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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, like, up to your elbows in, like, pizza toppings and party planning? Yeah. We're diving into something today that I think we've all experienced planning a pizza party, but, with a twist. Okay. We're looking at it through the lens of algebra.
Speaker 2:For sure.
Speaker 1:We've gotten our hands on a teacher's guide for a lesson called planning a pizza party.
Speaker 2:Yep.
Speaker 1:And it's part of the illustrative math algebra curriculum.
Speaker 2:Right.
Speaker 1:And, let me tell you, it's way more than just, like, dividing slices and figuring out tips.
Speaker 2:It is.
Speaker 1:Right.
Speaker 2:Yeah. This is really interesting how this lesson uses something as relatable as a pizza party Mhmm. To introduce students to the core concept of mathematical modeling.
Speaker 1:Okay. Mathematical modeling. Yeah. For those of us who maybe mentally checked out during algebra
Speaker 2:Right.
Speaker 1:What are we talking about here?
Speaker 2:So, really, it's all about, like, teaching students to use equations and inequalities to represent real world situations.
Speaker 1:Okay. Yeah.
Speaker 2:You can think that instead of just solving for x Right. They're learning how to translate a real life problem, like planning a party with a budget Mhmm. Into the language of mathematics.
Speaker 1:So it's less about just memorizing formulas and more about applying it to, like, situations that they actually care about.
Speaker 2:Exactly.
Speaker 1:Like pizza.
Speaker 2:Yeah.
Speaker 1:I wish my algebra class was this engaging.
Speaker 2:For sure.
Speaker 1:The guide even starts with a warm up activity. Right?
Speaker 2:It does. Yeah. They ease into it with a simplified scenario.
Speaker 1:Okay.
Speaker 2:So imagine, like, just putting together a simple meal, a main dish, a side or 2.
Speaker 1:Okay.
Speaker 2:The students start by using letters to represent costs.
Speaker 1:Mhmm.
Speaker 2:So, like, m for the main dish.
Speaker 1:So they're, like, dipping their toes into the world of variables without even realizing you're doing algebra. Exactly. Very sneaky. Yeah. Very smart.
Speaker 1:Yeah. So that's like setting the table for the main course Yeah. Which is, of course, the pizza party project.
Speaker 2:And that's where things get really interesting.
Speaker 1:Okay. The students are tasked with planning a real pizza party
Speaker 2:Wow. For their class with a budget, naturally.
Speaker 1:Okay. Now we're talking.
Speaker 2:Right.
Speaker 1:This is where the real life application comes in.
Speaker 2:Yeah.
Speaker 1:Suddenly, they're not just dealing with hypothetical numbers in a textbook. Mhmm.
Speaker 2:They
Speaker 1:need to think about how many students they need to feed.
Speaker 2:Yeah. How many slices per person?
Speaker 1:Maybe even dietary restrictions.
Speaker 2:Of course, that always comes up.
Speaker 1:Right.
Speaker 2:I think about who can have what and all that.
Speaker 1:Yeah. And let's not forget the cost.
Speaker 2:Oh, absolutely.
Speaker 1:It's not just about the price per pizza.
Speaker 2:Right.
Speaker 1:They have to factor in delivery fees
Speaker 2:Mhmm.
Speaker 1:Taxes, all those things that we forget about until we see the final bill.
Speaker 2:All the sneaky little things. Yeah.
Speaker 1:Oh, the the delivery fee always gets me.
Speaker 2:Yes.
Speaker 1:But that's such a good point.
Speaker 2:Yeah.
Speaker 1:It adds a layer of real world complexity that you just don't get from a textbook problem.
Speaker 2:Absolutely. And the guide encourages teachers to really highlight the different approaches that students use to solve these problems.
Speaker 1:Okay.
Speaker 2:Because some students are gonna be comfortable, like, estimating based on their own experiences. Others might go online and look up very specific pricing
Speaker 1:Sure.
Speaker 2:To come up with there.
Speaker 1:That's fantastic. Yeah. It shows that there isn't always one right way to approach a problem.
Speaker 2:Right.
Speaker 1:It encourages flexibility and problem solving.
Speaker 2:For sure.
Speaker 1:Okay. So we've got our pizza party planned. Yes. Our budget is hopefully under control. Right.
Speaker 1:What comes next?
Speaker 2:This is where the lesson introduces the concept of constraints.
Speaker 1:Constraints. Constraints. Yeah. Those fun little limitations that always seem to come up
Speaker 2:Exactly.
Speaker 1:In real life and in algebra too.
Speaker 2:Exactly. Think of it like a maximum budget set by the teacher.
Speaker 1:Okay.
Speaker 2:Or maybe the principal says, alright. Each student can only have 2 slices.
Speaker 1:Oh, so, like, when my budget says I can only order takeout once a week? Precisely. Those kinds of constraints?
Speaker 2:And this is where the students start to see, like, equations and inequalities in action.
Speaker 1:Okay.
Speaker 2:They learn to translate those limits into mathematical statements.
Speaker 1:Oh, okay.
Speaker 2:For example, each person gets fewer than 4 slices becomes the inequality s is less than 4.
Speaker 1:Wow. So they're not just planning a pizza party. They're basically learning to translate their cravings into another language.
Speaker 2:That's a great way to put it.
Speaker 1:It's like algebra for pizza lovers.
Speaker 2:I like it.
Speaker 1:Right.
Speaker 2:Yeah. And just like learning any new language, there are some common, hiccups along the way. Okay. The guide even points out some common misconceptions.
Speaker 1:Knowing students, I bet there are some common stumbling blocks.
Speaker 2:For sure.
Speaker 1:What are some of the misconceptions that teachers should be prepared for?
Speaker 2:Well, one common one is around those constraints.
Speaker 1:Okay.
Speaker 2:Students might see them as more like suggestions.
Speaker 1:Right. Because in a real life pizza party, it's flexible. Right? Exactly. In real life,
Speaker 2:if you go a dollar or 2 over budget
Speaker 1:Right.
Speaker 2:Or someone sneaks an extra slice, it's not the end of the world. Exactly. But in math, those constraints are nonnegotiable.
Speaker 1:Okay. If you
Speaker 2:go over budget even by a dollar, you've arrived at an incorrect solution.
Speaker 1:Interesting.
Speaker 2:So to help students grasp this, the guide recommends using real world examples where the constraints are set in stone.
Speaker 1:Now that you mentioned it, I do recall a few unbreakable rules from my school days.
Speaker 2:Yeah.
Speaker 1:Fire codes for maximum capacity in a room
Speaker 2:Oh, for sure. Or,
Speaker 1:like, a very strict budget set by the principal.
Speaker 2:Absolutely.
Speaker 1:Those are definitely constraints you don't wanna mess with.
Speaker 2:You don't wanna mess with those? No.
Speaker 1:Another area where students tend to trip up is inequalities. Okay. Translating phrases like at least or no more than into the correct mathematical symbols can be tricky. I can see how that would be confusing because it's like the difference between saying I want at least 2 slices of pizza Right. And I want more than 2 slices of pizza.
Speaker 1:They sound similar in conversation Yeah. But have very different meanings in math.
Speaker 2:You got it. Yeah. And to make those abstract symbols more concrete, the guide suggests using number lines.
Speaker 1:Okay.
Speaker 2:Visualizing it helps students grasp the range of numbers that fit the criteria.
Speaker 1:It's amazing how something as simple as a pizza party can open the door to these fundamental math concepts.
Speaker 2:Yeah.
Speaker 1:You know what really stood out to me in the lesson plan is the emphasis on allowing students to explore different approaches.
Speaker 2:Yeah.
Speaker 1:Some might be comfortable estimating
Speaker 2:Right.
Speaker 1:While others might wanna get really precise with online menus and calculators.
Speaker 2:And that's great.
Speaker 1:I love that flexibility.
Speaker 2:It's about meeting students where they are and acknowledging that there isn't always one right way to approach a problem.
Speaker 1:Right.
Speaker 2:Some students thrive on that exactness Yeah.
Speaker 1:Yeah.
Speaker 2:And others excel at that big picture thinking.
Speaker 1:It's so important to recognize those different strengths even in math. Yeah. And this approach encourages them to take ownership over the learning process.
Speaker 2:For sure.
Speaker 1:They're not just being handed formulas. They're making decisions, testing out strategies, and figuring out what works best for them.
Speaker 2:And that's such a valuable skill to develop, not just in math class, but in life in general.
Speaker 1:Right.
Speaker 2:This lesson plan goes beyond teaching equations and inequalities. It equips students with a toolkit for tackling real world problems.
Speaker 1:It's like they're learning to think like mathematicians without even realizing it. It's like we're secretly training up all these pizza loving mathematicians, ready to tackle any real world problem with a slice of pepperoni and a well placed inequality.
Speaker 2:And the best part is this lesson plan is really just the tip of the iceberg.
Speaker 1:Okay.
Speaker 2:You know, it's designed to be a springboard
Speaker 1:for exploring even more complex scenario. So instead of just wrapping things up with the pizza party, teachers could really push their students to apply these skills to other real world situations. Absolutely. What kind of delicious possibilities are we talking about?
Speaker 2:Oh, the possibilities are pretty much endless.
Speaker 1:Okay.
Speaker 2:Imagine adapting this framework to plan a school dance
Speaker 1:Okay.
Speaker 2:A fundraising event, or even just figuring out how to budget an allowance for the month. Mhmm.
Speaker 1:The core principles of that mathematical modeling are all still the same. So it's really cool that they can see how those mathematical concepts aren't confined to textbooks.
Speaker 2:Exactly.
Speaker 1:They're woven into just our everyday lives.
Speaker 2:It really is.
Speaker 1:It's like they're learning to see the matrix, but instead of code, it's all pizza toppings and budget constraints.
Speaker 2:You know what impresses me most about this lesson plan? Is that it really empowers those students.
Speaker 1:Okay.
Speaker 2:They're not just passively absorbing information. Yeah. They're actively engaged in solving a problem that feels relevant to their lives.
Speaker 1:It's a fantastic reminder that sometimes the best learning happens when you don't even realize you're being taught.
Speaker 2:Yeah. Absolutely. That's what makes this approach so powerful.
Speaker 1:Well said. This has been a really insightful deep dive.
Speaker 2:It has.
Speaker 1:I'm ready to grab a slice and brush up on my inequalities. How about you?
Speaker 2:Count me in. It's amazing how a simple topic like a pizza party can unlock all this mathematical thinking.
Speaker 1:A huge thank you to the creators of Illustrative Math for serving up such a creative and engaging lesson plan.
Speaker 2:You're here.
Speaker 1:And to you, dear listener, next time you find yourself planning a gathering, remember the power of math. You might be surprised at just how delicious those equations can be.
Speaker 2:That's right.
Speaker 1:This has been the deep dive. Until next time.