I’m a big fan of Andrew Stadel. If you haven’t checked out his awesome contributions to teaching math, please head on over to his blog, Divisible by 3. For years, I used resources from Estimation180 to get my students estimating and talking math. Last year, I decided to institute a more regular warm-up and cycled Estimation180 into my weekly rotation. Then, Mr. Stadel began stringing clotheslines all over the place as dynamic number lines. For no good reason, I did not string one up in my classroom last year – no clotheslines in China? (yea right) – but came back to the start of this year with a clothesline in my bag.
Talks surrounding Estimation180 have often been rich as students explain their reasoning. I’m a fan of the “too low” and “too high” bounds. I want my students to be able to set these limits. I want them to get the feeling of a range and that they do not have to zero in on a specific number. So, airtime in discussions leans towards setting these bounds, discussing the reasoning involved, and working as a class to develop (or recognize the levels of) confidence in our estimations.
To start this year, I decided to use a clothesline as a way to make the math talk a bit more dynamic.
Here is the flow from my first go – any suggestions / tweaks greatly appreciated!
- Start with the image – students Notice / Wonder to get their minds into the math class. We then bounce a few ideas around as to what we could possibly be getting ready to estimate.
- Individual – students work on a “too high” and a “too low” estimate. A focus is on paying attention to the thoughts and processes involved in setting the bounds.
- Table talk – after each student has made some individual progress, get them talking.
- Group talk – this is where the clothesline comes in
- Too Low – orange cards used to place values on the clothesline. Several students came up and shared.
- Too High – red cards used and again several students placed a value and shared reasoning.
- Table groups then had a few moments to agree upon one “just right” estimate. We just finished a lot of processing so they take it one step farther and decide upon a value that answers the estimate question.
- A group member comes up to place the group’s value on the clothesline. Yellow card tents used this time. No discussion at this point unless it is making observations about the values.
- Check out the actual value and move on…
That was the process yesterday. What did I like about using the clothesline?
- In the past, we had the conversations regarding low and high values but the lack of organization was clear. Students would write a value on the board and talk and it was challenging to visualize the range. Now, we begin to see the distribution of values.
- Developing more number sense – When final values were placed by a class, the value 185 cm was used on multiple occasions. However, these values were not stacked to represent the quantity but lined up to represent each group’s idea. A nice conversation ensued about value.
- Developing a sense of placement and spacing – As values are placed on the clothesline, we can begin talking about keeping a general sense of equal spacing. 10 cm on one end of the number line should represent the same value distribution as on another place on the clothesline.
- Visual Representation – Wow! My lack of organization from last year’s conversations was quite apparent. The clothesline immediately organized and the colors of the number tents allowed us to easily talk of the highs/lows. Maximum and minimum values were easy to discuss. Students can walk the range.
- Shift to students – I felt that more of the focus and attention was placed on students as they walked the number line and explained their reasoning. It is helping me fade to the background!
To improve upon? Time. I am looking for ways to tighten the process up a bit. I like the different colors of number tents to place onto the clothesline and wonder how I can better distribute them to students. Possible idea – provide each table group with a tent of each color (representing too low, too high and actual estimate). The too low and too high values are written first and at the same time a member from each group comes up for “too low”. They have to work together for placement purposes and then give an explanation. Repeat for “too high”. Have a number talk regarding patterns seen and explanations. Final estimates are placed. Other ideas?