Opening with Estimation180 on a clothesline

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.

FullSizeRender

Here is the flow from my first go – any suggestions / tweaks greatly appreciated!

  1. 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.
  2. 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.
  3. Table talk – after each student has made some individual progress, get them talking.
  4. Group talk – this is where the clothesline comes in
    1. Too Low – orange cards used to place values on the clothesline. Several students came up and shared.
    2. Too High – red cards used and again several students placed a value and shared reasoning.
    3. 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.
    4. 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.
    5. 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?

Fav -Class Start

unnamed

A favorite is when students walked into class and immediately began thinking and talking about mathematics. This year, I decided to kick-off the start of each class with a rotation touching on the mathematical practices. Tied to the current unit? Maybe, but not necessarily.

How much time? Well, it’s slowly been increasing as connections back to past or current topics become more apparent (funny how this increases the more it is practiced). Perfected? Nope, some days are magical and others not so much.

The Rotation

  • Monday – Graphing Stories
  • Tuesday – Visual Patterns
  • Wednesday – Estimation 180
  • Thursday – Math Talks
  • Friday – Reflection

The schedule at my school pretends to be a block (class length ranges from 60 to 80 minutes). So, I see students for math every other day and it takes two weeks to get through a rotation.

This post is a bit long as I attempt to lay out the flow of how these warm-ups take place. The first three days have a pretty good feel to them. Thursday Math Talks are the newest for me and need the most work. Friday Reflections seem a bit standard and good likely use an injection of inspiration. All of the days are a work in progress and have changed since the year began. With that in mind, any feedback on how to improve or suggestions to try is greatly appreciated.

Monday – Graphing Stories

A big thanks to Dan Meyer and others who put this project together. This awesome site has a collection of 15 second videos of an action. Students graph the action.

IMG_0329

Students come in and open their notebooks to the graphing story page. First, a quick What do you notice? What do you wonder? Then, what action do you think we will be graphing?  Time is always on the horizontal axis and we discuss what will be on the vertical axis and what units will be likely. Funny, how often this is prefaced with a reminder that most videos were created in the States. Yep, that means “feet”.

Begin watching. The videos are set up to run once (15 seconds) at normal speed and then again at half speed before providing a solution. We watch the normal and the half. Stop.

Students talk for 3-5 minutes in their table groups, come up with a “sketch” of the graph and determine areas of focus for the next viewing. They know that we will again watch the half speed section. At the end of this time, students share out. This has varied:

  • What do you notice? I’ve recently begun adding this in to the graphing stories. Students often struggle with the y-intercept. Where does the graph start? Before, this came out through groans as the solution was presented or by individual checks. Adding this step of each table sharing one “notice” brings it out from the students.
  • What do you wonder? This is the focus that students will have for their second viewing. I like shifting to this question versus “What will you look for?” as it feels as if the question opens the frame for students. Again, each table group shares out and if we get repeats, great.

Rewatch the half speed segment.

2 minutes – get a line on your graph. They are free to chat but after a quick burst, the class often gets quiet.

A few solutions – a couple of volunteers come up to the SmartBoard to put down their graphs. Three colors is the max for this. When we play the final moments of the video, the solution is drawn between the student lines.

IMG_0461 3

Solution – Students use a different color to draw in the solution to distinguish from their own.

That’s it. Unless, and this is when magic begins, the students don’t agree with the solution. We go down that lane. Talk it up. Convince us that your solution is a better description of the action.

Tuesday – Visual Patterns 

A big thanks to Fawn Nguyen and others for putting together this awesome site of patterns! There are many patterns and some great ideas to get going. For this, I like to print out a copy of the pattern for each student. They mark the sheet up!

Screen Shot 2016-01-20 at 3.57.50 AM

Students get the page into their notebook and begin working. Talk at the beginning is often minimal as students process the pattern on their own. The talk steadily builds as they make progress and start trying out ideas. I ask them to draw in the next figure as well as what could possibly be Figure 0.

One of the goals of this activity is for students to work in multiple representations to build connections between graphs, tables and equations while also reinforcing skills such as table set-up and graph design. Wait, the scale has to have an equal increment? 

The various ways that students approach patterns is fascinating. The check provided on the patterns page is Pattern #43. When two students reach a solution but have different equations it’s great hearing them talk when asked, do you have the same equation as G? They get down to it, break apart their solutions, talk about equations and then realize that yes, they have similar equations.

IMG_0300

For the 7th graders, the concept of variable is still developing for many and having this ongoing, yearly work with variable slowly builds familiarity. At the end of the first semester, most are now comfortable with having “n” placed into their table after the first few numbers (0, 1, 2, 3, 4, 5, n).

This warm-up is a bit more time intensive. Students work at their own pace as some can quickly see patterns and others take more time to get started and make various representations. Some need hints though a nice thing about having this on a regular cycle is that students have other patterns to refer back to. They are also increasing their ability to recognize patterns.

Wednesday – Estimation 180

Another big thanks to those putting out amazing resources for the math community. This time, it’s to Andrew Stadel for the Estimation180 site. This began as a quick warm-up activity. Students came in to see the image on the screen and quickly start thinking about their estimates. As with the other “warm-ups,” the value of estimations as a doorway to lots of math creeped in more and more now it takes a solid block. The presentation is a bit different as well:

IMG_0469

  1. Bring in the What do you notice? What do you wonder? framework. We start slowly. Students see the image and we talk about the things we notice. Then, what do you wonder? This is starting to edge us closer to the estimation.
  2. The next question for the students – What do you think we will be estimating today? Most of the time, this question has already come up though a curve ball was recently thrown to them as I worked in negative numbers.
  3. Now, we get into the estimation framework – What’s an estimate that you think is too high?   What’s an estimate that you think is too low?   Students are off and thinking. Our focus on the too high / too low is to begin developing a range of their estimates. “What is reasonable for you? How is your confidence of the estimation related to the range of your too high/too low?”
  4. We share with lots of questions. This is a great opportunity to review. “Explain how you got to that point…What does that mean?” Now, as a class we have a range. Sometimes it’s quite wide and others fairly tight.
  5. A few more minutes for students to get their just right estimate.
  6. We share and talk some more with students giving explanations as to how they arrived at their estimate.
  7. Show the actual amount to (often) cheers and (sometimes) groans.

Thursday – Math Talks

 

This is the “day” where I would love feedback. My goal is to get students talking. I want students to realize the difference in the ways each other think. I like that students are opened up to different ways of solving problems.

A few resources that I’m looking at:

I’m not quite sure what happens on Thursday and I’m afraid to say that we often hop into other activities without having a good number talk. Again, suggestions…

Friday – Reflection

Students need time to look back over their math and think about their progress. Reflections are used to also strengthen the connection to the mathematical practices. Questions may revolve around a problem of the week and asks students to write about a mathematical practice they used. This is also a bit in development and suggestions would be great!