Week 4: The Coordinate Plane

This is a bit delayed because I had the opportunity to head to Annapolis this weekend for one of the STEM Teacher Training events hosted by the US Naval Academy.  If you are involved in STEM teaching, I highly recommend this experience (and probably should blog about it, but...yknow, life).

So, a quick recap of this past week as we began exploring the Coordinate Plane...

Day 1: Creating a Need for Precise Vocabulary

If you haven't used the Polygraph activities by Desmos, you definitely need to incorporate them.  Students play a "Guess Who" type game with a random classmate requiring them to utilize precise vocabulary to determine which of a series of images has been selected via yes/no questions.

I usually start our Coordinate Plane week with Polygraph: Points.  While a few of my students come to me with the vocabulary needed for this topic, many do not.  This game develops the need for precise vocabulary as students discover that words like section, line, and corner result in miscommunication.  I pause periodically throughout the activity so that students can look at the questions their classmates are developing and we can throw in a new term to help us better communicate with our mystery partner.  By the time we log off, we have talked about terms like horizontal, vertical, x-axis, y-axis, quadrant, and even point (rather than dot).  All of this serves to help the notes the next day "stick" a bit better.

Day 2: Measuring Two Things at Once 

and Developing our Vocabulary

Before we start on our notes for the day, I want to start to expose the class to the idea that a coordinate plane is used to measure two variables simultaneously. In their Thinking Space, I give them two minutes to write what they notice from this Emoji Graph from Jo Boaler's Week of Inspiration which I had also posted on our class Instagram the previous night:

Students take turns sharing out their noticings which serve as launching points for some discussions.  The conversation that ensues when they share out varies a bit from class to class.  Several noticed that there were more emojis in the upper right quadrant than any other, so we made note of that.  There is a lot of prompting to recognize that we can read the graph horizontally if we want to look at frequency of use (i.e. "Which emoji do you think gets used the most often?  The least?") and vertically if we want to look at cuteness (i.e. "Which emoji does the creator of the graph think is the cutest? The least").
As a follow-up to our conversations, I posted this image on our Instagram that evening and asked them to comment about their noticings:

I also challenged them to decide on what measures they might use if they were creating such a graph. I am really sorry that it was a short week, because it would've been fun to have them work in groups to try to create graphs of different themes.  If I was teaching Sixth Grade next year, I would definitely incorporate that as a follow-up.
Notes time...
I write the notes under a document reader and do so anew for each class period.  This allows me to pause throughout the notes to check for understanding and often throw a formative assessment question or two at them to complete in their thinking space.  This week's notes were pretty standard.

Day 3: Find the Treasure

Practice Plotting Points

I let students know that fluency with plotting points is going to become incredibly important in their mathematical careers.  We spend our third day playing a variation of Battleship that I call Pirate Treasure Hunt. In previous years, I have launched the class with pirate themed music but the

selections this year sounded more to me like a beer pub so I wasn't feeling it.  Basically, I "hide" a treasure somewhere on my coordinate plane.  As teams, they take turns telling us where to "dig" and I let them know whether or not they have found treasure.
In previous years, I had each of them record the hits/misses on individual dry erase coordinate planes. This year, I gave each team one board and they had to pass it between members for each new dig.  I found that they seemed more engaged as they were checking on each other and I was able to more quickly determine whether they were plotting correctly.
We end class with a brief exit slip so that I can assess their understanding.

Day 4: Revisiting the Two Variable Idea and

Fluency with Point Plotting

We started our day by revisiting the idea that a coordinate plane allows us to measure two different things at the same time (I neglected to use the term variable with them just yet, and I'm second guessing that decision a bit).  We did this by doing an abbreviated exercise using Mathalicious' lesson, Origin Stories.  We rated breakfast foods on the healthiness and deliciousness scales being very careful to always rate healthiness first because that was our x-axis. The objective was to reinforce both the idea that a coordinate plane is using two number lines at once to measure two different things, and the idea that we plot on the x-axis first.  The kids enjoyed the activity and were incredibly animated. As with the Emoji graphs, I would definitely spend a bit more time with this lesson next year if time would allow.
Today was all about  providing them more practice in gaining fluency with point plotting.  In two of my classes, I have the support of a collaborative teacher.  We often use the results of our weekly exit slips to do some differentiation toward the end of the week. Today, one of them was absent so that hindered us a bit. However, in one class, my partner took those whose exit slip performance indicated some confusion and worked more directly with them on practice.  The rest of the students self-differentiated by selecting a graphing points picture by difficulty level and working independently. A little Damien Escobar music and a nice chill day practicing points. I didn't really require them to complete the assignment, just work for the duration of our class period. Several completed the Easy selection and then began working on the Medium difficulty.  Still others asked if it was okay to take it home and keep working on it. Ummmm, yes.

Next Week....Distance on the Coordinate Plane. :)

Week 3: Distance on a Number Line

I realized that it is definitely not sustainable for me to run a 180 blog and juggle the single mom with kids who play sports gig. Something had to give, and I learned long ago how to give myself grace when I need it. I've decided to try to run a #36weeks blog instead. I actually like this idea better anyway because I conceive of my classes in week sections anyway, so it takes the full week of lessons to explore the given topic.

This week was a bit disruptive because there was a family emergency that had me out unexpectedly mid-week which jumbled up the schedule a bit. I had the students work on Moby Max the day I was out and rearranged the rest of the week a bit.  So, I am going to focus on the four days we actually got to interact.

We were working on Distance on a Number Line this week.  In previous years, I have spent a chunk of time working with the students on very basic addition and subtraction of integers. We focused on creating models (number lines and integer counters) to represent it. My reading of the standards, however, seems to suggest that it is meant to be covered in seventh grade. I have decided to stick a bit more exclusively to my standards (or previous years') so that I set a stronger, firmer foundation for what the seventh grade teacher often ends up having to reteach anyway.

As a result, our goal this week was to work on absolute value and how that can be used to help represent distances on a number line.  There were a few misconceptions or weaknesses that tended to arise in our activities:

• Counting intervals rather than spaces on the number line - This tends to manifest during distance on the coordinate plane so I was glad to have the chance to address it early.
• Distance values as negative - This was much trickier to cover last year when I was trying to work on subtraction and distance simultaneously. Sticking to distance more exclusively allowed us to reinforce the idea that distance is always positive, while difference (which they will work on next year) can be negative, while not requiring them to make the distinction in practice yet.
• Naked numbers - We start early with the idea that attending to precision means that we label our values and this was an easy place to start setting that expectation. "The values aren't 7 apart, they are 7 units apart." (or in the case of a few of our tasks...7 degrees or 7 feet)

Day 1: Playing on the Number Line

I found these interactive number lines in a cabinet in my classroom last year:

They have a little skateboard on them, so we modified the Illustrative Mathematics Jumping Flea task to be about Charlie the Skateboarder. I put each of the task questions on a separate slide and we moved through the prompts allowing me time to formatively assess students understanding of movement and spacing on the line.  This activity also introduced the idea of absolute value, which is new to these students.  

The entire activity took around ten minutes or so, warming them up for an application with bigger numbers in the Yummy Math lesson, Extreme Weather. I've used this lesson for several years but have had to modify it greatly for my students, many of whom would be resistant to the amount of reading on the worksheet in its present format. This year, we started by talking about what they had been seeing in the news about Hurricane Harvey. I shared with them some of the latest information I'd been hearing on my way to work. I explained that today we were going to be talking about a different sort of extreme weather and then I started the video that I normally use for a hook here:

From this point, we draw the conversation to weather extremes in the United States.  I ask them to think about which state they think has the highest temperature on record. [Group discussion, share out, record...] Coldest temperature on record. [Group discussion, share out, record...] I then show them the data from Yummy Math and briefly explain how to read the chart. [Pass out laminated chart to groups.]

We talk then about states that have a big range of temperatures and use West Virginia to explore the way we can use a number line to model that range. Because who doesn't like a good 90s hip hop reference. Number lines are gonna make ya...Jump, Jump as we touch again on the idea of absolute value. The most difficult part of the lesson is having them work together to develop a sentence explaining what our distance means in context. The looming bell for the end of class adds a bit of unwelcome pressure to that concluding conversation.

Day 2: Interactive Notebook

It is always surprising to me how much some students love taking notes. I am pretty sure the Flair pen company should be sending me some sort of residual check from the students who weren't content to work with colored pencils and just had to have pens like Ms. Packer's. As I've mentioned before, my INBs are not particularly interactive. Traditional notes on the right which allows us to give formal structure to what we experienced the previous day, and Thinking Space on the left where I can formatively check that they are understanding as we move through the "lecture."  

We wanted to add a students friendly definition of absolute value to our notes, explore some examples of finding distance on a number line, and write equations to represent what we were doing. 

I model the notes on the document projector, pausing to assess their understanding as we go. We sometimes throw a few practice questions over in our Thinking Space.  When we do, I can monitor their responses and solicit members of each team to check on their teammates as well.  In some classes, we finished up with about 3-5 minutes remaining so I used the opportunity to remind them of the resources posted on our class website, which led us to include class with a few moments of Absolute Value Numberballs. I really thought they would be thrown by terms that had a negative sign outside the absolute value bars, but I was quite pleasantly surprised.  <3 div="">

Day 3: State Posters

Instead of a traditional exit slip this week (what I call quizzes in my class), we assess their understanding with the Extreme Weather lesson introduced on Monday.  After our notes, we revisit the task. Teams are given the temperature data. Each student has to choose a state (differing from their other team members) and create a poster that represents the distance between the high and low temperatures in their state.  Their work must include a number line model, some form of an equation to explain their thinking and an explanatory sentence. I haven't graded them yet, but I grabbed a few quick photos of some samples to share:

I always struggle grading things that have a neatness/artistic component to them because I'm not sure whether to ignore it completely or not. I really want to focus exclusively on the mathematics since I am using it as this week's formative assessment, so I will probably not penalize someone for not putting forth effort on the quality. I feel very conflicted about that though.

Day 4: The Scuba Problem

I'm not sure where the Scuba Problem originated, but I've used it in my class for the past few years. I think it might have been a sample question from the Smarter Balance test at one point.  I knew I was going to want students working on the large dry erase boards for it. Typically, that means I would group them in color groups (the colored pencil pouches attached to their desks), but when I encountered this desk of distance cards, I decided to use this as a grouping strategy.

Students were each given a card which led to groups of 3-4 when they found others whose cards represented the same distance on the number line. I then introduced the Scuba Problem (without the associated questions):

In most of my classes [more on that later], we had some time here to Notice and Wonder a bit (very informally...it's a structure I haven't really set up with them) and then work independently in our INB Thinking Space to draw a model of what is happening. They then worked in their groups on the large whiteboards to model the situation and answer the associated questions. In most of the classes, I was pleased with the quality of their work and managed to snag a few photos of them in action:

We ended those classes with a silent Gallery Walk where I encouraged them to look for ideas on how they could've improved their own boards. I posited this question, "If I were to hand you a poster board on your way out of class and ask you to redo this task independently for homework, how many of your found ideas on other boards that you would incorporate into your work?" and the response was almost unanimous. We then took a few moments to offer some specific praise of things we saw, but the time ran out...and we had to clean up and head quickly to the door for High Five Friday.

Double SPL Period

This was my last week to have a double period (two partial periods actually) with my Support for Personalized Learning class before we start Clubs next week. My primary goal with them is to strengthen their confidence with fractions, but I am debating also using this time to explore some Mathalicious lessons relevant to what we are doing in regular class (perhaps Origin Stories next week). This week, however, we continued the routines from last week.  We opened with a quick game of Fraction Math Match and worked through some Fraction Splats.  When the band students left us at the start of the second period, we did some Estimation 180 work and started having more conversation about the spacing choices in their number line models. 

Thorns and Roses

As I mentioned before, we close our week in a Developmental Guidance period where my students share their Thorns and Roses from the week. It is sometimes incredibly personal, often funny, and I thoroughly enjoy my time with them each week. It is, however, private and we stress the importance of us as a family that respects the privacy of what is being shared. So, I don't intend to blog about that each week. I do, however, want to honor the spirit of that experience by ending my blog post with my own Thorn/Roses reflection on the week in my classroom.  

Thorn - I am really struggling in a few of my classes. Especially at the end of the week. They are talkative and off-task in a way that hasn't responded yet to the structures and routines that I've put into place. We are losing a lot of time to redirection and it isn't always effective. The fact that things are going so beautifully in other classes makes the struggle all the more pronounced and I am doing a lot of thinking about how I can turn things around in there and not create an adversarial punishing climate or an overly reward-based system (which is terribly ineffective in eliciting the intrinsic motivation I'm hoping to tap into). I think I need to take some time this week to note some very concrete and specific strategies that I am going to have to be very cognizant of as those class periods begin.

Rose - I am already seeing the kids start to pull the conversations we have as a whole class into their work as groups. I overheard talk about units today, saw a few groups writing equations using absolute value bars, and saw increasing precision on the number line models from conversations that I'd had with some of the kids in SPL. I was also thrilled with how they recognized the idea of the opposite of an absolute value by applying it from what we'd learned last week about ways to interpret a negative symbol. 

Next week....the Coordinate Plane.  Polygraph, anyone???