Friday, September 7, 2012

Visions of PEMDAS Danced Through my Head

I woke up in the middle of the night with visions of lesson plans dancing in my head. Earlier in the day, I had gone over and over my plans, trying to find the best method of introducing my new crop of sixth graders to the infamous order of operations. I struggled with whether to use PEMDAS or not (I normally use a different acronym), but I really wanted to use Mr. Stadel's PEMDAS video; I knew my students would love it! Since I've started using foldables, I really wasn't happy with the normal graphic organizer I might have used and so I began searching for a foldable that fit my vision. Alas, nothing could be found and so I finally gave up, resorting to my tried and true graphic organizer.

Fast forward to the vision that woke me up...... My brain had been working on the problem while I got what little sleep most of us are used to the first few weeks of school. I saw the perfect foldable in my mind; now, I just had to construct it!

Have you ever tried to design a foldable at 3:30 AM???? It's far more difficult than one might expect! :) I wanted to make sure that my foldable emphasized the fact that multiplication and division are done as we move left to right through the equation and that it is true for addition and subtraction as well. In my mind, I could finally see what it needed to look like, but my brain just couldn't get it onto the paper.  Finally, at 4:45.... Success!  Here's what it looks like all folded and nice after one of my students constructed it today ....

Notice that the P and the E flaps extend across the foldable, but the M and D share a row, just as the A and S do.  I wanted to make sure that students graphically saw this on the foldable. And it worked!

I had students choose a color for writing the "P". They then chose a different color for the "E". They picked a third color that they used for the "M" and the "D" because, as my students said, they share a row. :) The fourth color was used for the "A" and the "D" for the same reason.

After we made the outside of the foldable, we turned to the inside. I wanted the students to label each step and we also worked through a problem together.

Once we finished the right side of our INB (our input side), we turned to the left page (our output).
We worked through a problem together, labeling each step as we went. Students then worked through a couple of problems on their own, underlining each step. Finally, I had the students answer a generalizing question at the bottom of the page.

All in all, this was the smoothest introduction to the order of operations I've ever experienced. Students LOVED the foldable, they LOVED getting to choose the four colors that they would use with intentionality (my word, not theirs :)), and I loved how easily students picked up the idea of doing multiplication and division and then addition and subtraction as they moved from left to right in their expression! :) :)  Success!

Here is the elusive foldable pattern I came up with early this morning.....

PEMDAS Foldable
Just cut out the larger rectangle, cut out the black spaces, and then cut on the dotted lines. Fold the smaller flaps in towards each other and fold the larger flaps across the foldable to the right.

I would love feedback..... If you try the foldable, how did it work for your students? Did you make any changes or modifications that worked well?

Some things I'm wondering.... How can the process be streamlined for my sixth graders (Some of them take forever to cut the foldable and even to write a single sentence!!!) but still keep the educational value intact?  What are the "have to haves" or the "have to do's that I need to keep in the lesson so that my students get that innate sense of the steps (especially MD and AS)? Suggestions? Ideas?


  1. This isn't exactly the type of help you were soliciting, but I would consider doing something much less ink-intensive with the part of the foldable that you're going to cut away. Light gray or just a big X in each section, something like that.

    As for one of the questions you *did* ask: Perhaps if you knew you had say, five students who take much longer than average to cut things out, you could do part of the cutting for them ahead of time. Cut away all the black (gray?) area, for example. Then they've got a little bit of a head start.

    Depending on the dynamics in your classroom you may need to be pretty subtle in passing out the "special" foldables. I find it's generally better to be straightforward about it, even joking with the students, but I teach high school so my students are a little less dependent on positive strokes from me for their emotional well-being, but you'll know what would work for your students, I'm sure.

  2. Steve,
    That's a great idea! I think I was focusing on making sure my sixth graders knew exactly where to cut, but I think a big X would have worked just as well. I'll try that next time.

    You're right; I have to be really careful when differentiating. My students are likely to yell out, "Why does he/she get their's cut for them?" I don't want to embarrass anyone! Still... I need to find ways to do that so the lesson can move at a good pace for everyone. I'll keep working on it! :) Thanks for the suggestions!

  3. "so that my students get that innate sense of the steps"

    What about creating a question for them (situation or word problem) where they can construct their own number equation to represent the situation. Then have them calculate it without knowing anything about PEMDAS.

    hopefully they'll come up with different answers. then it would be a good time to talk about why order of operations make sense -- and that it's not just a term to memorize.

    1. Jimmy, I do that first (before introducing the idea and the foldable) but some students seem to still forget to do all the multiplication and division or the addition and subtraction at the same time. Still trying to figure out why.... The foldable with the flaps for multiplication and division and then for addition and subtraction on the same rows are seeming to help with that...we chose the same colors for each flap because they were on the same row and we do them both as we move from left to right... the kids seemed to buy into it ... we'll see... :)

  4. Thanks for sharing - this is really cool! I like how you designed it with the M and D and A and S on the same row.

  5. I think I'll try this with my kids this year! Thanks!