SWBAT improve their mastery of all learning targets, explore extensions into ideas we haven't quite covered, or just finish their work.

I love teaching the binomial distribution - but what happens if there's no time for that?

If you take a look at the previous lesson, you'll see that it's kind of epic. Even with 75-minute periods like the ones I teach, this would be a lot to squeeze into one day. I wanted to share it like that because that's really how I plan. More than writing individual lessons, I think about the learning targets, and the series of activities - whole class, group, and individual - that will help students get there. I prepare these all as one "lesson," ready to teach, but usually take more than one day to get through everything.

I don't think I'm unique in this way, but just wanted to share because I think it works well. In particular, what I like about planning this way is that after each class meeting, I can reconsider how students are doing, and have time to adapt accordingly for the next day.

More generally, at the end of semester, I always find myself reflecting on all that I'd hoped to accomplish vs. what we actually got done. I reflect on that and how I use the time at the end of the semester in this video.

All of that is to say that today is a work period. As the semester winds down, most students will need time to finish the work of this unit. Some will want to dig back into older learning targets from the any of the first three units. Others are caught up with everything and loving it, and for them I have a few "extensions" drawn from some of the good stuff we didn't get to do.

I love these days: my class is an open workshop that runs itself, with students getting what they need from me, helping each other, and trying to finish strong. At any given moment, 25 kids might be working on a dozen different assignments. Online tools like Delta Math and Khan Academy help, but I also keep folders of old work available, and as I describe in the next section of this lesson, I have some extension ideas that are as simple as giving students a prompt and letting them run with it.

With many students finishing their work or mastering earlier learning targets, a few will be ready for some extensions. Keep in mind that kids who are extending what they know don't need many scaffolds -- they're the ones who have gotten everything done up to now. All it takes are a prompt or two, and kids can really run with the ideas. So as I noted in the previous section, I'd hoped to spend more time on expected value and to teach a few lessons about the binomial distribution when I was planning this course. Instead, I use the following approach to set students exploring these ideas independently as part of these differentiated days.

**(Mostly) Independent Investigation of the Binomial Distribution**

- First, I show students how to start Pascal's Triangle. I draw the first three or four rows so they get the idea, and then I say, "Continue until you have at least 10 rows complete, then show me what you've got." When students finish, a quick glance is usually enough (just familiarize yourself with the 10th row) to see how they did. From there, we can trouble-shoot or move on.
- When they're done with that, I say, "Go calculate "5 choose 0" through "5 choose 5" and tell me what you notice." When that's done I ask them to explain what they've seen, and to make some other predictions. Soon enough, I hope they can see that any value in Pascal's Triangle is the value of a combination.
- Next, I'll get them started expanding (x+1)^5. At the very least, students have seen FOIL previously, so now we're just taking it a step further. Again, I ask that everyone comes back to me with observations when they've got 'em!
- Finally a prompt: list all the possible outcomes of flipping a coin 2, 3, 4, and 5 times. Again, what do you notice?
- Note that at every step, the classroom workshop is in full effect. All students - whether remediating, finishing up, or extending - have access to each other and to me. So for any of these prompts, I'm there to answer questions and listen to student ideas. It is truly a joyful experience.

**More on Expected Value**

- Some students really love this topic when they see it for the first time. For anyone who wants to practice or see more applications, Khan Academy is a great place to start. In general, students should know about that site - whether we're talking about remediation or extension, it's a useful tool.
- If students want to go deeper, I simply ask if they've ever watched Deal or No Deal. If they have, I tell them to read this, and report back with their thoughts, questions, and ideas.