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Lesson by lesson podcasts for teachers of Illustrative Mathematics®.
(Based on IM 9-12 Math™ by Illustrative Mathematics®, available at www.illustrativemathematics.org.)
Hey, everyone, and welcome to another deep dive. Today, we're gonna be tackling something that, well, it might sound a little dry at first. We're talking about teaching students about associations in data.
Speaker 2:But trust me, it's way more interesting than it sounds.
Speaker 1:Exactly. This isn't like your average statistics lesson where you're just crunching numbers.
Speaker 2:Right. We're diving into a lesson plan from illustrative mathematics, and it's all about making this concept really click for algebra 1 students.
Speaker 1:And it does it in a really engaging way.
Speaker 2:Yeah. What I really like about this approach is that it focuses on what we call categorical data. So we're not just talking about numbers here. Mhmm. The colors, types of pets, you know, favorite desserts, things students can really, really grab onto.
Speaker 1:I love that. So it's relatable. Okay. So speaking of grabbing onto things, this lesson plan kicks off with an activity called, wait for it, cake or pie. Yum.
Speaker 1:Right? So it uses a table that shows whether people prefer, you guessed it, cake or pie, and then whether those same people are left or right handed. And then get this, students get to play data detective. They calculate percentages to see if there's any link between these two traits. You know?
Speaker 1:Are you more likely to be left handed if you love cake?
Speaker 2:It's a really brilliant way to introduce that idea of relative frequencies without making it too, you know, intimidating.
Speaker 1:Sneak it in there.
Speaker 2:Exactly. But it goes beyond that. See, this activity cleverly sets the stage for a much bigger idea.
Speaker 1:Yeah.
Speaker 2:And that's this. Just because two things show up together, doesn't mean they're actually connected.
Speaker 1:Okay. I see where you're going with this. So it's like saying, just because I wear my lucky socks on quiz day, doesn't mean that's the reason I'm gonna east the test.
Speaker 2:Exactly. And the lesson plan drives this point home with a really kind of a funny example. Car. Car seat color. Now do you really think that the color of your car seats actually influences whether you go back to the dealership for maintenance?
Speaker 1:Probably not, unless maybe if they, like, fade really badly or something, but I get your point.
Speaker 2:Yeah.
Speaker 1:It's about getting students to think critically and not just jump to conclusions based on what they see on the surface.
Speaker 2:Absolutely. And this this is where the lesson plan, it takes a really interesting turn. It actually dives into this real world example using data about coral health and, nitrate concentrations.
Speaker 1:Okay. Now hold on a second. I didn't sign up for marine biology here.
Speaker 2:No. No. No. But this is where those remember those relative frequencies we talked about? This is where they come back into play.
Speaker 1:Okay. So instead of cake or pie, we're talking about healthy coral versus stressed coral.
Speaker 2:Right.
Speaker 1:And instead of left or right handed, it's high versus low nitrate levels.
Speaker 2:Precisely. Students analyze this data using what we call a two way table just like they did with that cake or pie activity. But here's the thing, this time there's a higher chance of a real association. Yeah. And this helps them understand that data analysis isn't about, you know, just proving your assumptions.
Speaker 2:It's about uncovering these potential relationships that might actually be there.
Speaker 1:So it's like they're on a quest for knowledge. They're not just trying to force the data to fit into these preconceived notions they might have. But let's be real. We know students often come to these concepts with some some baggage. Right?
Speaker 2:Oh, absolutely. They have biases. They have misconceptions.
Speaker 1:For sure.
Speaker 2:And the lesson plan is really clever. It actually anticipates this by highlighting these common misconceptions that teachers might encounter.
Speaker 1:Okay. Like what? Give me an example.
Speaker 2:Well, for example, some students, they really struggle with when to compare frequencies in rows versus columns of a table.
Speaker 1:Oh, that's such a classic stumbling block. It's like trying to read a map without understanding which way is north.
Speaker 2:Exactly. Yeah. But here's the great part. Instead of just leaving teachers to fend for themselves, you know, figure it out. Good luck.
Speaker 2:The lesson plan actually provides really clear guidance on how to address that specific misconception.
Speaker 1:It's like it's like this lesson plan is like a treasure map. Right? Yeah. Guiding these teachers around all the common pitfalls and then leading them straight to those moments.
Speaker 2:Exactly. And, you know, here's another gem on that treasure map. It encourages students to actually become data creators themselves.
Speaker 1:Oh, interesting.
Speaker 2:Yeah. So the lesson plan suggests having them come up with their own examples of associated and unassociated variables.
Speaker 1:Okay. Now that sounds like now this sounds like where things could get really fun. So give me an example. What do we talk about here?
Speaker 2:Imagine students exploring whether, like, people who live in certain regions are more likely to enjoy, you know, skiing or, like, if there's a link between owning a saltwater fish tank and decorating it with, like, pirate treasure.
Speaker 1:Okay. Now I'm picturing, like, a fish tank with a little miniature black pearl, like, sailing around.
Speaker 2:Exactly.
Speaker 1:I love that. But, no, seriously, that's such a cool idea, letting them generate their own examples. It's brilliant.
Speaker 2:It is because not only does it encourage, like, deeper thinking, but it also allows them to connect these concepts to their own lives and their own interests. And, you know, speaking of connecting the dots, remember that section in the lesson plan? It's called, are you ready for more?
Speaker 1:Oh, yeah. Yeah. Yeah. The one with the extension activity. Yeah.
Speaker 1:Tell me about that.
Speaker 2:So it dives into this really, I think, relevant example. And it's using data about graduate school debt. And it's comparing universities in California and New York, you know, something a lot of people can relate to, unfortunately.
Speaker 1:Yeah. True. And it gives it gives students a chance to apply what they've learned about associations to, you know, a situation with some real world implications.
Speaker 2:Exactly.
Speaker 1:It's like taking those, you know, those data detective skills they've been they've been working on and, like, sending them out on a real case.
Speaker 2:Right. Exactly.
Speaker 1:But instead of, like, you know, tracking down suspects, they're tracking down trends and patterns and data.
Speaker 2:I love that analogy. That's great. Yeah. Yeah.
Speaker 1:This lesson plan is awesome. We've got relatable activities. We've got real world applications. We've even got this, like, this built in system for tackling those common misconceptions. What more could a teacher ask for?
Speaker 2:Well, I mean, on top of all of that, it provides, like, a a variety of practice problems at the end. So it gives them even more opportunities to apply what they've learned, whether they're just starting to grasp the basics or they're ready to tackle some of those more kind of challenging scenarios.
Speaker 1:It's like a data buffet.
Speaker 2:I like it.
Speaker 1:They can sample a little bit of everything or just load up their plate with extra helpings of whatever they're struggling with. This whole lesson plan, it just it feels like it was designed by teachers for teachers. Like, they really get it.
Speaker 2:They do. And, you know, it reminds us that teaching about associations in data, it's not just about, like, equations and formulas. Right? It's bigger than that. It's about fostering those critical thinking skills
Speaker 1:Mhmm.
Speaker 2:And encouraging students to, like, really question the world around them.
Speaker 1:Yeah. To be curious. Right?
Speaker 2:Exactly. To be curious.
Speaker 1:So so for all those teachers out there who are, like, you know, about to take this lesson plan for a spin, what's, like, the the one the one big takeaway they should keep in mind?
Speaker 2:I think it's it's crucial to remember that this is about, like, empowering those students to become, like you said earlier, those data detectives. Right?
Speaker 1:I love that.
Speaker 2:So encourage them to approach data with this, like curious mind, always asking themselves, okay. Could there be a connection here? Yeah. You know? It's about it's about nurturing that sense of wonder while also emphasizing just how important careful analysis is.
Speaker 1:Oh, I love that. It's like we're sending them off on this data expedition, right, armed with all the tools and the mindset to uncover these meaningful patterns and these insights.
Speaker 2:Precisely. And and remember, data, it's everywhere.
Speaker 1:It really is.
Speaker 2:So once they start to see the world through this lens, I mean, who knows what they'll find? They'll start to see connections and potential associations in the most unexpected places.
Speaker 1:That is such a powerful thought. I love that. Well said. And on that note, a huge, huge thank you to the creators of Illustrative Math for developing this incredible resource for teachers. And to all of you listening, thank you so much for joining us on this deep dive into the world of data and associations.
Speaker 1:We hope you've learned a lot and that you feel, you know, inspired to go out there and keep exploring these fascinating patterns all around us.