SWBAT construct number lines that represent different units with attention to scale.

Swapping units can change everything about a data display. Students build their background knowledge on this idea by constructing their own number lines for distance conversions.

5 minutes

Just like we did during one of the work periods last week, this class begins with everyone circling up. As students enter the room, I tell each to leave their stuff at a desk and to join the circle. When the bell rings, I provide the prompt: "What would you like to accomplish today?" I ask for a volunteer to start, then we whip around the circle with everyone answering that question.

This serves a few purposes: first, it's a chance for each student to identify what they'd like to accomplish today. Second, it's a chance for me to hear how each student is doing, and to know where and how I'll need to direct my attention. Third, it's a chance for classmates to hear each other, and to informally gauge their own progress in relation to classmates, and to identify who they may be able to work with as they finish whatever they will today.

After we go around the circle, I say that this period belongs to students for getting done whatever they need to do on the Number Line Project. Parts 3b and 3c are available. Everyone should work to finish whatever they need before the project is due tomorrow. There will not be much time during tomorrow's class to finish the project. We will circle up again at the end of the class for appreciations.

20 minutes

For the last two parts of the project, scaffolds come off entirely. I simply provide the task, and let students decide how they will do it. The thing is, if they've already been successful on everything else, this will be pretty straightforward. And that's precisely what I'm looking for. As kids undertake this final task, I want to see how comfortable they've become with the idea of lines and scale. I watch as they create these number lines. Usually, the only challenge is deciding *what to count by.* In Part 3b, this takes the form of which line to number first: yards, feet, or inches? Which makes it easiest? It seems to me that it's yards, but I don't give that away. If anyone labels feet first, then we can deal with fractions of a yard, and that's great. If anyone labels the inches line by 1's first, then I let them grapple with that, and I've had a few students complete this part successfully. Many would prefer not to use the fractions that such a design choice would necessitate, which gives us the chance to talk about changing initial choices in order to achieve a final goal.

For some students, these tasks provide a low-stress opportunity to review unit conversions. Some kids remember their conversions, others make reference to the back page of a notebook, and some even have smartphone apps for that. I show off Wolfram Alpha (on the high tech end) and a page in their school agendas (on the low). On Part 3c the main questions is of converting from miles to kilometers. The biggest challenge is determining if it's possible to label the integers for each line. What would that entail? Most students end up labeling the miles as integers, then counting by 1.609's on the km line. That's a finer detail that we can deal with later; I let students make their own decisions here, keeping the focus on scale.

5 minutes

Toward the end of today's work time, I circulate and return the patterns quizzes from the start of yesterday's class. Some students have improved their grades from the previous patterns quiz, and some have already lost some of the knowledge (or notes) from two weeks ago. I say, "No matter what your grade is on this quiz, you should keep this in your notebook. You can use these problems to review what you need to know and you can use this next time." For the least successful kids, I frame my responsibility to them: "I haven't been too helpful yet. But I'm going to help you our more next week."

We're still in the "building background knowledge" phase of this class, and whatever has happened so far is precisely what needs to happen in order for my students to understand me and my expectations, and for me to understand them and the skills they bring to the class.

5 minutes

Just as we did at the end of a work period last week, today's class ends with appreciations. I always look forward to doing this for the second time, because it makes more sense and kids dig it more than they did the first time.