^th grade Math I class. My unit on the order of operations (PEMDAS – Parenthesis, exponents, multiplication, division, addition, subtraction) encompassed six days. I originally thought I would start teaching a unit on adding/subtracting and multiplying/dividing decimals, but did not get to it. I have a separate pre-assessment for PEMDAS and one for only adding/subtracting decimals. PEMDAS was post-tested, but adding/subtracting decimals were not because we did not specifically go over it. The adding and subtracting part of the decimal unit is a 5^th grade standard and not technically a middle school one so many students have prior knowledge of how to do so. Throughout their 6^th grade year students will be able to find equivalent fractions, percents, decimals, understanding and skill with addition, subtraction, multiplication, and division of fractions, finding area and perimeter relationship of 2-dimensial shapes, addition, subtraction, multiplication, and division of decimals, calculate experimental and theoretical probabilities, in addition to learning about the order of operations.
            The unit on PEMDAS directly aligns standard 6.3.1. The standard directly requires the 6^th grade math student to be able to use PEMDAS, the order of operations, to solve and simplify mathematical equations. My unit directly addresses which steps to take and what order to take them to correctly solve a mathematical equation. The steps are broken down into parenthesis, exponents, multiply, divide, add and subtract. Students must do them in a particular order to get a correct answer that would be consistent with anyone who sits down to solve that equation. The unit on PEMDAS also encompasses a mini-lesson, which teaches students what to do when they see an exponent.
            The entire unit that I am teaching revolves around the one standard (6.3.1). Additionally, every goal and objective that I have thought out for the unit revolves around the standard 6.3.1 as well. Every goal and objective was written with the standard in mind.

STANDARD: 6.3.1 Use order of operations to simplify expressions that may include exponents and grouping symbols.

GOALS:
1) Students will be able to define the acronym,  PEMDAS,  and explain how it is used to solve mathematical equations.  
2) Students will be able evaluate a mathematical expression in order to choose the appropriate order in which  to do their operations.
3) Students will be able to accurately use the mathematical steps of the PEMDAS model to solve mathematical expressions.

STANDARD: 6.3.1 Use order of operations to simplify expressions that may include exponents and grouping symbols.

OBJECTIVES:
1) Students will be able to apply each of the process steps in the PEMDAS model to accurately solve 5 problems on a post-assessment. [Application]
2) Students will be able to label and EXPLAIN each letter in the PEMDAS acronym. [Comprehension]
3) Students will be able to create and solve their own exponent problem.  [Cognitive & Creating]
4) Students will be to use PEMDAS to find a path in order to do a search and rescue activity. [Cognitive & Evaluating]
5) Students will be able to insert an operation to an incorrect equation to make it true. [Cognitive & Application]