unit 2 math

One of the most important things you will learn in Unit 2 is order of operations. You may not usually think about it, but most of what you do in life is done in a certain order. What would happen if you put your shoes on and then your socks? It seems comical, but you do things in a certain order for a reason. The same thing is true in math. The order of operations will tell you how expressions should be simplified so that you always complete them in the same order. On the Unit 2 Discussion Board, you will investigate the order of operations. This Discussion topic has multiple parts. Please read and complete each part.
Original Response

1. Describe the order of operations and explain how it is used to simplify expressions. Explain specifically the order in which mathematical operations must be performed to correctly simplify an expression.  
2. Provide an example of a real life situation where a specific order of steps is necessary for a proper end result. What will happen if the proper order is not followed? (Humor and creativity are encouraged.) 
3. Develop an original mathematical expression which must be simplified using order of operations. Include addition, subtraction, multiplication, division, an exponent, and at least one set of parentheses. Simplify the expression incorrectly, showing each step as you simplify. You do not have to include the reasons for each step.  

First Response to a Classmate 

Find a classmate’s incorrectly simplified expression that has NOT already been corrected by a classmate. Simplify the expression correctly explaining each step. Identify the error, or errors, made.

Second Response to a Classmate 
Find and comment on at least one classmate’s correction of an expression. Make sure your comments are substantive and advance the Discussion. If the expression is not simplified correctly, tactfully identify the error and simplify the expression correctly.

Student 1 Response

1. The order of operations is a system that was developed to calculate mathematical expressions and verify the correct answers to equations. This order is expressed as PEMDAS, which is parentheses, exponents, multiplication, division, addition, and then subtraction.  As addition and subtraction are of the same order these operations can be done at the same time, just like multiplication and division, exponents and square roots, and parentheses and brackets.  This system is especially important when evaluating Algebraic expressions as they can include not only numbers and operation symbols, but also parentheses, and variables. When these multiple elements are used together to form an equation they may seem complicated. However, the order of operations simply breaks the different areas down so that the problem can be solved simply. If this order is not followed however, one could complete an equation with an incorrect solution. Maintaining the right sequence of PEMDAS ensures the correct answer.

2. Order is needed in many ways of our everyday lives. Simple things such as getting dressed, driving, cooking, cleaning and even work require some organization. As a homemaker I do fair amount all of these, but one thing I do a lot of is laundry. This is one of my least favorite things to do, but with two boys I always have an endless amount. The system for cleaning laundry is to put dirty clothes in a hamper, separate into correct colors/fabrics, put in a washing machine, place in dryer, or hang to dry, then fold or hang-up and put away. If I were to change the order by first separating the clothes by colors/fabrics, then folding or hanging-up them up, and next placing them in the dryer, then putting them in the washing machine, and finally placing the clothes into the hamper, I would have a pile of wet clothes sitting in a laundry basket instead fresh, clean, and dry clothes ready for my family to use. So, just as it is necessary to follow an order when performing a simple task such as washing clothes, one needs to follow the order of operations in order in perform correct solutions to equations.

3. Here is my expression, my incorrect simplified order, and incorrect answer.

23 + (8 – 2)6 + 18 ÷ (9 – 3) – 32

8 + (8 – 2)6 + 18 ÷ (9 – 3) – 9

16 – 2 ∙ 24 ÷ (9 – 3) – 9

14 ∙ 24 ÷ -3

336 ÷ -3

-112

Student 2 Response

Order of Operation: PEMDAS  = Parenthesis, Exponents, Multiply, Divide, Add, Subtract
2²X3²-(15/5)-10=11
2²X3²-(3)-10
4X6-(3)-10
24-3-10
21-10
 =11
Real example: It’s just like learning to ride a horse: 1- Catch the horse 2- Put the bridle/ reins on the horse 3- Put the saddle blanket on 4- Put the saddle on 5- Climb up on the left side of the horse using your left foot 6- Learn to walk the horse and give it directions 7- Learn to trot the horse while giving directions 8- Finally learn to canter the horse while giving directions