About this Task
Today is the first part of a summative assessment for Unit 3. The task is very similar to the Auto Depreciation, Moore's Law, and Cost of Storing MP3's investigations that students completed over the course of this unit. Kids will follow the same process of research, analysis, presentation, and interpretation that they've followed previously. You can see how students have learned this process by looking at any of the lesson linked above (the Cost of Storing MP3's investigation most closely mirrors what students will do today). The real difference is that today I won't offer as much help, because I want to see how much students can show me on their own.
Here is the handout that students receive. As students arrive, I greet them at the door and provide a copy. I say that they should grab a computer from the laptop cart, and get started right away, and we're rolling. Students will get the data by visiting this link: http://news.yahoo.com/number-active-users-facebook-over-230449748.html, they will plot the points on a graph (either on paper or digitally, although if anyone asks, I recommend using Desmos), they will run linear and exponential regressions on the data, and they will answer some questions in which they interpret the resulting models.
You can see the resulting graph by checking out this "answer key" on Desmos: https://www.desmos.com/calculator/ir7tsqt189.
What I'll Help With
Like I note above, I won't offer too much help today. I do allow students to talk to each other about their work, so I'll pay attention to student conversations - which students are particularly helpful, or which students lean the most on their classmates for help - and account for what I've seen when grade students on their performance.
The only real help I provide is to make sure everyone understands that we're counting months, not years, since December 2004. If students struggle, I'll sketch out the first few rows of a data table on the board. I tell students that whenever they see "End of [Year]" in the data, we can assume that to mean "December [Year]". I also double check to make sure that everyone is recording the number of users in millions.
Beyond that, kids are on their own, and I want to see how far they can go with this!
What I look for When I Assess
I want to assess all students on the process that I've tried to teach over the course of Unit 3. This assignment starts with the basics that I hope everyone can do, and grows gradually more demanding.
It's ok if students don't finish - there's more here than some students can finish in 75 minutes. Again, it's important to observe how students work, in addition to assessing the work they submit. I expect all students to be able to complete #1-13, by collecting the data, finding the regression models and creating a graph. #14-17 are within the grasp of most students: a gentle introduction the idea of piece-wise functions that help me see how comfortable students feel selecting a subset of data, and requiring kids to create precise graphs in which we can distinguish between all four models.
I hope that students get to #18 and #19 (I've debated whether or not these questions should go before #14-17), but if they don't, we might briefly revisit these questions as a group in a subsequent lesson. Finally, #20 is definitely a "Bonus Task," that is satisfying for anyone who gets that far.
Any student who can find and represent the models has certainly acquired "passing" knowledge for this unit. Interpretation is the next level up from that, so students who can give complete and coherent answers to all writing prompts from #1-13 are meeting the standards. Anyone who goes beyond #13 is in the range of meeting and exceeding expectations.
At the end of unit, I hope for students to complete a performance task like the one I've shared here, and a test consisting of multiple choice and open-response problems.
As a tool for creating that more "traditional" exam, I think that Problem Attic is currently the cream of the crop. This free site makes it easy to find questions by topic or browse old assessments from many states. I recommend checking it out. When the math department at my current school sat down to create some common assessments, we found Problem Attic indispensable. I talk a little more about creating exams and how I grade them in this lesson from my Algebra 1 course.
The key thing to remember about any assessment is that everything is formative. Giving a multiple-choice exam just for the sake of it, or as a "gotcha" to students, is not always a good idea. (And, to be fair, the same could be said of a "performance task".) But if we're thoughtful about its preparation and what it tells us, a set of multiple choice questions can be a great way to figure out what our students know and what our next steps should be.
When we use both kinds of assessment at the end of a unit, I think that we get a well-rounded snapshot of what our kids know and can do!