I had the opportunity to work with several K-5 instructional coaches last week during a one-day workshop on increasing student engagement and discourse in the math classroom. (My favorite workshop to lead!) Leadership in the district is making a focused effort to support teachers in their practice of creating classrooms where Math Practice 3 thrives and students are asked to share their thinking and reasoning with others. Creating such lively classrooms often means escaping the confines of a textbook, opening up math lessons to allow for more student choice and voice, anticipating student thinking, and embracing the surprise when they do something unexpectedly brilliant!

In our workshop, we explored ways to use estimation strategies to get all students participating in a conversation using mathematical reasoning. We then graphed our estimations on clotheslines, and that’s when the real magic started to happen! It was an enriching professional experience for all of us, and I’d like to tell you what we learned (and I will in Part 2 of this post). More importantly, I’d love to hear your thoughts on the questions below.

The workshop outcomes that framed the language and the focus for our day:

After grounding the group and framing our work for the day, we launched into an activity that required participants to make an estimate about how many Skittles were in a regular-sized bag. (I had a bag on hand to use as a visual.) Here were the prompts:

Participants wrote each of their estimates on folded sheets of paper. They were then divided into two groups of 4 and asked to do the following:

(A quick aside to say thank you to Andrew Stadel and Chris Shore for sharing their valuable and useful work around estimation and using clotheslines as a way to make number lines more engaging for learners.)

**“…in a way that makes sense to you”** is a phrase that I’m learning to add to many of my questions/prompts, and I’m encouraging teachers and leaders to do the same. The phrase creates an invitation that there is no “right way” but that there might be many sensible ways that could be worth exploring. This phrase invites students of all levels to make meaning for themselves. Compare that to the prompt: “Accurately scale your clothesline and locate your estimates appropriately.” This closed question has only one right answer and is riddled with language and ideas that are important to learn, but in this case, may turn off struggling learners from engaging in thinking and showing what they can do Again, the focus of the workshop was on finding ways to encourage discourse for all learners, and I’m discovering that “in a way that makes sense to you” is a great phrase to use when asking students to explore their thinking with each other.

Here’s what the groups (of 4) did with their estimates.

Group A:

(Note: The group above placed their two 20s and their two 100s on top of each other.)

Group B:

(Note: A “too high” estimate of 300 was written in green and got cut off on the right side.)

I invite you to take a moment to ponder each clothesline because I’m curious to know your thoughts.

What do you notice? What do you wonder?

How do they compare?

What questions could you ask to promote thinking? What further directions would you give the learners? Where would you take this with your students?

In Part 2, I’ll share our insights, wonderings, and the key pieces of learning and growth we made for ourselves as teachers and learners.

I notice that the spacing is not proportional (consistent units on the number line). I wonder if the teachers know that this is an important consideration on the clothesline. I suggest Andrew Stadel’s phrase of “Place, then Space.” Students are encouraged to just get the values in numerical order on the clothesline, then to work on appropriate spacing.

I dig the “Place, then Space” strategy for structuring conversations. Thank you for sharing it with me! Looking back, I could’ve phrased my follow-up directions/ questions so it focused only on the placement of numbers and had that conversation. Maybe “For now, let’s let go of how you spaced these numbers and talk about why you placed them where you did.”

It’s the placement of Group B’s number line that’s the interesting part to me since it makes sense but doesn’t put numbers in order of size.