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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.)
Ever find yourself looking at, like, a scatterplot of student test scores Mhmm. And you can just tell right away, are they, like, clustered together, or are they, like, confetti exploded all over the place?
Speaker 2:Oh, yeah. We've all been there.
Speaker 1:That, my friend, is variability in action. Yeah. And lucky for us, we're diving deep into a lesson plan today that's all about making that click for students.
Speaker 2:Yeah. We're gonna be tackling lesson 11, comparing and contrasting data distributions from Mathematics.
Speaker 1:Buckle up because they've got menus, math talk, who comes up with these names, kinda love it, and activities designed to make variability, there I say, dot engaging.
Speaker 2:Well, this lesson is really all about moving beyond just memorizing formulas, rote memorization, and really building a visual intuition for variability.
Speaker 1:Which let's be real. That's like a superpower. Right? Imagine a doctor, like, glancing a patient chart for an investor trying to figure out, like, market volatility. That ability to just grasp the spread of data is huge.
Speaker 2:Absolutely. And this lesson kicks off with something that seems kind of simple on the surface. It's called math talk. It's having students mentally calculate the mean of these perfectly symmetrical datasets, like 27, 30, 33.
Speaker 1:Okay. Seems pretty straightforward, but I'm sensing a but coming here.
Speaker 2:You know it. This, like, really basic task. It actually gets students to really understand why the mean works as a balancing point in that symmetrical data. It's not just some magic number. The math really works.
Speaker 1:Love it when that happens. K. So students have, like, flexed their mental math muscles. What's next?
Speaker 2:Time for a game. Well, kind of. The lesson plan calls it a matching activity where students connect these data displays, box plots, dot plots, the whole gangs here, to descriptions like skewed left or symmetrical.
Speaker 1:Sounds fun. But I feel like there's probably some classic misconceptions, you know, lurking in the shadows here ready to trip students up.
Speaker 2:Oh, absolutely. And one of the big ones is thinking that skewed left automatically means most of that data is hanging out over there on the left side of the graph. Ah, yes.
Speaker 1:The old skewed left means data
Speaker 2:on the left trap. I remember,
Speaker 1:you know, I used to always use the example of salaries at a company, you know, where you have a CEO. And even if it's just one data point way out there, that CEO's mega salary is pulling that whole distribution to the right, making it skewed right.
Speaker 2:Perfect example. It just highlights how even one little outlier can kinda throw off the whole game.
Speaker 1:Kinda like that optical illusion where it's like one line can make a whole shape look wonky. You know? Speaking of visual trickery, this lesson plan has an activity called visual variability smackdown. Oh. Okay.
Speaker 1:Are you intrigued yet?
Speaker 2:Oh, yeah. This is a good one. It's like box plots versus dot plots, but instead of, like, you know, actually fighting, they're, showing off, I guess, like, who displays variability the best.
Speaker 1:So let's fight and more, like, let's wow them with our visualization skills, kinda.
Speaker 2:Yeah. Exactly. And so students basically get to be these, like, data detectives. Right? They have to sort sets of plots from the least variable to the most variable, and they do it just by looking at it first, like, eyeballing it, and then they go back and actually, you know, do the calculations with the IQR and LME.
Speaker 1:Yes. IQR and MD are trusty measures of spread. Just in case, you know, someone hasn't had their second cup of coffee yet, can you remind us what those actually tell us about our data? Oh,
Speaker 2:yeah. For sure. So think about it this way. The IQR, that stands for interquartile range, and it's all about the middle ground. Right?
Speaker 2:Like, picture the box part of a box plot. The IQR is, like, how long is that box? The wider that box is, the more spread out those middle values are. And then MAD, which is the mean absolute deviation, that basically tells you the average distance each data point is from the mean.
Speaker 1:Okay. So back to this smack down. The students are like, I think this one's more variable just based on their gut, and then the calculations come in to either be, like, you're right or gotcha. Fooled you, that sneaky outlier.
Speaker 2:Exactly. Exactly. It's a really good way to show them that these formulas that they're learning aren't just these, like, abstract, you know, math things. They show, like, real things, real characteristics about the data.
Speaker 1:Which, you know, brings us to that classic stoopy question of, like, who cares? You know? Like, why do we care about IQR? Why do we care about them Nailies? I can practically hear them saying it now.
Speaker 2:Right. And that's where the lesson plan really shines because it brings in this really fun activity called, wait for it, the menu problem.
Speaker 1:Okay.
Speaker 2:Perfect. So imagine okay. You're a restaurant owner, and you wanna create a menu that has something for everybody. You know? You've got your budget friendly bites, but then you also have your fancy splurge worthy dishes.
Speaker 1:Wait. Now you're speaking my language. Get a menu in front of me, and then let's talk data.
Speaker 2:Exactly. And so the students, they analyze these different menus, and they all have different price distributions. And they use MED and IQR to, you know, tell the restaurant owner which menu actually offers the most variety but still makes sense.
Speaker 1:So it's not even just about calculating a number anymore. It's like understanding what did that number mean for, like, the customer experience. You know, if there's a a high amount on that menu, someone could have some serious sticker shock while another person's like, yes. This is what I'm talking about.
Speaker 2:Exactly. It's like all of a sudden variability. It's not just about formulas. It's about using data to make good choices, like, in a real situation. And, you know, the lesson plan, it doesn't just kinda throw you in the deep end.
Speaker 2:It actually talks about these common misconceptions that students might have, which is so smart, I think.
Speaker 1:Yes. It's like a cheat sheet for potential confusion. Mhmm. And we already talked about the skewed left misunderstanding, but what other, like, mental roadblocks does the lesson plan kinda, like, flag down for us as teachers to look out for?
Speaker 2:I think the other big one is that idea that IQR and math are just formulas. Right? Like, who cares?
Speaker 1:Right. Like, it's just a bunch of numbers. Who
Speaker 2:cares? Exactly. But this lesson plan, it suggests, like, connecting it back to that menu problem. You know?
Speaker 1:It's like, hey. That Mad D value that you just calculated, that could be the difference between a restaurant full of happy customers and one that's, like, totally empty. You know?
Speaker 2:Totally. And what I love about it is it takes something that feels kind of abstract, and it makes it real for them. Like, they're not just learning about statistics. They're learning about how to use data to, like, make good choices.
Speaker 1:Which, let's face it, that's a skill we could all use a little more of these days. Right? Yeah. Now before we wrap up this deep dive into variability, there was this little nugget in the lesson plan that I wanted to make sure we got to. They mentioned something called the five number summary.
Speaker 1:You ever heard of this?
Speaker 2:Oh, yeah. The five number summary, it's like, okay. Think of a box plot. This is like the decoder ring for box plots. It gives you this really quick snapshot of, like, the center of the data, the spread, just the overall shape.
Speaker 1:Okay. I'm listening. I'm intrigued. Break it down for me. What are these five magical numbers?
Speaker 2:Okay. So picture that box plot. Right? The five number summary gives you the values for each of those, like, key points on the box plot. You've got your minimum value, the first quartile that's, like, the bottom of the box.
Speaker 2:Right? Then you've got the medium, that's a line in the middle, then the third quartile, top of the box, and then that maximum value.
Speaker 1:So you're saying in just five numbers, you get this pretty complete picture of how that data is spread out. That's cool.
Speaker 2:Exactly. And what's really neat is you can use that to compare distributions really easily. You can spot outliers. You can even start to see, like, what story is the data telling. You know?
Speaker 1:See, I knew there was a reason why I thought this lesson plan was like a gold mine. We've got games. We've got real world connections. And now we've got this secret code for, like, unlocking even more data insights. I'm feeling a little bit more confident about teaching variability now.
Speaker 1:I'm not gonna lie.
Speaker 2:Me too. And, you know, that's what makes a good lesson plan great. It makes the teacher excited to share that with their students.
Speaker 1:That's such a good point. A huge thank you to the authors of Illustrative Math for this awesome lesson plan.
Speaker 2:Absolutely.
Speaker 1:And to you, dear listener, we wanna leave you with this. What if we embraced variability more? And I don't just mean, like, in our data, but, like, in our lives. What if we look for those differences, you know, those unexpected things? It makes data more fun.
Speaker 1:It might even make life a bit more interesting too. Right? Until next time.