Order of Operations Activity

29

August 10, 2012 by ray_emily

Last week for #MyFavFriday, I wrote about a totally silly non-academic game. This week, I want to share a game that I like lots, which actually has some academic substance. I’m honestly not sure if I thought up this activity on my own, or stole it from someone along the way. I am tempted to say that I devised this activity, myself, but … who knows.  (Please do let me know if it’s yours.) Also: Apologies, in advance, for the terrible photo quality. Going to need to work on that, I suppose. Hopefully you get the idea, anyway.

And, without further ado, THE ORDER OF OPERATIONS GAME!

The set-up:
My classroom has five tables, each of which seats five kids. I pass one laminated strip, like so, to each table. (All of the strips are exactly identical.)

Each table also gets an envelope with the following pieces:

[Update, 8/27/12: The one and only @jreulbach created a characteristically well-designed version of the game pieces that you see above. Check them out (download either the Word doc or PDF) and steal them! Now you’re set!]

How it works:
You start the game by calling out a number. (You will need to plan which numbers to call out — or feel free to use mine.)

So, let’s say you shout out, “77!”

Kids immediately start scurrying and scratchworking and talking and debating. (Their goal, if you hadn’t gathered, is to correctly place the operational symbols, and maybe some exponents, on the strip so that the numbers equal 77.) There is a frenetic, excited energy in the room: three points will go to the first team to get to 77! Second place earns your team two points, and third place gets you one point.

I weave around the room and eavesdrop.

Kid #1: “Let’s put the plus sign there!”
Kid #2: “Okay! So now we’re at 20. What next?”
Kid #1: “Umm…. we could… subtract?”
Kid #3: “Oooh, I know. Multiply by four–”
Kid #4: “Yeah, yeah! Multiply by four, then get rid of the three, and…”

Kid #5: “Yes, we got it!!!  OOOOH, ooh, pleasepleeeeaasecomecheckours!” (Hands wave wildly.)

They beam, proudly looking over their work as I head in their direction.

Suddenly–

Kid #5: “No… WAIT! Not yet!”

I shrug and head to another table. They join heads.

Kid #5: “We need to make it so the adding happens before we multiply,” I overhear.

Kid #1 eagerly retrieves the parentheses, and Kid #2 positions them around 18 + 2.

And, the hands go shooting into the air, for a second time. All around, groups of students are sharing similar exchanges—working together, working backwards, guessing and checking, arguing, persevering.

After a few minutes, the three winners have been established. I then write “18   2   4   3” on the board, and call up a student to fill in the holes. We talk about the wrong answers that they produced, and analyze what exactly caused the derailments. Error analysis melds with strategizing to do better next time melds with collaboration melds with total awesomeness.

… and then, we do it again!

Other stray thoughts and suggestions:
– “Let’s put the plus sign there,” and other similarly low-risk suggestions, offer a non-intimidating way for less confident kiddos to get involved. Finding a point of entry is simple (there are so many possibilities!), which means that this activity is welcoming to students of all ability levels.
– Make sure your kids know that as soon as you award them their points, they need to quickly remove the operational symbols that they’ve laid down. (Other teams will look; they won’t be able to resist.)
– If you have a class of eager beavers—kids so desperate to earn their points that they fail to stop and think and double-check—you can dock one point for a wrong answer, or require that everyone work for a minimum amount of time before summoning you.
– It amuses me, a little, that the kids get all worked up. I do not offer any sort of prize, but I think the competitive element spices things up a little bit. (It is probably not necessary, though, to tell the truth.)
– Encourage your kids to keep out a paper and pencil to test out their possible solutions. (An added bonus, which students generally fail to discover, is that occasionally, the wrong solution from early in the game is in fact a winning solution, later on.)
– There are many opportunities for easy differentiation. If I’ve got a group of kids that is not totally solid on applying the order of operations, I will tell them which three of the four operational symbols are needed for each problem. They still, of course, need to determine the correct order.  If kids are getting it and digging the activity, I will not tell them which symbols to use.  This increases the level of difficulty considerably.
– I start out with problems that do not require parentheses and exponents, and work my way to those that do, depending on kids’ success rates.

P.S. I am decidedly not crafty. For several years running, my kids received raggedy sheets of legal paper (with the numbers on them) and little pieces of chopped up note card (with the symbols) in wrinkly, worn-out plastic bags, when it was time to play this game. My desire to share this activity here compelled me, at last, to laminate those suckers. (I had to make a new set, of course. Mine had taken a beating.) I’m going to attempt be better about that, this year. (Something to add to my list of goals, I suppose.) I’ve developed enough games that I want to have on hand, that aren’t dingy and depressing and shame-inducing, that I think it’s time for me to step it up.