SWBAT develop some initial ideas about bivariate data. They will also practice working with percentages, which is a prerequisite for an upcoming lesson on relative frequency.

All parts of today's lesson involve the analysis, discussion, and collection of real data from inside and outside the walls of this classroom.

10 minutes

Today's opener is on slides 2 through 5 of today's Prezi. It is a series of true/false statements that indicate some sort of correlation between two variables. Many of them are absurd in some way, although I always include a reasonable one or two.

The idea here is get kids talking, to start a few arguments, and have some fun. The examples I've included here are a place to start, but you may decide to replace these. You can always find examples of dubious correlations by raising the topic at a math department meeting or by doing a quick search online. I usually adapt the examples I use to what I've learned about my students during our first unit. If I can sneak in some inside jokes that will really get them talking, I will.

Also, I decide in the moment how much I want to steer the conversation toward the relationship between correlation and causation. The ice cream sales vs. drowning example is good for this, because the two do correlate pretty well, but neither causes the other. This is always an interesting point to explore with the kids, who often report fun dinner-table conversations following our conversation of that example.

The last one, #7, says, "Students who completed the linear equation exercises on Delta Math improved the most from Linear Practice #1 to Linear Practice #2," which ties this exercise back into our Linear Practice trials from the previous unit.

To summarize, I show a list of all the relationships suggested by these statements (slide #6), and I say that when we answer questions like this, we are making relationships between two sets of data. I introduce the name of Unit 2, "Bivariate Data," and as slide #7 states, that the purpose of this unit is to explore the ways that two different data sets might be related.

30 minutes

One of the background skills that will come in handy over the course of this unit is the ability to work with percentages, and calculating percent change is one way to compare two data sets. The activity here provides students with a chance to review the concepts of percent and percent change, and to analyze how the class improved from Linear Practice #1 to Linear Practice #2. Additionally, "improvement from LP1 to LP2" is a variable that we'd like to be able to compare to Delta Math results in order to see if there's any relationship between those two data sets.

At the top of the handout (LP Analysis Percent Change, and appearing on slides 9 and 10 of today's Prezi), I provide students with brief notes consisting of an example and my favorite informal formula for percent change:

Then, students have time to practice applying this skill. I fill in the table with real results from the Linear Practice exercises for each class, and I've included one example of that here. LP Analysis Percent Change is a worksheet. It's a drill. But it's also a place to think about the behavior of numbers. As students move through this table, for example, they may notice a trend that % change is decreasing. When they do, I ask them why this is happening, and we're able to get at the idea that greater starting values will result in lower percentage changes, even if the amount of change is the same for two students. Ordered practice is an excellent tool for **making sense of structure**.

When it comes to sharing this data with the whole class, be sensitive. Even though the data is anonymous, some students may feel a little uncomfortable with it being public. I think it's important to use real data, however, and I say that this class is about growth. It's an opportunity for me to explain to kids that it doesn't matter where they're coming into my class - I just want everyone to end the semester knowing more than they did in September. This is a powerful message. But still, students are sensitive about looking smart or dumb. So I don't make it about that. It's all about the growth mindset: I want to talk about hard work and the ability to improve. Percent improvement is actually pretty cool, because that kid who only solved 9 equations right the first time can say, hey, I improved by over 100%! (How often does that kid say he got a 100 in math class?)

On the other side of the coin, it's no less impressive what student XXVIII did, even though the % change there is "only" 23%, this student made a pretty dramatic improvement in moving toward a perfect score on LP2.

After ~20-30 minutes, or when most students are done with the exercises, they will check their work when I post the results on an Excel spreadsheet, which motivates the next section of today's class. Please see the "Is there a relationship?" section that follows this one.

10 minutes

15 minutes

As Unit 2 begins, we're getting started on a new project. The mathematical purpose of this project is to **use two-way frequency tables to summarize categorical data (S-ID.B.5)**. Students will use the Part 1 handout, Stuff Part 1 Gathering Data, to collect data on where their stuff comes from. In the next part of the project, they will summarize the data they've collected in a two-way frequency table in which the categories are "Type of Stuff" and "Country of Origin".

The other purpose of this project is to analyze some trends in world trade. I have used this project in collaboration with the Global History teacher at my school, as this is a great opportunity to study geography and the economic reasons behind where our stuff comes from. I explain more about this over the next few lessons.

For now, we need to generate the data. I distribute the handout and I display it on slides 11-13 of today's Prezi. I explain the assignment as follows.

Everyone in the class must find a minimum of 20 items with origin labels. I define four categories of "stuff": Apparel, Electronics, Produce, and Other. I chose the first three categories because these types of items typically have a label with origin that's easy to find. My notes to students for each kind of stuff are on the handout, and I ask for volunteers to read through these descriptions before opening the floor to clarifying questions. Apparel and Electronics rarely present any issues from the class, because they've all seen the "Made In" labels on their clothes and electronics. For Produce, many students are unfamiliar with the "Product of" labels that appear on fruits and vegetables, and some students say that they can't count on having five different fruits and vegetables at home. I tell them that it's fine to go to grocery store and look at five different items with this information. For the "Other" category, I tell students to be creative and see what they can find. I say that toys are often a good place to start, as are books, beverages, and occasionally furniture, but they shouldn't limit themselves in any way. "If you can find the origin information for any of your random stuff, then use it!" I say.

I make a pretty firm point that students must come prepared with this handout completed for our next class, because we're going to use the data. With that in mind, I tell them that they can get started right away by looking at their own shoes and cell phones, and this gives me the chance to circulate for a few minutes and make sure everyone has the right idea. Everyone is usually pretty excited to get going, and soon they're all asking each other for help examining shirt tags so they can add that to the handout.

10 minutes

During today's class, we touched on a variety of topics, all of which lay groundwork for the more coherent narrative that we'll build over the course of the rest of the unit.

To that end, I use today's Exit Slip to gauge where my students are at on both percent change and the idea of correlation. The first problem on the exit slip is straightforward and will tell me which students need further remediation on the idea of percent change. The second prompt is totally open-ended, I look forward to seeing what kind of fun my students might have with it.

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