As students arrive, I tell them that today they'll complete a group quiz on learning target 2.1:
I can represent data with plots on the real number line. This means that I can create dot plots, box plots, and histograms that accurately represent a data set. (S-ID.1)
On an activity like this, where it's my goal to maximize the amount of class time for students to get the work done, I try to organize a series of mini-benchmarks for students to hit as they get started. This allows them to get to work as quickly as they are able. So the first such benchmark is written on the agenda as students arrive: find a group of 3-4 students, then tell me when you've found your group.
When groups confirm that they're formed and ready, I provide one copy of the group quiz. It's a double-sided handout. The first task is simply to write the name of everyone in the group. The second step is for the group to choose the data set that they'd like to use today. Each of the available data sets were generated on the survey that students took two days prior. Every group will work with different data today, and I provide it on a first-come-first-served basis. As each group chooses, they send a member to record their selection on the board, which I've set up like this (and by taking a quick picture of this, I can then remember who is doing what). I then provide one copy of the data for the group, all of which you can see here.
It's great to provide the data like this. When groups choose the data, and when it's from the survey that they completed two days prior, they’re invested. They're curious about the results, and they can't help but make informal conjectures about what the data will show.
As I distribute the data, I tell the class the that the quiz consists of the list of tasks listed on the back of the handout. I say that I've got plenty of graph paper, rulers, and crayons at the ready for anyone who needs them, and that students have the entire period to work together to complete the quiz.
What work time looks like.
I call this assignment a quiz, and I will grade it as evidence of whether or not students have mastered SLT 2.1, but I'm also prepared for it to be a learning experience for many of my students. It's important to go into this class thinking of this as both a formative and summative experience. Groups spend plenty of time working autonomously, but today's class is certainly a hands-on experience for me, with many opportunities to teach key ideas to a few kids at a time.
This is more work than one student can do in one class period, but a group that is focused and familiar with the work we've been doing should be able to get it done in about 30 minutes. In some sections, I don't have to say much at all to get everyone rolling, and in others kids will need a push in the right direction. Part of the challenge here is that I've given just one quiz handout and one data set to each group, because I want them to devise a collaborative plan for sharing that data.
If groups need help devising such a plan, I put up this slide and make a suggestion for how to get started. Every group needs to a make a dot plot and a frequency table. So if one person sets up the dot plot, one person sets up the frequency table and the third person reads the data and checks for errors, this will ensure that those two tasks done and that there are then other "copies" of this data set to be shared among the group.
I also mention that it's not worth it to take time ordering the data, because the dot plot does that for us. I walk around to make this point at each table, and I pay attention to how well each group understands what I'm saying. Part of my informal assessment of my kids is to see if they understand this utility of a dot plot.
Hints I offer.
Each data set is different, and the conversations I have with each group will reflect that. I can count on offering some guidance on how to set up the intervals on a frequency table. For the group who chooses the set of answers to, "What grade would you like to earn in this class?" we'll review the idea - also seen on a Delta Math assignment yesterday - that we're allowed to skip from zero to wherever we'd like on the x-axis, as long as we indicated what we've done.
I also plan to show students how to use a dot plot to calculate mean, which was also touched on in yesterday's Delta Math work, and where the median and quartiles will fall in a list of 99 numbers. I give these notes after students have been working for a while, and I don't make too big of deal out of it. After a few students ask questions that lead towards these hints, I head up the board and say that I've got some notes for anyone who might need them, and I quietly share these ideas.
Hints I don't offer.
On the other hand, I treat this very much like a quiz when it comes to questions that students can answer by referencing their class notes. So if someone asks, "What are the measures of center or spread?", "What are the steps to making a box plot?", "What is a histogram?", or "How do you make a _________?", I tell them to find the answer in their notebooks. That's what the quiz is about, I tell them. I know that students have these in their notes, and I want kids to continue to develop the habit of referencing notes to answer their own questions.
Kids who need the practice can continue to see the role of organization and self-sufficiency. A teacher can say “get organized” ad nauseum, but with some kids, until a need is generated for keeping up with the notes, the work, the handouts, that message is senseless. Now, when kids ask, “what are the measures of center” I can say that someone must have this in their notes. I remind them what we did on Friday, and to find those notes. These notes are simple, straightforward, clear and useful - if only students can find them.
And here's the thing: there’s a thrill to finding the notes. Kids go from being frustrated with me, that I won't just answer their simple question, to being proud that they had the answer all along. It's important to celebrate when students have what they need. This is a formative assessment of more than just the content.
What Kids Are Learning
As I mentioned above, there are different possibilities for conversation with each group of kids, depending on the data set they've chosen, and this is as much a chance to learn as it is to demonstrate mastery. All groups are getting a feel for working with a large set of data.
They're thinking about what is reasonable within their data. Some groups are developing an informal definition for outliers; for example, see how this group decided that they're not going to use certain answers in their dot plot. We won't work on a formal definition for outliers within this five-week stats unit, but tomorrow's lesson will be another chance to consider our options with extreme data points.
In addition to the continued practice at making these plots, this quiz is an opportunity to further develop the ideas of critique and revision. It only take a few moments for me to give some very specific feedback and suggested next steps to each group. I make a big point of not throwing anything away. "If your group made four different box plots, I want you to submit all four, labeled first, second, third and final draft," I say.
It is very likely that some classes will need a second class period to complete this work. One ideal is to collect the quizzes at the end of today's class, then return with brief feedback for day 2. I've seen this work well because students have an easier time digesting my feedback when it's directed at their group rather than the individual. When kids can discuss what I'm saying with each other, they’re processing the feedback.
With five minutes left in class, I ask for everyone's attention so I can explain how to finish up. On the front of the quiz handout, groups should assign grades on SLT 2.1 to each student in the group. Students must justify the grades they're giving in the next column. On the back of the quiz, I tell everyone to make sure that I can see who did what.
I distribute paper clips and remind each group to include all drafts of their work.
I will grade this generously. If all the parts are here and they're correct, I'm quick to give everyone a 4. If one of the three representations is missing, I make that very clear, so I can tell the group that they did great work but that I need too see mastery of the entire learning target.
Moving forward, I'm much more interested in getting students to compare data sets and interpret these graphs. So if I can see evidence that everyone in a group is ready to move on, I'm all about it. If I can see that students still need help here, I'll make a plan for that with individual students as the unit continues.