{
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  "segments": [
    {
      "speaker": "Speaker 1",
      "startTime": "0.08",
      "endTime": "5.46",
      "body": "Okay. So today, we are diving into Yeah. Percentage change."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "5.68",
      "endTime": "6.08",
      "body": "Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "6.08",
      "endTime": "10.639999",
      "body": "And this is something that I think Yeah. We probably all have to deal with at"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "10.639999",
      "endTime": "10.96",
      "body": "some point"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "10.96",
      "endTime": "11.36",
      "body": "in our lives."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "11.5199995",
      "endTime": "12.32",
      "body": "A lot of the time."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "12.32",
      "endTime": "18.975",
      "body": "Whether it's sales or taxes or tips or whatever. It's like these percentages are always floating around out there."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "18.975",
      "endTime": "19.375",
      "body": "Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "19.375",
      "endTime": "27.635",
      "body": "But, I think what's really interesting is that there's, like, a lot more really interesting math Absolutely. Behind the scenes of all those percentages."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "27.855",
      "endTime": "28.355",
      "body": "Absolutely."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "28.575",
      "endTime": "31.929998",
      "body": "So today, we're gonna be looking at a lesson plan"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "32.09",
      "endTime": "32.29",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "32.489998",
      "endTime": "33.79",
      "body": "That's designed for teachers."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "33.93",
      "endTime": "34.43",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "35.37",
      "endTime": "40.809998",
      "body": "But I think, honestly, this is something that, like, anybody can get something out of."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "40.809998",
      "endTime": "41.309998",
      "body": "Absolutely."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "41.69",
      "endTime": "44.805",
      "body": "And it's called recalling percent Change."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "45.185",
      "endTime": "46.785",
      "body": "Recalling Percent Change. Okay. Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "46.785",
      "endTime": "49.105",
      "body": "I like it. So what I think is so cool about this"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "49.345",
      "endTime": "49.505",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "49.665",
      "endTime": "56.305",
      "body": "Is that it, like, really breaks down all these, like Totally. Core concepts in a way that, like, makes it make sense."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "56.305",
      "endTime": "65.25",
      "body": "That's the key. Yeah. You know? I think so often people get caught up in, like, just trying to get the answers, and they don't understand, like, why Right. Why they're doing what"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "65.25",
      "endTime": "66.31",
      "body": "they're doing. Exactly."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "66.93",
      "endTime": "70.85",
      "body": "And so I think this lesson does a really nice job of breaking that down."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "70.85",
      "endTime": "76.415",
      "body": "Yeah. And it's not just about, like Right. How to calculate. Like, here's how you get a percentage."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "76.555",
      "endTime": "76.955",
      "body": "Yeah. Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "76.955",
      "endTime": "79.195",
      "body": "But it's, like, why that matters and, like"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "79.435",
      "endTime": "80.955",
      "body": "Why does it matter? What are the implications?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "80.955",
      "endTime": "84.235",
      "body": "Right. Exactly. Like, where do we even see this in the real world?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "84.235",
      "endTime": "85.055",
      "body": "Totally. Totally."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "85.115",
      "endTime": "87.675",
      "body": "And they actually have in this lesson plan"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "87.995",
      "endTime": "88.395",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "88.462494",
      "endTime": "98.15",
      "body": "All these different activities that cover, like, everything from, like, the price of scooters Just to, like, the mysteries of exponential growth."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "98.21",
      "endTime": "99.67",
      "body": "Right. I'm in. I'm in."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "100.21",
      "endTime": "100.93",
      "body": "So it's like"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "101.17",
      "endTime": "101.49",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "101.49",
      "endTime": "109.985",
      "body": "It runs the gamut. So our mission today is to kind of Okay. I don't know. Crack the code Yeah. Of these percentage changes"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "110.145004",
      "endTime": "110.545",
      "body": "I love that."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "110.625",
      "endTime": "115.045",
      "body": "And hopefully give you guys listening. Moment. Some"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "115.665",
      "endTime": "116.145004",
      "body": "I like it."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "116.145004",
      "endTime": "116.885",
      "body": "Yeah. Exactly."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "117.025",
      "endTime": "117.345",
      "body": "So good."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "117.345",
      "endTime": "119.75",
      "body": "So they start off with this activity called wheels."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "119.89",
      "endTime": "120.53",
      "body": "Wheels. Okay."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "120.53",
      "endTime": "124.39",
      "body": "And they're like, okay. Picture this. You're in the market for a new scooter."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "124.450005",
      "endTime": "124.950005",
      "body": "Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "125.25",
      "endTime": "128.07",
      "body": "And you find one for a $160."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "129.57",
      "endTime": "130.55",
      "body": "Okay. A $160."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "131.33",
      "endTime": "136.025",
      "body": "But then you see this bike that you like Mhmm. And it's 20% more expensive than the scooter."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "136.025",
      "endTime": "136.50499",
      "body": "Gotcha."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "136.50499",
      "endTime": "137.94499",
      "body": "So the question is"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "138.185",
      "endTime": "138.50499",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "138.58499",
      "endTime": "141.94499",
      "body": "How do we figure out the price of that bike?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "141.94499",
      "endTime": "148.025",
      "body": "Okay. So, I mean, the intuitive way to do that would be to just take 20% of the 160 and add that on."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "148.025",
      "endTime": "149.13",
      "body": "Right? Right. Exactly."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "149.13",
      "endTime": "152.01001",
      "body": "But I'm guessing this lesson is gonna give us some sort of, like"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "152.89",
      "endTime": "154.57",
      "body": "Well, so they shortcut? Or"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "154.97",
      "endTime": "156.73001",
      "body": "They do that, but then they're like Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "156.73001",
      "endTime": "159.39",
      "body": "But, also You could just multiply it by 1.2."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "159.69",
      "endTime": "160.635",
      "body": "Okay. There we go."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "160.955",
      "endTime": "166.655",
      "body": "And I'll be honest. If I were, like, on the fly trying to figure this out Yeah. Yeah. I would 100%."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "167.03499",
      "endTime": "168.39499",
      "body": "For sure. Add and subtract."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "168.39499",
      "endTime": "169.19499",
      "body": "Add and subtract."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "169.19499",
      "endTime": "169.69499",
      "body": "Totally."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "170.155",
      "endTime": "175.05",
      "body": "But I guess my question is, like Yeah. Why is this multiplication thing"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "175.29",
      "endTime": "177.45",
      "body": "Why is that important? Why do we care?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "177.45",
      "endTime": "178.49",
      "body": "Why do we care?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "178.49",
      "endTime": "179.85",
      "body": "Besides just speed. Right?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "179.85",
      "endTime": "183.45",
      "body": "Besides just speed. Right? Like, why is this important at all?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "183.45",
      "endTime": "184.17",
      "body": "Right. Right. Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "184.17",
      "endTime": "188.875",
      "body": "And what they say is that, like, it all has to do with this distributive property."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "188.935",
      "endTime": "190.615",
      "body": "Okay. The distributive property. Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "190.615",
      "endTime": "198.55501",
      "body": "So, basically, instead of adding that 20%, we can just multiply that scooter price by 1.20."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "198.935",
      "endTime": "201.41501",
      "body": "By 1.20 and get that bike price directly."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "201.41501",
      "endTime": "201.96",
      "body": "Right. Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "202.44",
      "endTime": "203.48001",
      "body": "So I get that."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "203.48001",
      "endTime": "206.94",
      "body": "Yeah. I'm also a little bit like Okay. Why does 1.20?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "207.40001",
      "endTime": "211.72",
      "body": "Yeah. Why does that why does that work? Yeah. Help me understand. Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "211.72",
      "endTime": "212.12001",
      "body": "Okay. Because,"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "212.12001",
      "endTime": "213.58",
      "body": "like, where does that come from?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "213.64",
      "endTime": "218.005",
      "body": "1.20, essentially, what we're doing there is we're saying a 100%"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "218.165",
      "endTime": "218.565",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "218.645",
      "endTime": "223.145",
      "body": "Plus 20%. Right. Because 1.20 is just, you know, that as a decimal."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "223.205",
      "endTime": "223.705",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "224.005",
      "endTime": "228.265",
      "body": "So when we multiply by that, we're multiplying by the original 100%"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "228.565",
      "endTime": "228.805",
      "body": "k."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "228.885",
      "endTime": "230.105",
      "body": "And the extra 20%."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "230.165",
      "endTime": "230.665",
      "body": "Gotcha."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "230.725",
      "endTime": "231.285",
      "body": "All at once."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "231.285",
      "endTime": "231.66",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "232.22",
      "endTime": "233.92",
      "body": "It's kind of a cool little shortcut."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "234.14",
      "endTime": "234.62001",
      "body": "Okay. You"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "234.62001",
      "endTime": "236.56",
      "body": "know? It's more elegant, I think."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "236.78",
      "endTime": "238.46",
      "body": "I mean, it is it is pretty elegant."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "238.46",
      "endTime": "239.66",
      "body": "It's slick. I like it."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "239.66",
      "endTime": "243.26001",
      "body": "Yeah. It's slick. So it's not just about speed then. It's about, like, this is like"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "243.42",
      "endTime": "244.62001",
      "body": "It's about the structure, man."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "244.62001",
      "endTime": "245.425",
      "body": "The structure of it."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "245.425",
      "endTime": "249.345",
      "body": "It's about the underlying structure of what we're doing. Yeah. It's It's deep, man."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "249.345",
      "endTime": "253.025",
      "body": "So I'm starting to see why this is called recalling percent change"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "253.185",
      "endTime": "253.385",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "253.58499",
      "endTime": "258.21002",
      "body": "Because it's like Yeah. It's not just about, like Great. Here's the formula, plug in the numbers."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "258.21002",
      "endTime": "262.05002",
      "body": "It's not a formula. It's like Effectively. Concept. Understanding. Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "262.05002",
      "endTime": "264.61002",
      "body": "It's a concept. How this works. That's right. How it"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "264.61002",
      "endTime": "264.93002",
      "body": "works."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "264.93002",
      "endTime": "270.29",
      "body": "Yeah. That's cool. Yeah. And then this multiplication mindset. Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "270.29",
      "endTime": "272.13",
      "body": "I love that's what they're calling it now."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "272.13",
      "endTime": "274.39502",
      "body": "Yes. The multiplication mindset."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "274.39502",
      "endTime": "276.155",
      "body": "The multiplication mindset. Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "276.155",
      "endTime": "276.95502",
      "body": "It's really important."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "276.95502",
      "endTime": "280.315",
      "body": "This is huge for understanding exponential growth."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "280.315",
      "endTime": "280.815",
      "body": "Yes."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "281.195",
      "endTime": "284.23502",
      "body": "This is, like, setting the stage. We gotta understand this now."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "284.23502",
      "endTime": "284.635",
      "body": "Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "284.635",
      "endTime": "286.555",
      "body": "So I'm excited to see where they go with that."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "286.555",
      "endTime": "289.49002",
      "body": "Yes. We'll get there. Right. But before we do"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "289.73",
      "endTime": "290.05002",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "290.13",
      "endTime": "293.51",
      "body": "Let's move on to the next activity in the lesson Let's do it. Which is"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "294.85",
      "endTime": "298.47",
      "body": "taxes and sales. Taxes and sales. Okay. Now we're talking."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "298.61002",
      "endTime": "299.73",
      "body": "Which I know is something that"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "299.89",
      "endTime": "303.205",
      "body": "Real world real world, we actually have to deal with."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "303.505",
      "endTime": "304.945",
      "body": "Come on. Now so they're like"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "305.105",
      "endTime": "306.245",
      "body": "So what's the scenario?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "306.54498",
      "endTime": "311.125",
      "body": "Okay. So say you wanna buy a car. Okay. And it's $12,000."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "311.82498",
      "endTime": "313.23",
      "body": "$12. Right?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "313.23",
      "endTime": "314.67",
      "body": "But there's sales tax."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "314.67",
      "endTime": "314.99002",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "314.99002",
      "endTime": "316.75",
      "body": "Of course. Right? Gotta have sales tax."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "316.75",
      "endTime": "317.49002",
      "body": "It's 8%."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "317.87",
      "endTime": "318.67",
      "body": "8%. Alright."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "318.67",
      "endTime": "320.99002",
      "body": "So they're saying there's 2 ways we can think about this."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "320.99002",
      "endTime": "321.79",
      "body": "Okay. Hit me."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "321.79",
      "endTime": "324.75",
      "body": "We can do the whole, like, 12,000 Mhmm."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "324.83002",
      "endTime": "327.97",
      "body": "Plus Plus 0.08 times 12,000."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "328.50497",
      "endTime": "329.32498",
      "body": "Times 12,000."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "329.54498",
      "endTime": "330.585",
      "body": "Right. The classic one."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "330.585",
      "endTime": "331.805",
      "body": "Or we can just do 1.08"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "332.345",
      "endTime": "333.145",
      "body": "I see where you're going."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "333.38498",
      "endTime": "334.205",
      "body": "Times 12,000."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "334.425",
      "endTime": "336.10498",
      "body": "Times 12,000. There it is again."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "336.10498",
      "endTime": "338.585",
      "body": "Right. So we're seeing this, like, pattern here."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "338.585",
      "endTime": "342.685",
      "body": "Okay. So, like, we were saying that multiplication mindset."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "342.745",
      "endTime": "345.80002",
      "body": "Yeah. Right? So, again, I'm like, okay. But Yeah."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "345.80002",
      "endTime": "351.1",
      "body": "So what's the big deal? Why? Why is that one multiplication so important?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "351.24002",
      "endTime": "352.94",
      "body": "Why is this important?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "353.48",
      "endTime": "355.58002",
      "body": "I mean, obviously, it's a little bit faster."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "355.64",
      "endTime": "356.14",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "356.44",
      "endTime": "358.965",
      "body": "But why else? Why do we care?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "358.965",
      "endTime": "359.685",
      "body": "Why we care?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "359.685",
      "endTime": "364.405",
      "body": "What does this allow us to do? Yeah. Okay. Okay. I think I see where they're going with this."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "364.405",
      "endTime": "364.805",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "364.805",
      "endTime": "374.21",
      "body": "This is really important because what if we have multiple percentage changes? Mhmm. What if we have you know, what if they tack on, like, a dealer markup"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "374.44998",
      "endTime": "375.01",
      "body": "Right. Exactly."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "375.25",
      "endTime": "376.38998",
      "body": "On top of that 8%."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "376.61",
      "endTime": "377.25",
      "body": "Like, what if"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "377.49",
      "endTime": "378.87",
      "body": "What if there's also a discount?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "379.00998",
      "endTime": "380.37",
      "body": "Right. Yeah. Yeah."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "380.37",
      "endTime": "383.27",
      "body": "Suddenly, we're talking about multiple percentage changes."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "383.40997",
      "endTime": "383.88998",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "383.88998",
      "endTime": "388.83502",
      "body": "And if we're thinking about it this way, it's just multiplication, multiplication, multiplication."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "388.975",
      "endTime": "390.83502",
      "body": "Yeah. Right. So it becomes like a chain?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "391.055",
      "endTime": "392.17502",
      "body": "Exactly. It's like a chain."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "392.17502",
      "endTime": "392.655",
      "body": "Okay. It's"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "392.655",
      "endTime": "393.635",
      "body": "like a chain reaction."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "393.775",
      "endTime": "394.255",
      "body": "Gotcha."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "394.255",
      "endTime": "399.055",
      "body": "You know? And I think that's where this idea of exponential growth is gonna come in."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "399.055",
      "endTime": "399.555",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "399.89",
      "endTime": "406.21002",
      "body": "Right? Because we're talking about things changing Uh-huh. As a percentage over and over and over again."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "406.21002",
      "endTime": "406.71002",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "407.09",
      "endTime": "409.11002",
      "body": "I'm picking up what they're putting down now."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "409.41",
      "endTime": "414.595",
      "body": "Yes. Yes. I think I am too. Alright. So this is really setting the stage for"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "415.155",
      "endTime": "417.395",
      "body": "Yeah. Big things to come. Yeah. We've got scooters."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "417.395",
      "endTime": "418.355",
      "body": "Or bigger ideas."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "418.355",
      "endTime": "420.45502",
      "body": "We've got taxes. We've got cars."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "420.515",
      "endTime": "420.835",
      "body": "Yes."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "420.835",
      "endTime": "423.075",
      "body": "I mean Yeah. Come on. This is exciting stuff."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "423.075",
      "endTime": "426.995",
      "body": "I know. I'm excited. Alright. Let's take a quick break Okay. And then we'll come back."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "426.995",
      "endTime": "427.815",
      "body": "Sounds good."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "428.09",
      "endTime": "433.45",
      "body": "And talk about more. Alright. So before we get too far into, like, the exponential growth stuff"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "433.61002",
      "endTime": "433.77002",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "433.93002",
      "endTime": "440.265",
      "body": "Let's talk about something a little bit more, I don't know, down to earth Yeah. A lot more fun, which is discounts. Okay. Everyone loves"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "440.265",
      "endTime": "444.457",
      "body": "a discount. Come on. Who doesn't love a good sale? Exactly. So remembering back to our wheels activity with the scooter Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "444.457",
      "endTime": "445.625",
      "body": "Yeah. And the bike."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "445.625",
      "endTime": "449.065",
      "body": "Mhmm. Let's say that scooter is now on"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "449.065",
      "endTime": "449.705",
      "body": "sale for 35% off."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "449.705",
      "endTime": "459.88998",
      "body": "Okay. Okay. So my inner bargain shopper is, like, perking up right now."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "460.51",
      "endTime": "463.15",
      "body": "How are you gonna figure that out? What are you gonna do?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "463.15",
      "endTime": "468.43",
      "body": "Well, I mean, I would probably figure out what 35% of a $160 is and then subtract it from the"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "468.43",
      "endTime": "472.845",
      "body": "total sick. Right. The old school way. But remember that multiplication mindset."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "472.845",
      "endTime": "473.885",
      "body": "Here we go. Here we go."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "473.885",
      "endTime": "475.105",
      "body": "We don't have to subtract."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "475.245",
      "endTime": "475.745",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "475.805",
      "endTime": "477.42502",
      "body": "We can multiply that 160"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "477.885",
      "endTime": "478.385",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "478.525",
      "endTime": "480.14502",
      "body": "By, in this case, 0.65"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "480.685",
      "endTime": "481.245",
      "body": "Hold on."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "481.325",
      "endTime": "481.965",
      "body": "To get our answer."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "481.965",
      "endTime": "483.98502",
      "body": "Where'd that come from? Okay. Where'd you get 0.65?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "484.52002",
      "endTime": "485.88",
      "body": "So if it's 35% off"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "486.04",
      "endTime": "486.24",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "486.44",
      "endTime": "489.66",
      "body": "That means we're paying 65%. Exactly."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "489.72",
      "endTime": "490.12003",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "490.12003",
      "endTime": "492.06",
      "body": "So we could just multiply by 0.65."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "492.44",
      "endTime": "493.24002",
      "body": "Gotcha. Gotcha."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "493.24002",
      "endTime": "495.66",
      "body": "Right? Okay. Instead of doing 2 separate things."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "495.88",
      "endTime": "497.895",
      "body": "It's so funny because I I never would have Yeah."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "497.895",
      "endTime": "498.935",
      "body": "It's not intuitive. Right?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "498.935",
      "endTime": "499.815",
      "body": "No. It's not intuitive."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "499.815",
      "endTime": "500.455",
      "body": "It's really not."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "500.455",
      "endTime": "502.775",
      "body": "But it's like yeah. Of course. That makes sense."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "502.775",
      "endTime": "503.415",
      "body": "Once you see it"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "503.655",
      "endTime": "503.775",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "503.895",
      "endTime": "505.675",
      "body": "It's like, oh, okay. Okay."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "505.735",
      "endTime": "506.935",
      "body": "Like, I get it. I get it."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "506.935",
      "endTime": "507.735",
      "body": "It makes sense."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "507.735",
      "endTime": "509.915",
      "body": "So this is, again, not just a shortcut."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "510.135",
      "endTime": "510.29498",
      "body": "This"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "510.29498",
      "endTime": "512.13",
      "body": "is, like, tying into this bigger picture."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "512.21",
      "endTime": "513.25",
      "body": "The bigger picture. Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "513.25",
      "endTime": "515.73",
      "body": "Right. Yeah. So we were talking about earlier"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "515.89",
      "endTime": "517.81",
      "body": "This is where the exponential growth comes in."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "517.81",
      "endTime": "519.19",
      "body": "Okay. Okay. Tell me more."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "519.57",
      "endTime": "525.855",
      "body": "So, basically, any time Yeah. We're multiplying by the same factor over and over again."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "526.01495",
      "endTime": "526.33496",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "526.33496",
      "endTime": "537.45496",
      "body": "Like, 1.20 for that 20% increase or 0.85 for a 15% decrease. Mhmm. We're essentially modeling what's called exponential change."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "537.45496",
      "endTime": "539.295",
      "body": "Yeah. Okay. So we've gone from"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "539.695",
      "endTime": "540.83496",
      "body": "I know. Right?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "541.135",
      "endTime": "544.07",
      "body": "Scooters to exponential growth."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "544.29004",
      "endTime": "545.25",
      "body": "It's a big jump."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "545.25",
      "endTime": "545.97003",
      "body": "It's wild."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "545.97003",
      "endTime": "547.25",
      "body": "But it's all connected, man."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "547.25",
      "endTime": "547.97003",
      "body": "It's all connected."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "547.97003",
      "endTime": "548.77",
      "body": "It's all connected."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "548.77",
      "endTime": "550.95",
      "body": "Okay. So, like, how? Give me an example."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "551.01",
      "endTime": "554.21",
      "body": "Okay. So think about compound interest. Right? It's like the magic of finance"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "554.45",
      "endTime": "554.69",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "554.77",
      "endTime": "556.05005",
      "body": "Where your money is making"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "556.29004",
      "endTime": "556.995",
      "body": "Money on money."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "557.075",
      "endTime": "559.635",
      "body": "Money on money. Exactly. Yeah. Because it's growing"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "559.795",
      "endTime": "560.195",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "560.275",
      "endTime": "563.71497",
      "body": "On the interest that it's already earned. Mhmm. That's exponential change."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "563.71497",
      "endTime": "564.21497",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "564.275",
      "endTime": "566.995",
      "body": "Or what about, like Okay. Population growth. Right?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "566.995",
      "endTime": "567.235",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "567.235",
      "endTime": "572.62",
      "body": "Like, let's say you have a population of rabbits. Okay. And they're growing by I don't know."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "572.62",
      "endTime": "574.06",
      "body": "Like, 10% a year?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "574.06",
      "endTime": "576.64",
      "body": "10% every year. Okay. That's exponential."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "576.86005",
      "endTime": "577.26",
      "body": "Gotcha."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "577.26",
      "endTime": "577.5",
      "body": "Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "577.5",
      "endTime": "577.82",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "577.82",
      "endTime": "580.8",
      "body": "Because it's 10% on top of the previous year's 10%."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "580.94",
      "endTime": "581.82",
      "body": "So it's like It"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "581.82",
      "endTime": "582.8",
      "body": "just keeps building."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "582.86005",
      "endTime": "583.42004",
      "body": "It builds."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "583.42004",
      "endTime": "583.74",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "583.74",
      "endTime": "585.525",
      "body": "Okay. So we're seeing this"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "586.405",
      "endTime": "587.04504",
      "body": "And that's the key."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "587.205",
      "endTime": "588.245",
      "body": "In the real world."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "588.245",
      "endTime": "589.765",
      "body": "Yeah. This is real world stuff."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "589.765",
      "endTime": "592.505",
      "body": "Like, this is actually how things change."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "592.565",
      "endTime": "595.685",
      "body": "This is not just some abstract math concept. Right?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "595.685",
      "endTime": "596.325",
      "body": "This is, like, how"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "596.565",
      "endTime": "597.36505",
      "body": "This is life."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "597.36505",
      "endTime": "599.54504",
      "body": "This is life. This is how things work."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "599.60504",
      "endTime": "600.10504",
      "body": "Wow."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "600.16504",
      "endTime": "600.885",
      "body": "It's pretty cool."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "600.885",
      "endTime": "601.66",
      "body": "It is really cool."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "601.66",
      "endTime": "602.16",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "602.62",
      "endTime": "607.6",
      "body": "But Okay. Let's be real. Yeah. This lesson plan isn't all sunshine and rainbows."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "607.66",
      "endTime": "608.62",
      "body": "No. Of course not."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "608.62",
      "endTime": "609.34",
      "body": "It's not just like"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "609.5",
      "endTime": "611.68",
      "body": "What are they what are they what are they missing?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "611.74",
      "endTime": "611.9",
      "body": "Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "611.9",
      "endTime": "613.52",
      "body": "What are they not telling us?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "614.005",
      "endTime": "617.46497",
      "body": "Because they do mention Yeah. That there are some common misconceptions"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "617.685",
      "endTime": "618.32495",
      "body": "Right. Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "618.565",
      "endTime": "627.225",
      "body": "That students and, honestly, probably all of us For sure. Have about percentages. Totally. So what are some of the stumbling blocks?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "627.445",
      "endTime": "629.58",
      "body": "Okay. Well, I think one of the biggest ones"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "629.74",
      "endTime": "629.9",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "630.06",
      "endTime": "632.24",
      "body": "Is knowing when to add or subtract"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "632.78",
      "endTime": "633.28",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "633.42004",
      "endTime": "634.8",
      "body": "Versus when to multiply."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "635.34",
      "endTime": "635.84",
      "body": "Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "635.98004",
      "endTime": "638.62",
      "body": "Right? Because it's easy to fall into that trap of thinking And that's"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "638.62",
      "endTime": "638.86005",
      "body": "all, like"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "638.94",
      "endTime": "640.22003",
      "body": "Oh, it's a 10% increase."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "640.22003",
      "endTime": "640.94",
      "body": "Just add 10%?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "640.94",
      "endTime": "642.38",
      "body": "I'm just gonna add 10% to this thing."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "642.38",
      "endTime": "644.94",
      "body": "Right. Exactly. Right. But as we've seen, like"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "645.32495",
      "endTime": "648.225",
      "body": "Not so fast. Not so fast. Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "648.365",
      "endTime": "651.82495",
      "body": "It's not always we gotta think about it multiplicatively."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "652.285",
      "endTime": "652.605",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "652.605",
      "endTime": "653.185",
      "body": "You know?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "653.485",
      "endTime": "655.005",
      "body": "Like, with that car and the sales tax"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "655.32495",
      "endTime": "655.56494",
      "body": "Exactly."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "655.805",
      "endTime": "657.18",
      "body": "We weren't adding 8%."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "657.42",
      "endTime": "657.82",
      "body": "Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "657.82",
      "endTime": "659.52",
      "body": "We were multiplying by 1.08."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "660.14",
      "endTime": "661.5",
      "body": "Right. To get that total amount."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "661.5",
      "endTime": "662.46",
      "body": "Right. Right. Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "662.46",
      "endTime": "663.33997",
      "body": "Right. So it's not"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "663.58",
      "endTime": "665.33997",
      "body": "It's a little bit counterintuitive sometimes."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "665.33997",
      "endTime": "666.3",
      "body": "Right. It's a little tricky."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "666.3",
      "endTime": "668.14",
      "body": "It's not what you would think at first glance."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "668.14",
      "endTime": "671.66",
      "body": "Okay. And then what else? What other pitfalls are there?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "671.66",
      "endTime": "676.635",
      "body": "Well, I think another big one is just, like Oh. Not understanding, like, why"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "677.115",
      "endTime": "677.275",
      "body": "Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "677.435",
      "endTime": "683.03503",
      "body": "The multiplication shortcuts work. Yeah. You know? Like, we kinda glazed over that a little bit."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "683.03503",
      "endTime": "685.38",
      "body": "I'll be honest. I'm still a little Right. Early on it."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "685.38",
      "endTime": "688.92",
      "body": "It's like we're just accepting it as truth. Right. We're like, why?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "688.98",
      "endTime": "689.48",
      "body": "Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "689.62",
      "endTime": "690.57996",
      "body": "Why does it work?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "690.57996",
      "endTime": "691.56",
      "body": "Tell me why."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "691.94",
      "endTime": "694.36",
      "body": "And it all comes back to that distributive property."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "694.5",
      "endTime": "694.98",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "694.98",
      "endTime": "698.98",
      "body": "Which, you know, again, we could easily just be like, okay. Here's the rule. Just memorize it."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "698.98",
      "endTime": "699.7",
      "body": "Right. Right. But if"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "699.7",
      "endTime": "701.435",
      "body": "we don't understand why it works"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "701.755",
      "endTime": "702.23505",
      "body": "Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "702.315",
      "endTime": "703.835",
      "body": "Then we're not really learning."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "703.835",
      "endTime": "707.455",
      "body": "Then what are we even doing here? Yeah. Exactly. We're just robots at that point."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "707.515",
      "endTime": "710.41504",
      "body": "Okay. So how do we avoid these pitfalls?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "710.635",
      "endTime": "712.47504",
      "body": "Okay. That's the $1,000,000 question. Right?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "712.47504",
      "endTime": "712.955",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "712.955",
      "endTime": "715.215",
      "body": "I think it's about asking why."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "715.35504",
      "endTime": "715.85504",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "716.24",
      "endTime": "718.39996",
      "body": "Like, don't be afraid to ask why."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "718.39996",
      "endTime": "719.86",
      "body": "Yeah. Just be curious."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "719.92",
      "endTime": "721.13995",
      "body": "Be curious. Explore."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "721.44",
      "endTime": "721.94",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "722.0",
      "endTime": "723.75995",
      "body": "Test things out. You know?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "723.75995",
      "endTime": "725.37994",
      "body": "You'll just take things for granted."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "725.44",
      "endTime": "727.62",
      "body": "Exactly. Yeah. Don't just accept the formulas."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "727.83997",
      "endTime": "729.27997",
      "body": "Like, really try to understand."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "729.27997",
      "endTime": "731.51996",
      "body": "Run around with it. Yeah. See what happens."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "731.51996",
      "endTime": "731.805",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "732.045",
      "endTime": "732.445",
      "body": "You know?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "732.445",
      "endTime": "734.305",
      "body": "So it's about fostering that curiosity."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "734.845",
      "endTime": "736.605",
      "body": "Yeah. And that's what makes learning fun."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "736.605",
      "endTime": "736.845",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "736.845",
      "endTime": "739.185",
      "body": "You know? Fun. When you're like, oh, that's cool."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "739.325",
      "endTime": "741.805",
      "body": "Right. Like that moment"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "742.045",
      "endTime": "742.685",
      "body": "I get it now."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "742.765",
      "endTime": "744.145",
      "body": "Where it finally clicks."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "744.205",
      "endTime": "745.31995",
      "body": "Yes. Exactly."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "745.37994",
      "endTime": "747.63995",
      "body": "Yes. Yeah. It's so satisfying."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "747.77997",
      "endTime": "748.89996",
      "body": "It is. It really is."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "748.89996",
      "endTime": "750.42",
      "body": "When you finally, like, get it."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "750.42",
      "endTime": "753.07996",
      "body": "Like, yes. Yes. Light bulb moment."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "753.37994",
      "endTime": "759.22",
      "body": "Totally. So And this lesson plan doesn't just, like, leave us hanging with all these formulas and, like"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "759.45996",
      "endTime": "759.86",
      "body": "Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "760.11",
      "endTime": "760.425",
      "body": "Concepts."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "760.505",
      "endTime": "760.825",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "760.825",
      "endTime": "762.745",
      "body": "They actually wrap it up with this really cool challenge."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "762.745",
      "endTime": "764.425",
      "body": "Right. I like it. I like it. Hit me with it."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "764.425",
      "endTime": "768.925",
      "body": "Okay. So imagine a school Okay. Where the student population grows"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "769.385",
      "endTime": "769.885",
      "body": "Mhmm."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "770.185",
      "endTime": "772.045",
      "body": "By 8% every year."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "772.105",
      "endTime": "773.46497",
      "body": "8% a year. Okay. That sounds"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "773.545",
      "endTime": "773.945",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "774.02496",
      "endTime": "774.665",
      "body": "Sounds pretty good."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "774.665",
      "endTime": "777.82",
      "body": "On the surface. Yeah. Yeah. Like, more students, more funding."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "777.82",
      "endTime": "779.26",
      "body": "Right. More teachers, potentially."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "779.26",
      "endTime": "781.18",
      "body": "Yeah. Exactly. Yeah. But then they're like"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "781.33997",
      "endTime": "781.83997",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "782.14",
      "endTime": "785.68",
      "body": "Is this sustainable forever? Oh,"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "786.06",
      "endTime": "786.88",
      "body": "good question."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "786.94",
      "endTime": "787.33997",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "787.33997",
      "endTime": "787.74",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "787.74",
      "endTime": "789.02",
      "body": "Like, it makes you think."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "789.02",
      "endTime": "794.185",
      "body": "So it's not just about the math. Right. It's about the real world."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "794.245",
      "endTime": "795.945",
      "body": "Like, what are the real world implications?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "796.005",
      "endTime": "796.485",
      "body": "That's yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "796.485",
      "endTime": "797.445",
      "body": "Because in the real world"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "797.525",
      "endTime": "797.925",
      "body": "Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "798.005",
      "endTime": "803.045",
      "body": "You can't just have Unlimited growth. Unlimited growth forever."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "803.045",
      "endTime": "805.125",
      "body": "Right. Exactly. It makes you think about things like"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "805.50995",
      "endTime": "806.70996",
      "body": "Right. Like, there's only so many"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "806.79",
      "endTime": "807.30994",
      "body": "Rim sources."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "807.58997",
      "endTime": "809.99",
      "body": "Resources. Like, how many kids can you fit"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "810.23",
      "endTime": "810.39",
      "body": "Space."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "810.55",
      "endTime": "811.29",
      "body": "In a classroom?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "811.58997",
      "endTime": "812.08997",
      "body": "Exactly."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "812.23",
      "endTime": "813.02997",
      "body": "Right. Yeah."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "813.02997",
      "endTime": "813.82996",
      "body": "Like, at some point"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "814.31",
      "endTime": "815.82996",
      "body": "Gotta factor all that stuff in."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "815.82996",
      "endTime": "816.14996",
      "body": "Mhmm."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "816.14996",
      "endTime": "817.50995",
      "body": "Right? It's gonna level off."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "817.50995",
      "endTime": "819.255",
      "body": "Yeah. Yeah. The real world is messy."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "819.335",
      "endTime": "820.615",
      "body": "The real world is messy."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "820.615",
      "endTime": "822.375",
      "body": "It's not as clean as our math equation."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "822.375",
      "endTime": "824.695",
      "body": "It's true. Unfortunately. That's a good point."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "824.695",
      "endTime": "826.955",
      "body": "But I think that's a good I'm some go It's a good reminder."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "827.015",
      "endTime": "828.075",
      "body": "Reality check."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "828.135",
      "endTime": "829.255",
      "body": "Yeah. Reality check."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "829.255",
      "endTime": "829.655",
      "body": "That, like"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "829.975",
      "endTime": "832.94",
      "body": "That the math is only part of the story."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "832.94",
      "endTime": "833.74",
      "body": "Right. Exactly."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "833.74",
      "endTime": "835.42",
      "body": "Like, it's a good starting point."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "835.42",
      "endTime": "835.74",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "835.74",
      "endTime": "836.94",
      "body": "But it's not the whole story."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "836.94",
      "endTime": "838.77997",
      "body": "What are the other factors at play?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "838.77997",
      "endTime": "841.18",
      "body": "Exactly. Yeah. Well, I think that's a perfect place to maybe"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "841.42",
      "endTime": "841.9",
      "body": "wrap it up."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "842.06",
      "endTime": "846.985",
      "body": "Wrap things up. So big thank you Yes. To the authors Absolutely."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "847.305",
      "endTime": "850.385",
      "body": "Of illustrative math For creating this awesome lesson."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "850.665",
      "endTime": "852.365",
      "body": "For this awesome lesson plan."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "852.425",
      "endTime": "852.90497",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "852.90497",
      "endTime": "854.425",
      "body": "And to you guys out there listening"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "854.745",
      "endTime": "854.94495",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "855.14496",
      "endTime": "856.105",
      "body": "Thanks for joining us"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "856.345",
      "endTime": "856.82495",
      "body": "As always."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "857.065",
      "endTime": "858.09",
      "body": "On this deep dive."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "858.25",
      "endTime": "860.19",
      "body": "Yeah. Thanks for diving deep with us."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "860.41003",
      "endTime": "861.13",
      "body": "Into the world"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "861.29004",
      "endTime": "862.35004",
      "body": "Into the world."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "862.57",
      "endTime": "863.45",
      "body": "Of percentage change"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "863.61005",
      "endTime": "864.29004",
      "body": "Of percentages."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "864.65",
      "endTime": "866.01",
      "body": "And exponential growth."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "866.01",
      "endTime": "867.69",
      "body": "It's more exciting than it sounds."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "867.69",
      "endTime": "869.93005",
      "body": "It is. It really is. Until next time."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "869.93005",
      "endTime": "870.84406",
      "body": "Until next time."
    }
  ]
}