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…
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!
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.
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…
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!