{"version":"1.0.0","segments":[{"speaker":"Pam","startTime":0.99,"endTime":4.32,"body":"Hey, fellow mathematicians!"},{"speaker":"Pam","startTime":0.99,"endTime":4.32,"body":"Welcome to the podcast where"},{"speaker":"Pam","startTime":4.32,"endTime":7.17,"body":"Math is Figure-Out-Able! I'm"},{"speaker":"Pam","startTime":4.32,"endTime":7.17,"body":"Pam."},{"speaker":"Kim","startTime":7.44,"endTime":8.16,"body":"And I'm Kim."},{"speaker":"Pam","startTime":8.37,"endTime":11.58,"body":"And you found a place where"},{"speaker":"Pam","startTime":8.37,"endTime":11.58,"body":"math is not about memorizing and"},{"speaker":"Pam","startTime":11.58,"endTime":15.27,"body":"mimicking, waiting to be told or"},{"speaker":"Pam","startTime":11.58,"endTime":15.27,"body":"shown what to do. But it's about"},{"speaker":"Pam","startTime":15.27,"endTime":19.2,"body":"making sense of problems,"},{"speaker":"Pam","startTime":15.27,"endTime":19.2,"body":"noticing patterns, and reasoning"},{"speaker":"Pam","startTime":19.2,"endTime":22.29,"body":"using mathematical"},{"speaker":"Pam","startTime":19.2,"endTime":22.29,"body":"relationships. Not only are"},{"speaker":"Pam","startTime":22.29,"endTime":25.71,"body":"algorithms not particularly"},{"speaker":"Pam","startTime":22.29,"endTime":25.71,"body":"helpful in teaching mathematics,"},{"speaker":"Pam","startTime":25.89,"endTime":29.01,"body":"but rotely repeating steps"},{"speaker":"Pam","startTime":25.89,"endTime":29.01,"body":"actually keep students from"},{"speaker":"Pam","startTime":29.01,"endTime":30.81,"body":"being the mathematicians they"},{"speaker":"Pam","startTime":29.01,"endTime":30.81,"body":"can be."},{"speaker":"Both Pam and Kim","startTime":30.81,"endTime":30.84,"body":"(laughing)"},{"speaker":"Pam","startTime":35.58,"endTime":41.7,"body":"What's so funny? Because I"},{"speaker":"Pam","startTime":35.58,"endTime":41.7,"body":"skipped a line in the intro that"},{"speaker":"Pam","startTime":41.7,"endTime":42.06,"body":"I hate?"},{"speaker":"Kim","startTime":42.06,"endTime":44.76,"body":"Listen, several weeks in a"},{"speaker":"Kim","startTime":42.06,"endTime":44.76,"body":"row, we've had a problem in the"},{"speaker":"Kim","startTime":44.76,"endTime":49.5,"body":"beginning. We're doing okay."},{"speaker":"Kim","startTime":44.76,"endTime":49.5,"body":"Alright. Hey, everyone. In our"},{"speaker":"Kim","startTime":49.5,"endTime":53.07,"body":"last episode, we answer the"},{"speaker":"Kim","startTime":49.5,"endTime":53.07,"body":"question from a follower in the"},{"speaker":"Kim","startTime":53.07,"endTime":56.13,"body":"Math is Figure-Out-Able, teacher"},{"speaker":"Kim","startTime":53.07,"endTime":56.13,"body":"Facebook group. We absolutely"},{"speaker":"Kim","startTime":56.13,"endTime":59.25,"body":"love hearing from listeners. And"},{"speaker":"Kim","startTime":56.13,"endTime":59.25,"body":"we're super excited about what"},{"speaker":"Kim","startTime":59.25,"endTime":61.8,"body":"you're interested in. So, join"},{"speaker":"Kim","startTime":59.25,"endTime":61.8,"body":"the group, tell us what you want"},{"speaker":"Kim","startTime":61.8,"endTime":65.37,"body":"to hear. We can't chat about"},{"speaker":"Kim","startTime":61.8,"endTime":65.37,"body":"everything, but we thought we'd"},{"speaker":"Kim","startTime":65.37,"endTime":68.19,"body":"answer some of the questions"},{"speaker":"Kim","startTime":65.37,"endTime":68.19,"body":"that people in the group"},{"speaker":"Kim","startTime":68.19,"endTime":68.88,"body":"requested."},{"speaker":"Pam","startTime":69.42,"endTime":71.4,"body":"I mean, at least we can't"},{"speaker":"Pam","startTime":69.42,"endTime":71.4,"body":"chat about everything at the"},{"speaker":"Pam","startTime":71.4,"endTime":72.51,"body":"moment. But we'll try."},{"speaker":"Kim","startTime":72.51,"endTime":74.28,"body":"I mean, we hope to do this"},{"speaker":"Kim","startTime":72.51,"endTime":74.28,"body":"a while, right?"},{"speaker":"Pam","startTime":74.34,"endTime":75.39,"body":"We'll keep going. Yeah."},{"speaker":"Pam","startTime":75.42,"endTime":78.06,"body":"Bring it on. Bring on your"},{"speaker":"Pam","startTime":75.42,"endTime":78.06,"body":"questions. Alright. So, Beth"},{"speaker":"Pam","startTime":78.09,"endTime":81.99,"body":"Roberts, thank you for your"},{"speaker":"Pam","startTime":78.09,"endTime":81.99,"body":"question. Beth, you said"},{"speaker":"Pam","startTime":82.05,"endTime":86.79,"body":"\"Division of fractions by a"},{"speaker":"Pam","startTime":82.05,"endTime":86.79,"body":"fraction. Without the 'Keep,"},{"speaker":"Pam","startTime":86.79,"endTime":89.94,"body":"Change, Flip', what would be a"},{"speaker":"Pam","startTime":86.79,"endTime":89.94,"body":"good model for this? How can I"},{"speaker":"Pam","startTime":89.94,"endTime":93.63,"body":"help teachers... How can I help"},{"speaker":"Pam","startTime":89.94,"endTime":93.63,"body":"teachers teach mathematize your"},{"speaker":"Pam","startTime":93.63,"endTime":96.33,"body":"way too...\" Sorry, I'm not"},{"speaker":"Pam","startTime":93.63,"endTime":96.33,"body":"reading this very well. \"How can"},{"speaker":"Pam","startTime":96.33,"endTime":99.24,"body":"I help teachers teach,"},{"speaker":"Pam","startTime":96.33,"endTime":99.24,"body":"mathematizing your way to"},{"speaker":"Pam","startTime":99.24,"endTime":102.72,"body":"division of a fraction by a"},{"speaker":"Pam","startTime":99.24,"endTime":102.72,"body":"fraction or mixed numbers for"},{"speaker":"Pam","startTime":102.72,"endTime":106.77,"body":"fifth grade?\" So, let's talk"},{"speaker":"Pam","startTime":102.72,"endTime":106.77,"body":"about division by fractions."},{"speaker":"Pam","startTime":106.98,"endTime":111.99,"body":"Division of fractions is an"},{"speaker":"Pam","startTime":106.98,"endTime":111.99,"body":"interesting thing. And I'm just"},{"speaker":"Pam","startTime":111.99,"endTime":115.02,"body":"going to mention this 'Keep,"},{"speaker":"Pam","startTime":111.99,"endTime":115.02,"body":"Change, Flip' thing is"},{"speaker":"Pam","startTime":115.02,"endTime":118.17,"body":"fascinating to me. A couple"},{"speaker":"Pam","startTime":115.02,"endTime":118.17,"body":"episodes ago, we talked about"},{"speaker":"Pam","startTime":118.44,"endTime":122.58,"body":"using words that aren't really"},{"speaker":"Pam","startTime":118.44,"endTime":122.58,"body":"well defined, and I will just"},{"speaker":"Pam","startTime":122.58,"endTime":127.47,"body":"note that 'Keep, Change, Flip'"},{"speaker":"Pam","startTime":122.58,"endTime":127.47,"body":"is often used for different"},{"speaker":"Pam","startTime":127.47,"endTime":131.76,"body":"things. So it could be used for"},{"speaker":"Pam","startTime":127.47,"endTime":131.76,"body":"fraction division. But I've also"},{"speaker":"Pam","startTime":131.76,"endTime":138.87,"body":"heard students say \"Keep,"},{"speaker":"Pam","startTime":131.76,"endTime":138.87,"body":"Change, Change\", for addition,"},{"speaker":"Pam","startTime":138.87,"endTime":143.67,"body":"subtraction of Integers. So,"},{"speaker":"Pam","startTime":138.87,"endTime":143.67,"body":"that's tricky because now we're"},{"speaker":"Pam","startTime":143.67,"endTime":147.27,"body":"using kind of the same words to"},{"speaker":"Pam","startTime":143.67,"endTime":147.27,"body":"mean drastically different"},{"speaker":"Pam","startTime":147.27,"endTime":151.05,"body":"things. And how about if we just"},{"speaker":"Pam","startTime":147.27,"endTime":151.05,"body":"don't use words at all? Because"},{"speaker":"Pam","startTime":151.05,"endTime":153.93,"body":"let's be clear, I'm going to"},{"speaker":"Pam","startTime":151.05,"endTime":153.93,"body":"call that fake math. I'm going"},{"speaker":"Pam","startTime":153.93,"endTime":158.01,"body":"to call that procedural math"},{"speaker":"Pam","startTime":153.93,"endTime":158.01,"body":"where my job is to help students"},{"speaker":"Pam","startTime":158.01,"endTime":162.33,"body":"get answers to questions, not"},{"speaker":"Pam","startTime":158.01,"endTime":162.33,"body":"the other way of thinking about"},{"speaker":"Pam","startTime":162.33,"endTime":164.94,"body":"mathematizing, the real way of"},{"speaker":"Pam","startTime":162.33,"endTime":164.94,"body":"thinking about Real Math. Which"},{"speaker":"Pam","startTime":164.94,"endTime":169.05,"body":"is, how can I help my students"},{"speaker":"Pam","startTime":164.94,"endTime":169.05,"body":"create relationships, think more"},{"speaker":"Pam","startTime":169.05,"endTime":172.32,"body":"sophisticatedly, actually get"},{"speaker":"Pam","startTime":169.05,"endTime":172.32,"body":"their brains thinking and"},{"speaker":"Pam","startTime":172.32,"endTime":175.83,"body":"reasoning like mathematicians"},{"speaker":"Pam","startTime":172.32,"endTime":175.83,"body":"with division of fractions? So,"},{"speaker":"Pam","startTime":175.83,"endTime":176.16,"body":"Kim."},{"speaker":"Kim","startTime":176.76,"endTime":177.15,"body":"Yep."},{"speaker":"Pam","startTime":177.3,"endTime":180.39,"body":"I'll never forget the day."},{"speaker":"Pam","startTime":177.3,"endTime":180.39,"body":"I could picture where I was in"},{"speaker":"Pam","startTime":180.39,"endTime":185.37,"body":"my kitchen. I'm cooking dinner."},{"speaker":"Pam","startTime":180.39,"endTime":185.37,"body":"My daughter storms in the house."},{"speaker":"Pam","startTime":186.06,"endTime":188.43,"body":"I think she was fifth grade. It"},{"speaker":"Pam","startTime":186.06,"endTime":188.43,"body":"might have been sixth grade. But"},{"speaker":"Pam","startTime":188.43,"endTime":191.55,"body":"she storms in the house, and I'm"},{"speaker":"Pam","startTime":188.43,"endTime":191.55,"body":"like, \"What's happening?\" And"},{"speaker":"Pam","startTime":191.55,"endTime":195.63,"body":"she is like, smoke is coming out"},{"speaker":"Pam","startTime":191.55,"endTime":195.63,"body":"of her ears. And she goes, \"Mom,"},{"speaker":"Pam","startTime":196.05,"endTime":198.33,"body":"divisions of fractions. Is"},{"speaker":"Pam","startTime":196.05,"endTime":198.33,"body":"division of fractions"},{"speaker":"Pam","startTime":198.33,"endTime":203.7,"body":"figure-out-able?\" I was like,"},{"speaker":"Pam","startTime":198.33,"endTime":203.7,"body":"\"Um, yes...\" And she goes, \"Oh,"},{"speaker":"Pam","startTime":203.73,"endTime":207.06,"body":"I knew it! I knew it! My teacher"},{"speaker":"Pam","startTime":203.73,"endTime":207.06,"body":"told me today, 'Ours is not to"},{"speaker":"Pam","startTime":207.06,"endTime":209.28,"body":"reason why, just invert and"},{"speaker":"Pam","startTime":207.06,"endTime":209.28,"body":"multiply'.\""},{"speaker":"Kim","startTime":209.37,"endTime":210.03,"body":"Yeah."},{"speaker":"Pam","startTime":210.6,"endTime":214.08,"body":"Now, I've heard that phrase"},{"speaker":"Pam","startTime":210.6,"endTime":214.08,"body":"a lot. But I've said it among"},{"speaker":"Pam","startTime":214.08,"endTime":216.99,"body":"teachers lately, and maybe it's"},{"speaker":"Pam","startTime":214.08,"endTime":216.99,"body":"not as ubiquitous as I thought"},{"speaker":"Pam","startTime":216.99,"endTime":220.89,"body":"it was. But \"Ours is not to"},{"speaker":"Pam","startTime":216.99,"endTime":220.89,"body":"reason why, just invert and"},{"speaker":"Pam","startTime":220.89,"endTime":225.66,"body":"multiply\" is kind of a very"},{"speaker":"Pam","startTime":220.89,"endTime":225.66,"body":"telling statement for me."},{"speaker":"Kim","startTime":225.9,"endTime":226.14,"body":"Yeah."},{"speaker":"Pam","startTime":226.14,"endTime":231.24,"body":"Because it says, \"Don't"},{"speaker":"Pam","startTime":226.14,"endTime":231.24,"body":"think about math. Just Keep,"},{"speaker":"Pam","startTime":231.24,"endTime":231.9,"body":"Change, Flip.\""},{"speaker":"Kim","startTime":231.93,"endTime":232.53,"body":"Yeah."},{"speaker":"Pam","startTime":232.77,"endTime":237.87,"body":"Like, \"Just invert and"},{"speaker":"Pam","startTime":232.77,"endTime":237.87,"body":"multiply.\" You can do that and"},{"speaker":"Pam","startTime":237.87,"endTime":242.85,"body":"get answers, but that doesn't"},{"speaker":"Pam","startTime":237.87,"endTime":242.85,"body":"build your reasoning about"},{"speaker":"Pam","startTime":242.85,"endTime":246.18,"body":"fraction division. And so, I"},{"speaker":"Pam","startTime":242.85,"endTime":246.18,"body":"took a deep breath, and I was"},{"speaker":"Pam","startTime":246.18,"endTime":249.21,"body":"like, \"Yes, fraction division is"},{"speaker":"Pam","startTime":246.18,"endTime":249.21,"body":"figure-out-able. Let's do some"},{"speaker":"Pam","startTime":249.21,"endTime":251.97,"body":"work.\" And I did. Go ahead."},{"speaker":"Kim","startTime":252.48,"endTime":254.31,"body":"Why didn't you put her in"},{"speaker":"Kim","startTime":252.48,"endTime":254.31,"body":"my fifth grade class?"},{"speaker":"Pam","startTime":254.64,"endTime":260.22,"body":"Oh, don't even go there."},{"speaker":"Pam","startTime":254.64,"endTime":260.22,"body":"Shh! So, listeners, what you"},{"speaker":"Pam","startTime":260.22,"endTime":264.06,"body":"might not know, Kim is rubbing"},{"speaker":"Pam","startTime":260.22,"endTime":264.06,"body":"salt in a wound. What you might"},{"speaker":"Pam","startTime":264.06,"endTime":268.29,"body":"not know is that Kim taught my"},{"speaker":"Pam","startTime":264.06,"endTime":268.29,"body":"number two. She taught my number"},{"speaker":"Pam","startTime":268.29,"endTime":271.86,"body":"three. And when my number four."},{"speaker":"Pam","startTime":268.29,"endTime":271.86,"body":"I have four kids. When my number"},{"speaker":"Pam","startTime":271.86,"endTime":277.2,"body":"four, who probably needed her"},{"speaker":"Pam","startTime":271.86,"endTime":277.2,"body":"the most, was about to have her,"},{"speaker":"Pam","startTime":278.34,"endTime":280.5,"body":"Kim's principal... So, Kim"},{"speaker":"Pam","startTime":278.34,"endTime":280.5,"body":"taught in a school that my kids"},{"speaker":"Pam","startTime":280.5,"endTime":283.02,"body":"went to. Kim's principal went"},{"speaker":"Pam","startTime":280.5,"endTime":283.02,"body":"and opened a new school. So, a"},{"speaker":"Pam","startTime":283.02,"endTime":285.36,"body":"new school was opening in the"},{"speaker":"Pam","startTime":283.02,"endTime":285.36,"body":"district. Kim's principal was"},{"speaker":"Pam","startTime":285.36,"endTime":289.2,"body":"leaving. We love that principal."},{"speaker":"Pam","startTime":285.36,"endTime":289.2,"body":"Hey, Jodi Weimer. And Kim went"},{"speaker":"Pam","startTime":289.2,"endTime":291.93,"body":"with her to open the new school."},{"speaker":"Pam","startTime":289.2,"endTime":291.93,"body":"And I said..."},{"speaker":"Kim","startTime":291.96,"endTime":292.41,"body":"(unclear) sorry."},{"speaker":"Pam","startTime":292.47,"endTime":295.77,"body":"And I had a very serious"},{"speaker":"Pam","startTime":292.47,"endTime":295.77,"body":"conversation with Kim, and I"},{"speaker":"Pam","startTime":295.77,"endTime":299.19,"body":"said, \"No, no, Kim. Kim. No, I"},{"speaker":"Pam","startTime":295.77,"endTime":299.19,"body":"need one more year here. Like,"},{"speaker":"Pam","startTime":299.19,"endTime":301.23,"body":"can you please just stay at this"},{"speaker":"Pam","startTime":299.19,"endTime":301.23,"body":"school for one more year, and"},{"speaker":"Pam","startTime":301.23,"endTime":304.89,"body":"then you can go anywhere you"},{"speaker":"Pam","startTime":301.23,"endTime":304.89,"body":"want. But I need my kid to have"},{"speaker":"Pam","startTime":304.89,"endTime":306.99,"body":"you for fifth grade. Please,"},{"speaker":"Pam","startTime":304.89,"endTime":306.99,"body":"pretty please, please, please,"},{"speaker":"Pam","startTime":306.99,"endTime":310.29,"body":"please, please, please.\" And she"},{"speaker":"Pam","startTime":306.99,"endTime":310.29,"body":"said, \"Pam, Abby will be fine."},{"speaker":"Pam","startTime":310.5,"endTime":314.49,"body":"There's fine... It'll be fine.\""},{"speaker":"Pam","startTime":310.5,"endTime":314.49,"body":"And you're laughing, Kim,"},{"speaker":"Pam","startTime":314.49,"endTime":317.49,"body":"because then. We had a"},{"speaker":"Pam","startTime":314.49,"endTime":317.49,"body":"conversation recently, right?"},{"speaker":"Pam","startTime":317.49,"endTime":320.04,"body":"You want to tell that? You can"},{"speaker":"Pam","startTime":317.49,"endTime":320.04,"body":"tell that story. Do you"},{"speaker":"Pam","startTime":320.04,"endTime":320.07,"body":"(unclear)?"},{"speaker":"Kim","startTime":320.16,"endTime":322.11,"body":"Oh, I don't remember what"},{"speaker":"Kim","startTime":320.16,"endTime":322.11,"body":"you're talking about, but"},{"speaker":"Kim","startTime":322.23,"endTime":322.26,"body":"(unclear)."},{"speaker":"Pam","startTime":322.29,"endTime":323.64,"body":"About your own personal"},{"speaker":"Pam","startTime":322.29,"endTime":323.64,"body":"kid."},{"speaker":"Kim","startTime":323.64,"endTime":328.44,"body":"Well, I think I called you"},{"speaker":"Kim","startTime":323.64,"endTime":328.44,"body":"one day and said, \"I get it.\""},{"speaker":"Kim","startTime":328.53,"endTime":332.34,"body":"Like, \"I'm in the same boat now,"},{"speaker":"Kim","startTime":328.53,"endTime":332.34,"body":"and I get it. And I'm really"},{"speaker":"Kim","startTime":332.34,"endTime":334.65,"body":"sorry I did that to you. And I'm"},{"speaker":"Kim","startTime":332.34,"endTime":334.65,"body":"really sorry I brought it up"},{"speaker":"Kim","startTime":334.65,"endTime":335.01,"body":"today.\""},{"speaker":"Pam","startTime":336.66,"endTime":339.06,"body":"Yeah, I think you started"},{"speaker":"Pam","startTime":336.66,"endTime":339.06,"body":"that conversation with \"I'm so"},{"speaker":"Pam","startTime":339.06,"endTime":342.33,"body":"sorry.\" And I said, \"What? For"},{"speaker":"Pam","startTime":339.06,"endTime":342.33,"body":"what? For what?\" Like, \"What's"},{"speaker":"Pam","startTime":342.33,"endTime":345.39,"body":"going on?\" You go, \"Oh, now I"},{"speaker":"Pam","startTime":342.33,"endTime":345.39,"body":"get it. I get what happened. I"},{"speaker":"Pam","startTime":345.39,"endTime":347.91,"body":"get why you were so desperate to"},{"speaker":"Pam","startTime":345.39,"endTime":347.91,"body":"have me stay and teach your"},{"speaker":"Pam","startTime":347.91,"endTime":350.52,"body":"daughter because...\" Because,"},{"speaker":"Pam","startTime":347.91,"endTime":350.52,"body":"ya'll, my daughter can"},{"speaker":"Pam","startTime":350.52,"endTime":354.51,"body":"absolutely mathematize with the"},{"speaker":"Pam","startTime":350.52,"endTime":354.51,"body":"best of them, but she wants to"},{"speaker":"Pam","startTime":354.51,"endTime":360.18,"body":"know why, and it makes her stir"},{"speaker":"Pam","startTime":354.51,"endTime":360.18,"body":"crazy. It infuriates her when"},{"speaker":"Pam","startTime":360.18,"endTime":363.78,"body":"teachers refuse to delve into"},{"speaker":"Pam","startTime":360.18,"endTime":363.78,"body":"the why. And in this case... Oh,"},{"speaker":"Pam","startTime":363.78,"endTime":366.3,"body":"and I have to say to her every"},{"speaker":"Pam","startTime":363.78,"endTime":366.3,"body":"time, \"Sweetheart, I don't think"},{"speaker":"Pam","startTime":366.3,"endTime":369.48,"body":"they know why.\" Like, you know,"},{"speaker":"Pam","startTime":366.3,"endTime":369.48,"body":"\"They don't know why. They're"},{"speaker":"Pam","startTime":369.48,"endTime":372.24,"body":"doing the best they can. You"},{"speaker":"Pam","startTime":369.48,"endTime":372.24,"body":"come home, we'll talk about it."},{"speaker":"Pam","startTime":372.24,"endTime":375.03,"body":"We'll do all the math together.\""},{"speaker":"Pam","startTime":372.24,"endTime":375.03,"body":"Alright, so we did some division"},{"speaker":"Pam","startTime":375.03,"endTime":378.12,"body":"of fractions. And sure enough,"},{"speaker":"Pam","startTime":375.03,"endTime":378.12,"body":"my daughter can divide fractions"},{"speaker":"Pam","startTime":378.15,"endTime":381.75,"body":"thinking and reasoning like"},{"speaker":"Pam","startTime":378.15,"endTime":381.75,"body":"we're going to today. So, Kim."},{"speaker":"Kim","startTime":382.38,"endTime":382.41,"body":"(unclear)."},{"speaker":"Pam","startTime":383.31,"endTime":387.84,"body":"That was kind of funny. So,"},{"speaker":"Pam","startTime":383.31,"endTime":387.84,"body":"Kim, let's do a Problem String"},{"speaker":"Pam","startTime":388.38,"endTime":392.13,"body":"to develop one of the major"},{"speaker":"Pam","startTime":388.38,"endTime":392.13,"body":"relationships in fraction"},{"speaker":"Pam","startTime":392.13,"endTime":396.18,"body":"division. And today, we're going"},{"speaker":"Pam","startTime":392.13,"endTime":396.18,"body":"to take a quotitive approach."},{"speaker":"Pam","startTime":396.63,"endTime":401.01,"body":"Okay, what do I mean by that?"},{"speaker":"Pam","startTime":396.63,"endTime":401.01,"body":"So, division has two major"},{"speaker":"Pam","startTime":401.01,"endTime":404.19,"body":"interpretations, two major ways"},{"speaker":"Pam","startTime":401.01,"endTime":404.19,"body":"of thinking about division, and"},{"speaker":"Pam","startTime":404.19,"endTime":406.92,"body":"so let's just sort of be clear"},{"speaker":"Pam","startTime":404.19,"endTime":406.92,"body":"on what I mean by quotitive"},{"speaker":"Pam","startTime":406.92,"endTime":412.98,"body":"division quickly. If I said 30"},{"speaker":"Pam","startTime":406.92,"endTime":412.98,"body":"divided by 5. If I'm thinking"},{"speaker":"Pam","startTime":413.01,"endTime":418.11,"body":"quotitively, then I'm thinking"},{"speaker":"Pam","startTime":413.01,"endTime":418.11,"body":"about how many 5s are in 30?"},{"speaker":"Pam","startTime":419.01,"endTime":421.92,"body":"That's a way of thinking about"},{"speaker":"Pam","startTime":419.01,"endTime":421.92,"body":"that division, and so that you"},{"speaker":"Pam","startTime":421.92,"endTime":425.25,"body":"can think about, \"Well, how many"},{"speaker":"Pam","startTime":421.92,"endTime":425.25,"body":"5s do I know?\" And then, I can"},{"speaker":"Pam","startTime":425.25,"endTime":429.45,"body":"sort of reason. Okay, there's"},{"speaker":"Pam","startTime":425.25,"endTime":429.45,"body":"six 5s in 30, so I can solve 30"},{"speaker":"Pam","startTime":429.45,"endTime":432.24,"body":"divided by 5 thinking"},{"speaker":"Pam","startTime":429.45,"endTime":432.24,"body":"quotitively. How many of the"},{"speaker":"Pam","startTime":432.24,"endTime":437.1,"body":"divisors are in the dividend?"},{"speaker":"Pam","startTime":432.24,"endTime":437.1,"body":"Okay. So, I know I didn't do. I"},{"speaker":"Pam","startTime":437.1,"endTime":439.53,"body":"just sort of told that. It would"},{"speaker":"Pam","startTime":437.1,"endTime":439.53,"body":"be much better if we'd"},{"speaker":"Pam","startTime":439.53,"endTime":441.15,"body":"experienced that with whole"},{"speaker":"Pam","startTime":439.53,"endTime":441.15,"body":"numbers."},{"speaker":"Kim","startTime":441.3,"endTime":441.57,"body":"Right."},{"speaker":"Pam","startTime":442.14,"endTime":444.75,"body":"I'm sure we did something"},{"speaker":"Pam","startTime":442.14,"endTime":444.75,"body":"on that earlier with partitive"},{"speaker":"Pam","startTime":444.75,"endTime":446.19,"body":"and quotitive somewhere on the"},{"speaker":"Pam","startTime":444.75,"endTime":446.19,"body":"podcast."},{"speaker":"Kim","startTime":446.4,"endTime":447.6,"body":"(unclear) Yeah, I feel like"},{"speaker":"Kim","startTime":446.4,"endTime":447.6,"body":"we have."},{"speaker":"Pam","startTime":448.44,"endTime":450.21,"body":"Maybe I'll search for that"},{"speaker":"Pam","startTime":448.44,"endTime":450.21,"body":"while you're solving one of"},{"speaker":"Pam","startTime":450.21,"endTime":454.02,"body":"these problems. Or not. Or we'll"},{"speaker":"Pam","startTime":450.21,"endTime":454.02,"body":"just let our... We have a"},{"speaker":"Pam","startTime":454.02,"endTime":458.04,"body":"wonderful podcast editor that"},{"speaker":"Pam","startTime":454.02,"endTime":458.04,"body":"will shoot me messages all the"},{"speaker":"Pam","startTime":458.04,"endTime":460.17,"body":"time. It's like, \"Okay, you"},{"speaker":"Pam","startTime":458.04,"endTime":460.17,"body":"mentioned this one in the"},{"speaker":"Pam","startTime":460.17,"endTime":464.1,"body":"podcast, what episode is that?"},{"speaker":"Pam","startTime":460.17,"endTime":464.1,"body":"It's not always so obvious.\""},{"speaker":"Pam","startTime":464.1,"endTime":467.85,"body":"Anyway. Alright, so if we're"},{"speaker":"Pam","startTime":464.1,"endTime":467.85,"body":"thinking quotitively. So, I'm"},{"speaker":"Pam","startTime":467.85,"endTime":471.66,"body":"just going to encourage you,"},{"speaker":"Pam","startTime":467.85,"endTime":471.66,"body":"Kim, to think quotitively about"},{"speaker":"Pam","startTime":471.66,"endTime":476.73,"body":"a problem like 1 divided by 1/3."},{"speaker":"Pam","startTime":471.66,"endTime":476.73,"body":"1 divided by 1/3. How would you"},{"speaker":"Pam","startTime":476.73,"endTime":477.96,"body":"think quotitively about that?"},{"speaker":"Pam","startTime":476.73,"endTime":477.96,"body":"Go."},{"speaker":"Kim","startTime":478.32,"endTime":481.56,"body":"Yeah, so how many 1/3s are"},{"speaker":"Kim","startTime":478.32,"endTime":481.56,"body":"in 1."},{"speaker":"Pam","startTime":481.56,"endTime":481.59,"body":"Mmhmm."},{"speaker":"Kim","startTime":481.89,"endTime":483.51,"body":"Are just three. Three 1/3s."},{"speaker":"Pam","startTime":484.02,"endTime":484.8,"body":"Yeah. And how do you know?"},{"speaker":"Kim","startTime":486.12,"endTime":488.04,"body":"One-third, two-thirds,"},{"speaker":"Kim","startTime":486.12,"endTime":488.04,"body":"three-thirds."},{"speaker":"Pam","startTime":488.07,"endTime":491.73,"body":"Sure. So, if a kid said"},{"speaker":"Pam","startTime":488.07,"endTime":491.73,"body":"something like Kim just said, I"},{"speaker":"Pam","startTime":491.73,"endTime":494.52,"body":"would quickly draw a candy bar."},{"speaker":"Pam","startTime":491.73,"endTime":494.52,"body":"I'm going to draw a rectangular"},{"speaker":"Pam","startTime":494.52,"endTime":498.42,"body":"candy bar, and I would say, \"So,"},{"speaker":"Pam","startTime":494.52,"endTime":498.42,"body":"you're saying that if I cut that"},{"speaker":"Pam","startTime":498.42,"endTime":502.02,"body":"candy bar into 3 equal shares,"},{"speaker":"Pam","startTime":498.42,"endTime":502.02,"body":"that those are some thirds."},{"speaker":"Pam","startTime":502.02,"endTime":504.6,"body":"You're saying there will be 3 of"},{"speaker":"Pam","startTime":502.02,"endTime":504.6,"body":"them?\" And that's kind of the"},{"speaker":"Pam","startTime":504.6,"endTime":509.19,"body":"definition of thirds, right?"},{"speaker":"Pam","startTime":504.6,"endTime":509.19,"body":"Like, I've separated the whole,"},{"speaker":"Pam","startTime":509.19,"endTime":512.73,"body":"the unit into 3 equal shares,"},{"speaker":"Pam","startTime":509.19,"endTime":512.73,"body":"and I call each of them"},{"speaker":"Pam","startTime":513.15,"endTime":515.88,"body":"one-third. And if the question"},{"speaker":"Pam","startTime":513.15,"endTime":515.88,"body":"is, \"How many one-thirds are in"},{"speaker":"Pam","startTime":515.91,"endTime":518.85,"body":"1 candy bar?\" we could"},{"speaker":"Pam","startTime":515.91,"endTime":518.85,"body":"clearly... And so on my paper"},{"speaker":"Pam","startTime":518.85,"endTime":521.1,"body":"right now, or on the board, or"},{"speaker":"Pam","startTime":518.85,"endTime":521.1,"body":"wherever I'm working with"},{"speaker":"Pam","startTime":521.1,"endTime":524.52,"body":"students, I've drawn this"},{"speaker":"Pam","startTime":521.1,"endTime":524.52,"body":"rectangle. I've cut it into 3"},{"speaker":"Pam","startTime":524.52,"endTime":528.3,"body":"equal pieces. I've labeled each"},{"speaker":"Pam","startTime":524.52,"endTime":528.3,"body":"of them one-third. And I've sort"},{"speaker":"Pam","startTime":528.3,"endTime":531.39,"body":"of got that on the board. Bam!"},{"speaker":"Pam","startTime":528.3,"endTime":531.39,"body":"So, that's what we often do in a"},{"speaker":"Pam","startTime":531.39,"endTime":533.94,"body":"Problem String, right? We ask a"},{"speaker":"Pam","startTime":531.39,"endTime":533.94,"body":"question everybody has access"},{"speaker":"Pam","startTime":533.94,"endTime":537.66,"body":"to. When they say their answer,"},{"speaker":"Pam","startTime":533.94,"endTime":537.66,"body":"I make that thinking visible. I,"},{"speaker":"Pam","startTime":537.66,"endTime":540.51,"body":"the teacher, make that thing"},{"speaker":"Pam","startTime":537.66,"endTime":540.51,"body":"visible. Next question. Kim,"},{"speaker":"Pam","startTime":540.54,"endTime":543.0,"body":"what is 2 divided by 1/3?"},{"speaker":"Kim","startTime":544.44,"endTime":545.13,"body":"Six."},{"speaker":"Pam","startTime":545.64,"endTime":546.3,"body":"And how do you know?"},{"speaker":"Kim","startTime":547.35,"endTime":553.62,"body":"There were three thirds in"},{"speaker":"Kim","startTime":547.35,"endTime":553.62,"body":"1, and so you doubled your"},{"speaker":"Kim","startTime":553.65,"endTime":556.65,"body":"amount of candy bars, and so now"},{"speaker":"Kim","startTime":553.65,"endTime":556.65,"body":"I have six 1/3s."},{"speaker":"Pam","startTime":557.07,"endTime":560.76,"body":"Cool. So, if there are"},{"speaker":"Pam","startTime":557.07,"endTime":560.76,"body":"three 1/3s in 1 candy bar, then"},{"speaker":"Pam","startTime":560.79,"endTime":563.91,"body":"you're saying there's double"},{"speaker":"Pam","startTime":560.79,"endTime":563.91,"body":"that. There's six 1/3s in 2"},{"speaker":"Pam","startTime":563.91,"endTime":564.96,"body":"candy bars. Cool."},{"speaker":"Kim","startTime":564.96,"endTime":565.14,"body":"Yep."},{"speaker":"Pam","startTime":565.17,"endTime":568.65,"body":"So, I've just now redrawn"},{"speaker":"Pam","startTime":565.17,"endTime":568.65,"body":"the first candy bar. But I"},{"speaker":"Pam","startTime":568.65,"endTime":571.44,"body":"didn't draw it in as much"},{"speaker":"Pam","startTime":568.65,"endTime":571.44,"body":"specificity. I slapped up a"},{"speaker":"Pam","startTime":571.44,"endTime":575.49,"body":"rectangle, I quickly cut it into"},{"speaker":"Pam","startTime":571.44,"endTime":575.49,"body":"thirds, and then I slapped up"},{"speaker":"Pam","startTime":575.49,"endTime":579.57,"body":"another rectangle next to it,"},{"speaker":"Pam","startTime":575.49,"endTime":579.57,"body":"quickly cut it into thirds. I've"},{"speaker":"Pam","startTime":579.57,"endTime":584.22,"body":"labeled one of the thirds, one"},{"speaker":"Pam","startTime":579.57,"endTime":584.22,"body":"of those pieces, with one-third."},{"speaker":"Pam","startTime":584.46,"endTime":587.34,"body":"And that's it. Like, I haven't"},{"speaker":"Pam","startTime":584.46,"endTime":587.34,"body":"spent time doing a whole lot of,"},{"speaker":"Pam","startTime":587.37,"endTime":590.07,"body":"but we can clearly see that"},{"speaker":"Pam","startTime":587.37,"endTime":590.07,"body":"there's 3 in the one, 3 in the"},{"speaker":"Pam","startTime":590.07,"endTime":594.06,"body":"other. I've doubled the number."},{"speaker":"Pam","startTime":590.07,"endTime":594.06,"body":"And that's 6. Cool. What if I"},{"speaker":"Pam","startTime":594.06,"endTime":598.29,"body":"had a problem like 4 divided by"},{"speaker":"Pam","startTime":594.06,"endTime":598.29,"body":"1/3? 4 divided by 1/3. Now,"},{"speaker":"Pam","startTime":598.29,"endTime":598.5,"body":"what?"},{"speaker":"Kim","startTime":600.21,"endTime":601.11,"body":"That would be 12."},{"speaker":"Pam","startTime":601.59,"endTime":602.13,"body":"Because?"},{"speaker":"Kim","startTime":602.46,"endTime":606.69,"body":"Because we just have six"},{"speaker":"Kim","startTime":602.46,"endTime":606.69,"body":"1/3s for 2 candy bars, and we"},{"speaker":"Kim","startTime":606.69,"endTime":609.63,"body":"have twice as many candy bars,"},{"speaker":"Kim","startTime":606.69,"endTime":609.63,"body":"so we need twice as many 1/3s."},{"speaker":"Kim","startTime":609.66,"endTime":610.92,"body":"So, twelve 1/3s."},{"speaker":"Pam","startTime":611.58,"endTime":615.18,"body":"Cool. And so, I've just"},{"speaker":"Pam","startTime":611.58,"endTime":615.18,"body":"sort of drawn quickly 4 candy"},{"speaker":"Pam","startTime":615.18,"endTime":619.47,"body":"bars. I've cut the first one"},{"speaker":"Pam","startTime":615.18,"endTime":619.47,"body":"into thirds, and I've labeled"},{"speaker":"Pam","startTime":619.47,"endTime":622.98,"body":"the first one 1/3. The first"},{"speaker":"Pam","startTime":619.47,"endTime":622.98,"body":"third, I've labeled it 1/3. And"},{"speaker":"Pam","startTime":622.98,"endTime":625.23,"body":"I haven't really done much with"},{"speaker":"Pam","startTime":622.98,"endTime":625.23,"body":"the other ones. I've got the 4"},{"speaker":"Pam","startTime":625.26,"endTime":628.74,"body":"candy bars up there. I've got"},{"speaker":"Pam","startTime":625.26,"endTime":628.74,"body":"the first one chunked into 3,"},{"speaker":"Pam","startTime":629.16,"endTime":632.04,"body":"and I'm kind of thinking about"},{"speaker":"Pam","startTime":629.16,"endTime":632.04,"body":"that. I'm a little curious,"},{"speaker":"Pam","startTime":632.07,"endTime":635.76,"body":"could you have thought about"},{"speaker":"Pam","startTime":632.07,"endTime":635.76,"body":"that? You went from the 2 candy"},{"speaker":"Pam","startTime":635.76,"endTime":638.4,"body":"bars, and you've doubled. And I"},{"speaker":"Pam","startTime":635.76,"endTime":638.4,"body":"love that. What if you didn't"},{"speaker":"Pam","startTime":638.4,"endTime":641.22,"body":"have the 2 candy bars? Could you"},{"speaker":"Pam","startTime":638.4,"endTime":641.22,"body":"have gone from the 1 candy bar"},{"speaker":"Pam","startTime":641.22,"endTime":641.64,"body":"divided by 1/3?"},{"speaker":"Kim","startTime":641.64,"endTime":644.25,"body":"Sure. Yeah, it would be 4"},{"speaker":"Kim","startTime":641.64,"endTime":644.25,"body":"times as many pieces."},{"speaker":"Pam","startTime":644.55,"endTime":645.33,"body":"Because?"},{"speaker":"Kim","startTime":645.99,"endTime":650.28,"body":"Because you went from 1"},{"speaker":"Kim","startTime":645.99,"endTime":650.28,"body":"candy bar to 4 candy bars and"},{"speaker":"Kim","startTime":650.28,"endTime":654.57,"body":"three 1/3s to 4 times as much as"},{"speaker":"Kim","startTime":650.28,"endTime":654.57,"body":"that."},{"speaker":"Pam","startTime":655.08,"endTime":656.25,"body":"Which is still that 12?"},{"speaker":"Kim","startTime":656.25,"endTime":656.94,"body":"Twelve thirds."},{"speaker":"Both Pam and Kim","startTime":657.0,"endTime":657.33,"body":"Yeah."},{"speaker":"Pam","startTime":657.33,"endTime":660.45,"body":"So, 4 divided by 1/3 has"},{"speaker":"Pam","startTime":657.33,"endTime":660.45,"body":"to, since you have 4, it would"},{"speaker":"Pam","startTime":660.45,"endTime":664.2,"body":"be 4 times as many thirds. Yeah,"},{"speaker":"Pam","startTime":660.45,"endTime":664.2,"body":"pieces. Cool. Alright, so 4"},{"speaker":"Pam","startTime":664.2,"endTime":668.94,"body":"divided by 1/3 is 12. Next"},{"speaker":"Pam","startTime":664.2,"endTime":668.94,"body":"question. How about 4 and 1/3"},{"speaker":"Pam","startTime":669.3,"endTime":672.39,"body":"divided by 1/3? 4 and 1/3"},{"speaker":"Pam","startTime":669.3,"endTime":672.39,"body":"divided by 1/3?"},{"speaker":"Kim","startTime":673.08,"endTime":674.43,"body":"That would be 13."},{"speaker":"Pam","startTime":675.18,"endTime":675.75,"body":"Because?"},{"speaker":"Kim","startTime":676.47,"endTime":681.6,"body":"We just had 4 divided by"},{"speaker":"Kim","startTime":676.47,"endTime":681.6,"body":"1/3. So, how many thirds in"},{"speaker":"Kim","startTime":681.6,"endTime":685.71,"body":"four, and that was 12. So, now"},{"speaker":"Kim","startTime":681.6,"endTime":685.71,"body":"you're just asking me one more"},{"speaker":"Kim","startTime":685.74,"endTime":689.19,"body":"third. (unclear)"},{"speaker":"Pam","startTime":689.19,"endTime":692.13,"body":"(unclear) Yeah. Sorry,"},{"speaker":"Pam","startTime":689.19,"endTime":692.13,"body":"didn't mean to interrupt. Cool."},{"speaker":"Kim","startTime":692.13,"endTime":692.43,"body":"It's okay."},{"speaker":"Pam","startTime":692.7,"endTime":697.86,"body":"So, I've just slapped down"},{"speaker":"Pam","startTime":692.7,"endTime":697.86,"body":"4 candy bars again, but I've"},{"speaker":"Pam","startTime":697.86,"endTime":702.21,"body":"tacked on kind of a ghost candy"},{"speaker":"Pam","startTime":697.86,"endTime":702.21,"body":"bar. And so my last, I've tacked"},{"speaker":"Pam","startTime":702.21,"endTime":706.71,"body":"on kind of a fifth candy bar,"},{"speaker":"Pam","startTime":702.21,"endTime":706.71,"body":"but I put it in dots. It's kind"},{"speaker":"Pam","startTime":706.71,"endTime":711.27,"body":"of like... But 1/3 of it, I've"},{"speaker":"Pam","startTime":706.71,"endTime":711.27,"body":"cut that into thirds. And that"},{"speaker":"Pam","startTime":711.27,"endTime":716.31,"body":"first third is solidly outlined."},{"speaker":"Pam","startTime":711.27,"endTime":716.31,"body":"So, you can see a fifth candy"},{"speaker":"Pam","startTime":716.31,"endTime":721.59,"body":"bar, but I've only like sort of"},{"speaker":"Pam","startTime":716.31,"endTime":721.59,"body":"sketched in that third. So, you"},{"speaker":"Pam","startTime":721.59,"endTime":726.03,"body":"can clearly see 4 and a 1/3"},{"speaker":"Pam","startTime":721.59,"endTime":726.03,"body":"candy bars. And I'm asking how"},{"speaker":"Pam","startTime":726.03,"endTime":729.63,"body":"many thirds are in that 4 and a"},{"speaker":"Pam","startTime":726.03,"endTime":729.63,"body":"1/3. We already have the 12 from"},{"speaker":"Pam","startTime":729.63,"endTime":732.45,"body":"the 4 candy bars, and there's"},{"speaker":"Pam","startTime":729.63,"endTime":732.45,"body":"just one more. And I'm not"},{"speaker":"Pam","startTime":732.45,"endTime":735.84,"body":"actually going to spend a lot of"},{"speaker":"Pam","startTime":732.45,"endTime":735.84,"body":"time on this problem. Like, I'm"},{"speaker":"Pam","startTime":735.84,"endTime":738.78,"body":"just going to. Like, we have the"},{"speaker":"Pam","startTime":735.84,"endTime":738.78,"body":"12. We got 1 more. Duh. We're"},{"speaker":"Pam","startTime":738.78,"endTime":745.41,"body":"moving on. Cool. How about 2 and"},{"speaker":"Pam","startTime":738.78,"endTime":745.41,"body":"2/3 divided by 1/3? 2 and 2/3s"},{"speaker":"Pam","startTime":745.44,"endTime":746.22,"body":"divided by 1/3."},{"speaker":"Kim","startTime":747.54,"endTime":753.03,"body":"That would be 8 because..."},{"speaker":"Pam","startTime":753.15,"endTime":753.66,"body":"Yeah?"},{"speaker":"Kim","startTime":754.14,"endTime":760.65,"body":"...there were six 1/3 in"},{"speaker":"Kim","startTime":754.14,"endTime":760.65,"body":"two candy bars, and I have two"},{"speaker":"Kim","startTime":760.65,"endTime":764.97,"body":"more 1/3. So, 2 and 2/3s is"},{"speaker":"Kim","startTime":760.65,"endTime":764.97,"body":"eight 1/3."},{"speaker":"Pam","startTime":765.3,"endTime":766.44,"body":"Two more 1/3s?"},{"speaker":"Kim","startTime":766.89,"endTime":767.1,"body":"Yeah."},{"speaker":"Pam","startTime":767.1,"endTime":770.7,"body":"So, as you were talking, I"},{"speaker":"Pam","startTime":767.1,"endTime":770.7,"body":"quickly slapped down 2 candy"},{"speaker":"Pam","startTime":770.7,"endTime":775.47,"body":"bars. And you said because we"},{"speaker":"Pam","startTime":770.7,"endTime":775.47,"body":"had 2 candy bars, and we had six"},{"speaker":"Pam","startTime":776.37,"endTime":779.88,"body":"1/3s in those 2 candy bars. And"},{"speaker":"Pam","startTime":776.37,"endTime":779.88,"body":"then you said, we had two more"},{"speaker":"Pam","startTime":779.91,"endTime":784.65,"body":"1/3s. So, I put another kind of"},{"speaker":"Pam","startTime":779.91,"endTime":784.65,"body":"ghost candy bar there, but I've"},{"speaker":"Pam","startTime":784.65,"endTime":791.31,"body":"solidly outlined two of those"},{"speaker":"Pam","startTime":784.65,"endTime":791.31,"body":"one-thirds. And the last third"},{"speaker":"Pam","startTime":791.55,"endTime":795.03,"body":"is kind of in dots. It's kind of"},{"speaker":"Pam","startTime":791.55,"endTime":795.03,"body":"just sort of sitting there. So,"},{"speaker":"Pam","startTime":795.03,"endTime":800.91,"body":"there's the 2 and 2/3. And then,"},{"speaker":"Pam","startTime":795.03,"endTime":800.91,"body":"I'm kind of circling a little"},{"speaker":"Pam","startTime":800.91,"endTime":805.29,"body":"bit the 2 candy bars, and I'm"},{"speaker":"Pam","startTime":800.91,"endTime":805.29,"body":"arrowing up to where we had 2"},{"speaker":"Pam","startTime":805.29,"endTime":809.43,"body":"candy bars before that we had 6."},{"speaker":"Pam","startTime":805.29,"endTime":809.43,"body":"And then I'm saying, \"Oh, and"},{"speaker":"Pam","startTime":809.43,"endTime":813.6,"body":"then there's those extra 2/3...\""},{"speaker":"Pam","startTime":809.43,"endTime":813.6,"body":"So, I've written by the problem,"},{"speaker":"Pam","startTime":813.6,"endTime":817.68,"body":"2 and 2/3 divided by 1/3. I've"},{"speaker":"Pam","startTime":813.6,"endTime":817.68,"body":"written 6 plus 2. Well,"},{"speaker":"Pam","startTime":817.68,"endTime":820.98,"body":"actually, I wrote 8, and then I"},{"speaker":"Pam","startTime":817.68,"endTime":820.98,"body":"wrote equals 6 plus 2."},{"speaker":"Kim","startTime":821.01,"endTime":821.13,"body":"Yeah."},{"speaker":"Pam","startTime":821.13,"endTime":826.44,"body":"Cool. Okay, next problem."},{"speaker":"Pam","startTime":821.13,"endTime":826.44,"body":"How about 2 and 2/3 divided by"},{"speaker":"Pam","startTime":826.53,"endTime":833.73,"body":"2/3? How many two 1/3s are in 2"},{"speaker":"Pam","startTime":826.53,"endTime":833.73,"body":"and 2/3?"},{"speaker":"Kim","startTime":835.14,"endTime":839.52,"body":"I think it's four 2/3s."},{"speaker":"Pam","startTime":840.06,"endTime":842.13,"body":"(unclear). There's four"},{"speaker":"Pam","startTime":840.06,"endTime":842.13,"body":"2/3s in 2 and 2/3?"},{"speaker":"Kim","startTime":842.16,"endTime":847.92,"body":"Yeah, because we just did 2"},{"speaker":"Kim","startTime":842.16,"endTime":847.92,"body":"and 2/3 divided by 1/3. And"},{"speaker":"Kim","startTime":847.92,"endTime":854.52,"body":"that, there were eight 1/3s. And"},{"speaker":"Kim","startTime":847.92,"endTime":854.52,"body":"so, now instead of one-thirds,"},{"speaker":"Kim","startTime":854.55,"endTime":859.59,"body":"you're asking me about"},{"speaker":"Kim","startTime":854.55,"endTime":859.59,"body":"two-thirds, so the... Think how"},{"speaker":"Kim","startTime":859.59,"endTime":864.03,"body":"to say this. The size of the"},{"speaker":"Kim","startTime":859.59,"endTime":864.03,"body":"pieces that you're asking about"},{"speaker":"Kim","startTime":864.09,"endTime":865.08,"body":"have doubled."},{"speaker":"Kim","startTime":866.34,"endTime":870.93,"body":"And so, I'm thinking about the"},{"speaker":"Kim","startTime":866.34,"endTime":870.93,"body":"size of the pieces have doubled,"},{"speaker":"Kim","startTime":870.96,"endTime":874.68,"body":"and so there's going to be less"},{"speaker":"Kim","startTime":870.96,"endTime":874.68,"body":"of them because the 2 and 2/3"},{"speaker":"Kim","startTime":874.68,"endTime":880.23,"body":"didn't change. So, instead of"},{"speaker":"Kim","startTime":874.68,"endTime":880.23,"body":"eight 1/3s, there's only going"},{"speaker":"Kim","startTime":880.23,"endTime":885.27,"body":"to be four 2/3s, which would be"},{"speaker":"Kim","startTime":880.23,"endTime":885.27,"body":"half as many pieces because the"},{"speaker":"Kim","startTime":885.27,"endTime":886.77,"body":"size of the piece doubled."},{"speaker":"Pam","startTime":887.58,"endTime":889.95,"body":"Half as many pieces that"},{"speaker":"Pam","startTime":887.58,"endTime":889.95,"body":"are twice as big."},{"speaker":"Kim","startTime":890.19,"endTime":890.76,"body":"Yeah."},{"speaker":"Pam","startTime":891.0,"endTime":893.61,"body":"I wonder if we could do a"},{"speaker":"Pam","startTime":891.0,"endTime":893.61,"body":"little more candy bar talk."},{"speaker":"Pam","startTime":893.82,"endTime":894.09,"body":"So..."},{"speaker":"Kim","startTime":894.09,"endTime":894.57,"body":"Okay."},{"speaker":"Pam","startTime":894.57,"endTime":898.71,"body":"...in the problem before."},{"speaker":"Pam","startTime":894.57,"endTime":898.71,"body":"I'm not... Yeah, well said. In"},{"speaker":"Pam","startTime":898.71,"endTime":902.01,"body":"the problem before, we had 2 and"},{"speaker":"Pam","startTime":898.71,"endTime":902.01,"body":"2/3 candy bars."},{"speaker":"Kim","startTime":902.25,"endTime":902.82,"body":"Yep."},{"speaker":"Pam","startTime":903.06,"endTime":907.23,"body":"And I kind of said, \"If I'm"},{"speaker":"Pam","startTime":903.06,"endTime":907.23,"body":"giving everybody a third of a"},{"speaker":"Pam","startTime":907.23,"endTime":910.56,"body":"candy bar, how many people can"},{"speaker":"Pam","startTime":907.23,"endTime":910.56,"body":"get a third of a candy bar? How"},{"speaker":"Pam","startTime":910.56,"endTime":914.85,"body":"many 1/3s can I get out of 2 and"},{"speaker":"Pam","startTime":910.56,"endTime":914.85,"body":"2/3 candy bars?\""},{"speaker":"Kim","startTime":914.88,"endTime":916.02,"body":"Yeah, that was 8."},{"speaker":"Pam","startTime":916.29,"endTime":920.46,"body":"You said there were 8."},{"speaker":"Pam","startTime":916.29,"endTime":920.46,"body":"Eight portions, eight of 1/3s I"},{"speaker":"Pam","startTime":920.46,"endTime":921.63,"body":"could sort of hand out to"},{"speaker":"Pam","startTime":920.46,"endTime":921.63,"body":"people."},{"speaker":"Kim","startTime":921.9,"endTime":922.29,"body":"Yep."},{"speaker":"Pam","startTime":922.32,"endTime":926.19,"body":"In the next problem, I said"},{"speaker":"Pam","startTime":922.32,"endTime":926.19,"body":"2 and 2/3 divided by 2/3? Could"},{"speaker":"Pam","startTime":926.19,"endTime":928.77,"body":"you tell me what that would mean"},{"speaker":"Pam","startTime":926.19,"endTime":928.77,"body":"in the candy bar problem?"},{"speaker":"Kim","startTime":928.8,"endTime":932.07,"body":"Yes. So, now each person..."},{"speaker":"Kim","startTime":928.8,"endTime":932.07,"body":"I have the same amount of candy"},{"speaker":"Kim","startTime":932.07,"endTime":936.24,"body":"bar total, but instead of people"},{"speaker":"Kim","startTime":932.07,"endTime":936.24,"body":"only getting a third, they're"},{"speaker":"Kim","startTime":936.24,"endTime":939.33,"body":"going to get two-thirds, so they"},{"speaker":"Kim","startTime":936.24,"endTime":939.33,"body":"get twice as much. And so, I'm"},{"speaker":"Kim","startTime":939.33,"endTime":943.17,"body":"thinking about how many people"},{"speaker":"Kim","startTime":939.33,"endTime":943.17,"body":"can I feed now? If I'm giving"},{"speaker":"Kim","startTime":943.2,"endTime":946.98,"body":"twice as much, then only the"},{"speaker":"Kim","startTime":943.2,"endTime":946.98,"body":"first 4 people are going to get"},{"speaker":"Kim","startTime":946.98,"endTime":947.46,"body":"some."},{"speaker":"Pam","startTime":948.0,"endTime":950.49,"body":"Yeah, because if you"},{"speaker":"Pam","startTime":948.0,"endTime":950.49,"body":"give... If you start with the"},{"speaker":"Pam","startTime":950.49,"endTime":953.82,"body":"total amount of candy bars, and"},{"speaker":"Pam","startTime":950.49,"endTime":953.82,"body":"you give each person twice as"},{"speaker":"Pam","startTime":953.82,"endTime":956.73,"body":"much, you can only give that out"},{"speaker":"Pam","startTime":953.82,"endTime":956.73,"body":"to half as many people."},{"speaker":"Kim","startTime":956.97,"endTime":957.33,"body":"Right."},{"speaker":"Pam","startTime":957.9,"endTime":961.41,"body":"So, that would be 4. 2 and"},{"speaker":"Pam","startTime":957.9,"endTime":961.41,"body":"2/3 divided by 2/3 is 4."},{"speaker":"Pam","startTime":963.21,"endTime":967.95,"body":"And that would be some beginning"},{"speaker":"Pam","startTime":963.21,"endTime":967.95,"body":"reasoning that I would want to"},{"speaker":"Pam","startTime":967.95,"endTime":971.28,"body":"do with students about fraction"},{"speaker":"Pam","startTime":967.95,"endTime":971.28,"body":"division."},{"speaker":"Kim","startTime":973.11,"endTime":973.47,"body":"Yeah."},{"speaker":"Pam","startTime":973.5,"endTime":977.7,"body":"Let's maybe parse out a few"},{"speaker":"Pam","startTime":973.5,"endTime":977.7,"body":"things that we did. So, one, we"},{"speaker":"Pam","startTime":977.7,"endTime":981.33,"body":"have to be able to think about"},{"speaker":"Pam","startTime":977.7,"endTime":981.33,"body":"division as quotitive division,"},{"speaker":"Pam","startTime":981.9,"endTime":988.89,"body":"as how many of the divisors are"},{"speaker":"Pam","startTime":981.9,"endTime":988.89,"body":"in the dividend? If I have this"},{"speaker":"Pam","startTime":988.89,"endTime":993.42,"body":"many candy bars, this much of a"},{"speaker":"Pam","startTime":988.89,"endTime":993.42,"body":"candy bar, and I want to dole"},{"speaker":"Pam","startTime":993.42,"endTime":996.72,"body":"out pieces of the candy bar,"},{"speaker":"Pam","startTime":993.42,"endTime":996.72,"body":"sections of the candy bar, how"},{"speaker":"Pam","startTime":996.72,"endTime":999.9,"body":"many people can I feed? So, like"},{"speaker":"Pam","startTime":996.72,"endTime":999.9,"body":"the first problem, if I had a"},{"speaker":"Pam","startTime":999.9,"endTime":1002.9,"body":"candy bar, and I'm giving out"},{"speaker":"Pam","startTime":999.9,"endTime":1002.9,"body":"one-third pieces, how many of"},{"speaker":"Pam","startTime":1002.9,"endTime":1006.26,"body":"them are there? You said there"},{"speaker":"Pam","startTime":1002.9,"endTime":1006.26,"body":"were 3. If I double the candy"},{"speaker":"Pam","startTime":1006.26,"endTime":1010.94,"body":"bars, and I have 2 candy bars,"},{"speaker":"Pam","startTime":1006.26,"endTime":1010.94,"body":"and I'm doling out one-third of"},{"speaker":"Pam","startTime":1010.94,"endTime":1013.85,"body":"the candy bar to the people, how"},{"speaker":"Pam","startTime":1010.94,"endTime":1013.85,"body":"many people can I feed? Well, I"},{"speaker":"Pam","startTime":1013.85,"endTime":1017.33,"body":"doubled the number of candy"},{"speaker":"Pam","startTime":1013.85,"endTime":1017.33,"body":"bars, but I'm still giving out"},{"speaker":"Pam","startTime":1017.33,"endTime":1020.81,"body":"the same amount. Well, then I"},{"speaker":"Pam","startTime":1017.33,"endTime":1020.81,"body":"can give that same amount to"},{"speaker":"Pam","startTime":1020.81,"endTime":1023.48,"body":"twice as many people, so it's 6"},{"speaker":"Pam","startTime":1020.81,"endTime":1023.48,"body":"pieces."},{"speaker":"Kim","startTime":1023.99,"endTime":1024.29,"body":"Yeah."},{"speaker":"Pam","startTime":1024.319,"endTime":1028.489,"body":"So, there's this"},{"speaker":"Pam","startTime":1024.319,"endTime":1028.489,"body":"relationship of, if I double the"},{"speaker":"Pam","startTime":1028.489,"endTime":1035.539,"body":"dividend, if I double the total,"},{"speaker":"Pam","startTime":1028.489,"endTime":1035.539,"body":"but I keep the divisor the same,"},{"speaker":"Pam","startTime":1035.839,"endTime":1040.909,"body":"I keep the share the same, then"},{"speaker":"Pam","startTime":1035.839,"endTime":1040.909,"body":"I could give that share to twice"},{"speaker":"Pam","startTime":1040.909,"endTime":1043.249,"body":"as many people. That's a big"},{"speaker":"Pam","startTime":1040.909,"endTime":1043.249,"body":"(unclear)."},{"speaker":"Kim","startTime":1043.369,"endTime":1045.439,"body":"Wait, wait, wait. You said"},{"speaker":"Kim","startTime":1043.369,"endTime":1045.439,"body":"if you double the amount, they"},{"speaker":"Kim","startTime":1045.439,"endTime":1045.949,"body":"get?"},{"speaker":"Pam","startTime":1046.43,"endTime":1046.61,"body":"Oh,"},{"speaker":"Pam","startTime":1046.609,"endTime":1051.049,"body":"no. Sorry. I double the total,"},{"speaker":"Pam","startTime":1046.609,"endTime":1051.049,"body":"but I keep the portion the same."},{"speaker":"Pam","startTime":1051.049,"endTime":1053.089,"body":"I keep the portion, the amount"},{"speaker":"Pam","startTime":1051.049,"endTime":1053.089,"body":"they get, the same."},{"speaker":"Kim","startTime":1053.09,"endTime":1053.72,"body":"(unclear). Yep."},{"speaker":"Pam","startTime":1053.87,"endTime":1056.84,"body":"Then, I could give that"},{"speaker":"Pam","startTime":1053.87,"endTime":1056.84,"body":"portion to twice as many people"},{"speaker":"Pam","startTime":1056.84,"endTime":1058.07,"body":"because I doubled the total."},{"speaker":"Kim","startTime":1058.34,"endTime":1058.61,"body":"Yep."},{"speaker":"Pam","startTime":1058.64,"endTime":1061.46,"body":"That relationship, ideally,"},{"speaker":"Pam","startTime":1058.64,"endTime":1061.46,"body":"we would have developed with"},{"speaker":"Pam","startTime":1061.46,"endTime":1062.27,"body":"whole numbers."},{"speaker":"Kim","startTime":1062.87,"endTime":1063.11,"body":"Yeah."},{"speaker":"Pam","startTime":1063.11,"endTime":1066.53,"body":"Before... Notice, the way I"},{"speaker":"Pam","startTime":1063.11,"endTime":1066.53,"body":"just said that. If I double the"},{"speaker":"Pam","startTime":1066.53,"endTime":1070.7,"body":"number of candy bars, but I keep"},{"speaker":"Pam","startTime":1066.53,"endTime":1070.7,"body":"the portion the same, I can give"},{"speaker":"Pam","startTime":1070.7,"endTime":1073.52,"body":"that portion to twice as many"},{"speaker":"Pam","startTime":1070.7,"endTime":1073.52,"body":"people because I doubled the"},{"speaker":"Pam","startTime":1073.52,"endTime":1076.64,"body":"number of candy bars. That"},{"speaker":"Pam","startTime":1073.52,"endTime":1076.64,"body":"relationship, ideally, we would"},{"speaker":"Pam","startTime":1076.64,"endTime":1081.08,"body":"have developed with whole"},{"speaker":"Pam","startTime":1076.64,"endTime":1081.08,"body":"numbers before we hit this place"},{"speaker":"Pam","startTime":1081.08,"endTime":1083.42,"body":"where we're trying to reason"},{"speaker":"Pam","startTime":1081.08,"endTime":1083.42,"body":"about division with fractions."},{"speaker":"Pam","startTime":1084.05,"endTime":1087.59,"body":"Now, if you haven't, you might"},{"speaker":"Pam","startTime":1084.05,"endTime":1087.59,"body":"want to do a Problem String with"},{"speaker":"Pam","startTime":1087.59,"endTime":1092.06,"body":"whole numbers into this Problem"},{"speaker":"Pam","startTime":1087.59,"endTime":1092.06,"body":"String with fractions. I think"},{"speaker":"Pam","startTime":1092.06,"endTime":1094.82,"body":"that would be a helpful thing."},{"speaker":"Pam","startTime":1092.06,"endTime":1094.82,"body":"But we still can reason."},{"speaker":"Pam","startTime":1094.85,"endTime":1097.82,"body":"Especially if I've got the candy"},{"speaker":"Pam","startTime":1094.85,"endTime":1097.82,"body":"bars up on the board, we still"},{"speaker":"Pam","startTime":1097.82,"endTime":1101.18,"body":"can reason about these chunks of"},{"speaker":"Pam","startTime":1097.82,"endTime":1101.18,"body":"candy bars with students. It's"},{"speaker":"Pam","startTime":1101.18,"endTime":1104.09,"body":"just going to be, you know,"},{"speaker":"Pam","startTime":1101.18,"endTime":1104.09,"body":"we're thinking about more"},{"speaker":"Pam","startTime":1104.09,"endTime":1108.41,"body":"complicated numbers. So, it's"},{"speaker":"Pam","startTime":1104.09,"endTime":1108.41,"body":"one of the reasons why I really"},{"speaker":"Pam","startTime":1108.47,"endTime":1113.57,"body":"encourage people to think and"},{"speaker":"Pam","startTime":1108.47,"endTime":1113.57,"body":"reason about division with whole"},{"speaker":"Pam","startTime":1113.57,"endTime":1117.17,"body":"numbers, not just do stuff, not"},{"speaker":"Pam","startTime":1113.57,"endTime":1117.17,"body":"just do an algorithm. If all"},{"speaker":"Pam","startTime":1117.17,"endTime":1119.45,"body":"we've done with division of"},{"speaker":"Pam","startTime":1117.17,"endTime":1119.45,"body":"whole numbers is stick numbers"},{"speaker":"Pam","startTime":1119.45,"endTime":1122.39,"body":"in an algorithm, and then"},{"speaker":"Pam","startTime":1119.45,"endTime":1122.39,"body":"perform a bunch of steps. \"Does"},{"speaker":"Pam","startTime":1122.42,"endTime":1126.05,"body":"McDonald's sell cheeseburgers?\""},{"speaker":"Pam","startTime":1122.42,"endTime":1126.05,"body":"And, \"Do dirty monkeys smell"},{"speaker":"Pam","startTime":1126.05,"endTime":1128.96,"body":"bad?\" Like, whatever that"},{"speaker":"Pam","startTime":1126.05,"endTime":1128.96,"body":"algorithm is that you've done"},{"speaker":"Pam","startTime":1128.96,"endTime":1131.42,"body":"for division with whole numbers."},{"speaker":"Pam","startTime":1128.96,"endTime":1131.42,"body":"If we've done that with division"},{"speaker":"Pam","startTime":1131.42,"endTime":1135.65,"body":"of whole numbers, thinking about"},{"speaker":"Pam","startTime":1131.42,"endTime":1135.65,"body":"division of fractions is going"},{"speaker":"Pam","startTime":1135.65,"endTime":1138.5,"body":"to be more difficult. We're"},{"speaker":"Pam","startTime":1135.65,"endTime":1138.5,"body":"going to have to do more"},{"speaker":"Pam","startTime":1138.5,"endTime":1142.13,"body":"building of \"Oh, like I can"},{"speaker":"Pam","startTime":1138.5,"endTime":1142.13,"body":"think quotitively.\" And not only"},{"speaker":"Pam","startTime":1142.16,"endTime":1146.21,"body":"quotitively, but this idea of if"},{"speaker":"Pam","startTime":1142.16,"endTime":1146.21,"body":"I double the dividend, keep the"},{"speaker":"Pam","startTime":1146.21,"endTime":1150.86,"body":"divisor the same, then I can"},{"speaker":"Pam","startTime":1146.21,"endTime":1150.86,"body":"double the quotient. That's a"},{"speaker":"Pam","startTime":1150.86,"endTime":1154.34,"body":"big idea that I wish kids owned,"},{"speaker":"Pam","startTime":1150.86,"endTime":1154.34,"body":"so that we can sort of just like"},{"speaker":"Pam","startTime":1154.34,"endTime":1158.6,"body":"then investigate it, make it"},{"speaker":"Pam","startTime":1154.34,"endTime":1158.6,"body":"strong with fractions. We can"},{"speaker":"Pam","startTime":1158.6,"endTime":1161.0,"body":"use that same understanding."},{"speaker":"Pam","startTime":1158.6,"endTime":1161.0,"body":"Maybe a... Well, do you want to"},{"speaker":"Pam","startTime":1161.0,"endTime":1162.95,"body":"say anything before I point out"},{"speaker":"Pam","startTime":1161.0,"endTime":1162.95,"body":"a couple other things I did?"},{"speaker":"Kim","startTime":1163.67,"endTime":1165.62,"body":"No, it's it's just"},{"speaker":"Kim","startTime":1163.67,"endTime":1165.62,"body":"interesting that you're talking"},{"speaker":"Kim","startTime":1165.62,"endTime":1169.91,"body":"about this right now because"},{"speaker":"Kim","startTime":1165.62,"endTime":1169.91,"body":"just last night, Cooper, my"},{"speaker":"Kim","startTime":1169.91,"endTime":1173.21,"body":"younger, was asked to do"},{"speaker":"Kim","startTime":1169.91,"endTime":1173.21,"body":"something with 90 divided by 5,"},{"speaker":"Kim","startTime":1173.24,"endTime":1173.84,"body":"and he was like,"},{"speaker":"Kim","startTime":1175.31,"endTime":1177.56,"body":"\"Ugh, I don't want to be about"},{"speaker":"Kim","startTime":1175.31,"endTime":1177.56,"body":"5s.\" And so, he thought about"},{"speaker":"Kim","startTime":1177.56,"endTime":1184.88,"body":"180 divided by 10. So, it's a"},{"speaker":"Kim","startTime":1177.56,"endTime":1184.88,"body":"nice example of how he thought"},{"speaker":"Kim","startTime":1184.88,"endTime":1190.73,"body":"about twice as much in a whole"},{"speaker":"Kim","startTime":1184.88,"endTime":1190.73,"body":"number setting, in order to get"},{"speaker":"Kim","startTime":1190.76,"endTime":1191.93,"body":"the answer that he needed."},{"speaker":"Pam","startTime":1192.32,"endTime":1197.18,"body":"Ah, very nice. I will point"},{"speaker":"Pam","startTime":1192.32,"endTime":1197.18,"body":"out that if he's going to solve"},{"speaker":"Pam","startTime":1197.18,"endTime":1203.12,"body":"90 divided by 5 by solving the"},{"speaker":"Pam","startTime":1197.18,"endTime":1203.12,"body":"equivalent problem 180 divided"},{"speaker":"Pam","startTime":1203.12,"endTime":1206.81,"body":"by 10. Brilliant, I love your"},{"speaker":"Pam","startTime":1203.12,"endTime":1206.81,"body":"kid. That's actually the"},{"speaker":"Pam","startTime":1206.81,"endTime":1208.82,"body":"partitive meaning of division."},{"speaker":"Kim","startTime":1208.82,"endTime":1209.87,"body":"Yes, you're right."},{"speaker":"Pam","startTime":1209.99,"endTime":1213.86,"body":"Yeah. Which we would want"},{"speaker":"Pam","startTime":1209.99,"endTime":1213.86,"body":"to develop. That's not what we"},{"speaker":"Pam","startTime":1213.86,"endTime":1217.76,"body":"were messing with today, but I"},{"speaker":"Pam","startTime":1213.86,"endTime":1217.76,"body":"wouldn't want to stifle Cooper"},{"speaker":"Pam","startTime":1217.79,"endTime":1222.74,"body":"when he does that. I would want"},{"speaker":"Pam","startTime":1217.79,"endTime":1222.74,"body":"to like absolutely celebrate the"},{"speaker":"Pam","startTime":1222.74,"endTime":1225.59,"body":"thinking he's doing. In the"},{"speaker":"Pam","startTime":1222.74,"endTime":1225.59,"body":"midst of this Problem String,"},{"speaker":"Pam","startTime":1225.59,"endTime":1229.91,"body":"though, I'm going to keep the"},{"speaker":"Pam","startTime":1225.59,"endTime":1229.91,"body":"context alive about candy bars"},{"speaker":"Pam","startTime":1229.91,"endTime":1233.99,"body":"and divvying them out to kids,"},{"speaker":"Pam","startTime":1229.91,"endTime":1233.99,"body":"which will kind of keep him"},{"speaker":"Pam","startTime":1233.99,"endTime":1237.38,"body":"thinking quotitively here. But"},{"speaker":"Pam","startTime":1233.99,"endTime":1237.38,"body":"I'm not going to like, \"Oh, no,"},{"speaker":"Pam","startTime":1237.38,"endTime":1239.51,"body":"we're not doing that today. Stop"},{"speaker":"Pam","startTime":1237.38,"endTime":1239.51,"body":"doing that.\" I'll totally"},{"speaker":"Pam","startTime":1239.51,"endTime":1242.36,"body":"support what he's doing, and"},{"speaker":"Pam","startTime":1239.51,"endTime":1242.36,"body":"I'll draw him into the context"},{"speaker":"Pam","startTime":1242.36,"endTime":1246.02,"body":"that we're using. Which leads me"},{"speaker":"Pam","startTime":1242.36,"endTime":1246.02,"body":"to a thing I was going to point"},{"speaker":"Pam","startTime":1246.02,"endTime":1250.91,"body":"out is. That we did it in"},{"speaker":"Pam","startTime":1246.02,"endTime":1250.91,"body":"context, right? So, context is"},{"speaker":"Pam","startTime":1251.15,"endTime":1254.33,"body":"hugely important. I think we"},{"speaker":"Pam","startTime":1251.15,"endTime":1254.33,"body":"need to have kids involved in"},{"speaker":"Pam","startTime":1254.33,"endTime":1258.92,"body":"contexts, and then get naked,"},{"speaker":"Pam","startTime":1254.33,"endTime":1258.92,"body":"then decontextualize, and help"},{"speaker":"Pam","startTime":1258.92,"endTime":1263.9,"body":"them think out of context. But"},{"speaker":"Pam","startTime":1258.92,"endTime":1263.9,"body":"as we decontextualize, draw back"},{"speaker":"Pam","startTime":1263.93,"endTime":1268.52,"body":"on major contexts that we've"},{"speaker":"Pam","startTime":1263.93,"endTime":1268.52,"body":"used until kids can solve"},{"speaker":"Pam","startTime":1268.52,"endTime":1271.43,"body":"contextual problems, and"},{"speaker":"Pam","startTime":1268.52,"endTime":1271.43,"body":"decontextualize problems, and go"},{"speaker":"Pam","startTime":1271.43,"endTime":1274.28,"body":"back. That we want the"},{"speaker":"Pam","startTime":1271.43,"endTime":1274.28,"body":"flexibility that they can go"},{"speaker":"Pam","startTime":1274.28,"endTime":1278.63,"body":"back and forth between them."},{"speaker":"Pam","startTime":1274.28,"endTime":1278.63,"body":"That's the ideal goal, and we do"},{"speaker":"Pam","startTime":1278.63,"endTime":1282.02,"body":"that by starting with context"},{"speaker":"Pam","startTime":1278.63,"endTime":1282.02,"body":"and helping kids really reason"},{"speaker":"Pam","startTime":1282.02,"endTime":1287.12,"body":"in context, and then moving more"},{"speaker":"Pam","startTime":1282.02,"endTime":1287.12,"body":"abstractly. There's one other"},{"speaker":"Pam","startTime":1287.12,"endTime":1290.21,"body":"thing I wanted to point out that"},{"speaker":"Pam","startTime":1287.12,"endTime":1290.21,"body":"I did. Kim, every time we did"},{"speaker":"Pam","startTime":1290.21,"endTime":1294.65,"body":"one of those problems, I did not"},{"speaker":"Pam","startTime":1290.21,"endTime":1294.65,"body":"command you to draw a model,"},{"speaker":"Pam","startTime":1294.68,"endTime":1295.1,"body":"right?"},{"speaker":"Kim","startTime":1295.52,"endTime":1295.88,"body":"Right."},{"speaker":"Pam","startTime":1296.24,"endTime":1298.37,"body":"Did I stop you from drawing"},{"speaker":"Pam","startTime":1296.24,"endTime":1298.37,"body":"a model?"},{"speaker":"Kim","startTime":1298.79,"endTime":1303.08,"body":"No. Actually, I sketched"},{"speaker":"Kim","startTime":1298.79,"endTime":1303.08,"body":"part of the Problem String with"},{"speaker":"Kim","startTime":1303.08,"endTime":1305.24,"body":"the model, and then I just kind"},{"speaker":"Kim","startTime":1303.08,"endTime":1305.24,"body":"of stopped."},{"speaker":"Pam","startTime":1305.9,"endTime":1311.3,"body":"And I wonder if I had been"},{"speaker":"Pam","startTime":1305.9,"endTime":1311.3,"body":"sketching your thinking where"},{"speaker":"Pam","startTime":1311.3,"endTime":1314.45,"body":"you could see it. You know,"},{"speaker":"Pam","startTime":1311.3,"endTime":1314.45,"body":"we're just audio recording your"},{"speaker":"Pam","startTime":1314.45,"endTime":1316.97,"body":"at your house, I'm at my house."},{"speaker":"Pam","startTime":1314.45,"endTime":1316.97,"body":"If I was sketching, so you could"},{"speaker":"Pam","startTime":1316.97,"endTime":1319.1,"body":"see it, you might not even have"},{"speaker":"Pam","startTime":1316.97,"endTime":1319.1,"body":"sketched those first couple"},{"speaker":"Pam","startTime":1319.1,"endTime":1319.64,"body":"ones, right?"},{"speaker":"Kim","startTime":1320.0,"endTime":1320.18,"body":"Right."},{"speaker":"Pam","startTime":1320.18,"endTime":1322.4,"body":"Because I would have had."},{"speaker":"Pam","startTime":1320.18,"endTime":1322.4,"body":"And you probably sketched them"},{"speaker":"Pam","startTime":1322.4,"endTime":1324.29,"body":"because you were wondering,"},{"speaker":"Pam","startTime":1322.4,"endTime":1324.29,"body":"\"Hey, maybe this is going to"},{"speaker":"Pam","startTime":1324.29,"endTime":1326.84,"body":"help me later on.\" And as you"},{"speaker":"Pam","startTime":1324.29,"endTime":1326.84,"body":"were reasoning, you're like, \"I"},{"speaker":"Pam","startTime":1326.87,"endTime":1328.16,"body":"don't need that to help me.\""},{"speaker":"Kim","startTime":1328.16,"endTime":1328.25,"body":"Right."},{"speaker":"Pam","startTime":1328.25,"endTime":1331.85,"body":"But I would have been. So,"},{"speaker":"Pam","startTime":1328.25,"endTime":1331.85,"body":"we're just going to suggest that"},{"speaker":"Pam","startTime":1331.85,"endTime":1336.17,"body":"with Problem Strings, often it"},{"speaker":"Pam","startTime":1331.85,"endTime":1336.17,"body":"is that we draw out students'"},{"speaker":"Pam","startTime":1336.17,"endTime":1338.18,"body":"thinking and we make it visible."},{"speaker":"Kim","startTime":1338.54,"endTime":1338.81,"body":"Right."},{"speaker":"Pam","startTime":1338.84,"endTime":1344.51,"body":"We choose the model, we"},{"speaker":"Pam","startTime":1338.84,"endTime":1344.51,"body":"make it visible, and we help put"},{"speaker":"Pam","startTime":1344.51,"endTime":1347.69,"body":"something on the board that we"},{"speaker":"Pam","startTime":1344.51,"endTime":1347.69,"body":"can point at, that we can"},{"speaker":"Pam","startTime":1348.05,"endTime":1351.56,"body":"compare, that we can have"},{"speaker":"Pam","startTime":1348.05,"endTime":1351.56,"body":"discussions about because it's"},{"speaker":"Pam","startTime":1351.56,"endTime":1355.49,"body":"visible. And that's a huge part"},{"speaker":"Pam","startTime":1351.56,"endTime":1355.49,"body":"of what we're recommending as"},{"speaker":"Pam","startTime":1355.49,"endTime":1360.68,"body":"we're developing all the things."},{"speaker":"Pam","startTime":1355.49,"endTime":1360.68,"body":"So, Kim, this was not enough. We"},{"speaker":"Pam","startTime":1360.68,"endTime":1365.45,"body":"have not done enough work with"},{"speaker":"Pam","startTime":1360.68,"endTime":1365.45,"body":"fraction division yet. How about"},{"speaker":"Pam","startTime":1365.45,"endTime":1369.38,"body":"if we... Are you up to doing a"},{"speaker":"Pam","startTime":1365.45,"endTime":1369.38,"body":"couple more podcasts where we'll"},{"speaker":"Pam","startTime":1369.38,"endTime":1370.88,"body":"dive deeper into fraction"},{"speaker":"Pam","startTime":1369.38,"endTime":1370.88,"body":"division?"},{"speaker":"Kim","startTime":1370.91,"endTime":1371.87,"body":"Sure, yeah."},{"speaker":"Pam","startTime":1371.93,"endTime":1374.72,"body":"Alright, we'll do that in"},{"speaker":"Pam","startTime":1371.93,"endTime":1374.72,"body":"our next episode. Listeners, you"},{"speaker":"Pam","startTime":1374.72,"endTime":1378.17,"body":"are not going to want to miss"},{"speaker":"Pam","startTime":1374.72,"endTime":1378.17,"body":"our next episode, or two, or"},{"speaker":"Pam","startTime":1378.2,"endTime":1381.95,"body":"three...I don't know how many"},{"speaker":"Pam","startTime":1378.2,"endTime":1381.95,"body":"we'll do...to dive into really,"},{"speaker":"Pam","startTime":1381.98,"endTime":1385.55,"body":"really developing fraction"},{"speaker":"Pam","startTime":1381.98,"endTime":1385.55,"body":"division. Ya'll, thanks for"},{"speaker":"Pam","startTime":1385.55,"endTime":1388.73,"body":"tuning in and teaching more and"},{"speaker":"Pam","startTime":1385.55,"endTime":1388.73,"body":"more real math. To find out more"},{"speaker":"Pam","startTime":1388.73,"endTime":1391.07,"body":"about the Math is"},{"speaker":"Pam","startTime":1388.73,"endTime":1391.07,"body":"Figure-Out-Able movement, visit"},{"speaker":"Pam","startTime":1391.19,"endTime":1394.88,"body":"mathisfigureoutable.com. Let's"},{"speaker":"Pam","startTime":1391.19,"endTime":1394.88,"body":"keep spreading the word that"},{"speaker":"Pam","startTime":1394.88,"endTime":1396.35,"body":"Math is Figure-Out-Able!"}]}