{
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  "segments": [
    {
      "speaker": "Speaker 1",
      "startTime": "0.08",
      "endTime": "12.4",
      "body": "Alright. Today, we're gonna do a deep dive into teaching parabolas and quadratic equations. Okay. And we're using this algebra 1612 lesson teacher guide to help us."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "12.4",
      "endTime": "13.12",
      "body": "Thank you."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "13.12",
      "endTime": "15.5199995",
      "body": "And, it's really amazing how these curves"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "15.759999",
      "endTime": "15.915",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "16.155",
      "endTime": "20.015",
      "body": "Show up, like, everywhere, right, from bridges to the path of, like, a football."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "20.154999",
      "endTime": "20.654999",
      "body": "Absolutely."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "20.875",
      "endTime": "24.895",
      "body": "So let's unpack how to make this concept really click for students."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "25.115",
      "endTime": "27.195",
      "body": "What I think is really clever about this lesson"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "27.435",
      "endTime": "27.675",
      "body": "Mhmm."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "27.755001",
      "endTime": "29.775",
      "body": "Is that it takes something that's familiar"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "30.075",
      "endTime": "30.575",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "30.84",
      "endTime": "35.260002",
      "body": "To students, like graphing linear equations Right. And it uses that as, like, a springboard."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "35.72",
      "endTime": "36.36",
      "body": "Right. Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "36.36",
      "endTime": "40.86",
      "body": "So instead of just Bimper Slope, now we're diving into the world of, like, a, b, and c."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "40.92",
      "endTime": "47.464996",
      "body": "Right. And it really emphasizes that this isn't just about, you know, plotting points on a graph."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "47.464996",
      "endTime": "47.784996",
      "body": "Mhmm."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "47.784996",
      "endTime": "52.104996",
      "body": "It's about understanding the relationship between the equation itself"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "52.425",
      "endTime": "52.824997",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "52.905",
      "endTime": "54.524998",
      "body": "And its visual representation."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "54.905",
      "endTime": "55.405",
      "body": "Absolutely."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "55.545",
      "endTime": "64.67",
      "body": "You know, it reminds me of that moment when students finally see how like, changing that in a linear equation Yep. Directly impacts the line's steepness."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "65.05",
      "endTime": "65.53",
      "body": "Totally."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "65.53",
      "endTime": "67.770004",
      "body": "Like, I bet you've seen those light bulb moments before."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "67.770004",
      "endTime": "71.05",
      "body": "Absolutely. Those are the best. Right. That's what it's all about. Yeah."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "71.05",
      "endTime": "75.33501",
      "body": "This lesson plan really sets the stage for that kind of understanding with quadratics."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "75.555",
      "endTime": "75.955",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "75.955",
      "endTime": "78.915",
      "body": "And it's all about giving students the tools to connect those equations"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "78.995",
      "endTime": "79.155",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "79.315",
      "endTime": "86.195",
      "body": "Tables and graphs Mhmm. Helping them to see those different representations as, like, facets of the same mathematical idea."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "86.195",
      "endTime": "88.115005",
      "body": "Okay. So let's get into, like, the nitty gritty."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "88.115005",
      "endTime": "88.38",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "89.74",
      "endTime": "99.74",
      "body": "The lesson really wants students to understand the standard form of a quadratic equation Mhmm. Which is y, of x plus, b x plus c."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "99.74",
      "endTime": "100.22",
      "body": "K."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "100.22",
      "endTime": "104.075005",
      "body": "And it seems like that a value has, like, a starring role here. It really does. Yeah. Yeah. The a value is all about the value is all"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "104.075005",
      "endTime": "108.40833",
      "body": "about the parabola's direction Okay. And its shape. Mhmm. So a positive a gives you a parabola that opens upwards Okay. And a negative a means it opens downwards."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "108.40833",
      "endTime": "108.92834",
      "body": "So a positive"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "108.92834",
      "endTime": "109.275",
      "body": "a means"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "109.275",
      "endTime": "111.69501",
      "body": "we're dealing with a parabola that looks like"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "119.090004",
      "endTime": "119.65",
      "body": "a smile"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "119.97",
      "endTime": "120.29",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "120.37",
      "endTime": "122.630005",
      "body": "And a negative one is more of a frown."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "122.85",
      "endTime": "123.41",
      "body": "You got it."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "123.41",
      "endTime": "129.19",
      "body": "Gotcha. Yep. So what else does it affect other than just the direction?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "129.65",
      "endTime": "133.505",
      "body": "A also controls the steepness of that smile or frown."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "133.565",
      "endTime": "134.045",
      "body": "K."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "134.045",
      "endTime": "139.905",
      "body": "So a larger a value means a much narrower and steeper parabola."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "140.445",
      "endTime": "140.925",
      "body": "Mhmm."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "140.925",
      "endTime": "143.88501",
      "body": "While a smaller a value creates a wider"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "144.125",
      "endTime": "144.39",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "144.71",
      "endTime": "145.99",
      "body": "More relaxed curve."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "145.99",
      "endTime": "149.19",
      "body": "So it's like a dictates how dramatic the parabola is."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "149.19",
      "endTime": "149.67",
      "body": "Totally."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "149.67",
      "endTime": "153.11",
      "body": "Whether it's like a subtle curve or a sharp climb or something, that makes sense."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "153.11",
      "endTime": "153.61",
      "body": "Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "154.06999",
      "endTime": "155.83",
      "body": "But what about the c value then?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "155.83",
      "endTime": "156.23",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "156.23",
      "endTime": "159.255",
      "body": "What role does that play in shaping our parabola?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "159.57501",
      "endTime": "164.975",
      "body": "So c is all about positioning that parabola on the graph. Okay. So just like with the y intercept in linear"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "165.255",
      "endTime": "165.375",
      "body": "Mhmm."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "165.49501",
      "endTime": "165.815",
      "body": "Equations"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "166.05501",
      "endTime": "166.55501",
      "body": "Mhmm."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "166.77501",
      "endTime": "168.85501",
      "body": "The c value shifts the entire parabola"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "168.935",
      "endTime": "169.175",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "169.255",
      "endTime": "170.535",
      "body": "Up or down the y axis."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "170.535",
      "endTime": "176.23",
      "body": "That's really helpful. Yeah. So a sets the basic shape. Mhmm. And then c determines where that shape sits vertically."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "176.37",
      "endTime": "176.85",
      "body": "Exactly."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "176.85",
      "endTime": "179.41",
      "body": "Because, like, c is choosing the parabola's starting point."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "179.41",
      "endTime": "180.05",
      "body": "I like that."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "180.05",
      "endTime": "183.57",
      "body": "Now we're cooking. This is starting to feel like a recipe for parabolas."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "183.57",
      "endTime": "183.97",
      "body": "Yes."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "183.97",
      "endTime": "190.28499",
      "body": "So we've talked about the theory, but, like, how does this lesson plan actually get students to internalize all of these concepts?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "190.42499",
      "endTime": "192.34499",
      "body": "Well, that's where things get really exciting. Right?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "192.34499",
      "endTime": "192.825",
      "body": "Mhmm."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "192.825",
      "endTime": "196.605",
      "body": "Because the lesson plan outlines some really brilliant hands on activities."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "196.745",
      "endTime": "197.245",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "198.905",
      "endTime": "203.0",
      "body": "For example, there's one called Quadratic Graphs Galore."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "203.54001",
      "endTime": "204.04001",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "204.18001",
      "endTime": "208.84001",
      "body": "And it encourages students to use graphing technology Mhmm. Like Desmos."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "208.90001",
      "endTime": "209.22",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "209.22",
      "endTime": "212.18001",
      "body": "And so they can experiment with changing the a and c values"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "212.26001",
      "endTime": "212.70001",
      "body": "That's right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "212.90001",
      "endTime": "217.785",
      "body": "And instantly see how the parabola, like, transforms on the screen."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "217.845",
      "endTime": "218.32501",
      "body": "Oh, wow."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "218.32501",
      "endTime": "222.565",
      "body": "Like, the dynamics. So they move that slider, and they can watch that parabola change."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "222.565",
      "endTime": "227.04501",
      "body": "Oh, that's cool. Yeah. So it's like a dynamic puzzle almost That's okay. Watching those connections come to life."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "227.04501",
      "endTime": "227.52501",
      "body": "Absolutely."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "227.52501",
      "endTime": "228.82501",
      "body": "I love that visual element."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "228.88501",
      "endTime": "229.38501",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "230.03",
      "endTime": "236.69",
      "body": "Speaking of visuals, though, what about those crucial x intercepts, you know, the points where the parabola crosses the x axis?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "236.75",
      "endTime": "237.23",
      "body": "Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "237.23",
      "endTime": "241.55",
      "body": "Those seem really important for students to grasp. Yeah. How does the lesson plan address that?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "241.55",
      "endTime": "246.22499",
      "body": "So it offers this great optional activity called what do these tables reveal?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "246.36499",
      "endTime": "246.765",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "246.765",
      "endTime": "251.985",
      "body": "And, basically, students calculate the a values for different x values."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "252.045",
      "endTime": "252.545",
      "body": "Mhmm."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "253.00499",
      "endTime": "258.63998",
      "body": "And in doing so, they see firsthand how those a and c values that we were just talking about"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "258.8",
      "endTime": "259.19998",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "259.36",
      "endTime": "262.98",
      "body": "Directly influence where that parabola hits that x axis."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "263.12",
      "endTime": "267.28",
      "body": "Ah, so they're building a deeper understanding of the relationship between, like"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "267.44",
      "endTime": "267.91998",
      "body": "The equation."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "268.16",
      "endTime": "273.125",
      "body": "Components and then the visual representation of those x intercepts."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "273.185",
      "endTime": "273.685",
      "body": "Absolutely."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "273.905",
      "endTime": "277.745",
      "body": "It sounds like this lesson plan is all about connecting those dots for those students."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "277.745",
      "endTime": "281.58502",
      "body": "Yeah. It provides a framework for students to develop a more intuitive understanding"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "281.745",
      "endTime": "282.14502",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "282.225",
      "endTime": "288.71002",
      "body": "Of these quadratic equations. Okay. But importantly, it doesn't shy away from addressing some of the common misconceptions."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "289.25",
      "endTime": "297.35",
      "body": "Which, let's be honest, can sometimes be, like, the most important part of teaching a new concept. For sure. So what are some of those potential stumbling blocks that the lesson highlights?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "297.57",
      "endTime": "297.89",
      "body": "Okay. And"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "297.89",
      "endTime": "300.205",
      "body": "then how does it recommend navigating those?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "300.205",
      "endTime": "305.485",
      "body": "So one very common misconception is that students will confuse the factors in factored form"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "305.645",
      "endTime": "305.84497",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "306.04498",
      "endTime": "307.585",
      "body": "With the x intercepts directly."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "307.645",
      "endTime": "308.365",
      "body": "Oh, interesting."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "308.365",
      "endTime": "314.16998",
      "body": "So that they might see something like x plus 1 Alright. And assume the x intercept is at positive one on the graph."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "314.16998",
      "endTime": "315.61",
      "body": "Yeah. You just pull it right out."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "315.61",
      "endTime": "322.83",
      "body": "Right. And they forget about that necessary step of setting that factored form equal to 0 and actually solving for x."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "323.05",
      "endTime": "324.73",
      "body": "Oh, that sneaky sign change."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "324.73",
      "endTime": "325.63",
      "body": "It's okay."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "325.69",
      "endTime": "327.975",
      "body": "It gets me sometimes even still."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "328.275",
      "endTime": "328.775",
      "body": "Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "330.035",
      "endTime": "340.13498",
      "body": "But it's great that the lesson emphasizes that solving for x is really key here Okay. Not just pulling a value straight from that factored form. Yeah. What other misconceptions do they discuss?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "340.54",
      "endTime": "344.48",
      "body": "Yeah. It's like they say sometimes you have to make the mistake to truly understand the rule."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "344.54",
      "endTime": "345.04",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "345.58002",
      "endTime": "347.92",
      "body": "So important to address those common missteps."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "347.98",
      "endTime": "348.48",
      "body": "Absolutely."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "349.42",
      "endTime": "352.22",
      "body": "Are there any other areas where students tend to get tripped up?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "352.22",
      "endTime": "359.565",
      "body": "Yeah. So the lesson plan also points out that students might assume that a positive a value k. Always means that the parabola's vertex"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "359.94498",
      "endTime": "360.10498",
      "body": "Mhmm."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "360.26498",
      "endTime": "362.185",
      "body": "Is gonna be above the x axis."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "362.185",
      "endTime": "365.72498",
      "body": "Right. Even though a positive a means we're dealing with a parabola that curves upwards."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "366.17",
      "endTime": "370.33002",
      "body": "That entire curve could be shifted downwards depending on the c value."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "370.33002",
      "endTime": "370.81",
      "body": "Exactly."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "370.81",
      "endTime": "371.13",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "371.13",
      "endTime": "387.125",
      "body": "It's a great opportunity to remind students that c really does play a role Yeah. In positioning that whole parabola on the graph. Right. So even a happy upward facing parabola might find itself, like, dipping below the x axis."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "387.125",
      "endTime": "389.525",
      "body": "That's a fantastic visual to keep in mind."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "389.525",
      "endTime": "390.005",
      "body": "Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "390.005",
      "endTime": "393.785",
      "body": "We've really broken down the roles of a and c today."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "393.845",
      "endTime": "394.165",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "394.165",
      "endTime": "396.085",
      "body": "But there's still that mysterious b"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "396.40997",
      "endTime": "396.72998",
      "body": "Right."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "396.72998",
      "endTime": "398.00998",
      "body": "In our standard form."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "398.00998",
      "endTime": "398.40997",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "398.40997",
      "endTime": "400.97",
      "body": "Y o x x plus b x plus c."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "400.97",
      "endTime": "401.47",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "402.09",
      "endTime": "404.18997",
      "body": "I'm curious. What can you tell us about b?"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "404.88998",
      "endTime": "408.99",
      "body": "Well, so unlike a and c, which have these, like Yeah. Really direct visual interpretations"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "409.28998",
      "endTime": "409.44998",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "409.61",
      "endTime": "410.88998",
      "body": "B is a little bit more subtle."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "410.88998",
      "endTime": "411.12997",
      "body": "Alright."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "411.12997",
      "endTime": "417.125",
      "body": "It doesn't just, like, stretch or shift the parabola on its own. Mhmm. B kinda works behind the scenes"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "417.365",
      "endTime": "417.685",
      "body": "Okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "417.76498",
      "endTime": "419.205",
      "body": "To influence the parabola's position"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "419.365",
      "endTime": "419.76498",
      "body": "I understand."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "419.845",
      "endTime": "420.805",
      "body": "In a more nuanced way."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "420.805",
      "endTime": "421.205",
      "body": "Gotcha."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "421.205",
      "endTime": "423.60498",
      "body": "So it's responsible for those, like, horizontal shifts"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "423.845",
      "endTime": "424.125",
      "body": "Oh, okay."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "424.32498",
      "endTime": "427.68",
      "body": "We see in some parabolas Right. Like moving them left or right on the graph."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "428.0",
      "endTime": "430.5",
      "body": "So b is, like, the quiet collaborator"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "431.12",
      "endTime": "431.32",
      "body": "Yes."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "431.52",
      "endTime": "435.68",
      "body": "Working in tandem with a and c to fine tune that parabolas' position."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "435.68",
      "endTime": "436.18",
      "body": "Exactly."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "436.32",
      "endTime": "441.22",
      "body": "Fascinating. And it sounds like the lesson plan intentionally leaves b as a little bit of a cliffhanger."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "441.52",
      "endTime": "451.075",
      "body": "It does. The authors pose this very thought provoking question to the students Okay. Which is, how do you think the b value might affect the parabolas graph?"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "451.135",
      "endTime": "452.095",
      "body": "Oh, that's cool."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "452.095",
      "endTime": "459.96",
      "body": "That's brilliant. Leaving that open ended question encourages students to go beyond just rote memorization"
    },
    {
      "speaker": "Speaker 1",
      "startTime": "460.25998",
      "endTime": "460.5",
      "body": "Right."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "460.58",
      "endTime": "462.19998",
      "body": "And delve into their own exploration."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "462.41998",
      "endTime": "465.72",
      "body": "I love that. Yeah. And this deep dive has been incredibly insightful."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "465.86",
      "endTime": "466.82",
      "body": "It's been fun."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "466.82",
      "endTime": "472.695",
      "body": "I think we've gone beyond just the mechanics of graphing these quadratic equations."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "472.755",
      "endTime": "473.415",
      "body": "For sure."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "473.635",
      "endTime": "477.075",
      "body": "We've really explored the why behind those graceful curves"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "477.23502",
      "endTime": "477.55502",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "477.635",
      "endTime": "481.155",
      "body": "And all those common pitfalls that students might encounter along the way."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "481.155",
      "endTime": "481.655",
      "body": "Absolutely."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "482.13",
      "endTime": "487.49002",
      "body": "And armed with these insights, I bet our listeners are gonna be amazing guides for their students."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "487.49002",
      "endTime": "488.37003",
      "body": "I hope so."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "488.37003",
      "endTime": "490.63",
      "body": "Helping them see those light bulb moments click."
    },
    {
      "speaker": "Speaker 2",
      "startTime": "490.85",
      "endTime": "491.60187",
      "body": "That's the goal."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "491.84186",
      "endTime": "495.92188",
      "body": "Right. Awesome. Well, a huge thank you to the authors of Illustrative Math"
    },
    {
      "speaker": "Speaker 2",
      "startTime": "496.08188",
      "endTime": "496.24188",
      "body": "Yeah."
    },
    {
      "speaker": "Speaker 1",
      "startTime": "496.40186",
      "endTime": "498.26187",
      "body": "For this insightful lesson plan."
    }
  ]
}