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Welcome to my math blog! The purpose of this blog is to help you stay informed about our learning and experiences that have taken place during our math class. I have also included links your child (and you) may want to use in order to supplement math learning in 5th grade.

Monday, October 13, 2014

Order of Operations: PEMDAS and The Power of Parentheses

To introduce our new topic, I asked the kids to write the following math problem on their desk (using dry erase markers):

3 + 3 x 4 + 2 x 3 + 3

Most students solved from left to right getting an answer of 81.  Other times, students had a variety of answers that when they explained their math thinking, were correct as they had no background knowledge of the Order of Operations.  We started to believe that all of the answers were correct.  Before we got too far into that, I explained that I had forgotten to add a piece of important information.... the parentheses.

I added in the parenthesis 

3 + (3 x 4) + 2 x (3 + 3)

we found yet another answer, but when we finally used the rules for PEMDAS, we found that the answer was 27.  This lead into my lesson objective:

We will understand the need for a standard order of operations by investigating the impact that changing the order has when performing a series of operations.

I explained to the classes that there is an agreed upon order of operations:  parenthesis, exponents, multiply/divide, then add/subtract.  To emphasize the new information we demonstrated PEMDAS using a paper hopscotch board and our fingers!  After playing hopscotch, we recorded our new learning in our journal.  I found another blog whose teacher used the hopscotch method in her classroom and then created the PEMDAS graphic organizer that we used in class today.  The video with information is at:  

I discussed that they need many different ways to help them remember the Order of Operations.  I explained that they needed something that would not allow them to mix up the order of the multiplication/division, and addition/subtraction.  At this point, I mentioned the acronym PEMDAS.  I also encouraged them to use a mnemonic device to remember the steps such as:

I really wanted to emphasize the importance of parentheses.  So we used a Mailbox Magazine page entitled "Parentheses in Numerical Expression" from the Dec/Jan 2013-14 edition.  We solved equations in which parentheses were missing.  We used PEMDAS and discovered that the equations were untrue.  We learned how placing the parentheses strategically would change our answer and allow the equation to be true.

Finally, I have the classes a choice of assignment (from the same Mailbox Magazine page):

  • Create a comic strip featuring a superhero named Captain Parentheses.  Use your creativity and sense of humor to have the superhero save the mathematical day.  in the comic strip, show that you understand how a set of parentheses can affect a mathematical expression.

  • If math parentheses could talk, how would they explain their work in mathematical expressions?  Write a conversation between the opening and closing parentheses about what they do in mathematical expressions.  Use correct punctuation.

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