{"version":"1.0.0","segments":[{"speaker":"Pam","startTime":0.72,"endTime":3.84,"body":"Hey, fellow mathematicians."},{"speaker":"Pam","startTime":0.72,"endTime":3.84,"body":"Welcome to the podcast where"},{"speaker":"Pam","startTime":3.84,"endTime":6.36,"body":"Math is Figure-Out-Able! I'm"},{"speaker":"Pam","startTime":3.84,"endTime":6.36,"body":"Pam."},{"speaker":"Kim","startTime":6.57,"endTime":7.32,"body":"And I'm Kim."},{"speaker":"Pam","startTime":7.65,"endTime":10.86,"body":"And you found a place where"},{"speaker":"Pam","startTime":7.65,"endTime":10.86,"body":"math is not about memorizing and"},{"speaker":"Pam","startTime":10.86,"endTime":14.16,"body":"mimicking, waiting to be told or"},{"speaker":"Pam","startTime":10.86,"endTime":14.16,"body":"shown what to do. But, ya'll,"},{"speaker":"Pam","startTime":14.16,"endTime":17.28,"body":"it's about making sense of"},{"speaker":"Pam","startTime":14.16,"endTime":17.28,"body":"problems, noticing patterns, and"},{"speaker":"Pam","startTime":17.28,"endTime":21.15,"body":"reasoning using mathematical"},{"speaker":"Pam","startTime":17.28,"endTime":21.15,"body":"relationships. We can mentor"},{"speaker":"Pam","startTime":21.15,"endTime":25.26,"body":"students to think and reason"},{"speaker":"Pam","startTime":21.15,"endTime":25.26,"body":"like mathematicians. Not only"},{"speaker":"Pam","startTime":25.26,"endTime":29.19,"body":"are algorithms not particularly"},{"speaker":"Pam","startTime":25.26,"endTime":29.19,"body":"helpful in teaching mathematics,"},{"speaker":"Pam","startTime":29.52,"endTime":32.73,"body":"but rotely repeating steps"},{"speaker":"Pam","startTime":29.52,"endTime":32.73,"body":"actually keep students from"},{"speaker":"Pam","startTime":32.73,"endTime":34.62,"body":"being the mathematicians they"},{"speaker":"Pam","startTime":32.73,"endTime":34.62,"body":"can be."},{"speaker":"Kim","startTime":35.58,"endTime":38.49,"body":"So, in today's episode, we"},{"speaker":"Kim","startTime":35.58,"endTime":38.49,"body":"are going to have some fun"},{"speaker":"Kim","startTime":38.52,"endTime":42.15,"body":"beating around a term that is"},{"speaker":"Kim","startTime":38.52,"endTime":42.15,"body":"often used in math classes."},{"speaker":"Pam","startTime":42.39,"endTime":47.34,"body":"Yeah! So, Kim, I just got"},{"speaker":"Pam","startTime":42.39,"endTime":47.34,"body":"back from spending time in Utah,"},{"speaker":"Pam","startTime":47.34,"endTime":49.38,"body":"which is totally cool because I"},{"speaker":"Pam","startTime":47.34,"endTime":49.38,"body":"got to see my kids. Yay!"},{"speaker":"Kim","startTime":49.41,"endTime":49.77,"body":"Yeah."},{"speaker":"Pam","startTime":50.1,"endTime":52.53,"body":"With some wonderful high"},{"speaker":"Pam","startTime":50.1,"endTime":52.53,"body":"school teachers. We've actually"},{"speaker":"Pam","startTime":52.53,"endTime":57.06,"body":"met a couple of times. And we"},{"speaker":"Pam","startTime":52.53,"endTime":57.06,"body":"had some great conversations. A"},{"speaker":"Pam","startTime":57.06,"endTime":60.99,"body":"super interesting conversation"},{"speaker":"Pam","startTime":57.06,"endTime":60.99,"body":"about some words we use in math"},{"speaker":"Pam","startTime":60.99,"endTime":65.76,"body":"teaching that have the potential"},{"speaker":"Pam","startTime":60.99,"endTime":65.76,"body":"to be super confusing because..."},{"speaker":"Pam","startTime":65.85,"endTime":68.1,"body":"Well, for many reasons. But I'm"},{"speaker":"Pam","startTime":65.85,"endTime":68.1,"body":"going to suggest today because"},{"speaker":"Pam","startTime":68.1,"endTime":70.26,"body":"they're not well defined."},{"speaker":"Kim","startTime":71.04,"endTime":71.07,"body":"Mmhmm."},{"speaker":"Pam","startTime":71.1,"endTime":73.89,"body":"Which is interesting for a"},{"speaker":"Pam","startTime":71.1,"endTime":73.89,"body":"group of people who are all"},{"speaker":"Pam","startTime":73.89,"endTime":74.94,"body":"about definitions."},{"speaker":"Kim","startTime":75.57,"endTime":76.11,"body":"Right?"},{"speaker":"Pam","startTime":76.14,"endTime":80.7,"body":"Right? So, it reminds me of"},{"speaker":"Pam","startTime":76.14,"endTime":80.7,"body":"a story that I heard Dylan"},{"speaker":"Pam","startTime":80.7,"endTime":84.48,"body":"Williams say one time. Which I"},{"speaker":"Pam","startTime":80.7,"endTime":84.48,"body":"think \"William\" not. There's no"},{"speaker":"Pam","startTime":84.51,"endTime":85.53,"body":"\"s\", right? Dylan William?"},{"speaker":"Kim","startTime":85.53,"endTime":85.65,"body":"Yeah, no."},{"speaker":"Pam","startTime":85.69,"endTime":87.88,"body":"Yeah. Sorry about that,"},{"speaker":"Pam","startTime":85.69,"endTime":87.88,"body":"Dylan. He's all about"},{"speaker":"Pam","startTime":87.88,"endTime":91.66,"body":"assessment. He's a good speaker."},{"speaker":"Pam","startTime":87.88,"endTime":91.66,"body":"I've learned some things from"},{"speaker":"Pam","startTime":91.66,"endTime":95.71,"body":"him. And I really appreciated"},{"speaker":"Pam","startTime":91.66,"endTime":95.71,"body":"this story. He talked about the"},{"speaker":"Pam","startTime":95.71,"endTime":99.88,"body":"word \"similar\" in mathematics."},{"speaker":"Pam","startTime":95.71,"endTime":99.88,"body":"So, the word \"similar\" in"},{"speaker":"Pam","startTime":99.88,"endTime":103.9,"body":"English has a very specific"},{"speaker":"Pam","startTime":99.88,"endTime":103.9,"body":"mathematical definition, but in"},{"speaker":"Pam","startTime":103.9,"endTime":107.56,"body":"everyday usage, we... (unclear)."},{"speaker":"Pam","startTime":103.9,"endTime":107.56,"body":"You know, Kim, you and I are"},{"speaker":"Pam","startTime":107.56,"endTime":111.61,"body":"similar in some ways, right? I"},{"speaker":"Pam","startTime":107.56,"endTime":111.61,"body":"mean, we live close, near each"},{"speaker":"Pam","startTime":111.61,"endTime":115.84,"body":"other. We both taught math"},{"speaker":"Pam","startTime":111.61,"endTime":115.84,"body":"(unclear). We're both women. We"},{"speaker":"Pam","startTime":115.84,"endTime":118.78,"body":"both have kids. I don't know."},{"speaker":"Pam","startTime":115.84,"endTime":118.78,"body":"There's some similarities that"},{"speaker":"Pam","startTime":118.78,"endTime":123.91,"body":"we have. We both like chips and"},{"speaker":"Pam","startTime":118.78,"endTime":123.91,"body":"salsa. Though, you might like it"},{"speaker":"Pam","startTime":123.91,"endTime":128.26,"body":"more than me. So, we have"},{"speaker":"Pam","startTime":123.91,"endTime":128.26,"body":"some...there's this word"},{"speaker":"Pam","startTime":128.29,"endTime":132.34,"body":"\"similar\" in everyday language"},{"speaker":"Pam","startTime":128.29,"endTime":132.34,"body":"that means, you know, we're kind"},{"speaker":"Pam","startTime":132.34,"endTime":135.61,"body":"of alike. We kind of have some"},{"speaker":"Pam","startTime":132.34,"endTime":135.61,"body":"things in common. But in"},{"speaker":"Pam","startTime":135.61,"endTime":139.36,"body":"mathematical definition, it's"},{"speaker":"Pam","startTime":135.61,"endTime":139.36,"body":"very particular. It has a very"},{"speaker":"Pam","startTime":139.36,"endTime":142.42,"body":"particular meaning. And he"},{"speaker":"Pam","startTime":139.36,"endTime":142.42,"body":"suggested that...and I don't"},{"speaker":"Pam","startTime":142.42,"endTime":144.7,"body":"remember the country he was in,"},{"speaker":"Pam","startTime":142.42,"endTime":144.7,"body":"but I'm pretty sure it was an"},{"speaker":"Pam","startTime":144.7,"endTime":148.9,"body":"Asian country...that in that"},{"speaker":"Pam","startTime":144.7,"endTime":148.9,"body":"particular country, when you get"},{"speaker":"Pam","startTime":148.9,"endTime":153.28,"body":"to \"similarity\", and you're"},{"speaker":"Pam","startTime":148.9,"endTime":153.28,"body":"talking about that shapes can"},{"speaker":"Pam","startTime":153.28,"endTime":159.04,"body":"have the same shape but"},{"speaker":"Pam","startTime":153.28,"endTime":159.04,"body":"different size; that the angles"},{"speaker":"Pam","startTime":159.04,"endTime":161.65,"body":"are congruent on a triangle,"},{"speaker":"Pam","startTime":159.04,"endTime":161.65,"body":"therefore the triangles are"},{"speaker":"Pam","startTime":161.65,"endTime":164.98,"body":"similar, but they can, you know,"},{"speaker":"Pam","startTime":161.65,"endTime":164.98,"body":"have a small triangle that's"},{"speaker":"Pam","startTime":164.98,"endTime":167.32,"body":"equalateral and a large triangle"},{"speaker":"Pam","startTime":164.98,"endTime":167.32,"body":"that's equalateral but they're"},{"speaker":"Pam","startTime":167.32,"endTime":172.33,"body":"similar; That definition of"},{"speaker":"Pam","startTime":167.32,"endTime":172.33,"body":"\"similar\", similar shapes, is"},{"speaker":"Pam","startTime":172.33,"endTime":177.7,"body":"very specific definition. That"},{"speaker":"Pam","startTime":172.33,"endTime":177.7,"body":"in that Asian language, they"},{"speaker":"Pam","startTime":177.7,"endTime":183.13,"body":"made up a word. That they don't"},{"speaker":"Pam","startTime":177.7,"endTime":183.13,"body":"use a commonly known word to"},{"speaker":"Pam","startTime":183.13,"endTime":187.24,"body":"then have a specific different"},{"speaker":"Pam","startTime":183.13,"endTime":187.24,"body":"definition. They made up a word."},{"speaker":"Pam","startTime":187.24,"endTime":189.73,"body":"And so, when kids in that"},{"speaker":"Pam","startTime":187.24,"endTime":189.73,"body":"country learn about"},{"speaker":"Pam","startTime":189.73,"endTime":193.36,"body":"\"similarity\", the mathematical"},{"speaker":"Pam","startTime":189.73,"endTime":193.36,"body":"definition of \"similarity\", they"},{"speaker":"Pam","startTime":193.36,"endTime":196.84,"body":"don't mess it up. That because"},{"speaker":"Pam","startTime":193.36,"endTime":196.84,"body":"there's this very. That's"},{"speaker":"Pam","startTime":196.84,"endTime":197.53,"body":"interesting, right?"},{"speaker":"Kim","startTime":197.55,"endTime":198.42,"body":"That is interesting."},{"speaker":"Pam","startTime":198.45,"endTime":201.99,"body":"There's this very specific"},{"speaker":"Pam","startTime":198.45,"endTime":201.99,"body":"word that has a very specific"},{"speaker":"Pam","startTime":201.99,"endTime":205.38,"body":"definition, and it's only used"},{"speaker":"Pam","startTime":201.99,"endTime":205.38,"body":"in that way. Kids don't mess up"},{"speaker":"Pam","startTime":205.41,"endTime":209.13,"body":"\"similarity\" in the same way"},{"speaker":"Pam","startTime":205.41,"endTime":209.13,"body":"that they do when the language"},{"speaker":"Pam","startTime":209.16,"endTime":212.82,"body":"is not well defined. That's what"},{"speaker":"Pam","startTime":209.16,"endTime":212.82,"body":"I mean. Like, we have this word"},{"speaker":"Pam","startTime":212.82,"endTime":215.4,"body":"that can mean so many different"},{"speaker":"Pam","startTime":212.82,"endTime":215.4,"body":"things. \"Oh, but in math, it"},{"speaker":"Pam","startTime":215.4,"endTime":218.19,"body":"should be this.\" But kids have a"},{"speaker":"Pam","startTime":215.4,"endTime":218.19,"body":"hard time parsing that out. And"},{"speaker":"Pam","startTime":218.22,"endTime":220.62,"body":"I don't know, maybe we as"},{"speaker":"Pam","startTime":218.22,"endTime":220.62,"body":"teachers could do a far better"},{"speaker":"Pam","startTime":220.62,"endTime":223.38,"body":"job of parsing out what the"},{"speaker":"Pam","startTime":220.62,"endTime":223.38,"body":"mathematical meaning of"},{"speaker":"Pam","startTime":223.38,"endTime":227.01,"body":"\"similarity\" is versus, you"},{"speaker":"Pam","startTime":223.38,"endTime":227.01,"body":"know, this sort of commonly used"},{"speaker":"Pam","startTime":227.01,"endTime":227.31,"body":"word."},{"speaker":"Kim","startTime":227.52,"endTime":229.02,"body":"Yeah. That's interesting."},{"speaker":"Pam","startTime":229.17,"endTime":230.67,"body":"Right? It's fascinating."},{"speaker":"Kim","startTime":230.73,"endTime":234.03,"body":"Yeah, it is really cool."},{"speaker":"Kim","startTime":230.73,"endTime":234.03,"body":"So, there are these words that"},{"speaker":"Kim","startTime":234.03,"endTime":237.54,"body":"we often say that have different"},{"speaker":"Kim","startTime":234.03,"endTime":237.54,"body":"meanings. And so, today, we'd"},{"speaker":"Kim","startTime":237.54,"endTime":242.64,"body":"like to focus on one of those"},{"speaker":"Kim","startTime":237.54,"endTime":242.64,"body":"words, which is \"simplify\". And"},{"speaker":"Kim","startTime":242.64,"endTime":245.16,"body":"we've actually mentioned this"},{"speaker":"Kim","startTime":242.64,"endTime":245.16,"body":"before because we did an"},{"speaker":"Kim","startTime":245.16,"endTime":247.86,"body":"episode... Oh gosh, way back"},{"speaker":"Kim","startTime":245.16,"endTime":247.86,"body":"when. I don't even know the"},{"speaker":"Kim","startTime":247.86,"endTime":249.0,"body":"number. It's like maybe"},{"speaker":"Kim","startTime":247.86,"endTime":249.0,"body":"(unclear)."},{"speaker":"Pam","startTime":249.0,"endTime":250.11,"body":"We'll put it in the show"},{"speaker":"Pam","startTime":249.0,"endTime":250.11,"body":"notes, yeah."},{"speaker":"Kim","startTime":250.14,"endTime":253.71,"body":"Yeah. That we did a \"This,"},{"speaker":"Kim","startTime":250.14,"endTime":253.71,"body":"Not That\" episode, and we"},{"speaker":"Kim","startTime":253.71,"endTime":257.22,"body":"tackled some of the words in"},{"speaker":"Kim","startTime":253.71,"endTime":257.22,"body":"mathematics that people use that"},{"speaker":"Kim","startTime":257.22,"endTime":261.18,"body":"make us cringe just a wee bit."},{"speaker":"Kim","startTime":257.22,"endTime":261.18,"body":"And one of the words that we"},{"speaker":"Kim","startTime":261.18,"endTime":265.8,"body":"said that we don't say is"},{"speaker":"Kim","startTime":261.18,"endTime":265.8,"body":"\"reduce\". And what I said at"},{"speaker":"Kim","startTime":265.8,"endTime":268.29,"body":"that time, and what you said at"},{"speaker":"Kim","startTime":265.8,"endTime":268.29,"body":"the time was, \"We kind of use"},{"speaker":"Kim","startTime":268.29,"endTime":271.26,"body":"the word 'simplify'.\" But I"},{"speaker":"Kim","startTime":268.29,"endTime":271.26,"body":"mentioned it, and you were like,"},{"speaker":"Kim","startTime":272.19,"endTime":274.02,"body":"\"Mmm...\" You know, \"Okay, but"},{"speaker":"Kim","startTime":272.19,"endTime":274.02,"body":"(unclear)."},{"speaker":"Pam","startTime":274.02,"endTime":275.13,"body":"Neither of us love it."},{"speaker":"Both Pam and Kim","startTime":275.22,"endTime":275.79,"body":"Yeah."},{"speaker":"Pam","startTime":275.82,"endTime":276.24,"body":"Yeah."},{"speaker":"Kim","startTime":276.24,"endTime":278.55,"body":"So, we're going to talk"},{"speaker":"Kim","startTime":276.24,"endTime":278.55,"body":"about that today."},{"speaker":"Pam","startTime":278.61,"endTime":281.49,"body":"Well, so to be clear. We"},{"speaker":"Pam","startTime":278.61,"endTime":281.49,"body":"for sure don't like the word"},{"speaker":"Pam","startTime":282.06,"endTime":285.84,"body":"\"reduce\" when we're talking"},{"speaker":"Pam","startTime":282.06,"endTime":285.84,"body":"about fractions."},{"speaker":"Kim","startTime":286.11,"endTime":286.32,"body":"Yeah."},{"speaker":"Pam","startTime":286.35,"endTime":288.96,"body":"Because if we're messing"},{"speaker":"Pam","startTime":286.35,"endTime":288.96,"body":"around with fractions, and we"},{"speaker":"Pam","startTime":288.96,"endTime":292.83,"body":"use the word \"reduce\" to mean"},{"speaker":"Pam","startTime":288.96,"endTime":292.83,"body":"\"create an equivalent fraction"},{"speaker":"Pam","startTime":292.86,"endTime":295.47,"body":"where there are no common"},{"speaker":"Pam","startTime":292.86,"endTime":295.47,"body":"factors between the numerator"},{"speaker":"Pam","startTime":295.47,"endTime":300.33,"body":"and denominator\", the word"},{"speaker":"Pam","startTime":295.47,"endTime":300.33,"body":"\"reduce\" feels like \"get"},{"speaker":"Pam","startTime":300.63,"endTime":304.8,"body":"smaller\". And often the"},{"speaker":"Pam","startTime":300.63,"endTime":304.8,"body":"numerator will be a smaller"},{"speaker":"Pam","startTime":304.8,"endTime":307.2,"body":"number than the previous"},{"speaker":"Pam","startTime":304.8,"endTime":307.2,"body":"numerator and the denominator"},{"speaker":"Pam","startTime":307.2,"endTime":309.63,"body":"will be a smaller number than"},{"speaker":"Pam","startTime":307.2,"endTime":309.63,"body":"the previous. I should give an"},{"speaker":"Pam","startTime":309.63,"endTime":312.03,"body":"example. We're being really"},{"speaker":"Pam","startTime":309.63,"endTime":312.03,"body":"esoteric here. So, if I was"},{"speaker":"Pam","startTime":312.03,"endTime":316.98,"body":"talking about twelve-fifteenths,"},{"speaker":"Pam","startTime":312.03,"endTime":316.98,"body":"and a textbook might say \"reduce"},{"speaker":"Pam","startTime":316.98,"endTime":320.19,"body":"that fraction\", then you might"},{"speaker":"Pam","startTime":316.98,"endTime":320.19,"body":"say, \"Well, okay. Like, I can"},{"speaker":"Pam","startTime":320.19,"endTime":322.38,"body":"see that there's a factor of 3"},{"speaker":"Pam","startTime":320.19,"endTime":322.38,"body":"in each of those. So,"},{"speaker":"Pam","startTime":322.38,"endTime":326.31,"body":"twelve-fifteenths. Divide a 3"},{"speaker":"Pam","startTime":322.38,"endTime":326.31,"body":"out of the 12, and that's 4. And"},{"speaker":"Pam","startTime":326.31,"endTime":329.34,"body":"I can divide a 3 out of 15, and"},{"speaker":"Pam","startTime":326.31,"endTime":329.34,"body":"that's 5. And so,"},{"speaker":"Pam","startTime":329.52,"endTime":332.73,"body":"twelve-fifteenths is equivalent"},{"speaker":"Pam","startTime":329.52,"endTime":332.73,"body":"to four-fifths. And you might"},{"speaker":"Pam","startTime":332.79,"endTime":335.82,"body":"say, \"Well, yeah. Like, 4 is"},{"speaker":"Pam","startTime":332.79,"endTime":335.82,"body":"smaller than 12. And 5 is"},{"speaker":"Pam","startTime":335.82,"endTime":340.11,"body":"smaller than 15. But the"},{"speaker":"Pam","startTime":335.82,"endTime":340.11,"body":"fraction four-fifths is not"},{"speaker":"Pam","startTime":340.11,"endTime":344.88,"body":"smaller than twelve-fifteenths.\""},{"speaker":"Pam","startTime":340.11,"endTime":344.88,"body":"So, we hate the word \"reduce\""},{"speaker":"Pam","startTime":345.18,"endTime":349.8,"body":"when we mean, \"find an"},{"speaker":"Pam","startTime":345.18,"endTime":349.8,"body":"equivalent fraction\". That maybe"},{"speaker":"Pam","startTime":349.8,"endTime":353.82,"body":"you've reduced common factors"},{"speaker":"Pam","startTime":349.8,"endTime":353.82,"body":"between the numerator and"},{"speaker":"Pam","startTime":353.82,"endTime":357.09,"body":"denominator. That's how some"},{"speaker":"Pam","startTime":353.82,"endTime":357.09,"body":"colleagues of mine once said,"},{"speaker":"Pam","startTime":357.09,"endTime":358.86,"body":"\"No, no, no. 'Reduce' totally"},{"speaker":"Pam","startTime":357.09,"endTime":358.86,"body":"makes sense because you're"},{"speaker":"Pam","startTime":358.86,"endTime":361.53,"body":"reducing the number of common"},{"speaker":"Pam","startTime":358.86,"endTime":361.53,"body":"factors. You reduce. There's no"},{"speaker":"Pam","startTime":361.53,"endTime":364.05,"body":"common factors now between the"},{"speaker":"Pam","startTime":361.53,"endTime":364.05,"body":"numerator and denominator.\" And"},{"speaker":"Pam","startTime":364.05,"endTime":365.73,"body":"I'm like, \"Yeah, okay (unclear)\""},{"speaker":"Kim","startTime":365.91,"endTime":368.25,"body":"But that's not what kids"},{"speaker":"Kim","startTime":365.91,"endTime":368.25,"body":"say."},{"speaker":"Pam","startTime":368.61,"endTime":369.72,"body":"Not in any way, right."},{"speaker":"Pam","startTime":368.61,"endTime":369.72,"body":"(unclear)"},{"speaker":"Kim","startTime":369.75,"endTime":370.11,"body":"Yeah."},{"speaker":"Pam","startTime":370.11,"endTime":372.93,"body":"(unclear) explain why we"},{"speaker":"Pam","startTime":370.11,"endTime":372.93,"body":"use this horrible word to mean"},{"speaker":"Pam","startTime":372.93,"endTime":375.78,"body":"what it doesn't really mean. But"},{"speaker":"Pam","startTime":372.93,"endTime":375.78,"body":"we don't like it because it"},{"speaker":"Pam","startTime":375.78,"endTime":378.66,"body":"sends such a... What? (unclear)."},{"speaker":"Kim","startTime":378.93,"endTime":380.4,"body":"A confusing message. Yeah."},{"speaker":"Pam","startTime":380.4,"endTime":382.71,"body":"A confusing message. Yeah,"},{"speaker":"Pam","startTime":380.4,"endTime":382.71,"body":"absolutely. And that's"},{"speaker":"Pam","startTime":382.71,"endTime":386.04,"body":"specifically when we're talking"},{"speaker":"Pam","startTime":382.71,"endTime":386.04,"body":"about fractions."},{"speaker":"Kim","startTime":386.46,"endTime":386.73,"body":"Right."},{"speaker":"Pam","startTime":387.05,"endTime":389.93,"body":"So, we said, \"So, we can"},{"speaker":"Pam","startTime":387.05,"endTime":389.93,"body":"use the word 'simplify'...\" But"},{"speaker":"Pam","startTime":389.93,"endTime":393.23,"body":"like you said, neither of us"},{"speaker":"Pam","startTime":389.93,"endTime":393.23,"body":"really love that. Because"},{"speaker":"Pam","startTime":393.92,"endTime":397.76,"body":"\"simplify\"? Does that really"},{"speaker":"Pam","startTime":393.92,"endTime":397.76,"body":"work when what we mean is \"find"},{"speaker":"Pam","startTime":397.76,"endTime":403.4,"body":"an equivalent fraction\". Like is"},{"speaker":"Pam","startTime":397.76,"endTime":403.4,"body":"four-fifths simpler than"},{"speaker":"Pam","startTime":403.43,"endTime":409.88,"body":"twelve-fifteenths? Yeah. Like,"},{"speaker":"Pam","startTime":403.43,"endTime":409.88,"body":"you could maybe make an argument"},{"speaker":"Pam","startTime":409.88,"endTime":413.78,"body":"that thinking about 4 pieces out"},{"speaker":"Pam","startTime":409.88,"endTime":413.78,"body":"of 5 pieces is simpler than"},{"speaker":"Pam","startTime":413.78,"endTime":417.59,"body":"thinking about 12 pieces out of"},{"speaker":"Pam","startTime":413.78,"endTime":417.59,"body":"15 pieces. You could try that"},{"speaker":"Pam","startTime":417.59,"endTime":421.94,"body":"argument. But again, we don't"},{"speaker":"Pam","startTime":417.59,"endTime":421.94,"body":"really love the word \"simplify\""},{"speaker":"Pam","startTime":421.97,"endTime":426.8,"body":"either when it comes to"},{"speaker":"Pam","startTime":421.97,"endTime":426.8,"body":"simplifying fractions."},{"speaker":"Kim","startTime":427.07,"endTime":429.92,"body":"And at the time, we just"},{"speaker":"Kim","startTime":427.07,"endTime":429.92,"body":"kind of left it. We were like,"},{"speaker":"Kim","startTime":430.76,"endTime":430.79,"body":"\"Ugh.\""},{"speaker":"Pam","startTime":431.81,"endTime":432.98,"body":"Yeah. Yeah."},{"speaker":"Kim","startTime":433.01,"endTime":435.59,"body":"But now you've had some"},{"speaker":"Kim","startTime":433.01,"endTime":435.59,"body":"more opportunities to think"},{"speaker":"Kim","startTime":435.59,"endTime":436.37,"body":"about that, right?"},{"speaker":"Pam","startTime":436.73,"endTime":440.63,"body":"I have. And so what's"},{"speaker":"Pam","startTime":436.73,"endTime":440.63,"body":"interesting is. Okay, I got to"},{"speaker":"Pam","startTime":440.63,"endTime":442.79,"body":"tell you, I've been trying to"},{"speaker":"Pam","startTime":440.63,"endTime":442.79,"body":"find the \"This, Not That\""},{"speaker":"Pam","startTime":442.79,"endTime":447.05,"body":"episode as we've been talking,"},{"speaker":"Pam","startTime":442.79,"endTime":447.05,"body":"and so I'm a little distracted."},{"speaker":"Pam","startTime":447.41,"endTime":451.7,"body":"It might be episode... No,"},{"speaker":"Pam","startTime":447.41,"endTime":451.7,"body":"that's not it. Okay. Oh, maybe I"},{"speaker":"Pam","startTime":451.7,"endTime":455.03,"body":"just found it. There it is. It's"},{"speaker":"Pam","startTime":451.7,"endTime":455.03,"body":"Episode 18. So, if you want to"},{"speaker":"Pam","startTime":455.03,"endTime":458.24,"body":"go back. And that was a while"},{"speaker":"Pam","startTime":455.03,"endTime":458.24,"body":"ago. So, episode 18. We talked"},{"speaker":"Pam","startTime":458.24,"endTime":460.61,"body":"about some of \"This, Not That\""},{"speaker":"Pam","startTime":458.24,"endTime":460.61,"body":"things. But like you said, we've"},{"speaker":"Pam","startTime":460.61,"endTime":465.26,"body":"gained some clarity. Hugely,"},{"speaker":"Pam","startTime":460.61,"endTime":465.26,"body":"this last weekend when I was in"},{"speaker":"Pam","startTime":465.5,"endTime":468.47,"body":"Utah, and I was talking to some"},{"speaker":"Pam","startTime":465.5,"endTime":468.47,"body":"teachers, I gained some clarity"},{"speaker":"Pam","startTime":468.74,"endTime":474.29,"body":"about the idea of the word"},{"speaker":"Pam","startTime":468.74,"endTime":474.29,"body":"\"simplify\". When I was dealing"},{"speaker":"Pam","startTime":474.29,"endTime":477.74,"body":"with these high school teachers"},{"speaker":"Pam","startTime":474.29,"endTime":477.74,"body":"in Utah. It occurred to me,"},{"speaker":"Pam","startTime":477.86,"endTime":481.04,"body":"partly because they were"},{"speaker":"Pam","startTime":477.86,"endTime":481.04,"body":"suggesting it, that we don't"},{"speaker":"Pam","startTime":481.04,"endTime":484.58,"body":"just use the word \"simplify\"..."},{"speaker":"Pam","startTime":481.04,"endTime":484.58,"body":"And I know this. But we don't"},{"speaker":"Pam","startTime":484.58,"endTime":489.14,"body":"just use it with fractions. We"},{"speaker":"Pam","startTime":484.58,"endTime":489.14,"body":"use it in lots of other places"},{"speaker":"Pam","startTime":489.35,"endTime":493.7,"body":"to mean other things. Like, the"},{"speaker":"Pam","startTime":489.35,"endTime":493.7,"body":"word \"simplify\" is super"},{"speaker":"Pam","startTime":494.27,"endTime":498.41,"body":"confusing, not just because it"},{"speaker":"Pam","startTime":494.27,"endTime":498.41,"body":"doesn't relate well with when"},{"speaker":"Pam","startTime":498.41,"endTime":501.71,"body":"we're finding an equivalent"},{"speaker":"Pam","startTime":498.41,"endTime":501.71,"body":"fraction, but it also has other"},{"speaker":"Pam","startTime":501.71,"endTime":505.34,"body":"places where it doesn't... It's"},{"speaker":"Pam","startTime":501.71,"endTime":505.34,"body":"not well defined. It can mean"},{"speaker":"Pam","startTime":505.34,"endTime":507.44,"body":"other things. So, let me give"},{"speaker":"Pam","startTime":505.34,"endTime":507.44,"body":"you some examples. Let's stay"},{"speaker":"Pam","startTime":507.44,"endTime":510.77,"body":"with fractions for just a"},{"speaker":"Pam","startTime":507.44,"endTime":510.77,"body":"second. Notice, that I could"},{"speaker":"Pam","startTime":510.77,"endTime":513.68,"body":"have that twelve-fifteenths"},{"speaker":"Pam","startTime":510.77,"endTime":513.68,"body":"being equivalent to that"},{"speaker":"Pam","startTime":513.68,"endTime":517.52,"body":"four-fifths, but you lose"},{"speaker":"Pam","startTime":513.68,"endTime":517.52,"body":"information or you run the"},{"speaker":"Pam","startTime":517.52,"endTime":521.3,"body":"potential of losing information"},{"speaker":"Pam","startTime":517.52,"endTime":521.3,"body":"about the context. So, for"},{"speaker":"Pam","startTime":521.3,"endTime":525.56,"body":"example, let's say if I was"},{"speaker":"Pam","startTime":521.3,"endTime":525.56,"body":"talking about making 63 out of"},{"speaker":"Pam","startTime":525.56,"endTime":529.91,"body":"119 free throws. You might be"},{"speaker":"Pam","startTime":525.56,"endTime":529.91,"body":"like, \"Okay. Well, I kind of"},{"speaker":"Pam","startTime":529.91,"endTime":533.09,"body":"have a feel for that.\" But if I"},{"speaker":"Pam","startTime":529.91,"endTime":533.09,"body":"just simplify that, so that it's"},{"speaker":"Pam","startTime":533.09,"endTime":536.66,"body":"about 2 out of 4. And it's just"},{"speaker":"Pam","startTime":533.09,"endTime":536.66,"body":"about 2 out of 4 on that one."},{"speaker":"Pam","startTime":536.96,"endTime":540.68,"body":"Then, you've lost some"},{"speaker":"Pam","startTime":536.96,"endTime":540.68,"body":"information. You don't know how"},{"speaker":"Pam","startTime":540.68,"endTime":543.5,"body":"many total free throws I was"},{"speaker":"Pam","startTime":540.68,"endTime":543.5,"body":"shooting. I mean, if I just said"},{"speaker":"Pam","startTime":543.5,"endTime":547.1,"body":"to the coach, \"Hey, you know"},{"speaker":"Pam","startTime":543.5,"endTime":547.1,"body":"like, 2 out of 4 free throws\""},{"speaker":"Pam","startTime":547.13,"endTime":551.0,"body":"versus \"63 out of 119.\" I might"},{"speaker":"Pam","startTime":547.13,"endTime":551.0,"body":"be like, Whoa, that kid shot a"},{"speaker":"Pam","startTime":551.0,"endTime":552.11,"body":"lot of free throws that day.\""},{"speaker":"Kim","startTime":552.41,"endTime":552.74,"body":"Yeah."},{"speaker":"Pam","startTime":552.77,"endTime":556.1,"body":"Versus... You know, like"},{"speaker":"Pam","startTime":552.77,"endTime":556.1,"body":"you run the potential of losing"},{"speaker":"Pam","startTime":556.1,"endTime":558.98,"body":"information. So, that's just one"},{"speaker":"Pam","startTime":556.1,"endTime":558.98,"body":"way of thinking about how it's"},{"speaker":"Pam","startTime":558.98,"endTime":563.54,"body":"not super with respect to"},{"speaker":"Pam","startTime":558.98,"endTime":563.54,"body":"finding equivalent fractions."},{"speaker":"Pam","startTime":563.99,"endTime":570.92,"body":"But also, we might send the"},{"speaker":"Pam","startTime":563.99,"endTime":570.92,"body":"impression to students that if"},{"speaker":"Pam","startTime":570.92,"endTime":574.49,"body":"they say...back to my"},{"speaker":"Pam","startTime":570.92,"endTime":574.49,"body":"twelve-fifteenths example...if"},{"speaker":"Pam","startTime":574.76,"endTime":577.85,"body":"they say twelve-fifteenths, and"},{"speaker":"Pam","startTime":574.76,"endTime":577.85,"body":"I mark it wrong because they"},{"speaker":"Pam","startTime":577.85,"endTime":580.28,"body":"didn't simplify it, or they"},{"speaker":"Pam","startTime":577.85,"endTime":580.28,"body":"didn't write an equivalent"},{"speaker":"Pam","startTime":580.28,"endTime":583.31,"body":"fraction that's in simplest"},{"speaker":"Pam","startTime":580.28,"endTime":583.31,"body":"form. See, we don't have really"},{"speaker":"Pam","startTime":583.31,"endTime":586.25,"body":"good words for this. They didn't"},{"speaker":"Pam","startTime":583.31,"endTime":586.25,"body":"write a fraction where the"},{"speaker":"Pam","startTime":586.28,"endTime":589.16,"body":"numerator, denominator are"},{"speaker":"Pam","startTime":586.28,"endTime":589.16,"body":"relatively prime. That's kind of"},{"speaker":"Pam","startTime":589.16,"endTime":592.4,"body":"complicated way of saying it."},{"speaker":"Pam","startTime":589.16,"endTime":592.4,"body":"Like, how could we say \"Write a"},{"speaker":"Pam","startTime":592.4,"endTime":595.58,"body":"fraction that's equivalent\"?"},{"speaker":"Pam","startTime":592.4,"endTime":595.58,"body":"\"Rewrite this fraction"},{"speaker":"Pam","startTime":595.67,"endTime":599.24,"body":"equivalent, so there's no common"},{"speaker":"Pam","startTime":595.67,"endTime":599.24,"body":"factors in the numerator"},{"speaker":"Pam","startTime":599.24,"endTime":601.4,"body":"denominator,\" that's a way of"},{"speaker":"Pam","startTime":599.24,"endTime":601.4,"body":"saying it. Boy, super"},{"speaker":"Pam","startTime":601.4,"endTime":605.18,"body":"complicated. If we mark"},{"speaker":"Pam","startTime":601.4,"endTime":605.18,"body":"twelve-fifteenths wrong because"},{"speaker":"Pam","startTime":605.18,"endTime":609.95,"body":"they didn't write four-fifths, I"},{"speaker":"Pam","startTime":605.18,"endTime":609.95,"body":"worry that students think, \"Oh,"},{"speaker":"Pam","startTime":609.95,"endTime":612.8,"body":"so twelve-fifteenths doesn't"},{"speaker":"Pam","startTime":609.95,"endTime":612.8,"body":"correctly represent the"},{"speaker":"Pam","startTime":612.8,"endTime":616.79,"body":"situation.\" When in reality, it"},{"speaker":"Pam","startTime":612.8,"endTime":616.79,"body":"might represent the situation"},{"speaker":"Pam","startTime":616.79,"endTime":618.86,"body":"better than four-fifths."},{"speaker":"Kim","startTime":618.95,"endTime":619.46,"body":"Right."},{"speaker":"Pam","startTime":619.49,"endTime":623.99,"body":"So, this is kind of a super"},{"speaker":"Pam","startTime":619.49,"endTime":623.99,"body":"tricky... Like, I understand"},{"speaker":"Pam","startTime":623.99,"endTime":627.59,"body":"that teachers often want to have"},{"speaker":"Pam","startTime":623.99,"endTime":627.59,"body":"four-fifths. They're like,"},{"speaker":"Pam","startTime":627.77,"endTime":630.68,"body":"\"Yeah. But, like, I want to be"},{"speaker":"Pam","startTime":627.77,"endTime":630.68,"body":"able to see, can students find"},{"speaker":"Pam","startTime":630.68,"endTime":634.55,"body":"the equivalent four-fifths to"},{"speaker":"Pam","startTime":630.68,"endTime":634.55,"body":"twelve-fifteenths?\" But I think"},{"speaker":"Pam","startTime":634.55,"endTime":638.15,"body":"we might want to be at least"},{"speaker":"Pam","startTime":634.55,"endTime":638.15,"body":"clear with students at least in"},{"speaker":"Pam","startTime":638.15,"endTime":641.42,"body":"a minimum. Teachers, may I"},{"speaker":"Pam","startTime":638.15,"endTime":641.42,"body":"invite you, be clear with"},{"speaker":"Pam","startTime":641.42,"endTime":643.52,"body":"students that twelve-fifteenths"},{"speaker":"Pam","startTime":641.42,"endTime":643.52,"body":"is not incorrect."},{"speaker":"Kim","startTime":644.15,"endTime":644.6,"body":"Right."},{"speaker":"Pam","startTime":644.84,"endTime":647.42,"body":"It's equivalent. It's just"},{"speaker":"Pam","startTime":644.84,"endTime":647.42,"body":"maybe not the answer you're"},{"speaker":"Pam","startTime":647.42,"endTime":652.88,"body":"looking for. And can we, then,"},{"speaker":"Pam","startTime":647.42,"endTime":652.88,"body":"maybe agree that it's convention"},{"speaker":"Pam","startTime":653.21,"endTime":656.9,"body":"that we're looking for that"},{"speaker":"Pam","startTime":653.21,"endTime":656.9,"body":"maybe easier to grade answer."},{"speaker":"Pam","startTime":657.41,"endTime":660.62,"body":"That maybe we're actually"},{"speaker":"Pam","startTime":657.41,"endTime":660.62,"body":"looking... Sometimes. Now, maybe"},{"speaker":"Pam","startTime":660.62,"endTime":663.08,"body":"not all the time. Maybe we"},{"speaker":"Pam","startTime":660.62,"endTime":663.08,"body":"really do want to know if"},{"speaker":"Pam","startTime":663.08,"endTime":666.26,"body":"students can factor out those"},{"speaker":"Pam","startTime":663.08,"endTime":666.26,"body":"common factors, divide out those"},{"speaker":"Pam","startTime":666.26,"endTime":669.8,"body":"common factors. Maybe we are"},{"speaker":"Pam","startTime":666.26,"endTime":669.8,"body":"really. We do want to say that."},{"speaker":"Pam","startTime":669.8,"endTime":672.29,"body":"But maybe we ought to say,"},{"speaker":"Pam","startTime":669.8,"endTime":672.29,"body":"\"Rewrite that fraction and"},{"speaker":"Pam","startTime":672.29,"endTime":674.3,"body":"divide out all the common"},{"speaker":"Pam","startTime":672.29,"endTime":674.3,"body":"factors from the numerator,"},{"speaker":"Pam","startTime":674.3,"endTime":677.9,"body":"denominator.\" Something like"},{"speaker":"Pam","startTime":674.3,"endTime":677.9,"body":"that, but not give the"},{"speaker":"Pam","startTime":677.9,"endTime":680.54,"body":"impression it's incorrect. But"},{"speaker":"Pam","startTime":677.9,"endTime":680.54,"body":"could we at least admit that"},{"speaker":"Pam","startTime":680.54,"endTime":683.6,"body":"sometimes we're asking for that"},{"speaker":"Pam","startTime":680.54,"endTime":683.6,"body":"simplified version of the"},{"speaker":"Pam","startTime":683.6,"endTime":688.25,"body":"fraction because it's easier to"},{"speaker":"Pam","startTime":683.6,"endTime":688.25,"body":"grade? And at least admit that"},{"speaker":"Pam","startTime":688.25,"endTime":688.85,"body":"to students?"},{"speaker":"Kim","startTime":688.85,"endTime":689.24,"body":"Yes, yes."},{"speaker":"Pam","startTime":689.27,"endTime":692.69,"body":"Like, it's easier to grade"},{"speaker":"Pam","startTime":689.27,"endTime":692.69,"body":"if all we're looking for is that"},{"speaker":"Pam","startTime":693.35,"endTime":695.66,"body":"fraction where there are no"},{"speaker":"Pam","startTime":693.35,"endTime":695.66,"body":"common factors in the numerator,"},{"speaker":"Pam","startTime":695.66,"endTime":698.42,"body":"denominator. Because it's easier"},{"speaker":"Pam","startTime":695.66,"endTime":698.42,"body":"to grade. So, at least admit it."},{"speaker":"Pam","startTime":698.42,"endTime":701.0,"body":"Tell students, \"Hey, it's just"},{"speaker":"Pam","startTime":698.42,"endTime":701.0,"body":"easier for me to grade if you'll"},{"speaker":"Pam","startTime":701.0,"endTime":704.36,"body":"do that, but they're not wrong.\""},{"speaker":"Pam","startTime":701.0,"endTime":704.36,"body":"Like, let's just say,"},{"speaker":"Pam","startTime":704.39,"endTime":708.41,"body":"\"Twelve-fifteenths is not"},{"speaker":"Pam","startTime":704.39,"endTime":708.41,"body":"incorrect. It just has common"},{"speaker":"Pam","startTime":708.41,"endTime":711.02,"body":"factors in the numerator,"},{"speaker":"Pam","startTime":708.41,"endTime":711.02,"body":"denominator. And I want to know,"},{"speaker":"Pam","startTime":711.02,"endTime":714.59,"body":"today, if you can factor out"},{"speaker":"Pam","startTime":711.02,"endTime":714.59,"body":"those common factors. Divide"},{"speaker":"Pam","startTime":714.59,"endTime":716.48,"body":"out, I should say. \"...divide"},{"speaker":"Pam","startTime":714.59,"endTime":716.48,"body":"out those common factors\". And"},{"speaker":"Pam","startTime":717.29,"endTime":720.92,"body":"let's at least be clear with"},{"speaker":"Pam","startTime":717.29,"endTime":720.92,"body":"kids on that. But then, in this"},{"speaker":"Pam","startTime":720.92,"endTime":724.07,"body":"conversation with those high"},{"speaker":"Pam","startTime":720.92,"endTime":724.07,"body":"school teachers, they helped me"},{"speaker":"Pam","startTime":724.07,"endTime":728.48,"body":"become a little bit more clear"},{"speaker":"Pam","startTime":724.07,"endTime":728.48,"body":"that's not the only time we use"},{"speaker":"Pam","startTime":728.48,"endTime":730.79,"body":"\"simplify\". And I got kind of"},{"speaker":"Pam","startTime":728.48,"endTime":730.79,"body":"interested in that. I started"},{"speaker":"Pam","startTime":730.79,"endTime":734.87,"body":"thinking about all the times we"},{"speaker":"Pam","startTime":730.79,"endTime":734.87,"body":"use \"simplify\" because we do."},{"speaker":"Pam","startTime":734.96,"endTime":738.92,"body":"So, then, one of the"},{"speaker":"Pam","startTime":734.96,"endTime":738.92,"body":"participants in the workshop,"},{"speaker":"Pam","startTime":738.92,"endTime":742.67,"body":"super guy. His name is Travis"},{"speaker":"Pam","startTime":738.92,"endTime":742.67,"body":"Lemon. Travis and I've actually"},{"speaker":"Pam","startTime":742.67,"endTime":745.25,"body":"worked together for several"},{"speaker":"Pam","startTime":742.67,"endTime":745.25,"body":"years. He reminded me that we"},{"speaker":"Pam","startTime":745.25,"endTime":750.17,"body":"met... Golly. My daughter is 22."},{"speaker":"Pam","startTime":745.25,"endTime":750.17,"body":"So, you might be like, \"Why are"},{"speaker":"Pam","startTime":750.17,"endTime":752.57,"body":"you talking about your daughter,"},{"speaker":"Pam","startTime":750.17,"endTime":752.57,"body":"Pam?\" Because we met when I was"},{"speaker":"Pam","startTime":752.57,"endTime":756.29,"body":"doing a workshop in Utah when"},{"speaker":"Pam","startTime":752.57,"endTime":756.29,"body":"she was, golly, probably six"},{"speaker":"Pam","startTime":756.29,"endTime":759.86,"body":"months old. That's how I know"},{"speaker":"Pam","startTime":756.29,"endTime":759.86,"body":"because I took her to the"},{"speaker":"Pam","startTime":759.86,"endTime":763.58,"body":"workshop with my cousin. Maybe"},{"speaker":"Pam","startTime":759.86,"endTime":763.58,"body":"she was... I think she was more"},{"speaker":"Pam","startTime":763.58,"endTime":766.52,"body":"like three months old. It was in"},{"speaker":"Pam","startTime":763.58,"endTime":766.52,"body":"Utah. And my husband and I, we"},{"speaker":"Pam","startTime":766.52,"endTime":768.26,"body":"took all the kids out and"},{"speaker":"Pam","startTime":766.52,"endTime":768.26,"body":"everything. And my husband,"},{"speaker":"Pam","startTime":768.29,"endTime":771.56,"body":"during the day of the workshop."},{"speaker":"Pam","startTime":768.29,"endTime":771.56,"body":"He took the kids to the dinosaur"},{"speaker":"Pam","startTime":771.56,"endTime":775.7,"body":"museum, and I took Abby to the"},{"speaker":"Pam","startTime":771.56,"endTime":775.7,"body":"workshop and did the workshop,"},{"speaker":"Pam","startTime":775.7,"endTime":777.77,"body":"and then at break, I would go"},{"speaker":"Pam","startTime":775.7,"endTime":777.77,"body":"nurse her because I was"},{"speaker":"Pam","startTime":777.77,"endTime":780.26,"body":"breastfeeding her at the time."},{"speaker":"Pam","startTime":777.77,"endTime":780.26,"body":"And my cousin sort of took care"},{"speaker":"Pam","startTime":780.26,"endTime":782.57,"body":"of her during the time. And"},{"speaker":"Pam","startTime":780.26,"endTime":782.57,"body":"then, during the break, I'd chat"},{"speaker":"Pam","startTime":782.57,"endTime":784.19,"body":"with my cousin while I nursed."},{"speaker":"Pam","startTime":782.57,"endTime":784.19,"body":"And I would go back into the"},{"speaker":"Pam","startTime":784.19,"endTime":786.8,"body":"workshop. So, I can tell you"},{"speaker":"Pam","startTime":784.19,"endTime":786.8,"body":"exactly when we met because I"},{"speaker":"Pam","startTime":786.83,"endTime":789.5,"body":"totally remember that's how old"},{"speaker":"Pam","startTime":786.83,"endTime":789.5,"body":"my daughter was. And I met"},{"speaker":"Pam","startTime":789.5,"endTime":792.56,"body":"Travis then, and I was doing"},{"speaker":"Pam","startTime":789.5,"endTime":792.56,"body":"some work with algebra. And it's"},{"speaker":"Pam","startTime":792.56,"endTime":796.04,"body":"so cool to have this long term"},{"speaker":"Pam","startTime":792.56,"endTime":796.04,"body":"relationship with this fantastic"},{"speaker":"Pam","startTime":796.04,"endTime":799.28,"body":"teacher. And he said, \"Yeah,"},{"speaker":"Pam","startTime":796.04,"endTime":799.28,"body":"we've really been working on"},{"speaker":"Pam","startTime":799.28,"endTime":803.09,"body":"that.\" So \"we\" being Travis is"},{"speaker":"Pam","startTime":799.28,"endTime":803.09,"body":"one of the authors on the Open"},{"speaker":"Pam","startTime":803.09,"endTime":807.53,"body":"Up Resources, curriculum for"},{"speaker":"Pam","startTime":803.09,"endTime":807.53,"body":"high school. So, it used to be"},{"speaker":"Pam","startTime":807.53,"endTime":812.48,"body":"called MVP, and then they went"},{"speaker":"Pam","startTime":807.53,"endTime":812.48,"body":"to, Open Up is now publishing"},{"speaker":"Pam","startTime":812.48,"endTime":817.19,"body":"them. You can get it for free. I"},{"speaker":"Pam","startTime":812.48,"endTime":817.19,"body":"highly recommend it. One of the"},{"speaker":"Pam","startTime":817.19,"endTime":821.66,"body":"main creators of MVP or Open Up"},{"speaker":"Pam","startTime":817.19,"endTime":821.66,"body":"Resources, high school is Scott"},{"speaker":"Pam","startTime":821.66,"endTime":826.22,"body":"Henderson, who was the teacher"},{"speaker":"Pam","startTime":821.66,"endTime":826.22,"body":"who hired me for my first"},{"speaker":"Pam","startTime":826.25,"endTime":830.3,"body":"teaching job, so I have a long"},{"speaker":"Pam","startTime":826.25,"endTime":830.3,"body":"connection with these folks that"},{"speaker":"Pam","startTime":830.3,"endTime":833.03,"body":"are writing this curriculum. And"},{"speaker":"Pam","startTime":830.3,"endTime":833.03,"body":"I really honor the fact that"},{"speaker":"Pam","startTime":833.03,"endTime":837.02,"body":"what they're doing is, in their"},{"speaker":"Pam","startTime":833.03,"endTime":837.02,"body":"latest version, they're trying"},{"speaker":"Pam","startTime":837.02,"endTime":841.55,"body":"to eliminate the verb or the"},{"speaker":"Pam","startTime":837.02,"endTime":841.55,"body":"command to \"simplify\". And as"},{"speaker":"Pam","startTime":841.55,"endTime":844.1,"body":"Travis was talking he said,"},{"speaker":"Pam","startTime":841.55,"endTime":844.1,"body":"\"Because there's so many"},{"speaker":"Pam","startTime":844.1,"endTime":848.06,"body":"different times we say"},{"speaker":"Pam","startTime":844.1,"endTime":848.06,"body":"'simplify' when we mean"},{"speaker":"Pam","startTime":848.06,"endTime":850.7,"body":"different things.\" And I said"},{"speaker":"Pam","startTime":848.06,"endTime":850.7,"body":"like, \"Give me some examples.\""},{"speaker":"Pam","startTime":850.7,"endTime":853.46,"body":"And the more he talked, the more"},{"speaker":"Pam","startTime":850.7,"endTime":853.46,"body":"examples I was coming up with."},{"speaker":"Pam","startTime":853.7,"endTime":856.91,"body":"And he actually sent me some"},{"speaker":"Pam","startTime":853.7,"endTime":856.91,"body":"screenshots of places where they"},{"speaker":"Pam","startTime":856.91,"endTime":861.47,"body":"were replacing. Well, I said..."},{"speaker":"Pam","startTime":856.91,"endTime":861.47,"body":"It wasn't me actually. Somebody"},{"speaker":"Pam","startTime":861.47,"endTime":864.32,"body":"in the workshop said, \"Well,"},{"speaker":"Pam","startTime":861.47,"endTime":864.32,"body":"what's a better word?\" And when"},{"speaker":"Pam","startTime":864.32,"endTime":868.25,"body":"I told the Dylan Williams story,"},{"speaker":"Pam","startTime":864.32,"endTime":868.25,"body":"Dylan William story. I keep"},{"speaker":"Pam","startTime":868.25,"endTime":871.19,"body":"giving you an \"S\". Sorry, Dylan."},{"speaker":"Pam","startTime":868.25,"endTime":871.19,"body":"When I told that story, they"},{"speaker":"Pam","startTime":871.19,"endTime":875.12,"body":"said, \"Oh, well then we should"},{"speaker":"Pam","startTime":871.19,"endTime":875.12,"body":"make up a word in English like,"},{"speaker":"Pam","startTime":875.12,"endTime":878.9,"body":"they did, you know like, for"},{"speaker":"Pam","startTime":875.12,"endTime":878.9,"body":"'similarity'. We should make up"},{"speaker":"Pam","startTime":878.9,"endTime":881.87,"body":"a word for 'simplify'.\" And"},{"speaker":"Pam","startTime":878.9,"endTime":881.87,"body":"Travis was like. \"No, because we"},{"speaker":"Pam","startTime":881.87,"endTime":885.2,"body":"use \"simplify\" to mean too many"},{"speaker":"Pam","startTime":881.87,"endTime":885.2,"body":"different things.\" And as"},{"speaker":"Pam","startTime":885.2,"endTime":888.29,"body":"they've tried to replace"},{"speaker":"Pam","startTime":885.2,"endTime":888.29,"body":"\"simplify\", they've actually"},{"speaker":"Pam","startTime":888.29,"endTime":892.01,"body":"replaced it with phrases. So,"},{"speaker":"Pam","startTime":888.29,"endTime":892.01,"body":"let me give you a couple of"},{"speaker":"Pam","startTime":892.01,"endTime":895.76,"body":"examples. So, for example, there"},{"speaker":"Pam","startTime":892.01,"endTime":895.76,"body":"was a place where they had"},{"speaker":"Pam","startTime":895.76,"endTime":902.39,"body":"problems like 5(3x - 2). 5 times"},{"speaker":"Pam","startTime":895.76,"endTime":902.39,"body":"the quantity 3x minus 2. So, you"},{"speaker":"Pam","startTime":902.39,"endTime":905.03,"body":"can picture 5 \"parenthese\" 3x"},{"speaker":"Pam","startTime":902.39,"endTime":905.03,"body":"minus two, end the"},{"speaker":"Pam","startTime":905.06,"endTime":908.93,"body":"\"parentheses\". And in a typical"},{"speaker":"Pam","startTime":905.06,"endTime":908.93,"body":"textbook, the instruction might"},{"speaker":"Pam","startTime":908.93,"endTime":911.39,"body":"be \"Simplify the following"},{"speaker":"Pam","startTime":908.93,"endTime":911.39,"body":"expressions\". And you would"},{"speaker":"Pam","startTime":911.39,"endTime":915.68,"body":"expect kids to then like. Well,"},{"speaker":"Pam","startTime":911.39,"endTime":915.68,"body":"here's the instruction that they"},{"speaker":"Pam","startTime":915.68,"endTime":918.5,"body":"wrote. So, it doesn't... In Open"},{"speaker":"Pam","startTime":915.68,"endTime":918.5,"body":"Up resources High School, it"},{"speaker":"Pam","startTime":918.5,"endTime":921.68,"body":"doesn't say \"Simplify the"},{"speaker":"Pam","startTime":918.5,"endTime":921.68,"body":"following expressions\". It says,"},{"speaker":"Pam","startTime":922.31,"endTime":924.32,"body":"\"Rewrite the following"},{"speaker":"Pam","startTime":922.31,"endTime":924.32,"body":"expressions using the"},{"speaker":"Pam","startTime":924.32,"endTime":927.56,"body":"distributive property.\" So,"},{"speaker":"Pam","startTime":924.32,"endTime":927.56,"body":"then, you would expect kids to"},{"speaker":"Pam","startTime":927.56,"endTime":932.06,"body":"use the distributive property to"},{"speaker":"Pam","startTime":927.56,"endTime":932.06,"body":"say 5 times 3x is 15x. And then,"},{"speaker":"Pam","startTime":932.66,"endTime":936.62,"body":"distribute that 5 times the"},{"speaker":"Pam","startTime":932.66,"endTime":936.62,"body":"negative 2. And minus 10. So,"},{"speaker":"Pam","startTime":937.07,"endTime":940.16,"body":"there is no instruction to"},{"speaker":"Pam","startTime":937.07,"endTime":940.16,"body":"simplify. It's \"Rewrite the"},{"speaker":"Pam","startTime":940.16,"endTime":942.8,"body":"following expressions using the"},{"speaker":"Pam","startTime":940.16,"endTime":942.8,"body":"distributive property\". Not sure"},{"speaker":"Pam","startTime":942.8,"endTime":945.74,"body":"I love, \"Rewrite the following"},{"speaker":"Pam","startTime":942.8,"endTime":945.74,"body":"expressions using distributive"},{"speaker":"Pam","startTime":945.74,"endTime":947.84,"body":"property\", but it's what they"},{"speaker":"Pam","startTime":945.74,"endTime":947.84,"body":"mean."},{"speaker":"Kim","startTime":948.05,"endTime":948.32,"body":"Yeah."},{"speaker":"Pam","startTime":948.32,"endTime":951.89,"body":"So, there you go. Here's"},{"speaker":"Pam","startTime":948.32,"endTime":951.89,"body":"another example. Let's say that"},{"speaker":"Pam","startTime":951.89,"endTime":954.2,"body":"you had... Now, I'll give you"},{"speaker":"Pam","startTime":951.89,"endTime":954.2,"body":"some high school examples. We'll"},{"speaker":"Pam","startTime":954.2,"endTime":956.69,"body":"give a couple of younger"},{"speaker":"Pam","startTime":954.2,"endTime":956.69,"body":"examples in minute. Let's say"},{"speaker":"Pam","startTime":956.69,"endTime":963.2,"body":"that you had 2x times the"},{"speaker":"Pam","startTime":956.69,"endTime":963.2,"body":"quantity 5x plus 3, plus 7 times"},{"speaker":"Pam","startTime":963.2,"endTime":964.73,"body":"the quantity 5x plus 3."},{"speaker":"Pam","startTime":966.4,"endTime":969.94,"body":"You could say \"simplify\". And"},{"speaker":"Pam","startTime":966.4,"endTime":969.94,"body":"often, the instructions in a"},{"speaker":"Pam","startTime":969.94,"endTime":972.55,"body":"typical textbook would say"},{"speaker":"Pam","startTime":969.94,"endTime":972.55,"body":"\"simplify\" when we mean...and"},{"speaker":"Pam","startTime":972.58,"endTime":975.43,"body":"here's the instructions that"},{"speaker":"Pam","startTime":972.58,"endTime":975.43,"body":"they wrote...\"Rewrite each"},{"speaker":"Pam","startTime":975.43,"endTime":979.03,"body":"expression as the product of two"},{"speaker":"Pam","startTime":975.43,"endTime":979.03,"body":"binomials.\" Now, I know that"},{"speaker":"Pam","startTime":979.03,"endTime":981.97,"body":"sounds like a lot of math speak"},{"speaker":"Pam","startTime":979.03,"endTime":981.97,"body":"to you, but you might notice"},{"speaker":"Pam","startTime":981.97,"endTime":985.42,"body":"that there was a 5x plus 3 that"},{"speaker":"Pam","startTime":981.97,"endTime":985.42,"body":"was common, And so you can sort"},{"speaker":"Pam","startTime":985.42,"endTime":989.26,"body":"of factor out that 5x plus 3,"},{"speaker":"Pam","startTime":985.42,"endTime":989.26,"body":"and you end up with the"},{"speaker":"Pam","startTime":989.26,"endTime":991.99,"body":"multiplication, the product of"},{"speaker":"Pam","startTime":989.26,"endTime":991.99,"body":"two binomials. And that's their"},{"speaker":"Pam","startTime":991.99,"endTime":995.08,"body":"sort of, \"Can you"},{"speaker":"Pam","startTime":991.99,"endTime":995.08,"body":"un-distribute?\" So, can you pull"},{"speaker":"Pam","startTime":995.08,"endTime":999.97,"body":"that 2x and that 7 out to get"},{"speaker":"Pam","startTime":995.08,"endTime":999.97,"body":"the quantity 2x plus 7 times the"},{"speaker":"Pam","startTime":999.97,"endTime":1002.94,"body":"quantity 5x plus 3? And I know"},{"speaker":"Pam","startTime":999.97,"endTime":1002.94,"body":"I'm doing a lot in the air here."},{"speaker":"Pam","startTime":1002.94,"endTime":1004.71,"body":"You'd almost have to write that"},{"speaker":"Pam","startTime":1002.94,"endTime":1004.71,"body":"down to be able to sort of see"},{"speaker":"Pam","startTime":1004.71,"endTime":1007.98,"body":"what's happening. But it's a way"},{"speaker":"Pam","startTime":1004.71,"endTime":1007.98,"body":"of kind of. Typically, kids"},{"speaker":"Pam","startTime":1007.98,"endTime":1012.42,"body":"would take the 2x plus 7 times"},{"speaker":"Pam","startTime":1007.98,"endTime":1012.42,"body":"the quantity 5x plus 3, and then"},{"speaker":"Pam","startTime":1012.45,"endTime":1015.66,"body":"you could distribute that. You"},{"speaker":"Pam","startTime":1012.45,"endTime":1015.66,"body":"could think about that as 2x"},{"speaker":"Pam","startTime":1015.72,"endTime":1019.86,"body":"times the quantity 5x plus 3,"},{"speaker":"Pam","startTime":1015.72,"endTime":1019.86,"body":"plus 7 times the quantity 5x"},{"speaker":"Pam","startTime":1019.86,"endTime":1023.31,"body":"plus 3. And so, in this case,"},{"speaker":"Pam","startTime":1019.86,"endTime":1023.31,"body":"they're kind of undoing that"},{"speaker":"Pam","startTime":1023.31,"endTime":1024.0,"body":"distribution."},{"speaker":"Kim","startTime":1024.03,"endTime":1024.39,"body":"Yeah."},{"speaker":"Pam","startTime":1024.42,"endTime":1026.88,"body":"But you're being clear"},{"speaker":"Pam","startTime":1024.42,"endTime":1026.88,"body":"about what's happening. So,"},{"speaker":"Pam","startTime":1026.88,"endTime":1027.27,"body":"here's another."},{"speaker":"Kim","startTime":1027.27,"endTime":1028.59,"body":"Yeah, you know what I love?"},{"speaker":"Kim","startTime":1027.27,"endTime":1028.59,"body":"Hang on one second."},{"speaker":"Pam","startTime":1028.59,"endTime":1028.83,"body":"Yeah, go ahead."},{"speaker":"Kim","startTime":1028.83,"endTime":1031.92,"body":"You know what I love about"},{"speaker":"Kim","startTime":1028.83,"endTime":1031.92,"body":"that is that the mathematical"},{"speaker":"Kim","startTime":1031.92,"endTime":1035.64,"body":"vocabulary that they're using"},{"speaker":"Kim","startTime":1031.92,"endTime":1035.64,"body":"here is so simplified. They're"},{"speaker":"Kim","startTime":1035.64,"endTime":1038.49,"body":"saying \"expression\", and"},{"speaker":"Kim","startTime":1035.64,"endTime":1038.49,"body":"\"product\", and \"binomials\"."},{"speaker":"Kim","startTime":1038.52,"endTime":1044.31,"body":"Like, it gives the kids a window"},{"speaker":"Kim","startTime":1038.52,"endTime":1044.31,"body":"into what is happening, but also"},{"speaker":"Kim","startTime":1044.31,"endTime":1048.18,"body":"using correct mathematical"},{"speaker":"Kim","startTime":1044.31,"endTime":1048.18,"body":"vocabulary that we want them to"},{"speaker":"Kim","startTime":1048.21,"endTime":1049.26,"body":"understand anyway."},{"speaker":"Pam","startTime":1049.59,"endTime":1053.49,"body":"Yeah. So, you might say,"},{"speaker":"Pam","startTime":1049.59,"endTime":1053.49,"body":"\"Kids can't use that kind of"},{"speaker":"Pam","startTime":1053.49,"endTime":1057.6,"body":"vocabulary.\" And what we're"},{"speaker":"Pam","startTime":1053.49,"endTime":1057.6,"body":"suggesting is, as you just say"},{"speaker":"Pam","startTime":1057.6,"endTime":1062.34,"body":"\"simplify\" but expect kids to"},{"speaker":"Pam","startTime":1057.6,"endTime":1062.34,"body":"know that they're supposed to do"},{"speaker":"Pam","startTime":1062.34,"endTime":1066.36,"body":"this other thing... Each of"},{"speaker":"Pam","startTime":1062.34,"endTime":1066.36,"body":"these instances that we're using"},{"speaker":"Pam","startTime":1066.36,"endTime":1069.3,"body":"so far, kids are expected to do"},{"speaker":"Pam","startTime":1066.36,"endTime":1069.3,"body":"something completely different."},{"speaker":"Pam","startTime":1069.66,"endTime":1073.98,"body":"And it's almost like we have the"},{"speaker":"Pam","startTime":1069.66,"endTime":1073.98,"body":"secret club, and if you've done"},{"speaker":"Pam","startTime":1073.98,"endTime":1078.69,"body":"1 through 29 odd 29 times, you"},{"speaker":"Pam","startTime":1073.98,"endTime":1078.69,"body":"kind of get a feel for when"},{"speaker":"Pam","startTime":1078.69,"endTime":1081.36,"body":"\"simplify\" means \"use the"},{"speaker":"Pam","startTime":1078.69,"endTime":1081.36,"body":"distributive property\", and you"},{"speaker":"Pam","startTime":1081.36,"endTime":1084.51,"body":"get a feel for when it means"},{"speaker":"Pam","startTime":1081.36,"endTime":1084.51,"body":"\"undistribute\", and you get a"},{"speaker":"Pam","startTime":1084.51,"endTime":1089.43,"body":"feel for when it means \"rewrite"},{"speaker":"Pam","startTime":1084.51,"endTime":1089.43,"body":"the fraction so that there are"},{"speaker":"Pam","startTime":1089.43,"endTime":1092.01,"body":"no common factors in the"},{"speaker":"Pam","startTime":1089.43,"endTime":1092.01,"body":"numerator, denominator\". You get"},{"speaker":"Pam","startTime":1092.01,"endTime":1095.25,"body":"a feel for what \"simplify\""},{"speaker":"Pam","startTime":1092.01,"endTime":1095.25,"body":"means. But if you don't ever get"},{"speaker":"Pam","startTime":1095.25,"endTime":1097.98,"body":"that feel? We haven't been"},{"speaker":"Pam","startTime":1095.25,"endTime":1097.98,"body":"explicit about what \"simplify\""},{"speaker":"Pam","startTime":1097.98,"endTime":1101.58,"body":"means in these different cases."},{"speaker":"Pam","startTime":1097.98,"endTime":1101.58,"body":"We're kind of expecting kids to"},{"speaker":"Pam","startTime":1101.58,"endTime":1102.81,"body":"guess what's in our head."},{"speaker":"Kim","startTime":1103.11,"endTime":1103.5,"body":"Yes!"},{"speaker":"Pam","startTime":1103.5,"endTime":1105.78,"body":"We're kind of expecting"},{"speaker":"Pam","startTime":1103.5,"endTime":1105.78,"body":"them to just like know, \"Oh, in"},{"speaker":"Pam","startTime":1105.78,"endTime":1108.45,"body":"this case, this is what it"},{"speaker":"Pam","startTime":1105.78,"endTime":1108.45,"body":"means. But not in that case.\""},{"speaker":"Pam","startTime":1109.14,"endTime":1113.55,"body":"So, let's actually be clear. And"},{"speaker":"Pam","startTime":1109.14,"endTime":1113.55,"body":"I think these guys are doing a"},{"speaker":"Pam","startTime":1113.55,"endTime":1117.69,"body":"great job of at least admitting,"},{"speaker":"Pam","startTime":1113.55,"endTime":1117.69,"body":"\"Hey, this is what we mean in"},{"speaker":"Pam","startTime":1117.69,"endTime":1121.56,"body":"this case. We actually mean"},{"speaker":"Pam","startTime":1117.69,"endTime":1121.56,"body":"that.\" And I think, yes, it"},{"speaker":"Pam","startTime":1121.56,"endTime":1125.19,"body":"might mean that in this case, we"},{"speaker":"Pam","startTime":1121.56,"endTime":1125.19,"body":"actually have to help explain"},{"speaker":"Pam","startTime":1125.19,"endTime":1131.4,"body":"those terms that these commands"},{"speaker":"Pam","startTime":1125.19,"endTime":1131.4,"body":"are sort of meaning. But that's"},{"speaker":"Pam","startTime":1131.4,"endTime":1134.55,"body":"better than saying, \"Guess what"},{"speaker":"Pam","startTime":1131.4,"endTime":1134.55,"body":"we mean here by 'simplify'.\""},{"speaker":"Kim","startTime":1134.79,"endTime":1135.27,"body":"Yeah."},{"speaker":"Pam","startTime":1135.51,"endTime":1137.25,"body":"Yeah, cool. Alright, let me"},{"speaker":"Pam","startTime":1135.51,"endTime":1137.25,"body":"give you a couple other"},{"speaker":"Pam","startTime":1137.25,"endTime":1141.51,"body":"examples. Here was one where it"},{"speaker":"Pam","startTime":1137.25,"endTime":1141.51,"body":"was x times the quantity x plus"},{"speaker":"Pam","startTime":1141.51,"endTime":1147.51,"body":"9, plus 2 times the quantity x"},{"speaker":"Pam","startTime":1141.51,"endTime":1147.51,"body":"minus two. And often, we could"},{"speaker":"Pam","startTime":1147.51,"endTime":1151.8,"body":"just say \"simplify\". It might..."},{"speaker":"Pam","startTime":1147.51,"endTime":1151.8,"body":"I've seen places where it would"},{"speaker":"Pam","startTime":1151.8,"endTime":1155.46,"body":"say \"simplify and collect like"},{"speaker":"Pam","startTime":1151.8,"endTime":1155.46,"body":"terms\". In this case they said,"},{"speaker":"Pam","startTime":1155.52,"endTime":1158.52,"body":"\"Multiply using the distributive"},{"speaker":"Pam","startTime":1155.52,"endTime":1158.52,"body":"property, then add like terms.\""},{"speaker":"Pam","startTime":1159.81,"endTime":1162.51,"body":"Giving a clear instruction about"},{"speaker":"Pam","startTime":1159.81,"endTime":1162.51,"body":"what to do. You know, I can"},{"speaker":"Pam","startTime":1162.51,"endTime":1165.15,"body":"almost picture some of the"},{"speaker":"Pam","startTime":1162.51,"endTime":1165.15,"body":"colleagues that I've talked with"},{"speaker":"Pam","startTime":1165.15,"endTime":1168.63,"body":"saying, \"No, we're giving away"},{"speaker":"Pam","startTime":1165.15,"endTime":1168.63,"body":"too much. We're telling the"},{"speaker":"Pam","startTime":1168.63,"endTime":1171.84,"body":"student what to do too much."},{"speaker":"Pam","startTime":1168.63,"endTime":1171.84,"body":"They should know that. They"},{"speaker":"Pam","startTime":1171.84,"endTime":1174.57,"body":"should be able to look at that"},{"speaker":"Pam","startTime":1171.84,"endTime":1174.57,"body":"and know what to do.\" I'm going"},{"speaker":"Pam","startTime":1174.57,"endTime":1178.32,"body":"to push back on that. I think"},{"speaker":"Pam","startTime":1174.57,"endTime":1178.32,"body":"it's actually... It's almost"},{"speaker":"Pam","startTime":1178.32,"endTime":1181.32,"body":"like we're saying, \"If we do"},{"speaker":"Pam","startTime":1178.32,"endTime":1181.32,"body":"that, we'll level the playing"},{"speaker":"Pam","startTime":1181.32,"endTime":1184.86,"body":"field too much.\" How about if we"},{"speaker":"Pam","startTime":1181.32,"endTime":1184.86,"body":"level the playing field?"},{"speaker":"Kim","startTime":1185.16,"endTime":1185.64,"body":"Right."},{"speaker":"Pam","startTime":1185.73,"endTime":1189.63,"body":"Like, I don't think it's"},{"speaker":"Pam","startTime":1185.73,"endTime":1189.63,"body":"necessarily a nice thing to make"},{"speaker":"Pam","startTime":1189.63,"endTime":1193.98,"body":"kids have to guess what we mean."},{"speaker":"Pam","startTime":1189.63,"endTime":1193.98,"body":"Here's another example. \"Rewrite"},{"speaker":"Pam","startTime":1194.01,"endTime":1198.27,"body":"each of the radical expressions"},{"speaker":"Pam","startTime":1194.01,"endTime":1198.27,"body":"to remove perfect squares from"},{"speaker":"Pam","startTime":1198.27,"endTime":1202.53,"body":"inside the radical.\" Now, if all"},{"speaker":"Pam","startTime":1198.27,"endTime":1202.53,"body":"those words are like crazy to"},{"speaker":"Pam","startTime":1202.53,"endTime":1205.77,"body":"you, let me give you an example."},{"speaker":"Pam","startTime":1202.53,"endTime":1205.77,"body":"If I write the square root of"},{"speaker":"Pam","startTime":1205.8,"endTime":1208.38,"body":"50. So, you can picture the"},{"speaker":"Pam","startTime":1205.8,"endTime":1208.38,"body":"square root symbol with a 50"},{"speaker":"Pam","startTime":1208.38,"endTime":1213.12,"body":"inside. If I right square root"},{"speaker":"Pam","startTime":1208.38,"endTime":1213.12,"body":"of 50 and say \"simplify\", you"},{"speaker":"Pam","startTime":1213.12,"endTime":1215.52,"body":"might look at that and go, \"It"},{"speaker":"Pam","startTime":1213.12,"endTime":1215.52,"body":"looks pretty simple to me.\""},{"speaker":"Pam","startTime":1216.48,"endTime":1220.71,"body":"Like, you know, what does the"},{"speaker":"Pam","startTime":1216.48,"endTime":1220.71,"body":"word \"simple\" mean? And in fact,"},{"speaker":"Pam","startTime":1220.71,"endTime":1223.35,"body":"I probably could have said that,"},{"speaker":"Pam","startTime":1220.71,"endTime":1223.35,"body":"for all of those expressions"},{"speaker":"Pam","startTime":1223.35,"endTime":1227.04,"body":"that I just said above, it's"},{"speaker":"Pam","startTime":1223.35,"endTime":1227.04,"body":"kind of in the eye of the"},{"speaker":"Pam","startTime":1227.04,"endTime":1231.18,"body":"beholder whether one of the"},{"speaker":"Pam","startTime":1227.04,"endTime":1231.18,"body":"versions is more simple than the"},{"speaker":"Pam","startTime":1231.18,"endTime":1234.96,"body":"other. In fact, two of the"},{"speaker":"Pam","startTime":1231.18,"endTime":1234.96,"body":"examples that I gave a minute"},{"speaker":"Pam","startTime":1234.96,"endTime":1239.1,"body":"ago were the exact inverse of"},{"speaker":"Pam","startTime":1234.96,"endTime":1239.1,"body":"each other. So, if you say"},{"speaker":"Pam","startTime":1239.13,"endTime":1242.34,"body":"\"simplify\" when I mean \"multiply"},{"speaker":"Pam","startTime":1239.13,"endTime":1242.34,"body":"them out\", and I say \"simplify\""},{"speaker":"Pam","startTime":1242.34,"endTime":1246.75,"body":"when I mean \"factor them back to"},{"speaker":"Pam","startTime":1242.34,"endTime":1246.75,"body":"the other direction\", then"},{"speaker":"Pam","startTime":1246.78,"endTime":1250.08,"body":"you've used the same term to"},{"speaker":"Pam","startTime":1246.78,"endTime":1250.08,"body":"mean \"go one direction, and then"},{"speaker":"Pam","startTime":1250.08,"endTime":1251.34,"body":"reverse and go the other"},{"speaker":"Pam","startTime":1250.08,"endTime":1251.34,"body":"direction\"."},{"speaker":"Kim","startTime":1251.38,"endTime":1251.95,"body":"Yep."},{"speaker":"Pam","startTime":1252.07,"endTime":1254.53,"body":"So, being more clear. So,"},{"speaker":"Pam","startTime":1252.07,"endTime":1254.53,"body":"if I have the square root of 50,"},{"speaker":"Pam","startTime":1255.13,"endTime":1257.41,"body":"I might look at and go, \"I don't"},{"speaker":"Pam","startTime":1255.13,"endTime":1257.41,"body":"know what you mean.\" Oh, except"},{"speaker":"Pam","startTime":1257.41,"endTime":1261.07,"body":"it just said, \"Rewrite this"},{"speaker":"Pam","startTime":1257.41,"endTime":1261.07,"body":"radical expression to remove"},{"speaker":"Pam","startTime":1261.07,"endTime":1263.56,"body":"perfect squares from inside the"},{"speaker":"Pam","startTime":1261.07,"endTime":1263.56,"body":"radicals.\" So, then I got to"},{"speaker":"Pam","startTime":1263.56,"endTime":1266.95,"body":"think to myself, \"Are there"},{"speaker":"Pam","startTime":1263.56,"endTime":1266.95,"body":"perfect squares in 50?\" Oh, sure"},{"speaker":"Pam","startTime":1266.95,"endTime":1271.27,"body":"enough. Like, I can think about"},{"speaker":"Pam","startTime":1266.95,"endTime":1271.27,"body":"25 times 2. So, now I'm thinking"},{"speaker":"Pam","startTime":1271.27,"endTime":1274.18,"body":"about the square root of 25"},{"speaker":"Pam","startTime":1271.27,"endTime":1274.18,"body":"times a square root of 2. Square"},{"speaker":"Pam","startTime":1274.18,"endTime":1278.17,"body":"root of 25 is 5. So, square root"},{"speaker":"Pam","startTime":1274.18,"endTime":1278.17,"body":"of 2. There's no perfect squares"},{"speaker":"Pam","startTime":1278.17,"endTime":1280.75,"body":"inside 2. And so, then, I can"},{"speaker":"Pam","startTime":1278.17,"endTime":1280.75,"body":"say to myself, The square root"},{"speaker":"Pam","startTime":1280.75,"endTime":1284.05,"body":"of 50 is equivalent to 5 times"},{"speaker":"Pam","startTime":1280.75,"endTime":1284.05,"body":"the square root of 2. I have"},{"speaker":"Pam","startTime":1284.05,"endTime":1288.79,"body":"removed a perfect square from"},{"speaker":"Pam","startTime":1284.05,"endTime":1288.79,"body":"inside the radical. It's so much"},{"speaker":"Pam","startTime":1288.79,"endTime":1292.12,"body":"more clear, kids kind of know"},{"speaker":"Pam","startTime":1288.79,"endTime":1292.12,"body":"what to do. One last example"},{"speaker":"Pam","startTime":1292.15,"endTime":1294.58,"body":"that Travis sent me...Thank you,"},{"speaker":"Pam","startTime":1292.15,"endTime":1294.58,"body":"Travis, by the way. Super enjoy"},{"speaker":"Pam","startTime":1294.58,"endTime":1299.86,"body":"working with you...was \"Rewrite"},{"speaker":"Pam","startTime":1294.58,"endTime":1299.86,"body":"each expression by performing"},{"speaker":"Pam","startTime":1299.86,"endTime":1303.61,"body":"the indicated operation. Each"},{"speaker":"Pam","startTime":1299.86,"endTime":1303.61,"body":"new expression should contain"},{"speaker":"Pam","startTime":1303.61,"endTime":1306.85,"body":"only one square root.\" And so,"},{"speaker":"Pam","startTime":1303.61,"endTime":1306.85,"body":"these were examples where there"},{"speaker":"Pam","startTime":1306.85,"endTime":1311.32,"body":"were lots of square roots"},{"speaker":"Pam","startTime":1306.85,"endTime":1311.32,"body":"happening, and that you could"},{"speaker":"Pam","startTime":1311.32,"endTime":1315.37,"body":"combine, so that you only have"},{"speaker":"Pam","startTime":1311.32,"endTime":1315.37,"body":"one square root. So, it's almost"},{"speaker":"Pam","startTime":1315.37,"endTime":1317.47,"body":"like you're kind of going the"},{"speaker":"Pam","startTime":1315.37,"endTime":1317.47,"body":"other direction. You're taking"},{"speaker":"Pam","startTime":1317.47,"endTime":1319.72,"body":"now a bunch of square roots, and"},{"speaker":"Pam","startTime":1317.47,"endTime":1319.72,"body":"you sort of squishing them all"},{"speaker":"Pam","startTime":1319.72,"endTime":1322.24,"body":"under the radical, instead of"},{"speaker":"Pam","startTime":1319.72,"endTime":1322.24,"body":"like that square root of 50"},{"speaker":"Pam","startTime":1322.24,"endTime":1324.67,"body":"where you're taking one square"},{"speaker":"Pam","startTime":1322.24,"endTime":1324.67,"body":"root, and you're kind of"},{"speaker":"Pam","startTime":1324.97,"endTime":1327.19,"body":"like...or at least one number"},{"speaker":"Pam","startTime":1324.97,"endTime":1327.19,"body":"under square root...and now you"},{"speaker":"Pam","startTime":1327.19,"endTime":1329.65,"body":"end up with 5 times the square"},{"speaker":"Pam","startTime":1327.19,"endTime":1329.65,"body":"root of 2. Now, you have like"},{"speaker":"Pam","startTime":1330.4,"endTime":1332.74,"body":"multiple things happening. So,"},{"speaker":"Pam","startTime":1330.4,"endTime":1332.74,"body":"it's kind of, again, that sort"},{"speaker":"Pam","startTime":1332.74,"endTime":1336.46,"body":"of different direction. That's"},{"speaker":"Pam","startTime":1332.74,"endTime":1336.46,"body":"kind of important. Like, we can"},{"speaker":"Pam","startTime":1336.49,"endTime":1340.15,"body":"actually help students"},{"speaker":"Pam","startTime":1336.49,"endTime":1340.15,"body":"understand what we mean, what"},{"speaker":"Pam","startTime":1340.15,"endTime":1345.4,"body":"their task is by replacing the"},{"speaker":"Pam","startTime":1340.15,"endTime":1345.4,"body":"word \"simplify\" with what we"},{"speaker":"Pam","startTime":1345.4,"endTime":1348.55,"body":"actually want them to do. Okay,"},{"speaker":"Pam","startTime":1345.4,"endTime":1348.55,"body":"so let me think of a younger"},{"speaker":"Pam","startTime":1348.55,"endTime":1352.24,"body":"example. I think the best"},{"speaker":"Pam","startTime":1348.55,"endTime":1352.24,"body":"example I can think of with"},{"speaker":"Pam","startTime":1352.75,"endTime":1356.53,"body":"younger numbers... Younger"},{"speaker":"Pam","startTime":1352.75,"endTime":1356.53,"body":"numbers. Students that dealing"},{"speaker":"Pam","startTime":1356.53,"endTime":1360.73,"body":"with younger... Younger"},{"speaker":"Pam","startTime":1356.53,"endTime":1360.73,"body":"students. Would be simplifying"},{"speaker":"Pam","startTime":1360.73,"endTime":1363.07,"body":"fractions. I'm not sure I can"},{"speaker":"Pam","startTime":1360.73,"endTime":1363.07,"body":"think of. Kim, can you think of"},{"speaker":"Pam","startTime":1363.07,"endTime":1365.77,"body":"an example where? Would you"},{"speaker":"Pam","startTime":1363.07,"endTime":1365.77,"body":"write \"simplify a division"},{"speaker":"Pam","startTime":1365.77,"endTime":1367.33,"body":"expression\" or \"simplify...\"?"},{"speaker":"Kim","startTime":1368.95,"endTime":1370.06,"body":"Not off the top of my head."},{"speaker":"Pam","startTime":1370.1,"endTime":1374.07,"body":"Yeah, really I can think of"},{"speaker":"Pam","startTime":1370.1,"endTime":1374.07,"body":"simplifying fractions, and then"},{"speaker":"Pam","startTime":1374.137,"endTime":1378.175,"body":"it kind of comes in more when we"},{"speaker":"Pam","startTime":1374.137,"endTime":1378.175,"body":"have variables. So, I could"},{"speaker":"Pam","startTime":1378.243,"endTime":1382.415,"body":"picture something like 2x plus"},{"speaker":"Pam","startTime":1378.243,"endTime":1382.415,"body":"3x minus 5y plus y. And I could"},{"speaker":"Pam","startTime":1382.483,"endTime":1386.588,"body":"picture a textbook that says"},{"speaker":"Pam","startTime":1382.483,"endTime":1386.588,"body":"\"simplify\", when in reality what"},{"speaker":"Pam","startTime":1386.655,"endTime":1389.953,"body":"they mean is \"collect like"},{"speaker":"Pam","startTime":1386.655,"endTime":1389.953,"body":"terms\" or \"rewrite the"},{"speaker":"Pam","startTime":1390.02,"endTime":1393.991,"body":"expression, so that...\" How did"},{"speaker":"Pam","startTime":1390.02,"endTime":1393.991,"body":"they say that? \"Rewrite the"},{"speaker":"Pam","startTime":1394.058,"endTime":1395.27,"body":"expression, so...\""},{"speaker":"Kim","startTime":1396.19,"endTime":1397.27,"body":"(unclear)."},{"speaker":"Pam","startTime":1398.59,"endTime":1401.53,"body":"Yeah, yeah. Or \"Add like"},{"speaker":"Pam","startTime":1398.59,"endTime":1401.53,"body":"terms\"."},{"speaker":"Kim","startTime":1401.68,"endTime":1401.92,"body":"Yeah."},{"speaker":"Pam","startTime":1401.95,"endTime":1404.68,"body":"\"Combine like terms\"? \"Add"},{"speaker":"Pam","startTime":1401.95,"endTime":1404.68,"body":"like terms\"? Either way. Yeah."},{"speaker":"Pam","startTime":1405.01,"endTime":1409.42,"body":"So, I think we can use phrases"},{"speaker":"Pam","startTime":1405.01,"endTime":1409.42,"body":"to say what we actually mean."},{"speaker":"Pam","startTime":1409.57,"endTime":1414.43,"body":"You might have a textbook that"},{"speaker":"Pam","startTime":1409.57,"endTime":1414.43,"body":"is replete everywhere. It just"},{"speaker":"Pam","startTime":1414.43,"endTime":1418.48,"body":"says \"simplify\" all over the"},{"speaker":"Pam","startTime":1414.43,"endTime":1418.48,"body":"place. May I encourage you to at"},{"speaker":"Pam","startTime":1418.48,"endTime":1423.43,"body":"least begin you thinking about"},{"speaker":"Pam","startTime":1418.48,"endTime":1423.43,"body":"what it actually wants kids to"},{"speaker":"Pam","startTime":1423.43,"endTime":1428.32,"body":"do in that case? Like, are you"},{"speaker":"Pam","startTime":1423.43,"endTime":1428.32,"body":"clear? Yeah. Could you replace"},{"speaker":"Pam","startTime":1428.32,"endTime":1431.17,"body":"\"simplify\" with what you're"},{"speaker":"Pam","startTime":1428.32,"endTime":1431.17,"body":"actually expecting kids to do in"},{"speaker":"Pam","startTime":1431.17,"endTime":1435.04,"body":"that case? Ya'll, listeners, I'd"},{"speaker":"Pam","startTime":1431.17,"endTime":1435.04,"body":"love to hear some examples that"},{"speaker":"Pam","startTime":1435.04,"endTime":1439.78,"body":"you find as your teaching. Where"},{"speaker":"Pam","startTime":1435.04,"endTime":1439.78,"body":"do you see the word \"simplify\","},{"speaker":"Pam","startTime":1439.96,"endTime":1445.69,"body":"asking students to do something?"},{"speaker":"Pam","startTime":1439.96,"endTime":1445.69,"body":"And then, either send us what"},{"speaker":"Pam","startTime":1445.69,"endTime":1449.71,"body":"phrase could you replace that"},{"speaker":"Pam","startTime":1445.69,"endTime":1449.71,"body":"with? Or ask. Let's ask the"},{"speaker":"Pam","startTime":1449.71,"endTime":1453.16,"body":"world. How could we all come up"},{"speaker":"Pam","startTime":1449.71,"endTime":1453.16,"body":"with better ways to ask students"},{"speaker":"Pam","startTime":1453.16,"endTime":1455.14,"body":"what we actually mean for them"},{"speaker":"Pam","startTime":1453.16,"endTime":1455.14,"body":"to do when they see that word"},{"speaker":"Pam","startTime":1455.14,"endTime":1455.65,"body":"\"simplify\"."},{"speaker":"Kim","startTime":1455.77,"endTime":1458.95,"body":"Right, right. Because if"},{"speaker":"Kim","startTime":1455.77,"endTime":1458.95,"body":"our gig is to make math more and"},{"speaker":"Kim","startTime":1458.95,"endTime":1462.28,"body":"more figure-out-able, we can't"},{"speaker":"Kim","startTime":1458.95,"endTime":1462.28,"body":"leave them guessing what's in"},{"speaker":"Kim","startTime":1462.28,"endTime":1462.85,"body":"our head."},{"speaker":"Pam","startTime":1463.39,"endTime":1464.08,"body":"Exactly."},{"speaker":"Kim","startTime":1464.14,"endTime":1467.86,"body":"Or what's in the textbook's"},{"speaker":"Kim","startTime":1464.14,"endTime":1467.86,"body":"head, right? So, let's cancel"},{"speaker":"Kim","startTime":1467.86,"endTime":1470.77,"body":"the word \"simplify\" and say what"},{"speaker":"Kim","startTime":1467.86,"endTime":1470.77,"body":"we actually mean."},{"speaker":"Pam","startTime":1471.1,"endTime":1474.28,"body":"Nice, nice. Alright, ya'll,"},{"speaker":"Pam","startTime":1471.1,"endTime":1474.28,"body":"thanks for tuning in and"},{"speaker":"Pam","startTime":1474.28,"endTime":1477.4,"body":"teaching more and more Real"},{"speaker":"Pam","startTime":1474.28,"endTime":1477.4,"body":"Math! To find out more about the"},{"speaker":"Pam","startTime":1477.4,"endTime":1479.29,"body":"Math is Figure-Out-Able."},{"speaker":"Pam","startTime":1477.4,"endTime":1479.29,"body":"Movement, visit"},{"speaker":"Pam","startTime":1480.34,"endTime":1483.28,"body":"mathisfigureoutable.com. Let's"},{"speaker":"Pam","startTime":1480.34,"endTime":1483.28,"body":"keep spreading the word that"},{"speaker":"Pam","startTime":1483.28,"endTime":1484.66,"body":"Math is Figure-Out-Able!"}]}