# Let the students show the way (spreadsheets to Desmos)

Recently, I posted about the CER structure that I was starting to use more with my 7th graders in science. There, time was spent on representing evidence from multiple trials as well as different measures of center. I wondered about the use of Desmos in creating graphs. The goal is for students to be able to quickly create graphical displays so that the bulk of their time is spent discussing patterns within their evidence. Honestly, I hadn’t poked around in Desmos enough recently to know if it would be challenging or not. Graphing in Excel/gSheets often opens up the destructive side of me as it is quite cumbersome to make and modify graphs (at least at my skill level).

Today, students were finishing up assessments and and I tasked them with getting into Desmos and graphing the data they had recently done by hand. The goal was to explore, learn skills, reproduce the graph and then share out if it is possible.

Students got to cracking! I had them work individually to both allow for quiet in order for others to finish up assessments and to also allow for each student’s creativity in finding a solution. They were quite resourceful. Some began by putting in individual points. Others typed in entire tables. I nudged to find a way to copy and paste from the data in the spreadsheet. (I’m fully onboard in the power of spreadsheets to analyze data – I just can’t get the displays I want without frustration.) They reported back that they had. Entire tables can be copied from a spreadsheet and pasted into Desmos! Yeah! That’s quick! However, we had to do some restructuring of tables to make better meaning.

The trials and averages went into two different Desmos tables so that the formatting could be differentiated.

Desmos Graph

Desmos Tip from students: Holding down on the color in the table provides extra options such as adding in a line between points if that is desired.

By the end of class, students were telling me that they were quite comfortable bringing tables into Desmos and then creating a graphical display. Desmos Tip: The wrench in the top right corner allows labels to be put on each axis as well as adjusting the scale.

So, I’m pretty excited both in having a potential system to make graphical displays and with the reward of putting my trust in the students. They could and did dive into the Desmos and finished by increasing the understanding of our community.

# Fav -Class Start

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.

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.

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!

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.

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:

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!