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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.)
Welcome back to the deep dive. Ready to dive into some algebra? Today, it's all about inequalities. And get this, we're looking at how they pop up in some pretty surprising places.
Speaker 2:And hopefully, we can help some teachers out there rediscover how much fun teaching this stuff can be.
Speaker 1:Absolutely. So listeners, just a heads up. We're getting our inspiration today from a lesson plan designed for teachers.
Speaker 2:Yeah.
Speaker 1:It's all about making any qualities, you know, those greater than, less than symbols relatable.
Speaker 2:Which is a challenge. Let's be real.
Speaker 1:Mhmm. But
Speaker 2:what I think is so smart about this particular lesson plan is that it starts with these everyday scenarios, things students actually experience to show them how relevant this stuff really is.
Speaker 1:And one of those scenarios is, drum roll, please,
Speaker 2:Mhmm.
Speaker 1:An elevator. I told you, surprising places.
Speaker 2:Right. I mean, who knew elevators were so mathematical?
Speaker 1:Right. It's brilliant. And this is where the lesson plan really shines. They use this super relatable example of an elevator with, you know, its weight restrictions, how many people it can hold, to introduce this idea of constraints, basically, limits on what's possible.
Speaker 2:And suddenly, those greater than and less than symbols, they have this real world purpose. We're not just comparing random numbers anymore. We're trying to figure out, like, how many people can actually fit in this elevator.
Speaker 1:It's like, oh, that's why we need inequalities. It finally clicks.
Speaker 2:Exactly. And the lesson plan actually encourages teachers to have their students come up with their own equations, their own inequalities based on this elevator scenario. Like, how much weight can it handle? What if it's kids versus adults?
Speaker 1:So instead of just, like, interpreting someone else's math, they're actually building it themselves. Way more engaging
Speaker 2:product. And as they're figuring that out, they see how these kind of abstract math symbols translate into, like, practical applications.
Speaker 1:Okay. But real talk. Remember how tricky inequalities could be back in the day? Like, there wasn't always one right answer. At least that's how it felt to me.
Speaker 2:Totally. And this lesson plan gets that. It acknowledges that right up front. So for example, some students might write the weight limit of the elevator as, say, w is less than or equal to 1500 kilograms, where w stands for weight.
Speaker 1:Right. Makes sense.
Speaker 2:While other students might flip it and say, 1500 kilograms is greater than or equal to w o. Both are totally right.
Speaker 1:I love that they highlight that. I think that messed me up sometimes. Like, which way to write it?
Speaker 2:It shows that it's about understanding the concept, not just memorizing one specific way to write it down.
Speaker 1:So we've got this elevator, which is already a way more exciting example than I ever got in algebra, but it gets even better. This lesson plan, it also throws in planning a senior bowl.
Speaker 2:Yes. The senior bowl, rife with mathematical possibilities.
Speaker 1:Right. And just like with the elevator, the lesson plan uses this scenario, this whole Senior Bowl thing, to show how inequalities they're everywhere, especially if you're working with a budget.
Speaker 2:Oh, absolutely. Ticket prices, how many chaperones you need, what your profit margin needs to be, like, it's all constraints, all inequalities in disguise.
Speaker 1:And here's where it gets good. The lesson plan guides teachers to use inequalities, like, it is less than or equal to 20 to show the ticket price. And just so everyone's on the same page, that t, that represents the ticket price.
Speaker 2:Yeah. It seems simple, but what it's doing is getting students to connect those symbols, those greater than, less than signs to, like, real world meaning.
Speaker 1:And it gets even more nuanced because then they bring in the chaperone requirement, which involves an inequality with division. They use c is greater than or equal to p divided by 20, where c represents the number of chaperones, and p is the total number of people at the Senior Bowl.
Speaker 2:So smart because now it's not just about comparing two numbers. It's like, how do we take a ratio like chaperones to students and write that mathematically?
Speaker 1:And that's where the magic happens, right, when students see that these aren't just, you know, random math rules. They're actually problem solving tools.
Speaker 2:Yeah. It's like those light bulb moments are the best part of teaching. Yeah. You know?
Speaker 1:Yeah.
Speaker 2:Seeing it click for them.
Speaker 1:Oh, for sure.
Speaker 2:Yeah.
Speaker 1:And speaking of helping things click, this lesson plan, it doesn't just, like, throw these scenarios at you and wish you luck. They've got these awesome notes and guidance for teachers too.
Speaker 2:Oh, yeah. These notes for deep dive presenters. Pure gold. They call out those common mistakes students make with inequalities, and then boom, they give you strategies to address them head on.
Speaker 1:Like, we were talking about how that variable placement can be confusing. Right?
Speaker 2:Yeah.
Speaker 1:Well, the notes actually tell teachers to have students read the inequalities out loud. You know, like, substitute the words for the symbols.
Speaker 2:So simple. But it works. It makes them slow down, really think about what those symbols mean in the problem. Because they might write something down that looks right, but then they say it.
Speaker 1:And they're like, wait a minute. That's not right. If we've got more chaperones, we can have more students, not less.
Speaker 2:Exactly. And that's how those light bulb moments happen. Catching those mistakes out loud helps them get that connection between the symbols and what's actually going on.
Speaker 1:So not only does this lesson plan have these relatable examples, but it also gives teachers, like, actual tools to help their students get through the tough parts.
Speaker 2:It's so well thought out. And I love that because it's not just about teaching inequalities, you know, in isolation. It's about building those bigger mathematical thinking skills, problem solving skills that they can use anywhere.
Speaker 1:And honestly, anything that helps kids not be scared of math is a win in my book.
Speaker 2:A 100%. When students aren't afraid to try things, to make mistakes even, that's when the real learning happens.
Speaker 1:Oh, and speaking of trying things, one thing that really struck me about this lesson plan is that it stresses that there are lots of different ways to look at things, different ways to show things. Like, it's not just about one right answer.
Speaker 2:Right. Which is so true with inequalities because there often isn't just one right answer. There are a bunch of ways to write the same thing.
Speaker 1:Like with that weight limit we were talking about. It's totally cool to write w is less than or equal to 1500 kilograms, or 1500 kilograms is greater than or equal to w. They both work. And these notes, they tell teachers to show all those different ways of writing it to drive that point home that there's some flexibility in math.
Speaker 2:Yeah. And it even goes beyond just showing different ways to write the inequality. They also suggest that teachers encourage students to come up with their own real world scenarios.
Speaker 1:Oh, I love that. So it's not just about following someone else's examples. Now they can get creative and use these ideas in ways that make sense to them.
Speaker 2:Exactly. I mean, the possibilities are endless. Planning a trip with their friends, designing a video game, they could even analyze stats for their favorite sports team.
Speaker 1:That is so cool. It lets them be in charge of their own learning Yeah. Which is, like, the holy grail of teaching. Am I right?
Speaker 2:Totally. When kids are into it, when it matters to them, that's when the learning sticks.
Speaker 1:So let's see. We've talked about how this lesson plan uses real life examples, addresses those common misconceptions, shows how there can be more than one way to write things, and encourages kids to come up with their own problems. That's that's pretty comprehensive. It really is. It's like they've given teachers this whole road map for teaching inequalities from those first moments all the way to helping students use these ideas in their own way.
Speaker 2:And it all comes back to meeting students where they are. Right? Like, not every kid is gonna get excited about math symbols, but everyone can connect with things they experience in their own lives.
Speaker 1:So true. And that's what makes this lesson plan so cool. It doesn't just teach students about inequalities. It gives them the tools to actually use them to understand the world around them.
Speaker 2:And to think, we started with an elevator. I love that. Math is everywhere if you know where to look.
Speaker 1:It really is all connected, isn't it? And this lesson plan does such a good job of showing those connections both for teachers and students.
Speaker 2:A 100%. It reminds us that teaching and learning should be about exploring, discovering new things, and having fun while we're at it.
Speaker 1:Couldn't agree more. So to wrap up our deep dive today, we've seen how a really well designed lesson plan can take something like inequalities, which some people might find intimidating, and turn it into a really engaging and empowering learning experience.
Speaker 2:We talked about how using those relatable real world scenarios combined with some smart teaching strategies can help students really grasp those core concepts. They start to see the power of inequalities and how they can use them to solve problems, not just in math class, but in their own lives.
Speaker 1:And we also saw how something as simple as an elevator ride can actually spark a love of learning. It's all about making those connections between math and our everyday experiences.
Speaker 2:Before we go, we wanna leave you with this. What other everyday things can we use to teach math? What other hidden mathematical gems are out there just waiting to be discovered?
Speaker 1:We love a good challenge. Keep exploring, keep asking questions, and keep diving deep. And a huge thank you to the amazing team at Illustrative Math for the inspiration for today's episode. Until next time.