Order of Operations: Solving Simple Equations Using PEMDAS
Lesson 10 of 12
Objective: SWBAT solve whole number numeric expressions using the order of operations.
Warm Up: Stop That Creature!
Just to review simple in and out charts, we used this game to have some fun and strengthen our thinking. Stop that Creature. Everyone took a turn and the class supported each other as sometimes they were stumped with the negative out puts. They love this game. It is simple, but the music and concept is just too fun.
Math Timed Tests
Students logged onto their iPads to work on Timed Tests. I am doing this everyday now and am seeing great improvement using this ap. I highly recommend it. I think the old fashioned paper and pencil tests are fine as long as there isn't a stress on time. This ap helps me adjust and individualize for students to help them with achieving math fact fluency.
Listing Factor Pairs
Since we were working on reviewing skills and fluency, I took 5 minutes to review creating factor pairs 1-100. I wrote the number 73, 91 and 62 on the board and told them to list factor pairs for as many as they could in 5 minutes.
Afterward we stopped and solved.We discussed how 91 looks like it might be prime. We talked about how we can use our fact knowledge to solve it since listing factor pairs for this will be long and drawn out. "Let's use some mental math and facts we know to solve." They knew it wasn't divisible by 3...but questioned 4. So we started with 4 x20, 4x 21 would be 4x20 + 4x1 , ect and 4 x22 is 88. 88 + 4 is 92. Nope. Not 4. When we tried 6, one student started right away with 6 x 12 being 72, 6 x13 being 78, and he kept guessing and checking like that until he came up with 6x 16 and said to stop. Nope. Not six. Maybe it is prime, one girl said.
I told her no, she needed to keep trying. Move to seven. So we did it together starting with 7x11 being 77, then 7x12 and then adding seven more to make 91. Bingo! There it is! 7x13. We checked it with our calculator. Sure enough, we had found them all. They worked the last two on their own. We had a quick discussion about them and stopped. I plan to practice every day with just a few products for them to fine factor pairs for without using the calculator until they felt they had found them all.
Core Lesson: The reason that students in 4th grade benefit from having order of operations introduced revolves around Math Practice Standard 2 & 7.
Rationale: This lesson gets kids to reason quantaties and fluently use the operations, as well as make use of structure. The order of operations standard is addressed by standard 6.EE.A.2. This lesson could be used for a remedial 6th grade or a more advanced 4th or 5th grade lesson. I am teaching it because it is part of our curriculum and is caught up in the transition to CCSS.
I had the whiteboard ready with a simple example of a numerical expression that included parenthesis, addition and multiplication, (3+4) x 2 = n. I also had written PEMDAS on the board. I asked them to copy down PEMDAS at the top of the notebook page and copy the equation as a sample.Notebook notes PEMDAS
When all were ready, I began the lesson using a slide show that I developed. This slide show,Order of Operations also contains material for 5th grade students. Simply touch upon exponents and then focus on parenthesis for this lesson. Students sat around my feet by the Smart Board with their iPads and Math Notebooks and took notes as the lesson progressed.
They copied down the information on first page of the lesson into their notebook. This page is very clear in explaining the order of operations. I taught step by step the concepts from that page and we read it together out loud, as I stopped the video when needed.
I asked students if they all knew what parenthesis were. I checked for understanding that they know the concept of solving left to right and had them make the motion with their hands of left to right. The next pages teach the process of solving a problem using PEMDAS. It contains exponents and I stopped the movie and talked about not practicing with exponents in our work today, but it was good to see what exponent meant. We would solve it, but not to expect it in their homework today. I explained that they would see more exponents in the future and reminded them that I had shown them this when we were learning about square numbers.
We listened to how the problem was solved and talked about the steps involved. They noted all of the V's under each section that was solved as the "v" acts as a guide to keep things neat. I pointed out the steps that she used in the video to solve the problems.
When she discussed the "common mistake", I paused the film and we copied down the "common mistake" and then discussed it in detail. I asked if they thought when they were practicing later if they would make that mistake. They all said no! I am pretty certain at least three students will forget to consider order of operations unless they are taught the system of remembering by writing PEMDAS next to every problem. This lesson needs to be taught sytematically. I told them I need them to follow PEMDAS exactly.
I asked them why order of operations would be a good thing to use when we solve? Their answers mainly were about getting the problem right. I told them that is part of it but was more about making sure that solving expressions were a consistent thing...that everyone would solve it the same way to ensure accuracy.
Smart Board Practice
I brought up the Notebook file to create a practice board for my students ( PEMDAS Smart Board Practice) to start them on whole class practice.( Look through the file to see the examples of what we were doing as the lesson progressed.)
While they waited for me to get it running ( because it was giving me a problem!), I had them recite PEMDAS rules. Reciting PEMDAS It sounded great... They seemed excited when I told them they were learning a 6th grade standard. "See how smart you are? You can do 6th grade work, right now!" I just smiled and they beamed back. It set the tone for solving the first problem. They were "pumped". I wrote a challenging expression on purpose because I wanted to challenge students to think at a higher level. We solved the problem with my guidance as I helped a volunteer student keep things lined up and organized. Students took the notes as we solved it together. The V's and copying the equation helped students completely understand what was going on. We talked about accuracy and how organization helps us be accurate and we have to consistently solve it by recopying the new sections of the problem down as we go. Showing the V's and rewriting the equation.
One student explained her confusion and realized she had made the mistake of not copying the next equation down. Recognizing her mistakes.
After three practice tries on the Smart Board, I asked if they felt confident to go and try it on their own. They were anxious to try!
Just before everyone went back to their seats, I posed the question: What will our "thinking voice" be saying to us? I heard this term from our reading specialist who happened to be in the room and fed off of it as a whole class question. I think that was a great question.... "our thinking voice" is a good term to use when getting math students to think things through systematically. I wanted to see if they knew what they needed to say to themselves as they went.
I assigned IXL.com Level F G.4 (as many problems as time allowed in class) I told them it was a good strategy to use their notes and to write PEMDAS on top of their notebook as they solved. Practicing PEMDAS I caught one student doing the "common mistake". When I questioned him, he smiled and threw his head back and let out a big "aw"!!!. We talked about how we think that we aren't going to make a common mistake...but when we stop thinking, we often do.