One of the many great take-aways from the recent Professional Development day in October was an activity that begins with a clothesline (thanks to Estimation180 and Andrew Stadel). Students are shown an image or given a question and asked to estimate their solution. As the teacher circulates, they ask some students for estimates that they think are too high or too low. Students write these estimates on red (or pink) pieces of paper, and add them to the clothesline. Other students are given green pieces of paper and asked to write an estimate that they think is the correct solution. These are also added to the clothesline.
The result is a collection of numbers that can be used to develop students’ number sense around the magnitude of numbers and proportional reasoning. Inevitably, students will place their numbers on the clothesline in a way that doesn’t accurately depict the relationship between each number. The number talk around how the values can be arranged differently and how we can appropriately space the numbers is a great sense-making activity! The conversation inevitably comes around to the fact that using benchmarks would make the adjustments to the number line much easier to figure out. There were some excellent observations and conversations around what benchmarks would be most useful, and which ones might not be helpful.
I’ve been trying it for the past couple of weeks and have found it really neat how students asked for benchmark numbers at first, and how it’s evolved even in a short time span. In the picture above, my students initially asked for benchmark numbers like 20 and 15 (rather than what I thought would be easiest, 0).
I left it up during class and allowed students to rearrange the numbers thoughout the class if they wanted to… with 10 minutes to spare, one student asked if she could have another benchmark number… she wanted a 30, placed it at the opposite edge of the wall and began rearranging. It was such a GREAT teacher moment to see that she had been thinking about it all class and wanted to make that change!
I will definitely be using Estimation 180 and my surroundings to come up with other images for students to make predictions about. I would like to find some that would have estimates that stretch student’s thinking to other place values (such as the thousands, millions, etc.). Overall this is a great activity with MANY extensions! (In fact, at the conference we were using it to solve equations… it was cool.)