Sometimes the saying “better to be lucky than good” applies to teaching as well. Today I stumbled across a new routine by little more than blind luck.

Inspired by the sleepy looks on several faces, I interrupted my middle school class with a shout: “Everybody stand up! Head to the back of the room. Make a circle around those two tables.”

At this point, I had no idea what we were going to do. But it was going to be *on our feet *and it was going to *involve everyone*.

On the way to the back of the room, I snagged an empty water bottle. And then…

### Round 1

Holding the plastic bottle in my hands, I announced: “2, 4, 6.” Then I passed the bottle to the student on my right, and gave her no directions.

Her response was beautiful: “2, 4, 6, 8?”

“Nice. But leave off the 2, 4, 6. Just say 8.” We started over. “2, 4, 6.” Then, “8.”

“Alright! Pass it along.”

The next student: “10.”

And with that, the rhythm was established. We went all the way around the circle. And guess what?! Eighth graders can count by twos!

### Round 2

With the bottle back in my hands, I started a new routine: “5, 10, 15.” But then I passed it off to the left. And they rocked this direct variation sequence just as easily as the first round.

### Round 3 (and a surprise!)

“Okay, let’s ramp up the difficulty just a bit. Ready? Here goes: 1, 4, 7.”

I passed the bottle along (back to the right now), and with no hesitation: “10.”

Then followed 13, 16, and 19 without any trouble. And to be honest, much of the progress was smooth, as you’d hope for a group of middle schoolers.

But once every third or fourth student, there was a pause. Not a long one. Not necessarily awkward. Just a pause. And that up-and-to-the-left-as-if-the-answer-is-on-the-ceiling look that means someone is lying (or telling the truth; I can never remember). There was a fair bit of whispering, followed by a shout: “20… 21… 22!” And even some twitching fingers as students accessed old-school strategies for continuing the pattern.

This was magic for me. I’ve only been teaching this group for about three weeks. (It’s a long story.) As such, I don’t know their strengths and weaknesses quite as well as if I’d been their teacher all year. But this simple activity gave me instant insight into the basic number sense skills my students possess.

There was another bonus at the end of this round. We briefly discussed the “starting number” and the “change” (1 and 3, respectively). Since we’ve been rocking linear visual patterns recently, we turned this into the equation y = 1 + 3x rather quickly and moved on. (Assuming that we’re beginning with the *zeroth* term here.)

### Round 4 (another surprise!)

We had time for one more: “5, 9, 13.” I passed the bottle left, and we were off. “17,” “21,” and so forth. But then we hit a snag. Someone forgot the previous numbers. So we invented a new rule: If someone gets stuck, they can ask the previous three people to repeat their numbers. No other hints are allowed.

On track. Off track. Hint. Back on track. And so on until we make it back to the beginning.

### Looking Ahead

I’m excited to try this again next week. I’ve already started thinking about ways to adjust and/or extend:

- Introduce a higher starting number, and/or negative change. (A student actually suggested 10, 8, 6, etc. as we wandered back to our seats.)
- Introduce sequences involving fractions or decimals.
- Invite
*students*to generate the pattern by kicking a round off with their own sequence of three numbers. - Mix things up—and simultaneously encourage more students to focus on each response—so that if a student needs help, I call on a random student to repeat the last 2-3 numbers.

### One More Thing…

I can’t help but think I may be subconsciously ripping off Sadie Estrella’s counting circles here. Whatever the case, I’m excited to see where this routine leads us in the weeks ahead.

If you do something similar with your students, or if you decide to give this a try with your own class, drop a line in the comments so we can benefit from your experience.

And if your name is Sadie and you hail from the lovely state of Hawaii, there’s a special spot in the comments reserved just for you. Let me know what you think!

## Comments 9

We are going to start equations and expressions. This will be a cool activity for my 6th graders.

I’d love to hear how it goes, Frank. Especially if you let your students create their own.

As I was reading I was thinking about Sadie. I like your version as well. Thanks for sharing.

Love it! I could use this when we are studying the unit circle. This be a great way to practice those crazy fractions of pi.

Thanks for sharing. Like you say, these are those magic moments, when teaching is definitely the best job in the world!

I was doing the same thing in 3rd grade a few weeks ago but in small group. I was trying to use patterns that foster algebraic thinking.

One example: we used skip counting by 9 but starting at 3 (3, 12, 21….). As students gave the next number I wrote them down to make the number pattern more accessible. We discussed efficient strategies to add 9 and students described how they’d add 10 to the previous number then subtract 1.

As you begin to dive in to more complex number patterns maybe think about recording the numbers and have students describe their strategy. Kind of like a MathTalk…Just a thought.

Thanks for sharing Michael!

Sounds fun!

Here’s an idea to keep the quickest ones entertained too: Simultaneous contest to predict what number the last student will call out. (Make sure everybody knows how many people will be calling out numbers.)

They could skip-count fast, but probably the winners will be figuring out what f(x) is and then applying it to f(31) or whatever.

Maybe there’s a way to expand this so there’s more than one winner.

I thought of this because my students have trouble making the jump from “y increases by 3 every time” to “this is how y depends on x.”

Author

Julie, thanks for the amazing comment! I love that idea of keeping the quickest students engaged. I might push a little further… Maybe five terms beyond the last student. That way the last student gets to share his/her response, then the rest can call out the “five later” response (maybe on the count of three).

@shouldbequiltin, @mathnerdjet, @mhorley, and @Graham: Thanks for stopping by to read and to comment!