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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 feel like spreadsheets are just rows and columns, you know, just craving to be filled with student boredom?
Speaker 2:Mhmm.
Speaker 1:What if I told you they're actually secret weapons
Speaker 2:Right.
Speaker 1:For unlocking algebra 1? Okay. Today's deep dive is all about turning lesson 8 Alright. Specifically spreadsheet shortcuts
Speaker 2:Yeah.
Speaker 1:Into a smash hit for your classroom.
Speaker 2:That's good.
Speaker 1:So we're diving into algebra 118 lesson teacher guide 2 dot PDF.
Speaker 2:Okay.
Speaker 1:And let me tell you, the curriculum creators were clever with this one.
Speaker 2:Really? How so?
Speaker 1:They use a classic birthday math trick as a hook Oh,
Speaker 2:okay. To
Speaker 1:introduce cell referencing.
Speaker 2:That's a I mean, that's really effective
Speaker 1:Yeah.
Speaker 2:When you think about it.
Speaker 1:It is.
Speaker 2:You ask students to, you know, input their birth month and day
Speaker 1:Right.
Speaker 2:Into this, like, seemingly simple spreadsheet.
Speaker 1:Yeah.
Speaker 2:And unbeknownst to them Yeah. It's carefully crafted formula disguised as a magic trick Right. Uses those inputs to eventually, like, spit out a number Uh-huh. That magically reveals their birth date.
Speaker 1:Okay. That sounds really cool, but how does it actually work?
Speaker 2:So let's imagine a student's birthday is January 5th.
Speaker 1:Uh-huh.
Speaker 2:In cell a one, they input 1 for January.
Speaker 1:Okay.
Speaker 2:In b one, they put 5 for the day. Mhmm. Now the magic unfolds in the formula.
Speaker 1:Okay.
Speaker 2:In cell c 1, you might have something like a 12. Right. In the next cell, d one, you continue the pattern using another formula.
Speaker 1:Okay.
Speaker 2:Let's say c 1+5 and so on. Okay. Each step kinda builds on the previous one. Right?
Speaker 1:Right.
Speaker 2:Yeah. Eventually, including their birth date within the final result.
Speaker 1:So it's not just about that final trick at the end.
Speaker 2:Exactly.
Speaker 1:It's about the students seeing how
Speaker 2:Yeah.
Speaker 1:Changing the values in cells a 1 and b 1 Right. Directly impact that final result.
Speaker 2:It sparks that initial curiosity Yeah. Like a sneak peek into the power of cell referencing.
Speaker 1:Yeah. For sure.
Speaker 2:But the true magic
Speaker 1:Yeah.
Speaker 2:Happens when we transition from this, like, playful trick Right. To a core algebraic concept.
Speaker 1:Okay.
Speaker 2:Equivalent ratios.
Speaker 1:So this is where the lesson shifts Yeah. From just a fun activity That's Right. Powerful learning tool. Right? Absolutely.
Speaker 1:Because instead of just presenting tables of numbers
Speaker 2:Mhmm.
Speaker 1:This lesson has students use a spreadsheet to discover Right. And understand equivalent ratios.
Speaker 2:Think about it.
Speaker 1:Okay.
Speaker 2:In a traditional table
Speaker 1:Mhmm.
Speaker 2:The relationship between those numbers might seem static.
Speaker 1:Yeah.
Speaker 2:But on a spreadsheet Yeah. Students can manipulate those numbers
Speaker 1:Right.
Speaker 2:Change one cell
Speaker 1:Mhmm.
Speaker 2:And instantly see the impact on the others.
Speaker 1:Yes. So they go from Exact. Passive observers to active participants
Speaker 2:Yes.
Speaker 1:In uncovering these mathematical relationships.
Speaker 2:You've hit the nail on the head.
Speaker 1:I like that.
Speaker 2:And the beauty of this approach is it seamlessly integrates technology Right. While still emphasizing Mhmm. The fundamental concepts.
Speaker 1:Yeah.
Speaker 2:For instance k. Students are tasked with
Speaker 1:Yes.
Speaker 2:Finding missing values in a table of equivalent ratios.
Speaker 1:Right.
Speaker 2:So this not only reinforces their understanding of ratios
Speaker 1:Mhmm.
Speaker 2:But also prompts them to kinda decipher the underlying rule.
Speaker 1:Mhmm.
Speaker 2:Connecting those numbers, it's like they're piecing together a puzzle.
Speaker 1:Right.
Speaker 2:But instead of cardboard pieces
Speaker 1:Yeah.
Speaker 2:They're manipulating numbers and formulas. And this sets the
Speaker 1:stage for understanding Yeah. How formulas actually work in a spreadsheet. Right? Exactly. And the guide cleverly highlights Okay.
Speaker 1:A common misconception
Speaker 2:Okay. Students might have about recursive formulas.
Speaker 1:Oh, you mean, like Yeah. The idea that each row builds upon the one before it?
Speaker 2:Exactly.
Speaker 1:Like, instead of always going back to the original starting values
Speaker 2:Right.
Speaker 1:They need to use the results from the previous calculation.
Speaker 2:Precisely. Yeah. It's a subtle Right. But crucial concept.
Speaker 1:Okay.
Speaker 2:And the guide suggests using visual aids
Speaker 1:Okay.
Speaker 2:To help students grasp this.
Speaker 1:Yeah.
Speaker 2:Imagine using, like, color coding or arrows Yeah. To visually link the cells involved in a formula.
Speaker 1:Oh, I see. So Yeah. Instead of just seeing, you know, a string of numbers and symbols Mhmm. They can actually visualize the relationship between the cells. Yeah.
Speaker 1:I can see how that would be a game changer
Speaker 2:Right.
Speaker 1:For visual learners.
Speaker 2:And speaking of visual learning
Speaker 1:Yeah.
Speaker 2:Remember that birthday trick we talked about? Yeah. The guide mentions a digital version of that activity.
Speaker 1:Now that's interesting. Yeah. How does that work?
Speaker 2:Well, in the digital version Okay. Students input their birth date.
Speaker 1:Mhmm.
Speaker 2:And the spreadsheet does the calculations in real time.
Speaker 1:Oh, wow.
Speaker 2:So they can experiment with different birth dates
Speaker 1:Okay.
Speaker 2:And actually see those changes reflected immediately.
Speaker 1:So instead of passively following steps on paper and getting instant feedback. Exactly. I like it. And because the digital version handles, like, the heavy lifting Yeah.
Speaker 2:Calculations Mhmm. Students are free to focus on Yeah. The underlying patterns Right. And the magic of cell references.
Speaker 1:This is reminding me of another key feature of this lesson. Okay. The fill down function.
Speaker 2:Oh, yeah.
Speaker 1:It's like a superpower for spreadsheets.
Speaker 2:It certainly is.
Speaker 1:Like, you can just
Speaker 2:The guide uses another activity Okay. With equivalent ratios Mhmm. To introduce this.
Speaker 1:Okay.
Speaker 2:Imagine this. Students start by, like, writing a formula in one cell
Speaker 1:Yeah.
Speaker 2:And then with a simple, like, drag or click Uh-huh. They can apply that same formula k. To an entire column of cells.
Speaker 1:So it's, like, super, Yeah.
Speaker 2:Incredibly efficient.
Speaker 1:Efficient. Yeah. Right. But I do wonder
Speaker 2:Yeah.
Speaker 1:Could this lead students to make mistakes?
Speaker 2:That's a great point.
Speaker 1:Yeah.
Speaker 2:If they don't fully understand the formula Right. Exactly. They're replicating.
Speaker 1:Right. They're just like, oh, I can just drag this down.
Speaker 2:Yeah. And it underscores the importance of having students engage with Yes. The why behind the formula Yeah. Not just the how.
Speaker 1:Right. Not just the mechanics of it.
Speaker 2:And what's fascinating Uh-huh. The guide acknowledges that students might come up with different
Speaker 1:Okay.
Speaker 2:But equally valid formulas
Speaker 1:Okay.
Speaker 2:To achieve the same result.
Speaker 1:Interesting.
Speaker 2:So some might gravitate towards, you know, a recursive formula, the one that references the previous cell Mhmm. While others might discover an explicit formula
Speaker 1:Right.
Speaker 2:That directly links back to the initial values.
Speaker 1:So it encourages them to find their own kind of problem solving
Speaker 2:Exactly.
Speaker 1:Pathways.
Speaker 2:Yeah. And it reinforces that idea that Yeah. In math, there isn't always a single right way Exactly. To approach a problem.
Speaker 1:I'm curious, though.
Speaker 2:Yeah.
Speaker 1:We keep mentioning recursive formulas.
Speaker 2:Mhmm.
Speaker 1:Can you break down why they're so important Yeah. Absolutely. For students to grasp.
Speaker 2:Recursive formulas are fundamental
Speaker 1:Okay.
Speaker 2:In math, particularly in algebra and beyond. Okay. They form the building blocks for understanding more complex concepts later on.
Speaker 1:Mhmm.
Speaker 2:Like, you'll find students will encounter them time and time again.
Speaker 1:So by mastering them now
Speaker 2:Right.
Speaker 1:They're setting themselves up for success
Speaker 2:Precisely.
Speaker 1:In future math courses.
Speaker 2:And what this lesson does so brilliantly is it makes those formulas Yeah. Tangible and visual. Okay. Students can see how changing one value ripples through the entire spreadsheet.
Speaker 1:Right. Like a domino effect.
Speaker 2:Yeah. Making the concept of recursion less abstract Right. And more concrete.
Speaker 1:So they go from memorizing formulas to truly understanding them.
Speaker 2:Yes. The cause and effect.
Speaker 1:The cause and effect relationships within them.
Speaker 2:This is pure gold.
Speaker 1:This is great.
Speaker 2:And it highlights the true power of spreadsheets as teaching tools.
Speaker 1:Mhmm.
Speaker 2:They're not just about crunching numbers.
Speaker 1:Right.
Speaker 2:They're about making math dynamic and engaging.
Speaker 1:It's about bringing those abstract concepts to life.
Speaker 2:Exactly.
Speaker 1:Speaking of which, the guide emphasizes going beyond the lesson itself.
Speaker 2:Yeah.
Speaker 1:How do they suggest extending the learning?
Speaker 2:Well, they encourage teachers to, you know Yeah. Challenge students to create their own patterns using formulas
Speaker 1:Okay.
Speaker 2:Or even come up with their own spreadsheet math tricks.
Speaker 1:Oh, that's fun.
Speaker 2:Yeah. So it's about giving them the tools
Speaker 1:Right.
Speaker 2:And then empowering them to explore and discover on their own.
Speaker 1:So you could even have them Exactly. Use spreadsheets to you Imagine
Speaker 2:the excitement Yeah. When students realize they can use spreadsheets to model Yes. Real world scenarios.
Speaker 1:So, like, they could calculate the cost of a trip or something?
Speaker 2:Absolutely. Yeah. Or track their favorite sports team stats.
Speaker 1:That's a good idea.
Speaker 2:Or even design a simple video game.
Speaker 1:Like Right. The possibilities are endless.
Speaker 2:The possibilities are truly endless.
Speaker 1:It really opens up a world of possibilities, doesn't it?
Speaker 2:It does.
Speaker 1:Now while we've been, you know, laser focused on the student experience Mhmm. I'm curious about your perspective as an educator. Sure. What, key takeaways
Speaker 2:Yeah.
Speaker 1:Would you offer teachers?
Speaker 2:1st and foremost, I think the guide does an excellent job
Speaker 1:Okay.
Speaker 2:Of anticipating potential pitfalls.
Speaker 1:Like what?
Speaker 2:Like that misconception around recursive formulas.
Speaker 1:Right.
Speaker 2:By highlighting this early on. Yeah. Teachers can address it proactively Mhmm. Perhaps by incorporating those visual aids we discussed.
Speaker 1:Yeah. It's about, like, guiding students toward those moments and minimizing confusion.
Speaker 2:But beyond that Yeah. I'd say the true strength of this lesson Okay. Lies in its adaptability. In what way? While the guide provides a solid framework
Speaker 1:Mhmm.
Speaker 2:Teachers can easily tailor the activities
Speaker 1:Okay.
Speaker 2:To match their students' interests
Speaker 1:Right.
Speaker 2:And learning styles.
Speaker 1:Well, if I have a class that's, you know, super into video games, I could have them create a spreadsheet that Absolutely. Like, tracks character stats or something like that.
Speaker 2:Or if you have a class interested in, like, entrepreneurship Okay. They could model the costs and profits Mhmm. Of a hypothetical business.
Speaker 1:So it's about making those connections between math
Speaker 2:Yes.
Speaker 1:And the real world.
Speaker 2:And the real world and making it meaningful to them.
Speaker 1:It's about showing them that algebra isn't Yeah. Confined to textbooks. It's a tool they can use to understand the world around them.
Speaker 2:Precisely.
Speaker 1:This has been great.
Speaker 2:And that's what makes this lesson so powerful. It's not just about teaching, like spreadsheet mechanics. It's about fostering a deeper understanding Yeah. Of mathematical concepts
Speaker 1:For sure.
Speaker 2:And empowering students to see themselves as mathematicians.
Speaker 1:And who knows? Right. Maybe we'll even spark a lifelong love Yeah. Of spreadsheets in the process.
Speaker 2:Yeah. Wouldn't that be something?
Speaker 1:A big thank you to the authors of Illustrative Math for this insightful lesson.
Speaker 2:Yes. Absolutely.
Speaker 1:So the next time you open up a spreadsheet, remember, it's not just about rows and columns. Right. It's about unlocking patterns.
Speaker 2:It's about making it fun. Yes. It's about making it engaging.
Speaker 1:And empowering your students to see the magic of math.
Speaker 2:Absolutely. Yeah.
Speaker 1:This has been a fascinating deep dive. Until next time.