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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. Welcome back. Ever feel like when your students hear the words compound interest, it's just like instant eye glaze?
Speaker 2:Yeah. It's definitely one of those things that can be tough to make, well, exciting for them.
Speaker 1:Yeah. For sure. So that's why we're doing this deep dive. We're gonna equip you to teach compound interest in a way that really clicks with algebra students. Like, we're talking going way past just the formulas and really digging into, like, how does this actually show up in their
Speaker 2:lives Exactly.
Speaker 1:Ready to break it down.
Speaker 2:Absolutely. Let's, let's jump into this lesson plan.
Speaker 1:Perfect. So the lesson is called different compounding intervals, and it gets into some pretty key stuff like nominal versus effective interest rates.
Speaker 2:And let's be real. That trips up a lot of adults.
Speaker 1:Oh, totally. Totally. But can you imagine giving your students, like, the power to actually avoid some of those financial pitfalls that a lot of us fall into just because they actually get how interest works. That's what I love about this lesson. So where does it start?
Speaker 1:Well, it starts with a really clever warm up
Speaker 2:activity all about equivalent expressions. So they're given these two different expressions, but they actually represent the exact same investment.
Speaker 1:Interesting.
Speaker 2:It's this subtle way to kinda ease them into thinking about how interest is calculated over different periods, you know, like monthly versus annually in this case.
Speaker 1:So it's like they're already building that foundation without realizing it.
Speaker 2:Yeah. Exactly. It's laying the groundwork for that big moment, you know, where they finally get the difference between nominal and effective interest rates.
Speaker 1:Okay. Yes. Break that down for me because I think that's super important. But it can be one of those, like, wait. What?
Speaker 1:Kind of things.
Speaker 2:For sure. For sure. Think of it this way. The nominal rate is like that friend who's always making big promises. Okay.
Speaker 2:It sounds good on paper. Right? It's the advertised rate, but it doesn't tell you the whole story.
Speaker 1:Because it doesn't account for how often that interest is actually calculated.
Speaker 2:You got it. Yeah. And that's where the effective rate comes in. It's the real deal. Like, what are you actually paying, or what are you actually earning after you factor in how often that interest is being compounded?
Speaker 1:And I feel like that's the piece that a lot of people miss, and it can have some real consequences.
Speaker 2:Absolutely. Huge consequences. That's why this lesson dives into, well, a scenario that I think we're all familiar with, credit cards.
Speaker 1:Oh, yeah. That's where those nominal versus effective rates can be brutal.
Speaker 2:Absolutely. Brutal. So they use this example of a credit card with a 24% APR.
Speaker 1:Which sounds, you know, pretty standard.
Speaker 2:Right. Until you realize that it's compounded monthly, and then suddenly
Speaker 1:Suddenly, 24% is not what you thought it was.
Speaker 2:Exactly. And this is where having those visuals can be so helpful.
Speaker 1:Oh, absolutely.
Speaker 2:Seeing those numbers actually climb on a graph month after month as that interest compounds, that can really drive the point home.
Speaker 1:It's one thing to talk about it. It's another thing to see it.
Speaker 2:Exactly. And this lesson goes a step further because it doesn't just explain the problem. It actually encourages teachers to have students build the expressions that represent these real world situations.
Speaker 1:Oh, I like that. So they're not just, you know, passively learning about it. They're actually getting their hands dirty.
Speaker 2:Yes. They're getting hands on. They're analyzing. They're comparing. It's giving them the tools to really understand how these financial scenarios actually play out.
Speaker 1:Which is so perfect for our algebra students because it's taking those core math concepts and making them relevant to their lives.
Speaker 2:And that's actually a perfect segue into what comes next because after they've had that credit card moment, the lesson shifts gears a little bit Mhmm. And starts talking about comparing different investment options.
Speaker 1:Okay.
Speaker 2:And this is where things get really interesting because it's not as simple as just, you know, picking the option with the higher interest rate.
Speaker 1:Right. Because it's not always that simple, is it?
Speaker 2:Not at all. In fact, the lesson gives us example with 2 options, one that has a 3% interest rate that's compounded every 3 months and then another one with a 4% rate, but it's compounded every 4 months.
Speaker 1:So at first glance, you might think, oh, 4%, that's gotta be better.
Speaker 2:Right. Exactly. But and this is the sneaky part. They intentionally leave out one crucial piece of information, the length of the investment. Uh-huh.
Speaker 2:And that's where students can get tripped up if they're not careful because, you know, that 4% might seem better initially. But if that 3% is compounding more frequently
Speaker 1:It could totally catch up or even surpass it.
Speaker 2:Right? Exactly. Especially over a longer period. Yeah. So that's a really important takeaway here.
Speaker 2:It's not just about the interest rate itself. It's about how often that interest is being applied.
Speaker 1:The whole picture. I like it. So how does the lesson kinda nudge them towards that realization?
Speaker 2:Well, it encourages them to actually experiment a bit.
Speaker 1:Right.
Speaker 2:Like, plug in some different numbers for the investment length and see what happens. They might be surprised by the results.
Speaker 1:I love that. So it's like they're becoming financial detectives.
Speaker 2:Right? Exactly. Testing out different scenarios and seeing how those compounding periods can make all the difference.
Speaker 1:Very cool. Now before I move on, I do wanna touch on that optional activity that deals with college tuition increases. Because even though it's optional, it just feels so timely and relevant. You know?
Speaker 2:It's definitely an eye opener. So they use this function that models tuition growing at a rate of 7% per year.
Speaker 1:Which, I mean, 7% on its own might not sound like a ton, but
Speaker 2:But compound that over 4 years of college and then maybe even more for grad school and suddenly
Speaker 1:It starts to feel a little more significant.
Speaker 2:Exactly. And that's exactly what they want students to grasp, the power of compounding, especially over those longer time frames.
Speaker 1:And it seems like this activity goes even beyond the math itself. Right? Like, encouraging students to think critically about what actually drives those tuition increases in the first place.
Speaker 2:Absolutely. It's not just about crunching numbers. Have them consider things like inflation, what's happening with government funding for education, you know, even the demand for certain degrees. It's about connecting those abstract mathematical concepts to what's actually happening in the world. And, you know, that's something I really like about this lesson plan.
Speaker 2:It seems like they were really thoughtful about anticipating those places where students might get stuck. Yeah. And it gives teachers strategies to kinda help them work through it.
Speaker 1:Yeah. It's like they're giving you the map and the compass.
Speaker 2:Exactly. Like, take that whole thing about nominal versus effective interest rates.
Speaker 1:Right.
Speaker 2:They specifically call that out as a prime area for confusion.
Speaker 1:Which makes sense because it can be one of things that's, like, it's a small difference on paper, but then
Speaker 2:Huge implications in the real world. Yeah.
Speaker 1:Huge.
Speaker 2:Yeah. Totally. It's, like, it's one thing to look at a map, and it's another thing to actually, like, have to navigate through a maze.
Speaker 1:Right. But
Speaker 2:one's just giving you a sense of a layout, but the other one, you're really in it. You know? Yeah. And that's where those real world examples become so key.
Speaker 1:Absolutely.
Speaker 2:It's one thing to talk about credit card statements and stuff, but it's another thing to, like, pull up an actual statement or pull up, like, you know, an offer for a loan and be like, alright. Let's dissect this. Let's see where this is.
Speaker 1:It makes it real.
Speaker 2:Yeah. Exactly. Totally.
Speaker 1:Totally. What about that we were talking about that idea where, you know, depending on the time frame, what seems like the better investment option might not actually be the case. It's kind of mind blowing for them, I would think, at that age.
Speaker 2:Totally. And that's why visuals are so powerful. You know? Yeah. Like, actually plotting out those different growth scenarios on a graph so they can see how over time, you know, those lines might intersect or they might diverge depending on how long that money's being invested.
Speaker 2:That's powerful stuff.
Speaker 1:So powerful. Now one other thing that the lesson mentions is that students might struggle with just wrapping their heads around those exponential expressions in general. Like, even once they get the concept Yeah.
Speaker 2:It's a whole other thing to then have to work with the actual expressions. Right?
Speaker 1:Right. It's a lot it's a lot of moving parts.
Speaker 2:Totally. So that's where, you know, it's not just about one thing. It's about making those connections to real world situations. It's about breaking it down step by step. It's about using those visual aids to really support that understanding.
Speaker 1:Staff holding it. Yeah.
Speaker 2:Yeah. Exactly. Because when students feel supported, they're a lot more likely to, you know, lean into that challenge.
Speaker 1:Yeah. Sure. Absolutely. Now one last thing I wanna touch on because I think this is huge is the power of those class discussions.
Speaker 2:Oh, yeah. Absolutely. Some of the best learning happens when they're bouncing ideas off of each other. Right?
Speaker 1:Totally. And the lesson plan specifically calls this out, especially when they're comparing those different investment options.
Speaker 2:Right. Because there's so many layers to it. So just hearing those different perspectives can be so helpful.
Speaker 1:It's like they're teaching each other at that point.
Speaker 2:Yeah. And they're catching those misconceptions that they might have. Or maybe someone's like, oh, I didn't even think about it that way. You know?
Speaker 1:Absolutely. So as we kind of wrap up this deep dive here, I'm hoping that our listeners are walking away feeling like, okay. I can do this. I can make this make sense for my students. It's about so much more than just memorizing formulas.
Speaker 1:Totally. It's about giving them the
Speaker 2:tools, right Yes. To
Speaker 1:actually make those decisions, those smart financial decisions for
Speaker 2:their future. We've explored kind of, like, the ins and outs of how compound interest works. But I think where it really comes alive is when you can connect it to those real world scenarios.
Speaker 1:Yeah.
Speaker 2:And you can see that light bulb go off for your students.
Speaker 1:Absolutely. And for that, a huge thank you to the authors of Illustrative Math for providing the source material for this deep dive.
Speaker 2:Yes. Thank you, Illustrative Math.
Speaker 1:And to all of you listening, keep those learning curves going up. We'll see you next time.