{"version":"1.0.0","segments":[{"speaker":"Pam","startTime":1.35,"endTime":4.83,"body":"Hey, fellow mathematicians!"},{"speaker":"Pam","startTime":1.35,"endTime":4.83,"body":"Welcome to the podcast where"},{"speaker":"Pam","startTime":4.83,"endTime":7.83,"body":"Math is Figure-Out-Able. I'm"},{"speaker":"Pam","startTime":4.83,"endTime":7.83,"body":"Pam."},{"speaker":"Kim","startTime":8.16,"endTime":8.88,"body":"And I'm Kim."},{"speaker":"Pam","startTime":9.18,"endTime":12.12,"body":"And you have found a place"},{"speaker":"Pam","startTime":9.18,"endTime":12.12,"body":"where math is not about"},{"speaker":"Pam","startTime":12.12,"endTime":15.24,"body":"memorizing and mimicking,"},{"speaker":"Pam","startTime":12.12,"endTime":15.24,"body":"waiting to be told or shown what"},{"speaker":"Pam","startTime":15.24,"endTime":18.63,"body":"to do. But it's about making"},{"speaker":"Pam","startTime":15.24,"endTime":18.63,"body":"sense of problems, noticing"},{"speaker":"Pam","startTime":18.63,"endTime":22.32,"body":"patterns, and reasoning using"},{"speaker":"Pam","startTime":18.63,"endTime":22.32,"body":"mathematical relationships. We"},{"speaker":"Pam","startTime":22.32,"endTime":27.36,"body":"can mentor students to think and"},{"speaker":"Pam","startTime":22.32,"endTime":27.36,"body":"reason like mathematicians. Not"},{"speaker":"Pam","startTime":27.36,"endTime":30.81,"body":"only are algorithms not"},{"speaker":"Pam","startTime":27.36,"endTime":30.81,"body":"particularly helpful in teaching"},{"speaker":"Pam","startTime":30.81,"endTime":34.32,"body":"mathematics, but rotely"},{"speaker":"Pam","startTime":30.81,"endTime":34.32,"body":"repeating steps actually keep"},{"speaker":"Pam","startTime":34.32,"endTime":37.05,"body":"students from being the"},{"speaker":"Pam","startTime":34.32,"endTime":37.05,"body":"mathematicians they can be."},{"speaker":"Kim","startTime":37.59,"endTime":40.41,"body":"In our last episode, we"},{"speaker":"Kim","startTime":37.59,"endTime":40.41,"body":"started answering a question"},{"speaker":"Kim","startTime":40.41,"endTime":43.2,"body":"from a follower of our Math is"},{"speaker":"Kim","startTime":40.41,"endTime":43.2,"body":"Figure-Out-Able, teacher"},{"speaker":"Kim","startTime":43.23,"endTime":46.05,"body":"Facebook group, and so today,"},{"speaker":"Kim","startTime":43.23,"endTime":46.05,"body":"we've decided we're going to"},{"speaker":"Kim","startTime":46.05,"endTime":49.47,"body":"continue to answer Beth's"},{"speaker":"Kim","startTime":46.05,"endTime":49.47,"body":"question. And, Pam, I wanted to"},{"speaker":"Kim","startTime":49.47,"endTime":52.5,"body":"tell you that this is also"},{"speaker":"Kim","startTime":49.47,"endTime":52.5,"body":"timely because not too long ago,"},{"speaker":"Kim","startTime":52.5,"endTime":56.61,"body":"I got a text from a good friend"},{"speaker":"Kim","startTime":52.5,"endTime":56.61,"body":"of mine that you know well, and"},{"speaker":"Kim","startTime":56.61,"endTime":60.12,"body":"she said, \"Hey, Kim! Here's a"},{"speaker":"Kim","startTime":56.61,"endTime":60.12,"body":"problem that my kid has to"},{"speaker":"Kim","startTime":60.12,"endTime":63.51,"body":"solve. How can I think about"},{"speaker":"Kim","startTime":60.12,"endTime":63.51,"body":"this?\" And I loved her question"},{"speaker":"Kim","startTime":63.51,"endTime":65.61,"body":"because it wasn't \"What's the"},{"speaker":"Kim","startTime":63.51,"endTime":65.61,"body":"answer?\" Like, \"Just tell me"},{"speaker":"Kim","startTime":65.61,"endTime":68.7,"body":"what to tell my kid.\" She's"},{"speaker":"Kim","startTime":65.61,"endTime":68.7,"body":"interested in thinking. So, I"},{"speaker":"Kim","startTime":68.7,"endTime":73.11,"body":"think there are probably plenty"},{"speaker":"Kim","startTime":68.7,"endTime":73.11,"body":"of people out there who want to"},{"speaker":"Kim","startTime":73.11,"endTime":76.29,"body":"learn how to think about"},{"speaker":"Kim","startTime":73.11,"endTime":76.29,"body":"division of fractions."},{"speaker":"Pam","startTime":76.35,"endTime":78.75,"body":"Absolutely. And so, Beth"},{"speaker":"Pam","startTime":76.35,"endTime":78.75,"body":"Roberts, thanks for asking the"},{"speaker":"Pam","startTime":78.75,"endTime":83.28,"body":"question about how to teach"},{"speaker":"Pam","startTime":78.75,"endTime":83.28,"body":"division of fractions. So, we"},{"speaker":"Pam","startTime":83.28,"endTime":85.62,"body":"started last time. We did some"},{"speaker":"Pam","startTime":83.28,"endTime":85.62,"body":"whole number divided by"},{"speaker":"Pam","startTime":85.62,"endTime":88.92,"body":"fraction. We also did some mixed"},{"speaker":"Pam","startTime":85.62,"endTime":88.92,"body":"number divided by fraction."},{"speaker":"Pam","startTime":88.92,"endTime":92.58,"body":"Let's dive in more to some"},{"speaker":"Pam","startTime":88.92,"endTime":92.58,"body":"reasoning that we would want to"},{"speaker":"Pam","startTime":92.58,"endTime":97.8,"body":"develop about fraction division."},{"speaker":"Pam","startTime":92.58,"endTime":97.8,"body":"Last week, we did some problems"},{"speaker":"Pam","startTime":97.8,"endTime":102.72,"body":"like 3 and a 1/3 divided by 1/3,"},{"speaker":"Pam","startTime":97.8,"endTime":102.72,"body":"and we thought about how many"},{"speaker":"Pam","startTime":102.72,"endTime":108.15,"body":"unit fractions are in a bigger"},{"speaker":"Pam","startTime":102.72,"endTime":108.15,"body":"number. So, all of the problems"},{"speaker":"Pam","startTime":108.15,"endTime":113.4,"body":"last week had dividends, or the"},{"speaker":"Pam","startTime":108.15,"endTime":113.4,"body":"sort of first number in the"},{"speaker":"Pam","startTime":113.4,"endTime":117.39,"body":"division problem, that were"},{"speaker":"Pam","startTime":113.4,"endTime":117.39,"body":"bigger than the divisor. Like, 3"},{"speaker":"Pam","startTime":117.39,"endTime":122.34,"body":"and 1/3 divided by 1/3. So, 3"},{"speaker":"Pam","startTime":117.39,"endTime":122.34,"body":"and 1/3 is bigger. The divisor's"},{"speaker":"Pam","startTime":122.37,"endTime":126.93,"body":"1/3. How many 1/3s can we get"},{"speaker":"Pam","startTime":122.37,"endTime":126.93,"body":"out of 3 and 1/3. It's very"},{"speaker":"Pam","startTime":126.93,"endTime":131.67,"body":"quotitative approach to thinking"},{"speaker":"Pam","startTime":126.93,"endTime":131.67,"body":"about division. In a way what we"},{"speaker":"Pam","startTime":131.67,"endTime":136.83,"body":"did last time was really focus"},{"speaker":"Pam","startTime":131.67,"endTime":136.83,"body":"on the definition of a unit"},{"speaker":"Pam","startTime":136.83,"endTime":139.38,"body":"fraction. What's a unit"},{"speaker":"Pam","startTime":136.83,"endTime":139.38,"body":"fraction? It's when the"},{"speaker":"Pam","startTime":139.41,"endTime":143.67,"body":"numerator's 1. So, it's like my"},{"speaker":"Pam","startTime":139.41,"endTime":143.67,"body":"fair share when I'm thinking"},{"speaker":"Pam","startTime":143.67,"endTime":147.15,"body":"about sharing. So, if I'm"},{"speaker":"Pam","startTime":143.67,"endTime":147.15,"body":"sharing a candy bar, and I'm"},{"speaker":"Pam","startTime":147.15,"endTime":150.09,"body":"going to share it with 4 other"},{"speaker":"Pam","startTime":147.15,"endTime":150.09,"body":"people. So, 5 of us are sharing,"},{"speaker":"Pam","startTime":150.51,"endTime":154.92,"body":"and I share it fairly, then what"},{"speaker":"Pam","startTime":150.51,"endTime":154.92,"body":"do I call my piece? I call my"},{"speaker":"Pam","startTime":154.92,"endTime":158.31,"body":"piece one-fifth because 5 people"},{"speaker":"Pam","startTime":154.92,"endTime":158.31,"body":"are sharing. Well, what if 7"},{"speaker":"Pam","startTime":158.31,"endTime":162.36,"body":"people were sharing? Then I call"},{"speaker":"Pam","startTime":158.31,"endTime":162.36,"body":"it one-seventh. The definition"},{"speaker":"Pam","startTime":162.45,"endTime":166.74,"body":"of a unit fraction is sort of"},{"speaker":"Pam","startTime":162.45,"endTime":166.74,"body":"one person's fair share. If you"},{"speaker":"Pam","startTime":166.74,"endTime":170.55,"body":"share the thing fairly with that"},{"speaker":"Pam","startTime":166.74,"endTime":170.55,"body":"many people. That's important."},{"speaker":"Pam","startTime":170.55,"endTime":174.27,"body":"We need to know what one-twelfth"},{"speaker":"Pam","startTime":170.55,"endTime":174.27,"body":"looks like, one-eighth looks"},{"speaker":"Pam","startTime":174.27,"endTime":178.32,"body":"like, one-half looks like. We"},{"speaker":"Pam","startTime":174.27,"endTime":178.32,"body":"need kids to reason about the"},{"speaker":"Pam","startTime":178.32,"endTime":183.66,"body":"relationships between that unit"},{"speaker":"Pam","startTime":178.32,"endTime":183.66,"body":"fraction and a whole, the unit"},{"speaker":"Pam","startTime":183.69,"endTime":186.24,"body":"that were sort of cutting up and"},{"speaker":"Pam","startTime":183.69,"endTime":186.24,"body":"dividing fairly. Yeah?"},{"speaker":"Kim","startTime":186.66,"endTime":186.99,"body":"Yep."},{"speaker":"Pam","startTime":187.44,"endTime":191.28,"body":"So, today, we're going to"},{"speaker":"Pam","startTime":187.44,"endTime":191.28,"body":"continue to take a quotitive"},{"speaker":"Pam","startTime":191.61,"endTime":195.42,"body":"approach, how many of the"},{"speaker":"Pam","startTime":191.61,"endTime":195.42,"body":"divisors are in the dividend?"},{"speaker":"Pam","startTime":195.66,"endTime":198.33,"body":"So, for example, if I was"},{"speaker":"Pam","startTime":195.66,"endTime":198.33,"body":"dividing a whole number problem"},{"speaker":"Pam","startTime":198.33,"endTime":204.96,"body":"like 210 divided by 10. If I'm"},{"speaker":"Pam","startTime":198.33,"endTime":204.96,"body":"looking at quotitively, that's"},{"speaker":"Pam","startTime":204.96,"endTime":210.63,"body":"asking the question, \"How many"},{"speaker":"Pam","startTime":204.96,"endTime":210.63,"body":"10s are in 210? So, if I was"},{"speaker":"Pam","startTime":210.63,"endTime":214.05,"body":"going to reason about how many"},{"speaker":"Pam","startTime":210.63,"endTime":214.05,"body":"10s are in 210, I might reason"},{"speaker":"Pam","startTime":214.05,"endTime":217.83,"body":"about how many 10s are in 100"},{"speaker":"Pam","startTime":214.05,"endTime":217.83,"body":"because I know that, and then I"},{"speaker":"Pam","startTime":217.83,"endTime":221.58,"body":"could double that to think about"},{"speaker":"Pam","startTime":217.83,"endTime":221.58,"body":"how many 10s are in 200, and I"},{"speaker":"Pam","startTime":221.58,"endTime":225.57,"body":"can just tack on that extra one"},{"speaker":"Pam","startTime":221.58,"endTime":225.57,"body":"more 10 in 210. So, that would"},{"speaker":"Pam","startTime":225.57,"endTime":229.59,"body":"be a way of me sort of reasoning"},{"speaker":"Pam","startTime":225.57,"endTime":229.59,"body":"about the number of 10s is 210."},{"speaker":"Pam","startTime":230.34,"endTime":233.25,"body":"I wonder if we could use similar"},{"speaker":"Pam","startTime":230.34,"endTime":233.25,"body":"reasoning that we just did with"},{"speaker":"Pam","startTime":233.25,"endTime":236.16,"body":"whole numbers. Could we use"},{"speaker":"Pam","startTime":233.25,"endTime":236.16,"body":"similar reasoning to think about"},{"speaker":"Pam","startTime":236.16,"endTime":240.78,"body":"division fractions? So here we"},{"speaker":"Pam","startTime":236.16,"endTime":240.78,"body":"go. Alright, Kim. If I had a"},{"speaker":"Pam","startTime":240.78,"endTime":246.45,"body":"candy bar, and I'm going to"},{"speaker":"Pam","startTime":240.78,"endTime":246.45,"body":"split it up, and share it. And"},{"speaker":"Pam","startTime":246.45,"endTime":250.23,"body":"I'm thinking about sharing it"},{"speaker":"Pam","startTime":246.45,"endTime":250.23,"body":"with 4 other people, so five"},{"speaker":"Pam","startTime":250.23,"endTime":255.87,"body":"people are sharing. What is 1"},{"speaker":"Pam","startTime":250.23,"endTime":255.87,"body":"candy bar divided by 1/5? How"},{"speaker":"Pam","startTime":255.87,"endTime":259.56,"body":"many 1/5s can I get out of 1"},{"speaker":"Pam","startTime":255.87,"endTime":259.56,"body":"candy bar?"},{"speaker":"Kim","startTime":261.6,"endTime":266.55,"body":"Well, your going to have 5"},{"speaker":"Kim","startTime":261.6,"endTime":266.55,"body":"because you just told me how"},{"speaker":"Kim","startTime":266.55,"endTime":269.28,"body":"many people you have. So,"},{"speaker":"Kim","startTime":266.55,"endTime":269.28,"body":"one-fifth. There are five 1/5s"},{"speaker":"Kim","startTime":269.31,"endTime":269.85,"body":"in 1."},{"speaker":"Pam","startTime":270.54,"endTime":273.93,"body":"Did I do too much there?"},{"speaker":"Pam","startTime":270.54,"endTime":273.93,"body":"Too much of your own thinking?"},{"speaker":"Pam","startTime":274.53,"endTime":277.14,"body":"So, I want to start in a place"},{"speaker":"Pam","startTime":274.53,"endTime":277.14,"body":"where kind of everybody can"},{"speaker":"Pam","startTime":277.14,"endTime":279.21,"body":"access. Again, we're kind of"},{"speaker":"Pam","startTime":277.14,"endTime":279.21,"body":"reminding ourselves what we did"},{"speaker":"Pam","startTime":279.21,"endTime":282.54,"body":"last time. And so, you're saying"},{"speaker":"Pam","startTime":279.21,"endTime":282.54,"body":"that the answer to 1 divided by"},{"speaker":"Pam","startTime":282.54,"endTime":286.74,"body":"1/5 is 5 because there's five"},{"speaker":"Pam","startTime":282.54,"endTime":286.74,"body":"1/5s in one. So, I've quickly"},{"speaker":"Pam","startTime":286.74,"endTime":290.94,"body":"sketched a candy bar. I've sort"},{"speaker":"Pam","startTime":286.74,"endTime":290.94,"body":"of eyeballed dividing it into 5"},{"speaker":"Pam","startTime":290.94,"endTime":293.85,"body":"equal pieces. I've kind of"},{"speaker":"Pam","startTime":290.94,"endTime":293.85,"body":"dotted those, put some dotted"},{"speaker":"Pam","startTime":293.85,"endTime":298.05,"body":"lines, so we can see 5 chunks of"},{"speaker":"Pam","startTime":293.85,"endTime":298.05,"body":"that rectangle. And I've labeled"},{"speaker":"Pam","startTime":298.38,"endTime":302.49,"body":"the first chunk. I've labeled it"},{"speaker":"Pam","startTime":298.38,"endTime":302.49,"body":"one-fifth. So, a little bit less"},{"speaker":"Pam","startTime":302.49,"endTime":304.74,"body":"labeling then I did in the"},{"speaker":"Pam","startTime":302.49,"endTime":304.74,"body":"Problem String that we talked"},{"speaker":"Pam","startTime":304.74,"endTime":309.81,"body":"about in the last episode. Okay,"},{"speaker":"Pam","startTime":304.74,"endTime":309.81,"body":"next problem. I've only got half"},{"speaker":"Pam","startTime":309.81,"endTime":315.06,"body":"a candy bar, Kim. So, what is"},{"speaker":"Pam","startTime":309.81,"endTime":315.06,"body":"1/2 divided by 1/5? And what"},{"speaker":"Pam","startTime":315.06,"endTime":317.13,"body":"does that mean with our candy"},{"speaker":"Pam","startTime":315.06,"endTime":317.13,"body":"bar scenario?"},{"speaker":"Kim","startTime":318.24,"endTime":324.66,"body":"So, when you had a whole"},{"speaker":"Kim","startTime":318.24,"endTime":324.66,"body":"candy bar, 1 divided by a 1/5,"},{"speaker":"Kim","startTime":325.08,"endTime":330.21,"body":"then you had 5 people or 5"},{"speaker":"Kim","startTime":325.08,"endTime":330.21,"body":"pieces. But now you have only"},{"speaker":"Kim","startTime":330.21,"endTime":335.34,"body":"half as much candy bar, so"},{"speaker":"Kim","startTime":330.21,"endTime":335.34,"body":"you're going to have half as"},{"speaker":"Kim","startTime":335.34,"endTime":339.48,"body":"much people or per person. Let"},{"speaker":"Kim","startTime":335.34,"endTime":339.48,"body":"me think about what you... I"},{"speaker":"Kim","startTime":339.48,"endTime":343.38,"body":"can't remember exactly what your"},{"speaker":"Kim","startTime":339.48,"endTime":343.38,"body":"scenario was. 1/2 divided by 1/5"},{"speaker":"Kim","startTime":344.37,"endTime":350.19,"body":"is 2 and a 1/2. Because in the"},{"speaker":"Kim","startTime":344.37,"endTime":350.19,"body":"previous problem, you said 1"},{"speaker":"Kim","startTime":350.22,"endTime":354.57,"body":"divided by 1/5, and now we have"},{"speaker":"Kim","startTime":350.22,"endTime":354.57,"body":"1/2 divided by 1/5, so the"},{"speaker":"Kim","startTime":354.57,"endTime":356.07,"body":"answer is going to be half as"},{"speaker":"Kim","startTime":354.57,"endTime":356.07,"body":"much."},{"speaker":"Pam","startTime":356.73,"endTime":359.01,"body":"Since the answer to the"},{"speaker":"Pam","startTime":356.73,"endTime":359.01,"body":"first problem is 5, the answer"},{"speaker":"Pam","startTime":359.01,"endTime":361.2,"body":"to the next problem is going to"},{"speaker":"Pam","startTime":359.01,"endTime":361.2,"body":"be half as much, which is 2 and"},{"speaker":"Pam","startTime":361.2,"endTime":363.09,"body":"a 1/2. 1/2 of 5 is 2 and a 1/2."},{"speaker":"Pam","startTime":361.2,"endTime":363.09,"body":"Yeah."},{"speaker":"Kim","startTime":363.09,"endTime":363.3,"body":"Yeah."},{"speaker":"Pam","startTime":363.45,"endTime":365.94,"body":"So, you were like, \"What"},{"speaker":"Pam","startTime":363.45,"endTime":365.94,"body":"was the scenario again?\" So,"},{"speaker":"Pam","startTime":365.94,"endTime":368.49,"body":"that's a good question. Like, I"},{"speaker":"Pam","startTime":365.94,"endTime":368.49,"body":"said I have a whole candy bar,"},{"speaker":"Pam","startTime":368.82,"endTime":372.33,"body":"and I want to share it with 5"},{"speaker":"Pam","startTime":368.82,"endTime":372.33,"body":"people, so they each get..."},{"speaker":"Pam","startTime":372.75,"endTime":374.91,"body":"Well, I guess what I should say"},{"speaker":"Pam","startTime":372.75,"endTime":374.91,"body":"is, I've got a whole candy bar,"},{"speaker":"Pam","startTime":374.91,"endTime":377.07,"body":"and I've cut it into 5 equal"},{"speaker":"Pam","startTime":374.91,"endTime":377.07,"body":"sections."},{"speaker":"Kim","startTime":377.07,"endTime":377.58,"body":"There you go. Yeah."},{"speaker":"Kim","startTime":377.07,"endTime":377.58,"body":"(unclear)."},{"speaker":"Pam","startTime":377.58,"endTime":380.31,"body":"I've cut it into 5"},{"speaker":"Pam","startTime":377.58,"endTime":380.31,"body":"sections. Cut it into fifths."},{"speaker":"Pam","startTime":380.55,"endTime":385.17,"body":"How many people can I give a"},{"speaker":"Pam","startTime":380.55,"endTime":385.17,"body":"fifth of a candy bar to?"},{"speaker":"Kim","startTime":385.2,"endTime":387.27,"body":"I think that's why I was"},{"speaker":"Kim","startTime":385.2,"endTime":387.27,"body":"like, \"Wait a second...\" because"},{"speaker":"Kim","startTime":387.6,"endTime":389.7,"body":"in this scenario, it'd be 2 and"},{"speaker":"Kim","startTime":387.6,"endTime":389.7,"body":"a 1/2 people."},{"speaker":"Pam","startTime":390.63,"endTime":393.66,"body":"Yeah. So, that's kind of"},{"speaker":"Pam","startTime":390.63,"endTime":393.66,"body":"weird, right? How many fifths"},{"speaker":"Pam","startTime":393.84,"endTime":396.21,"body":"can I get out of 1/2 a candy"},{"speaker":"Pam","startTime":393.84,"endTime":396.21,"body":"bar? (unclear)."},{"speaker":"Kim","startTime":396.21,"endTime":397.5,"body":"Two and half 1/5s. Yeah."},{"speaker":"Pam","startTime":397.56,"endTime":400.65,"body":"I can only get two and a"},{"speaker":"Pam","startTime":397.56,"endTime":400.65,"body":"half of those 1/5s. So, that's"},{"speaker":"Pam","startTime":400.65,"endTime":403.89,"body":"not so great, right, for 2 and a"},{"speaker":"Pam","startTime":400.65,"endTime":403.89,"body":"1/2 people, so... Yeah, that's"},{"speaker":"Pam","startTime":403.89,"endTime":407.07,"body":"kind of weird to think about."},{"speaker":"Pam","startTime":403.89,"endTime":407.07,"body":"But I can think about. I can"},{"speaker":"Pam","startTime":407.07,"endTime":411.0,"body":"only give that same amount to"},{"speaker":"Pam","startTime":407.07,"endTime":411.0,"body":"half as many people."},{"speaker":"Kim","startTime":411.24,"endTime":411.84,"body":"Yes."},{"speaker":"Pam","startTime":412.26,"endTime":416.85,"body":"Cool. Yeah. Okay. So, what"},{"speaker":"Pam","startTime":412.26,"endTime":416.85,"body":"if I had a problem like... I'm"},{"speaker":"Pam","startTime":416.85,"endTime":419.97,"body":"back to a whole candy bar, but"},{"speaker":"Pam","startTime":416.85,"endTime":419.97,"body":"this time I'm going to split it"},{"speaker":"Pam","startTime":419.97,"endTime":421.02,"body":"into tenths."},{"speaker":"Kim","startTime":421.41,"endTime":421.89,"body":"Okay."},{"speaker":"Pam","startTime":422.04,"endTime":425.97,"body":"How many tenths can I get"},{"speaker":"Pam","startTime":422.04,"endTime":425.97,"body":"out of that candy bar?"},{"speaker":"Kim","startTime":426.87,"endTime":427.26,"body":"Ten.(unclear)"},{"speaker":"Pam","startTime":428.28,"endTime":428.7,"body":"Because?"},{"speaker":"Kim","startTime":429.18,"endTime":432.21,"body":"One-tenth because there's"},{"speaker":"Kim","startTime":429.18,"endTime":432.21,"body":"ten-tenths in a whole."},{"speaker":"Pam","startTime":432.57,"endTime":436.14,"body":"Ten-tenths in a whole. So,"},{"speaker":"Pam","startTime":432.57,"endTime":436.14,"body":"1 divided by 1/10 is 10. How"},{"speaker":"Pam","startTime":436.14,"endTime":438.96,"body":"does that relate to the problem"},{"speaker":"Pam","startTime":436.14,"endTime":438.96,"body":"1 divided by 1/5?"},{"speaker":"Kim","startTime":440.82,"endTime":444.81,"body":"Oh, good question. I hadn't"},{"speaker":"Kim","startTime":440.82,"endTime":444.81,"body":"thought about that."},{"speaker":"Pam","startTime":446.19,"endTime":450.48,"body":"I like it when I get Kim to"},{"speaker":"Pam","startTime":446.19,"endTime":450.48,"body":"think. Bam! That's a good day."},{"speaker":"Kim","startTime":451.05,"endTime":453.42,"body":"Let me think if I can say"},{"speaker":"Kim","startTime":451.05,"endTime":453.42,"body":"this right. I still have 1 candy"},{"speaker":"Kim","startTime":453.42,"endTime":463.95,"body":"bar, but instead of fifths, now"},{"speaker":"Kim","startTime":453.42,"endTime":463.95,"body":"the size of the piece is half is"},{"speaker":"Kim","startTime":463.95,"endTime":467.58,"body":"big. Right, so instead of fifth,"},{"speaker":"Kim","startTime":463.95,"endTime":467.58,"body":"now I have tenths. The size of"},{"speaker":"Kim","startTime":467.58,"endTime":469.95,"body":"the piece is half as big, so I'm"},{"speaker":"Kim","startTime":467.58,"endTime":469.95,"body":"going to have twice as many of"},{"speaker":"Kim","startTime":469.95,"endTime":470.91,"body":"those pieces."},{"speaker":"Pam","startTime":471.78,"endTime":477.0,"body":"Right? Yeah. Because before"},{"speaker":"Pam","startTime":471.78,"endTime":477.0,"body":"I had five 1/5s, but I've cut"},{"speaker":"Pam","startTime":477.0,"endTime":480.0,"body":"the, now I'd have tenths. And"},{"speaker":"Pam","startTime":477.0,"endTime":480.0,"body":"tenths are half as big as"},{"speaker":"Pam","startTime":480.0,"endTime":482.46,"body":"fifths. That's like the"},{"speaker":"Pam","startTime":480.0,"endTime":482.46,"body":"definition of a tenth, right?"},{"speaker":"Kim","startTime":482.49,"endTime":483.09,"body":"Yep."},{"speaker":"Pam","startTime":483.3,"endTime":486.6,"body":"In fact, often if we say to"},{"speaker":"Pam","startTime":483.3,"endTime":486.6,"body":"kids, \"Hey, draw a rectangle,"},{"speaker":"Pam","startTime":486.6,"endTime":490.71,"body":"and cut it into tenths.\" Some of"},{"speaker":"Pam","startTime":486.6,"endTime":490.71,"body":"them will cut it into fifths,"},{"speaker":"Pam","startTime":491.04,"endTime":493.41,"body":"and then they'll cut each of"},{"speaker":"Pam","startTime":491.04,"endTime":493.41,"body":"those fifths in half."},{"speaker":"Kim","startTime":493.98,"endTime":494.25,"body":"Yep."},{"speaker":"Pam","startTime":494.25,"endTime":496.11,"body":"And then, they've got"},{"speaker":"Pam","startTime":494.25,"endTime":496.11,"body":"tenths. Cool. So, you're saying"},{"speaker":"Pam","startTime":496.11,"endTime":501.18,"body":"that if there's five 1/5s in 1,"},{"speaker":"Pam","startTime":496.11,"endTime":501.18,"body":"1 divided by 1/5 is 5, then"},{"speaker":"Pam","startTime":501.18,"endTime":505.11,"body":"there's ten 1/10s in 1 because"},{"speaker":"Pam","startTime":501.18,"endTime":505.11,"body":"you've cut the pieces in half,"},{"speaker":"Pam","startTime":505.11,"endTime":510.33,"body":"so there's twice as many. Nice."},{"speaker":"Pam","startTime":505.11,"endTime":510.33,"body":"What if... Oh, so on my candy"},{"speaker":"Pam","startTime":510.33,"endTime":513.81,"body":"bar, I went ahead and cut the"},{"speaker":"Pam","startTime":510.33,"endTime":513.81,"body":"candy bar into fifths again. So,"},{"speaker":"Pam","startTime":513.81,"endTime":516.6,"body":"I've kind of underneath the one"},{"speaker":"Pam","startTime":513.81,"endTime":516.6,"body":"I had before. I've cut it into"},{"speaker":"Pam","startTime":516.6,"endTime":520.53,"body":"fifths, and then each of"},{"speaker":"Pam","startTime":516.6,"endTime":520.53,"body":"those... Actually, I've only cut"},{"speaker":"Pam","startTime":520.53,"endTime":523.26,"body":"the first one in half to be"},{"speaker":"Pam","startTime":520.53,"endTime":523.26,"body":"honest with you, and I've"},{"speaker":"Pam","startTime":523.26,"endTime":527.97,"body":"labeled that piece as 1/10, and"},{"speaker":"Pam","startTime":523.26,"endTime":527.97,"body":"I've labeled the second"},{"speaker":"Pam","startTime":528.0,"endTime":532.17,"body":"one-tenth as 1/10. So, I have 2"},{"speaker":"Pam","startTime":528.0,"endTime":532.17,"body":"little pieces labeled as 1/10."},{"speaker":"Pam","startTime":532.62,"endTime":534.84,"body":"And I kind of have an"},{"speaker":"Pam","startTime":532.62,"endTime":534.84,"body":"overarching one of those"},{"speaker":"Pam","startTime":534.87,"endTime":538.68,"body":"bracketty things above the two"},{"speaker":"Pam","startTime":534.87,"endTime":538.68,"body":"1/10s and I've labeled that as"},{"speaker":"Pam","startTime":538.68,"endTime":539.16,"body":"one-fifth."},{"speaker":"Kim","startTime":539.25,"endTime":539.34,"body":"Okay."},{"speaker":"Pam","startTime":539.97,"endTime":542.13,"body":"Does that make sense? So, I"},{"speaker":"Pam","startTime":539.97,"endTime":542.13,"body":"kinda have a one-fifth labeled,"},{"speaker":"Pam","startTime":542.28,"endTime":544.11,"body":"and I've cut it in half, and"},{"speaker":"Pam","startTime":542.28,"endTime":544.11,"body":"I've labeled each of those"},{"speaker":"Pam","startTime":544.11,"endTime":548.85,"body":"halves as one-tenth. Alright,"},{"speaker":"Pam","startTime":544.11,"endTime":548.85,"body":"cool. Next problem. How about if"},{"speaker":"Pam","startTime":548.85,"endTime":553.65,"body":"I ask you for 3/5 divided by"},{"speaker":"Pam","startTime":548.85,"endTime":553.65,"body":"1/5?"},{"speaker":"Kim","startTime":554.76,"endTime":558.18,"body":"Three. Three 1/5s in 3/5."},{"speaker":"Pam","startTime":559.29,"endTime":562.41,"body":"There's three 1/5s in 3 is"},{"speaker":"Pam","startTime":559.29,"endTime":562.41,"body":"your answer? That's your final"},{"speaker":"Pam","startTime":562.41,"endTime":562.8,"body":"answer?"},{"speaker":"Kim","startTime":563.07,"endTime":563.19,"body":"Yep."},{"speaker":"Pam","startTime":563.19,"endTime":567.54,"body":"Cool. So, I might draw that"},{"speaker":"Pam","startTime":563.19,"endTime":567.54,"body":"whole candy bar, and I might"},{"speaker":"Pam","startTime":567.54,"endTime":572.73,"body":"divide it into fifths, and then"},{"speaker":"Pam","startTime":567.54,"endTime":572.73,"body":"I might circle three-fifths,"},{"speaker":"Pam","startTime":572.76,"endTime":577.14,"body":"three of those 1/5s. And then, I"},{"speaker":"Pam","startTime":572.76,"endTime":577.14,"body":"might say, \"So, that's what"},{"speaker":"Pam","startTime":577.14,"endTime":579.81,"body":"you're focused on is those three"},{"speaker":"Pam","startTime":577.14,"endTime":579.81,"body":"1/5s?\" Because you just were"},{"speaker":"Pam","startTime":579.81,"endTime":583.38,"body":"like, \"Bam! 3.\" And in those"},{"speaker":"Pam","startTime":579.81,"endTime":583.38,"body":"three 1/5s, you can see three"},{"speaker":"Pam","startTime":583.41,"endTime":586.71,"body":"1/5s. So, it's interesting"},{"speaker":"Pam","startTime":583.41,"endTime":586.71,"body":"because I actually want to"},{"speaker":"Pam","startTime":586.71,"endTime":591.15,"body":"call... So, the problem is 3/5"},{"speaker":"Pam","startTime":586.71,"endTime":591.15,"body":"divided by 1/5. I actually want"},{"speaker":"Pam","startTime":591.15,"endTime":596.46,"body":"to say, three 1/5s divided by"},{"speaker":"Pam","startTime":591.15,"endTime":596.46,"body":"1/5. How many 1/5 are in three"},{"speaker":"Pam","startTime":596.46,"endTime":598.74,"body":"1/5s. And I think you said that."},{"speaker":"Pam","startTime":596.46,"endTime":598.74,"body":"How many 1/5 are in three 1/5s."},{"speaker":"Pam","startTime":598.92,"endTime":602.76,"body":"There's 3 of them. So,"},{"speaker":"Pam","startTime":598.92,"endTime":602.76,"body":"listeners, you might recognize"},{"speaker":"Pam","startTime":602.76,"endTime":607.47,"body":"that I'm calling the non-unit"},{"speaker":"Pam","startTime":602.76,"endTime":607.47,"body":"fraction three-fifths. I'm"},{"speaker":"Pam","startTime":607.47,"endTime":611.52,"body":"actually naming it three-fifths,"},{"speaker":"Pam","startTime":607.47,"endTime":611.52,"body":"but I'm also naming it three"},{"speaker":"Pam","startTime":611.55,"endTime":618.54,"body":"1/5s. Not 3 and 1/5, but three"},{"speaker":"Pam","startTime":611.55,"endTime":618.54,"body":"1/5s. And I'm simply writing the"},{"speaker":"Pam","startTime":618.54,"endTime":624.72,"body":"fraction 3 \"fraction bar\" 5, but"},{"speaker":"Pam","startTime":618.54,"endTime":624.72,"body":"it can have two names, and one"},{"speaker":"Pam","startTime":624.72,"endTime":627.99,"body":"of the names is three-fifths and"},{"speaker":"Pam","startTime":624.72,"endTime":627.99,"body":"one of the names is three 1/5s."},{"speaker":"Pam","startTime":628.17,"endTime":631.92,"body":"And we find that helpful. We"},{"speaker":"Pam","startTime":628.17,"endTime":631.92,"body":"find it helpful to talk about"},{"speaker":"Pam","startTime":632.13,"endTime":636.15,"body":"these non-unit fractions in"},{"speaker":"Pam","startTime":632.13,"endTime":636.15,"body":"terms of their unit fractions."},{"speaker":"Pam","startTime":636.18,"endTime":639.81,"body":"That can be helpful in some"},{"speaker":"Pam","startTime":636.18,"endTime":639.81,"body":"cases. Alright, cool. How about"},{"speaker":"Pam","startTime":639.81,"endTime":643.71,"body":"the next problem? The next"},{"speaker":"Pam","startTime":639.81,"endTime":643.71,"body":"problem is 3/5 divided by 1/10."},{"speaker":"Both Pam and Kim","startTime":649.83,"endTime":649.95,"body":"(unclear)"},{"speaker":"Pam","startTime":652.53,"endTime":654.33,"body":"Yes. I want to know what"},{"speaker":"Pam","startTime":652.53,"endTime":654.33,"body":"you really thought about, and"},{"speaker":"Pam","startTime":654.33,"endTime":655.77,"body":"then I'm going to ask you a"},{"speaker":"Pam","startTime":654.33,"endTime":655.77,"body":"question. Go ahead. What are you"},{"speaker":"Pam","startTime":655.77,"endTime":656.16,"body":"really thinking?"},{"speaker":"Kim","startTime":656.31,"endTime":660.0,"body":"So, what I really thought."},{"speaker":"Kim","startTime":656.31,"endTime":660.0,"body":"I know that we're living in land"},{"speaker":"Kim","startTime":660.0,"endTime":662.64,"body":"of fractions, and I see a"},{"speaker":"Kim","startTime":660.0,"endTime":662.64,"body":"relationship between..."},{"speaker":"Pam","startTime":662.64,"endTime":664.59,"body":"Oh, no. Oh, no. I know"},{"speaker":"Pam","startTime":662.64,"endTime":664.59,"body":"where you went."},{"speaker":"Kim","startTime":664.8,"endTime":665.97,"body":"In a previous problem,"},{"speaker":"Kim","startTime":665.97,"endTime":670.17,"body":"but I really thought $0.60"},{"speaker":"Kim","startTime":665.97,"endTime":670.17,"body":"divided by $0.10. Like."},{"speaker":"Pam","startTime":670.17,"endTime":672.69,"body":"Because you're just like"},{"speaker":"Pam","startTime":670.17,"endTime":672.69,"body":"this percent girl. You were..."},{"speaker":"Kim","startTime":672.87,"endTime":676.14,"body":"Well, I mean, percents, or"},{"speaker":"Kim","startTime":672.87,"endTime":676.14,"body":"dimes, or whatever. Like, all of"},{"speaker":"Kim","startTime":676.14,"endTime":677.88,"body":"it. Like, it's all connected."},{"speaker":"Kim","startTime":676.14,"endTime":677.88,"body":"So."},{"speaker":"Pam","startTime":677.91,"endTime":678.33,"body":"Yeah."},{"speaker":"Kim","startTime":678.39,"endTime":680.58,"body":"Yeah, I thought about how"},{"speaker":"Kim","startTime":678.39,"endTime":680.58,"body":"many dimes were in $0.60."},{"speaker":"Pam","startTime":680.91,"endTime":684.75,"body":"Because three-fifths is"},{"speaker":"Pam","startTime":680.91,"endTime":684.75,"body":"$0.60. And one-tenth... I have"},{"speaker":"Pam","startTime":684.75,"endTime":687.54,"body":"to say it out loud. And"},{"speaker":"Pam","startTime":684.75,"endTime":687.54,"body":"one-tenth is $0.10. So, it's"},{"speaker":"Pam","startTime":687.54,"endTime":691.14,"body":"like you said $0.60 divided by"},{"speaker":"Pam","startTime":687.54,"endTime":691.14,"body":"$0.10. How many $0.10 are in"},{"speaker":"Pam","startTime":691.14,"endTime":693.9,"body":"$0.60? And so, you said the"},{"speaker":"Pam","startTime":691.14,"endTime":693.9,"body":"answer's 6. Cool. Okay. I have"},{"speaker":"Pam","startTime":693.9,"endTime":697.8,"body":"no problem with that. I just"},{"speaker":"Pam","startTime":693.9,"endTime":697.8,"body":"realized, I totally leaned away"},{"speaker":"Pam","startTime":697.8,"endTime":702.57,"body":"from my microphone. Sorry about"},{"speaker":"Pam","startTime":697.8,"endTime":702.57,"body":"that. If I was working with"},{"speaker":"Pam","startTime":702.57,"endTime":706.41,"body":"kids, and I saw someone with"},{"speaker":"Pam","startTime":702.57,"endTime":706.41,"body":"that strategy. I'm circulating"},{"speaker":"Pam","startTime":706.41,"endTime":710.19,"body":"around. I'm listening and stuff."},{"speaker":"Pam","startTime":706.41,"endTime":710.19,"body":"Or even if a kid... Well, let's"},{"speaker":"Pam","startTime":710.19,"endTime":712.77,"body":"say I'm circling around, and I"},{"speaker":"Pam","startTime":710.19,"endTime":712.77,"body":"saw that strategy, I might say"},{"speaker":"Pam","startTime":712.77,"endTime":714.96,"body":"to that kid. I might give him a"},{"speaker":"Pam","startTime":712.77,"endTime":714.96,"body":"fist bump and go, \"Nice"},{"speaker":"Pam","startTime":714.96,"endTime":719.13,"body":"thinking. Hey, can you think"},{"speaker":"Pam","startTime":714.96,"endTime":719.13,"body":"about it in terms of fractions"},{"speaker":"Pam","startTime":719.13,"endTime":721.62,"body":"and the candy bar I have on the"},{"speaker":"Pam","startTime":719.13,"endTime":721.62,"body":"board?\""},{"speaker":"Kim","startTime":722.04,"endTime":722.37,"body":"Yeah."},{"speaker":"Pam","startTime":722.88,"endTime":726.78,"body":"So, I'm going to say like,"},{"speaker":"Pam","startTime":722.88,"endTime":726.78,"body":"\"Nice thinking. Can you also"},{"speaker":"Pam","startTime":726.78,"endTime":728.79,"body":"think about it in terms of like"},{"speaker":"Pam","startTime":726.78,"endTime":728.79,"body":"the candy bar I have on the"},{"speaker":"Pam","startTime":728.79,"endTime":729.12,"body":"board?\""},{"speaker":"Kim","startTime":729.48,"endTime":729.78,"body":"Yeah."},{"speaker":"Pam","startTime":730.14,"endTime":732.42,"body":"So, Kim, I'm curious. Can"},{"speaker":"Pam","startTime":730.14,"endTime":732.42,"body":"you? Can you think about it in"},{"speaker":"Pam","startTime":732.42,"endTime":734.91,"body":"terms? Especially like the"},{"speaker":"Pam","startTime":732.42,"endTime":734.91,"body":"problem before? So, I know you"},{"speaker":"Pam","startTime":734.91,"endTime":736.8,"body":"guys... A lot of listeners are"},{"speaker":"Pam","startTime":734.91,"endTime":736.8,"body":"probably listening. So, the"},{"speaker":"Pam","startTime":736.8,"endTime":739.92,"body":"problem before was \"How many"},{"speaker":"Pam","startTime":736.8,"endTime":739.92,"body":"one-fifths are in three-fifths?"},{"speaker":"Kim","startTime":740.04,"endTime":740.55,"body":"Yeah."},{"speaker":"Pam","startTime":740.76,"endTime":743.64,"body":"How would you say that"},{"speaker":"Pam","startTime":740.76,"endTime":743.64,"body":"quotitively for the problem we"},{"speaker":"Pam","startTime":743.64,"endTime":746.04,"body":"just said? How would you say the"},{"speaker":"Pam","startTime":743.64,"endTime":746.04,"body":"problem we just did quotitively?"},{"speaker":"Kim","startTime":746.85,"endTime":752.82,"body":"So, when it was 3/5 divided"},{"speaker":"Kim","startTime":746.85,"endTime":752.82,"body":"by 1/5, then there were three"},{"speaker":"Kim","startTime":752.82,"endTime":759.84,"body":"1/5s. Now, I have smaller"},{"speaker":"Kim","startTime":752.82,"endTime":759.84,"body":"pieces. The pieces are half as"},{"speaker":"Kim","startTime":759.87,"endTime":761.82,"body":"big, and so I have..."},{"speaker":"Pam","startTime":761.88,"endTime":763.14,"body":"Because you have one-tenth."},{"speaker":"Kim","startTime":763.59,"endTime":766.32,"body":"Yeah. One-tenth. They're"},{"speaker":"Kim","startTime":763.59,"endTime":766.32,"body":"half as big as a fifth, and so"},{"speaker":"Kim","startTime":766.32,"endTime":768.06,"body":"I'm going to have twice as many"},{"speaker":"Kim","startTime":766.32,"endTime":768.06,"body":"pieces."},{"speaker":"Pam","startTime":769.5,"endTime":772.29,"body":"And so, you're still"},{"speaker":"Pam","startTime":769.5,"endTime":772.29,"body":"getting 6 dimes and $0.60, but"},{"speaker":"Pam","startTime":772.29,"endTime":777.09,"body":"you're also getting 6... I'm"},{"speaker":"Pam","startTime":772.29,"endTime":777.09,"body":"going to try to let you finish"},{"speaker":"Pam","startTime":777.09,"endTime":777.93,"body":"that sentence. You're also..."},{"speaker":"Kim","startTime":777.96,"endTime":779.46,"body":"Oh, sorry. I zoned out."},{"speaker":"Pam","startTime":779.82,"endTime":782.94,"body":"That's okay. Alright, so"},{"speaker":"Pam","startTime":779.82,"endTime":782.94,"body":"you're getting 6 dimes... It's"},{"speaker":"Pam","startTime":782.94,"endTime":786.57,"body":"okay. It's a real thing. You're"},{"speaker":"Pam","startTime":782.94,"endTime":786.57,"body":"getting 6 dimes in $0.60. Now,"},{"speaker":"Pam","startTime":786.57,"endTime":788.43,"body":"I'm looking at the fractions,"},{"speaker":"Pam","startTime":786.57,"endTime":788.43,"body":"and if I was pointing to the"},{"speaker":"Pam","startTime":788.43,"endTime":789.54,"body":"board, you see I was pointing"},{"speaker":"Pam","startTime":788.43,"endTime":789.54,"body":"at?"},{"speaker":"Kim","startTime":789.81,"endTime":791.37,"body":"Six 1/10s in three-fifths."},{"speaker":"Pam","startTime":791.4,"endTime":792.96,"body":"Six 1/10s in three-fifths."},{"speaker":"Both Pam and Kim","startTime":792.99,"endTime":793.5,"body":"Yeah."},{"speaker":"Pam","startTime":793.59,"endTime":796.77,"body":"Cool. And you kind of"},{"speaker":"Pam","startTime":793.59,"endTime":796.77,"body":"compared that to the problem"},{"speaker":"Pam","startTime":796.77,"endTime":802.95,"body":"before. So, if we have three"},{"speaker":"Pam","startTime":796.77,"endTime":802.95,"body":"1/5s in 3/5. Now, you have"},{"speaker":"Pam","startTime":803.04,"endTime":805.89,"body":"smaller pieces. You've cut the"},{"speaker":"Pam","startTime":803.04,"endTime":805.89,"body":"pieces in half. You'd have twice"},{"speaker":"Pam","startTime":805.89,"endTime":809.49,"body":"as many pieces, right? What if"},{"speaker":"Pam","startTime":805.89,"endTime":809.49,"body":"you just were thinking about"},{"speaker":"Pam","startTime":809.49,"endTime":813.0,"body":"this problem? If I literally"},{"speaker":"Pam","startTime":809.49,"endTime":813.0,"body":"just said for cold one-tenths?"},{"speaker":"Pam","startTime":813.3,"endTime":818.1,"body":"How many 1/10 in 3/5? I'm just"},{"speaker":"Pam","startTime":813.3,"endTime":818.1,"body":"curious if there's any other"},{"speaker":"Pam","startTime":818.1,"endTime":823.11,"body":"thinking that comes to mind. And"},{"speaker":"Pam","startTime":818.1,"endTime":823.11,"body":"I'm pointing. You can't see. I'm"},{"speaker":"Pam","startTime":823.11,"endTime":827.1,"body":"pointing at the picture that I"},{"speaker":"Pam","startTime":823.11,"endTime":827.1,"body":"had on the board when we were"},{"speaker":"Pam","startTime":827.1,"endTime":829.62,"body":"talking about how many. I'm"},{"speaker":"Pam","startTime":827.1,"endTime":829.62,"body":"interrupting your thinking."},{"speaker":"Pam","startTime":829.62,"endTime":830.31,"body":"Sorry, Kim."},{"speaker":"Kim","startTime":830.4,"endTime":831.03,"body":"No, go ahead."},{"speaker":"Pam","startTime":831.09,"endTime":832.44,"body":"You want me to tell you"},{"speaker":"Pam","startTime":831.09,"endTime":832.44,"body":"where I'm pointing? Okay, I'm"},{"speaker":"Pam","startTime":832.44,"endTime":835.02,"body":"going to say where I'm pointing."},{"speaker":"Pam","startTime":832.44,"endTime":835.02,"body":"So, on the board, when we did"},{"speaker":"Pam","startTime":835.05,"endTime":838.68,"body":"3/5 divided by 1/5, I drew a"},{"speaker":"Pam","startTime":835.05,"endTime":838.68,"body":"whole candy bar. I cut it into"},{"speaker":"Pam","startTime":838.68,"endTime":843.84,"body":"fifths, and I circled three of"},{"speaker":"Pam","startTime":838.68,"endTime":843.84,"body":"the 1/5s. And I said, \"How many"},{"speaker":"Pam","startTime":843.84,"endTime":848.94,"body":"1/5 are in 3/5.\" Now, I'm still"},{"speaker":"Pam","startTime":843.84,"endTime":848.94,"body":"looking at a candy bar that's"},{"speaker":"Pam","startTime":848.94,"endTime":855.0,"body":"cut into fifths, and I've"},{"speaker":"Pam","startTime":848.94,"endTime":855.0,"body":"circled three of the 1/5s. And"},{"speaker":"Pam","startTime":855.0,"endTime":858.75,"body":"now I'm asking how many 1/10 are"},{"speaker":"Pam","startTime":855.0,"endTime":858.75,"body":"in 3/5?"},{"speaker":"Kim","startTime":859.59,"endTime":862.71,"body":"So, within each one of"},{"speaker":"Kim","startTime":859.59,"endTime":862.71,"body":"those fifths, there's"},{"speaker":"Kim","startTime":862.71,"endTime":864.24,"body":"two-tenths. Is that what you're"},{"speaker":"Kim","startTime":862.71,"endTime":864.24,"body":"asking?"},{"speaker":"Pam","startTime":864.81,"endTime":867.24,"body":"Mmhmm. So, if there's..."},{"speaker":"Kim","startTime":867.24,"endTime":868.44,"body":"I don't think I understand"},{"speaker":"Kim","startTime":867.24,"endTime":868.44,"body":"your question."},{"speaker":"Pam","startTime":868.65,"endTime":871.56,"body":"Yeah. So, where you just"},{"speaker":"Pam","startTime":868.65,"endTime":871.56,"body":"said. So, in each of those"},{"speaker":"Pam","startTime":871.56,"endTime":874.77,"body":"fifths. I've circled"},{"speaker":"Pam","startTime":871.56,"endTime":874.77,"body":"three-fifths, right? And the"},{"speaker":"question is","startTime":874.77,"endTime":877.23,"body":"How many tenths are"},{"speaker":"question is","startTime":874.77,"endTime":877.23,"body":"in three-fifths? And you just"},{"speaker":"question is","startTime":877.23,"endTime":879.96,"body":"said, \"Well, in each of those"},{"speaker":"question is","startTime":877.23,"endTime":879.96,"body":"tenths, there's two 1/5s.\" So,"},{"speaker":"question is","startTime":879.96,"endTime":881.79,"body":"you've kind of got two 1/5s, two"},{"speaker":"question is","startTime":879.96,"endTime":881.79,"body":"1/5s, two 1/5s."},{"speaker":"Kim","startTime":881.82,"endTime":883.53,"body":"The other way around. In"},{"speaker":"Kim","startTime":881.82,"endTime":883.53,"body":"each of those fifths, there's"},{"speaker":"Kim","startTime":883.53,"endTime":884.13,"body":"two-tenths."},{"speaker":"Pam","startTime":884.13,"endTime":886.14,"body":"Ha, I said it backwards."},{"speaker":"Pam","startTime":884.13,"endTime":886.14,"body":"You're right. In each of those"},{"speaker":"Pam","startTime":886.14,"endTime":889.95,"body":"fifths is two-tenths. So, you've"},{"speaker":"Pam","startTime":886.14,"endTime":889.95,"body":"got two 1/10s, two 1/10s, two"},{"speaker":"Pam","startTime":889.95,"endTime":893.55,"body":"1/10s, so you've got six of"},{"speaker":"Pam","startTime":889.95,"endTime":893.55,"body":"those 1/10s in 3/5."},{"speaker":"Kim","startTime":894.12,"endTime":894.39,"body":"Yes."},{"speaker":"Pam","startTime":894.39,"endTime":896.76,"body":"Just kind of sort of"},{"speaker":"Pam","startTime":894.39,"endTime":896.76,"body":"looking at the picture."},{"speaker":"Kim","startTime":896.76,"endTime":897.6,"body":"Oh, the model. Yeah."},{"speaker":"Pam","startTime":897.63,"endTime":901.41,"body":"The model where I kind of"},{"speaker":"Pam","startTime":897.63,"endTime":901.41,"body":"had 2/10 in each of those 1/5s."},{"speaker":"Kim","startTime":901.53,"endTime":901.8,"body":"Yes."},{"speaker":"Pam","startTime":901.8,"endTime":902.97,"body":"And so, I could sort of"},{"speaker":"Pam","startTime":901.8,"endTime":902.97,"body":"like. Well, if there's"},{"speaker":"Pam","startTime":903.0,"endTime":906.42,"body":"two-tenths in one-fifth, and"},{"speaker":"Pam","startTime":903.0,"endTime":906.42,"body":"I've got three of those 1/5s,"},{"speaker":"Pam","startTime":906.45,"endTime":909.06,"body":"then I have three times those"},{"speaker":"Pam","startTime":906.45,"endTime":909.06,"body":"two would be?"},{"speaker":"Kim","startTime":909.06,"endTime":909.63,"body":"Six 1/10s."},{"speaker":"Pam","startTime":909.9,"endTime":912.12,"body":"Yeah, I wish I was"},{"speaker":"Pam","startTime":909.9,"endTime":912.12,"body":"pointing. It's so much better"},{"speaker":"Pam","startTime":912.12,"endTime":917.73,"body":"pointing. Maybe, Kim, we should"},{"speaker":"Pam","startTime":912.12,"endTime":917.73,"body":"do a video podcast one day, and"},{"speaker":"Pam","startTime":917.73,"endTime":923.25,"body":"we can actually be pointing at"},{"speaker":"Pam","startTime":917.73,"endTime":923.25,"body":"stuff. Ya'll, we thought about"},{"speaker":"Pam","startTime":923.25,"endTime":926.13,"body":"doing a video podcast, and every"},{"speaker":"Pam","startTime":923.25,"endTime":926.13,"body":"time we do, it's me that's the"},{"speaker":"Pam","startTime":926.13,"endTime":928.83,"body":"holdout because I'm like, \"I'd"},{"speaker":"Pam","startTime":926.13,"endTime":928.83,"body":"have to like brush my hair,"},{"speaker":"Pam","startTime":928.86,"endTime":929.07,"body":"and...\""},{"speaker":"Kim","startTime":929.7,"endTime":930.78,"body":"Stop it. That's not true."},{"speaker":"Pam","startTime":930.78,"endTime":933.39,"body":"Like, I mean, right now"},{"speaker":"Pam","startTime":930.78,"endTime":933.39,"body":"what am I wearing? I'm wearing"},{"speaker":"Pam","startTime":933.39,"endTime":936.57,"body":"jeans and a hoodie? And my"},{"speaker":"Pam","startTime":933.39,"endTime":936.57,"body":"glasses."},{"speaker":"Kim","startTime":937.11,"endTime":937.14,"body":"(unclear)."},{"speaker":"Pam","startTime":938.76,"endTime":940.95,"body":"I did brush my hair this"},{"speaker":"Pam","startTime":938.76,"endTime":940.95,"body":"morning, but I didn't do"},{"speaker":"Pam","startTime":940.95,"endTime":941.85,"body":"anything else to it."},{"speaker":"Pam","startTime":942.87,"endTime":943.35,"body":"Anyway, okay, so."},{"speaker":"Kim","startTime":943.35,"endTime":945.51,"body":"We would just laugh at each"},{"speaker":"Kim","startTime":943.35,"endTime":945.51,"body":"other the whole time. (unclear)"},{"speaker":"Pam","startTime":945.57,"endTime":948.75,"body":"Well, you know the other"},{"speaker":"Pam","startTime":945.57,"endTime":948.75,"body":"reason we've pushed back on"},{"speaker":"Pam","startTime":948.75,"endTime":950.82,"body":"doing any video podcast. We"},{"speaker":"Pam","startTime":948.75,"endTime":950.82,"body":"would laugh at each other the"},{"speaker":"Pam","startTime":950.82,"endTime":955.14,"body":"whole time. But is we worry"},{"speaker":"Pam","startTime":950.82,"endTime":955.14,"body":"that... Well, like right now,"},{"speaker":"Pam","startTime":955.17,"endTime":957.69,"body":"I'm really cognizant that I'm"},{"speaker":"Pam","startTime":955.17,"endTime":957.69,"body":"talking to people who are just"},{"speaker":"Pam","startTime":957.69,"endTime":958.17,"body":"listening."},{"speaker":"Kim","startTime":958.5,"endTime":958.71,"body":"Yes."},{"speaker":"Pam","startTime":958.71,"endTime":962.37,"body":"And if we could point, we"},{"speaker":"Pam","startTime":958.71,"endTime":962.37,"body":"would probably say less because"},{"speaker":"Pam","startTime":962.37,"endTime":965.37,"body":"we would be able to point, and"},{"speaker":"Pam","startTime":962.37,"endTime":965.37,"body":"then anybody listening. So, hey,"},{"speaker":"Pam","startTime":965.37,"endTime":968.28,"body":"podcast listeners? We'd be super"},{"speaker":"Pam","startTime":965.37,"endTime":968.28,"body":"interested to know would it be"},{"speaker":"Pam","startTime":968.28,"endTime":971.04,"body":"worth it? Would you be like,"},{"speaker":"Pam","startTime":968.28,"endTime":971.04,"body":"\"Oh, really do a video one"},{"speaker":"Pam","startTime":971.04,"endTime":972.75,"body":"because we'd understand so much"},{"speaker":"Pam","startTime":971.04,"endTime":972.75,"body":"better!\" Or you're like, \"No."},{"speaker":"Pam","startTime":972.75,"endTime":975.33,"body":"Really, I'm listening in my car,"},{"speaker":"Pam","startTime":972.75,"endTime":975.33,"body":"and I would not be working, so"},{"speaker":"Pam","startTime":975.33,"endTime":977.88,"body":"keep...\" Yeah, I'd be super"},{"speaker":"Pam","startTime":975.33,"endTime":977.88,"body":"curious. Alright. Our last"},{"speaker":"Pam","startTime":977.88,"endTime":980.58,"body":"problem was how many tenths are"},{"speaker":"Pam","startTime":977.88,"endTime":980.58,"body":"in three-fifths. Or 3/5 divided"},{"speaker":"Pam","startTime":980.58,"endTime":981.15,"body":"by 1/10?"},{"speaker":"Kim","startTime":981.3,"endTime":981.51,"body":"Yeah."},{"speaker":"Pam","startTime":981.54,"endTime":986.88,"body":"The next problem is 1 and"},{"speaker":"Pam","startTime":981.54,"endTime":986.88,"body":"3/5 divided by 1/10? 1 and 3/5"},{"speaker":"Pam","startTime":986.91,"endTime":988.41,"body":"divided by 1/10. What are you"},{"speaker":"Pam","startTime":986.91,"endTime":988.41,"body":"thinking about?"},{"speaker":"Kim","startTime":989.43,"endTime":990.12,"body":"$1.60."},{"speaker":"Pam","startTime":992.43,"endTime":995.46,"body":"Alright, how many? How many"},{"speaker":"Pam","startTime":992.43,"endTime":995.46,"body":"dimes? Well, go ahead. How many"},{"speaker":"Pam","startTime":995.46,"endTime":995.94,"body":"dimes are in $1.60?"},{"speaker":"Kim","startTime":995.94,"endTime":997.47,"body":"How many dimes are in"},{"speaker":"Kim","startTime":995.94,"endTime":997.47,"body":"$1.60?"},{"speaker":"Pam","startTime":997.5,"endTime":998.13,"body":"Yeah, how many?"},{"speaker":"Kim","startTime":998.16,"endTime":1002.96,"body":"So, 16. But also, I've been"},{"speaker":"Kim","startTime":998.16,"endTime":1002.96,"body":"writing down the problems. I"},{"speaker":"Kim","startTime":1002.96,"endTime":1005.06,"body":"have not been drawing them all"},{"speaker":"Kim","startTime":1002.96,"endTime":1005.06,"body":"model, but I've been writing"},{"speaker":"Kim","startTime":1005.06,"endTime":1010.16,"body":"down the problems. And you asked"},{"speaker":"Kim","startTime":1005.06,"endTime":1010.16,"body":"me 1 divided by 1/10, and you"},{"speaker":"Kim","startTime":1010.16,"endTime":1012.02,"body":"asked me 3/5 divided by 1/10."},{"speaker":"Pam","startTime":1012.02,"endTime":1012.53,"body":"Mmhmm."},{"speaker":"Kim","startTime":1012.92,"endTime":1017.45,"body":"So, when it was 1 divided"},{"speaker":"Kim","startTime":1012.92,"endTime":1017.45,"body":"by 1/10, it was 10. And 3/5"},{"speaker":"Kim","startTime":1017.63,"endTime":1022.4,"body":"divided by 1/10 was 6. So, if"},{"speaker":"Kim","startTime":1017.63,"endTime":1022.4,"body":"you put those together, 1 and"},{"speaker":"Kim","startTime":1022.43,"endTime":1025.82,"body":"3/5 divided by a 1/10 would be"},{"speaker":"Kim","startTime":1022.43,"endTime":1025.82,"body":"the same 16."},{"speaker":"Pam","startTime":1026.15,"endTime":1028.49,"body":"Would be that 10 plus the 6"},{"speaker":"Pam","startTime":1026.15,"endTime":1028.49,"body":"is 16."},{"speaker":"Kim","startTime":1028.52,"endTime":1028.76,"body":"Yeah."},{"speaker":"Pam","startTime":1028.76,"endTime":1031.7,"body":"Yeah, nice. Nice. I love"},{"speaker":"Pam","startTime":1028.76,"endTime":1031.7,"body":"that reasoning. Super. And if"},{"speaker":"Pam","startTime":1031.7,"endTime":1033.77,"body":"I'm doing this Problem String"},{"speaker":"Pam","startTime":1031.7,"endTime":1033.77,"body":"with students those things are"},{"speaker":"Pam","startTime":1033.77,"endTime":1038.45,"body":"on the board, so students have"},{"speaker":"Pam","startTime":1033.77,"endTime":1038.45,"body":"access to those. I wonder then"},{"speaker":"Pam","startTime":1038.45,"endTime":1043.49,"body":"if I might grab that problem 1"},{"speaker":"Pam","startTime":1038.45,"endTime":1043.49,"body":"divided by 1/10 and that model"},{"speaker":"Pam","startTime":1043.52,"endTime":1048.59,"body":"that we used to see that one"},{"speaker":"Pam","startTime":1043.52,"endTime":1048.59,"body":"1/10 in that whole candy bar."},{"speaker":"Pam","startTime":1048.8,"endTime":1051.29,"body":"And then, I might also grab the"},{"speaker":"Pam","startTime":1048.8,"endTime":1051.29,"body":"model where I had the 3/5"},{"speaker":"Pam","startTime":1051.29,"endTime":1054.92,"body":"divided by 1/10 and grab that"},{"speaker":"Pam","startTime":1051.29,"endTime":1054.92,"body":"piece of it, and show those six"},{"speaker":"Pam","startTime":1054.92,"endTime":1058.31,"body":"1/10s. And I've got the ten"},{"speaker":"Pam","startTime":1054.92,"endTime":1058.31,"body":"1/10s, and the six 1/10s would"},{"speaker":"Pam","startTime":1058.31,"endTime":1061.64,"body":"be the sixteen 1/10. Nice. Next"},{"speaker":"Pam","startTime":1058.31,"endTime":1061.64,"body":"question. How about if I asked"},{"speaker":"Pam","startTime":1061.64,"endTime":1064.67,"body":"you 1 divided by 1/3?"},{"speaker":"Kim","startTime":1065.9,"endTime":1069.5,"body":"That would be 3. Three 1/3"},{"speaker":"Kim","startTime":1065.9,"endTime":1069.5,"body":"thirds, in 1 whole."},{"speaker":"Pam","startTime":1070.07,"endTime":1072.02,"body":"Cool. Because we just got a"},{"speaker":"Pam","startTime":1070.07,"endTime":1072.02,"body":"whole, and you're asking how"},{"speaker":"Pam","startTime":1072.02,"endTime":1074.6,"body":"many one-thirds are in 1. That's"},{"speaker":"Pam","startTime":1072.02,"endTime":1074.6,"body":"just three. I don't know why I"},{"speaker":"Pam","startTime":1074.6,"endTime":1076.85,"body":"repeat what you say every time,"},{"speaker":"Pam","startTime":1074.6,"endTime":1076.85,"body":"but it helps me think about"},{"speaker":"Pam","startTime":1076.85,"endTime":1081.17,"body":"what... It really helps me think"},{"speaker":"Pam","startTime":1076.85,"endTime":1081.17,"body":"about what you just said. So, I"},{"speaker":"Pam","startTime":1081.17,"endTime":1083.15,"body":"know sometimes listeners, you"},{"speaker":"Pam","startTime":1081.17,"endTime":1083.15,"body":"might be like, \"Why does she"},{"speaker":"Pam","startTime":1083.15,"endTime":1085.43,"body":"repeat what Kim says?\" Well,"},{"speaker":"Pam","startTime":1083.15,"endTime":1085.43,"body":"it's because I have to think"},{"speaker":"Pam","startTime":1085.43,"endTime":1087.95,"body":"about what Kim said, and it"},{"speaker":"Pam","startTime":1085.43,"endTime":1087.95,"body":"helps me think about it. Okay,"},{"speaker":"Pam","startTime":1087.95,"endTime":1089.12,"body":"so you said that was 3."},{"speaker":"Kim","startTime":1089.42,"endTime":1089.6,"body":"Yep."},{"speaker":"Pam","startTime":1090.08,"endTime":1093.56,"body":"Now, I'm going to ask you"},{"speaker":"Pam","startTime":1090.08,"endTime":1093.56,"body":"two-thirds divided by one-third."},{"speaker":"Pam","startTime":1093.89,"endTime":1095.0,"body":"Two-thirds divided by one-third."},{"speaker":"Kim","startTime":1095.45,"endTime":1096.14,"body":"Two."},{"speaker":"Pam","startTime":1097.31,"endTime":1097.91,"body":"And how do you know?"},{"speaker":"Kim","startTime":1098.27,"endTime":1100.43,"body":"I feel like we're going"},{"speaker":"Kim","startTime":1098.27,"endTime":1100.43,"body":"somewhere fun. I'm excited."},{"speaker":"Pam","startTime":1101.54,"endTime":1101.63,"body":"Okay."},{"speaker":"Kim","startTime":1102.59,"endTime":1104.87,"body":"Two 1/3s is 2/3."},{"speaker":"Pam","startTime":1105.56,"endTime":1108.77,"body":"So, you're thinking"},{"speaker":"Pam","startTime":1105.56,"endTime":1108.77,"body":"quotitively. You're saying how"},{"speaker":"Pam","startTime":1108.77,"endTime":1111.17,"body":"many one-thirds are in"},{"speaker":"Pam","startTime":1108.77,"endTime":1111.17,"body":"two-thirds? And like there's two"},{"speaker":"Pam","startTime":1111.17,"endTime":1114.35,"body":"of those. There's two. And we"},{"speaker":"Pam","startTime":1111.17,"endTime":1114.35,"body":"mentioned earlier that we could"},{"speaker":"Pam","startTime":1114.35,"endTime":1117.47,"body":"say \"two-thirds\" as two 1/3s."},{"speaker":"Pam","startTime":1117.92,"endTime":1118.1,"body":"Yeah."},{"speaker":"Pam","startTime":1118.1,"endTime":1122.12,"body":"So, when I say that problem like"},{"speaker":"Pam","startTime":1118.1,"endTime":1122.12,"body":"that two 1/3s divided by 1/3."},{"speaker":"Pam","startTime":1122.15,"endTime":1124.85,"body":"You could be like, \"Well, how"},{"speaker":"Pam","startTime":1122.15,"endTime":1124.85,"body":"many 1/3 are in two 1/3? Two.\""},{"speaker":"Pam","startTime":1125.15,"endTime":1128.45,"body":"Alright, so 2/3 divided by 1/3"},{"speaker":"Pam","startTime":1125.15,"endTime":1128.45,"body":"is 2. Cool. Next question. How"},{"speaker":"Pam","startTime":1128.45,"endTime":1132.38,"body":"about two-thirds divided by"},{"speaker":"Pam","startTime":1128.45,"endTime":1132.38,"body":"one-sixth? Two-thirds divided by"},{"speaker":"Pam","startTime":1132.38,"endTime":1133.1,"body":"one-sixth?"},{"speaker":"Kim","startTime":1134.33,"endTime":1136.22,"body":"That's going to be 4."},{"speaker":"Pam","startTime":1137.51,"endTime":1138.14,"body":"Because?"},{"speaker":"Kim","startTime":1139.01,"endTime":1141.89,"body":"Because just like we were"},{"speaker":"Kim","startTime":1139.01,"endTime":1141.89,"body":"talking about with the fifth and"},{"speaker":"Kim","startTime":1141.89,"endTime":1146.54,"body":"the tenths, when you asked me"},{"speaker":"Kim","startTime":1141.89,"endTime":1146.54,"body":"about how many 1/3 are in 2/3,"},{"speaker":"Kim","startTime":1146.6,"endTime":1150.86,"body":"then that was 2. But now, the"},{"speaker":"Kim","startTime":1146.6,"endTime":1150.86,"body":"size of the piece is half as"},{"speaker":"Kim","startTime":1150.86,"endTime":1153.92,"body":"big, so there's going to be"},{"speaker":"Kim","startTime":1150.86,"endTime":1153.92,"body":"twice as many pieces."},{"speaker":"Pam","startTime":1154.97,"endTime":1156.98,"body":"Cool. I love that"},{"speaker":"Pam","startTime":1154.97,"endTime":1156.98,"body":"relationship."},{"speaker":"Kim","startTime":1157.49,"endTime":1157.7,"body":"Yeah."},{"speaker":"Pam","startTime":1157.7,"endTime":1160.37,"body":"That's a little bit more"},{"speaker":"Pam","startTime":1157.7,"endTime":1160.37,"body":"sophisticated than maybe I might"},{"speaker":"Pam","startTime":1160.37,"endTime":1166.1,"body":"ask a kid to describe first. I"},{"speaker":"Pam","startTime":1160.37,"endTime":1166.1,"body":"might have a kid say \"Well, I"},{"speaker":"Pam","startTime":1166.1,"endTime":1169.19,"body":"know there's two-sixth in every"},{"speaker":"Pam","startTime":1166.1,"endTime":1169.19,"body":"one-third.\""},{"speaker":"Kim","startTime":1169.85,"endTime":1170.21,"body":"Yeah."},{"speaker":"Pam","startTime":1170.24,"endTime":1174.35,"body":"So, if there's two 1/3s, I"},{"speaker":"Pam","startTime":1170.24,"endTime":1174.35,"body":"can sort of picture those. That"},{"speaker":"Pam","startTime":1174.35,"endTime":1177.77,"body":"1/3 and that 1/3. I know there's"},{"speaker":"Pam","startTime":1174.35,"endTime":1177.77,"body":"two of them in two-thirds. In"},{"speaker":"Pam","startTime":1177.8,"endTime":1182.6,"body":"each of those one-third, there's"},{"speaker":"Pam","startTime":1177.8,"endTime":1182.6,"body":"two-sixths. And so, yeah. Kind"},{"speaker":"Pam","startTime":1182.6,"endTime":1184.64,"body":"of like your twice as many. But"},{"speaker":"Pam","startTime":1182.6,"endTime":1184.64,"body":"I might be looking a little more"},{"speaker":"Pam","startTime":1184.64,"endTime":1188.24,"body":"additively at first. There was a"},{"speaker":"Pam","startTime":1184.64,"endTime":1188.24,"body":"reason I mentioned that is I"},{"speaker":"Pam","startTime":1188.24,"endTime":1190.61,"body":"want to make sure people are"},{"speaker":"Pam","startTime":1188.24,"endTime":1190.61,"body":"understanding. Yes, I want kids"},{"speaker":"Pam","startTime":1190.61,"endTime":1193.28,"body":"thinking multiplicatively about"},{"speaker":"Pam","startTime":1190.61,"endTime":1193.28,"body":"these. And that's what Kim just"},{"speaker":"Pam","startTime":1193.28,"endTime":1195.41,"body":"did. \"Well, if the pieces are"},{"speaker":"Pam","startTime":1193.28,"endTime":1195.41,"body":"half as big, then there's going"},{"speaker":"Pam","startTime":1195.41,"endTime":1198.86,"body":"to be twice as many.\" But I also"},{"speaker":"Pam","startTime":1195.41,"endTime":1198.86,"body":"can allow kids to enter as"},{"speaker":"Pam","startTime":1198.86,"endTime":1201.08,"body":"they're sort of thinking about"},{"speaker":"Pam","startTime":1198.86,"endTime":1201.08,"body":"it as additively. I want to help"},{"speaker":"Pam","startTime":1201.08,"endTime":1204.26,"body":"kids enter thinking about"},{"speaker":"Pam","startTime":1201.08,"endTime":1204.26,"body":"additively, and then also help"},{"speaker":"Pam","startTime":1204.29,"endTime":1207.38,"body":"them transition to thinking"},{"speaker":"Pam","startTime":1204.29,"endTime":1207.38,"body":"about it more multiplicatively."},{"speaker":"Pam","startTime":1207.89,"endTime":1211.34,"body":"Alright, what is two-thirds"},{"speaker":"Pam","startTime":1207.89,"endTime":1211.34,"body":"divided by one-twelfth?"},{"speaker":"Kim","startTime":1214.64,"endTime":1215.18,"body":"Eight."},{"speaker":"Pam","startTime":1216.74,"endTime":1217.49,"body":"And how do you know?"},{"speaker":"Kim","startTime":1218.78,"endTime":1225.05,"body":"When it was 2/3 divided by"},{"speaker":"Kim","startTime":1218.78,"endTime":1225.05,"body":"1/6, that was 4. So, now again"},{"speaker":"Kim","startTime":1225.62,"endTime":1229.31,"body":"the pieces are half as big, so"},{"speaker":"Kim","startTime":1225.62,"endTime":1229.31,"body":"there's going to be twice as"},{"speaker":"Kim","startTime":1229.31,"endTime":1233.63,"body":"many, which is 8. But also I"},{"speaker":"Kim","startTime":1229.31,"endTime":1233.63,"body":"could."},{"speaker":"Pam","startTime":1233.93,"endTime":1236.24,"body":"Oh, go ahead. Well, let me"},{"speaker":"Pam","startTime":1233.93,"endTime":1236.24,"body":"just repeat that a slightly"},{"speaker":"Pam","startTime":1236.24,"endTime":1236.63,"body":"different way."},{"speaker":"Kim","startTime":1236.81,"endTime":1237.05,"body":"Yeah."},{"speaker":"Pam","startTime":1237.05,"endTime":1241.4,"body":"So, if I'm asking how many"},{"speaker":"Pam","startTime":1237.05,"endTime":1241.4,"body":"1/6 are in 2/3, and you're"},{"speaker":"Pam","startTime":1241.4,"endTime":1245.51,"body":"saying there's 4. And then, I"},{"speaker":"Pam","startTime":1241.4,"endTime":1245.51,"body":"ask how many there is of"},{"speaker":"Pam","startTime":1245.51,"endTime":1249.53,"body":"something half as big in"},{"speaker":"Pam","startTime":1245.51,"endTime":1249.53,"body":"two-thirds. How many"},{"speaker":"Pam","startTime":1249.53,"endTime":1251.87,"body":"one-twelfths are in two-thirds,"},{"speaker":"Pam","startTime":1249.53,"endTime":1251.87,"body":"then you're like, \"There's got"},{"speaker":"Pam","startTime":1251.87,"endTime":1254.75,"body":"to be twice as many. There's got"},{"speaker":"Pam","startTime":1251.87,"endTime":1254.75,"body":"to be 8.\" Okay. Okay, what else"},{"speaker":"Pam","startTime":1254.75,"endTime":1255.98,"body":"we're you going to do?"},{"speaker":"Kim","startTime":1256.01,"endTime":1258.71,"body":"Well, you had asked me"},{"speaker":"Kim","startTime":1256.01,"endTime":1258.71,"body":"earlier, two-thirds divided by"},{"speaker":"Kim","startTime":1258.71,"endTime":1259.4,"body":"one-third."},{"speaker":"Pam","startTime":1259.4,"endTime":1259.43,"body":"Mmhmm."},{"speaker":"Kim","startTime":1261.8,"endTime":1265.61,"body":"So, I'm thinking that I"},{"speaker":"Kim","startTime":1261.8,"endTime":1265.61,"body":"know the relationship between"},{"speaker":"Kim","startTime":1265.88,"endTime":1270.92,"body":"one-twelfth and one-third, and"},{"speaker":"Kim","startTime":1265.88,"endTime":1270.92,"body":"it's going to be... It's a"},{"speaker":"Kim","startTime":1270.92,"endTime":1275.03,"body":"fourth as big. So, we just did"},{"speaker":"Kim","startTime":1270.92,"endTime":1275.03,"body":"the half, half, and double"},{"speaker":"Kim","startTime":1275.03,"endTime":1275.81,"body":"relationship."},{"speaker":"Pam","startTime":1275.84,"endTime":1275.87,"body":"Mmhmm."},{"speaker":"Kim","startTime":1276.53,"endTime":1279.92,"body":"But there's also a"},{"speaker":"Kim","startTime":1276.53,"endTime":1279.92,"body":"quadrupling, quartering"},{"speaker":"Kim","startTime":1279.92,"endTime":1284.12,"body":"relationship to the previous"},{"speaker":"Kim","startTime":1279.92,"endTime":1284.12,"body":"problem, two-thirds divided by"},{"speaker":"Kim","startTime":1284.12,"endTime":1284.72,"body":"one-third."},{"speaker":"Pam","startTime":1286.28,"endTime":1288.41,"body":"So, if a twelfth. Oh, keep"},{"speaker":"Pam","startTime":1286.28,"endTime":1288.41,"body":"going,"},{"speaker":"Kim","startTime":1288.68,"endTime":1294.62,"body":"If a twelfth is one-fourth"},{"speaker":"Kim","startTime":1288.68,"endTime":1294.62,"body":"as big as a third, then I'm"},{"speaker":"Kim","startTime":1294.62,"endTime":1296.84,"body":"going to need four times as many"},{"speaker":"Kim","startTime":1294.62,"endTime":1296.84,"body":"pieces."},{"speaker":"Pam","startTime":1297.86,"endTime":1301.19,"body":"So, instead of getting two"},{"speaker":"Pam","startTime":1297.86,"endTime":1301.19,"body":"1/3s in two-thirds, you're going"},{"speaker":"Pam","startTime":1301.19,"endTime":1305.78,"body":"to have eight 1/12s in"},{"speaker":"Pam","startTime":1301.19,"endTime":1305.78,"body":"two-thirds. Nice. And I didn't"},{"speaker":"Pam","startTime":1305.78,"endTime":1309.17,"body":"talk about the modeling here,"},{"speaker":"Pam","startTime":1305.78,"endTime":1309.17,"body":"but I would also be making sure"},{"speaker":"Pam","startTime":1309.17,"endTime":1312.98,"body":"that I have a whole candy bar."},{"speaker":"Pam","startTime":1309.17,"endTime":1312.98,"body":"And when we talked about thirds,"},{"speaker":"Pam","startTime":1313.4,"endTime":1316.04,"body":"I would have, you know like,"},{"speaker":"Pam","startTime":1313.4,"endTime":1316.04,"body":"sketched out the two-thirds of"},{"speaker":"Pam","startTime":1316.04,"endTime":1320.03,"body":"the candy bar. So, I've got the"},{"speaker":"Pam","startTime":1316.04,"endTime":1320.03,"body":"whole candy bar. I've sort of"},{"speaker":"Pam","startTime":1320.03,"endTime":1322.76,"body":"circled the two-thirds because"},{"speaker":"Pam","startTime":1320.03,"endTime":1322.76,"body":"that's the whole that we're"},{"speaker":"Pam","startTime":1322.76,"endTime":1325.04,"body":"dealing with, that's the unit"},{"speaker":"Pam","startTime":1322.76,"endTime":1325.04,"body":"we're dealing with every time."},{"speaker":"Pam","startTime":1325.34,"endTime":1327.8,"body":"And then, the first question I"},{"speaker":"Pam","startTime":1325.34,"endTime":1327.8,"body":"asked: How many one-thirds were"},{"speaker":"Pam","startTime":1327.8,"endTime":1329.87,"body":"in there? And you were like 2?"},{"speaker":"Pam","startTime":1327.8,"endTime":1329.87,"body":"And then, I asked how many"},{"speaker":"Pam","startTime":1329.9,"endTime":1332.57,"body":"one-sixth were in there. We"},{"speaker":"Pam","startTime":1329.9,"endTime":1332.57,"body":"would have cut each of the"},{"speaker":"Pam","startTime":1332.57,"endTime":1334.67,"body":"thirds in half to show those"},{"speaker":"Pam","startTime":1332.57,"endTime":1334.67,"body":"one-sixth. And you're like,"},{"speaker":"Pam","startTime":1334.82,"endTime":1337.1,"body":"\"There's the four.\" And then, I"},{"speaker":"Pam","startTime":1334.82,"endTime":1337.1,"body":"would have said, \"Like where are"},{"speaker":"Pam","startTime":1337.1,"endTime":1339.35,"body":"twelfths? Like, how are you"},{"speaker":"Pam","startTime":1337.1,"endTime":1339.35,"body":"thinking about twelfths? How"},{"speaker":"Pam","startTime":1339.35,"endTime":1342.2,"body":"would you even cut a candy bar"},{"speaker":"Pam","startTime":1339.35,"endTime":1342.2,"body":"into twelfths?\" And we would"},{"speaker":"Pam","startTime":1342.2,"endTime":1344.63,"body":"have talked about how twelfths"},{"speaker":"Pam","startTime":1342.2,"endTime":1344.63,"body":"were half as big as the sixths"},{"speaker":"Pam","startTime":1344.63,"endTime":1351.5,"body":"like you said, but they're also"},{"speaker":"Pam","startTime":1344.63,"endTime":1351.5,"body":"a fourth of the thirds. And"},{"speaker":"Pam","startTime":1351.5,"endTime":1354.38,"body":"there's that quarter, quadruple"},{"speaker":"Pam","startTime":1351.5,"endTime":1354.38,"body":"relationship. Nice."},{"speaker":"Kim","startTime":1354.38,"endTime":1355.25,"body":"I have a question."},{"speaker":"Pam","startTime":1355.91,"endTime":1355.94,"body":"(unclear)"},{"speaker":"Kim","startTime":1356.0,"endTime":1359.72,"body":"I don't want to derail this"},{"speaker":"Kim","startTime":1356.0,"endTime":1359.72,"body":"because I'm afraid we'll go a"},{"speaker":"Kim","startTime":1359.72,"endTime":1362.36,"body":"little too long. But I wonder"},{"speaker":"Kim","startTime":1359.72,"endTime":1362.36,"body":"what you think about this."},{"speaker":"Pam","startTime":1362.54,"endTime":1362.69,"body":"Okay."},{"speaker":"Kim","startTime":1362.69,"endTime":1366.92,"body":"Sometimes, I think that"},{"speaker":"Kim","startTime":1362.69,"endTime":1366.92,"body":"when we have numbers like"},{"speaker":"Kim","startTime":1366.92,"endTime":1370.67,"body":"two-thirds and one-twelfth,"},{"speaker":"Kim","startTime":1366.92,"endTime":1370.67,"body":"sometimes that can be maybe a"},{"speaker":"Kim","startTime":1370.67,"endTime":1375.53,"body":"little bit overwhelming or a"},{"speaker":"Kim","startTime":1370.67,"endTime":1375.53,"body":"little bit like, \"Oh my gosh. I"},{"speaker":"Kim","startTime":1375.53,"endTime":1379.19,"body":"don't really know\" kind of"},{"speaker":"Kim","startTime":1375.53,"endTime":1379.19,"body":"situation for kids until they"},{"speaker":"Kim","startTime":1379.19,"endTime":1381.56,"body":"have, you know, a lot more"},{"speaker":"Kim","startTime":1379.19,"endTime":1381.56,"body":"experience or at least some more"},{"speaker":"Kim","startTime":1381.56,"endTime":1385.52,"body":"experience. But I wonder what"},{"speaker":"Kim","startTime":1381.56,"endTime":1385.52,"body":"you think about going back to"},{"speaker":"Kim","startTime":1385.52,"endTime":1389.51,"body":"the unit fraction of instead of"},{"speaker":"Kim","startTime":1385.52,"endTime":1389.51,"body":"two-thirds saying \"Okay, do you"},{"speaker":"Kim","startTime":1389.51,"endTime":1391.49,"body":"know how many 1/12 are in 1/3?\""},{"speaker":"Kim","startTime":1393.17,"endTime":1396.68,"body":"And then, once you know that,"},{"speaker":"Kim","startTime":1393.17,"endTime":1396.68,"body":"getting back to the unit"},{"speaker":"Kim","startTime":1396.68,"endTime":1399.44,"body":"fraction stuff, and then going"},{"speaker":"Kim","startTime":1396.68,"endTime":1399.44,"body":"\"Okay, but now we don't need"},{"speaker":"Kim","startTime":1399.47,"endTime":1401.93,"body":"one-third divided by"},{"speaker":"Kim","startTime":1399.47,"endTime":1401.93,"body":"one-twelfth. We need 2/3 divided"},{"speaker":"Kim","startTime":1401.93,"endTime":1404.51,"body":"by 12. Do you have any Problem"},{"speaker":"Kim","startTime":1401.93,"endTime":1404.51,"body":"Strings that..."},{"speaker":"Pam","startTime":1406.31,"endTime":1408.59,"body":"Let's do one next week!"},{"speaker":"Pam","startTime":1406.31,"endTime":1408.59,"body":"(unclear)."},{"speaker":"Kim","startTime":1408.77,"endTime":1409.94,"body":"Yeah! Okay, okay, okay."},{"speaker":"Pam","startTime":1409.94,"endTime":1412.07,"body":"(unclear) get that"},{"speaker":"Pam","startTime":1409.94,"endTime":1412.07,"body":"relationship. Maybe. Okay. So,"},{"speaker":"Pam","startTime":1412.1,"endTime":1414.74,"body":"we'll see what happens next"},{"speaker":"Pam","startTime":1412.1,"endTime":1414.74,"body":"week. But absolutely. We would"},{"speaker":"Pam","startTime":1414.74,"endTime":1418.67,"body":"absolutely want to develop the"},{"speaker":"Pam","startTime":1414.74,"endTime":1418.67,"body":"relationship that if we can"},{"speaker":"Pam","startTime":1418.67,"endTime":1422.12,"body":"think about how many"},{"speaker":"Pam","startTime":1418.67,"endTime":1422.12,"body":"one-twelfths are in one-third."},{"speaker":"Kim","startTime":1422.27,"endTime":1422.63,"body":"Yeah."},{"speaker":"Pam","startTime":1422.63,"endTime":1425.21,"body":"How can that help us think"},{"speaker":"Pam","startTime":1422.63,"endTime":1425.21,"body":"about how many one-twelfths are"},{"speaker":"Pam","startTime":1425.21,"endTime":1428.81,"body":"in two-thirds? And let's like"},{"speaker":"Pam","startTime":1425.21,"endTime":1428.81,"body":"actually answer that question."},{"speaker":"Pam","startTime":1428.81,"endTime":1431.06,"body":"So, how many one-twelfths are in"},{"speaker":"Pam","startTime":1428.81,"endTime":1431.06,"body":"one-third?"},{"speaker":"Kim","startTime":1433.61,"endTime":1434.33,"body":"Four."},{"speaker":"Pam","startTime":1434.96,"endTime":1435.65,"body":"How do you know?"},{"speaker":"Kim","startTime":1436.61,"endTime":1439.01,"body":"I'm trying to think of how"},{"speaker":"Kim","startTime":1436.61,"endTime":1439.01,"body":"I know. Because if you have a"},{"speaker":"Kim","startTime":1439.01,"endTime":1447.29,"body":"third, you would have to cut it."},{"speaker":"Kim","startTime":1439.01,"endTime":1447.29,"body":"Half would be a sixth. Then a"},{"speaker":"Kim","startTime":1447.29,"endTime":1448.64,"body":"fourth would be a twelfth."},{"speaker":"Pam","startTime":1449.06,"endTime":1451.94,"body":"Yeah. And as you said that,"},{"speaker":"Pam","startTime":1449.06,"endTime":1451.94,"body":"I drew a candy bar, and I cut it"},{"speaker":"Pam","startTime":1451.94,"endTime":1455.42,"body":"into 3 pieces. Because you said,"},{"speaker":"Pam","startTime":1451.94,"endTime":1455.42,"body":"\"Well, if you have a third...\""},{"speaker":"Pam","startTime":1455.42,"endTime":1457.73,"body":"So, I drew a candy bar and cut"},{"speaker":"Pam","startTime":1455.42,"endTime":1457.73,"body":"it into 3 pieces. You said,"},{"speaker":"Pam","startTime":1457.73,"endTime":1460.94,"body":"\"Well, if I cut that third in"},{"speaker":"Pam","startTime":1457.73,"endTime":1460.94,"body":"half, I'd have sixths.\" Right?"},{"speaker":"Kim","startTime":1460.94,"endTime":1461.81,"body":"Yeah, yep."},{"speaker":"Pam","startTime":1461.84,"endTime":1464.15,"body":"And you're like, \"Okay, so"},{"speaker":"Pam","startTime":1461.84,"endTime":1464.15,"body":"there's the sixth.\" And then you"},{"speaker":"Pam","startTime":1464.15,"endTime":1467.15,"body":"said, \"But then, I'd have to cut"},{"speaker":"Pam","startTime":1464.15,"endTime":1467.15,"body":"those in half to get twelfths.\""},{"speaker":"Pam","startTime":1467.48,"endTime":1470.84,"body":"And I've only really cut that"},{"speaker":"Pam","startTime":1467.48,"endTime":1470.84,"body":"one-third. I've just that one"},{"speaker":"Pam","startTime":1470.84,"endTime":1474.47,"body":"1/3, I cut it into two-sixths."},{"speaker":"Pam","startTime":1470.84,"endTime":1474.47,"body":"And I cut each of those sixths"},{"speaker":"Pam","startTime":1474.5,"endTime":1479.78,"body":"into two-twelfths. So, in that"},{"speaker":"Pam","startTime":1474.5,"endTime":1479.78,"body":"third, I now see four-twelfths."},{"speaker":"Pam","startTime":1480.89,"endTime":1483.83,"body":"So, that one-third has"},{"speaker":"Pam","startTime":1480.89,"endTime":1483.83,"body":"four-twelfths in it."},{"speaker":"Pam","startTime":1484.61,"endTime":1484.88,"body":"Right?"},{"speaker":"Kim","startTime":1484.88,"endTime":1484.91,"body":"Mmhmm."},{"speaker":"Pam","startTime":1485.39,"endTime":1486.02,"body":"Yeah."},{"speaker":"Kim","startTime":1486.08,"endTime":1487.85,"body":"But we don't need"},{"speaker":"Kim","startTime":1486.08,"endTime":1487.85,"body":"one-third. We need two-thirds."},{"speaker":"Kim","startTime":1487.85,"endTime":1488.78,"body":"(unclear)."},{"speaker":"Pam","startTime":1489.44,"endTime":1491.42,"body":"Because the problem is"},{"speaker":"Pam","startTime":1489.44,"endTime":1491.42,"body":"two-thirds divided by"},{"speaker":"Pam","startTime":1491.45,"endTime":1495.83,"body":"one-twelfth. Right, so we don't"},{"speaker":"Pam","startTime":1491.45,"endTime":1495.83,"body":"just have. So, 1/3 divided by"},{"speaker":"Pam","startTime":1495.83,"endTime":1501.08,"body":"one-twelfth is 4, so 2/3, twice"},{"speaker":"Pam","startTime":1495.83,"endTime":1501.08,"body":"as much, divided by 1/3 is twice"},{"speaker":"Pam","startTime":1501.08,"endTime":1507.17,"body":"as much, 8. Nice. Well, I almost"},{"speaker":"Pam","startTime":1501.08,"endTime":1507.17,"body":"wonder if your problem was a"},{"speaker":"Pam","startTime":1507.17,"endTime":1509.75,"body":"better... Well, is that your"},{"speaker":"Pam","startTime":1507.17,"endTime":1509.75,"body":"problem or is that just a"},{"speaker":"Pam","startTime":1509.75,"endTime":1511.1,"body":"different way of thinking about?"},{"speaker":"Pam","startTime":1512.72,"endTime":1513.65,"body":"Yeah. Anyway."},{"speaker":"Kim","startTime":1513.65,"endTime":1514.61,"body":"A different way of. Yeah."},{"speaker":"Pam","startTime":1514.85,"endTime":1516.53,"body":"A different way of thinking"},{"speaker":"Pam","startTime":1514.85,"endTime":1516.53,"body":"about that last problem. I'm"},{"speaker":"Pam","startTime":1516.53,"endTime":1518.9,"body":"going to give you one last"},{"speaker":"Pam","startTime":1516.53,"endTime":1518.9,"body":"problem for this string."},{"speaker":"Kim","startTime":1518.99,"endTime":1519.5,"body":"Okay."},{"speaker":"Pam","startTime":1519.65,"endTime":1523.82,"body":"Okay. So, I'm just going to"},{"speaker":"Pam","startTime":1519.65,"endTime":1523.82,"body":"note the recent problem we did"},{"speaker":"Pam","startTime":1523.82,"endTime":1527.12,"body":"was two-thirds divided by"},{"speaker":"Pam","startTime":1523.82,"endTime":1527.12,"body":"one-twelfth, and you got 8. Now,"},{"speaker":"Pam","startTime":1527.12,"endTime":1531.2,"body":"I'm going to ask you 1 and 2/3"},{"speaker":"Pam","startTime":1527.12,"endTime":1531.2,"body":"divided by 1/12. In other words,"},{"speaker":"Pam","startTime":1531.2,"endTime":1533.75,"body":"how many 1/12 are in 1 and 2/3?"},{"speaker":"Kim","startTime":1534.68,"endTime":1539.33,"body":"So, we just did two-thirds"},{"speaker":"Kim","startTime":1534.68,"endTime":1539.33,"body":"divided by a twelfth a couple of"},{"speaker":"Kim","startTime":1539.33,"endTime":1543.35,"body":"different ways, and talked about"},{"speaker":"Kim","startTime":1539.33,"endTime":1543.35,"body":"how that was 8. And so then, I'm"},{"speaker":"Kim","startTime":1543.35,"endTime":1548.72,"body":"going to also think about the"},{"speaker":"Kim","startTime":1543.35,"endTime":1548.72,"body":"extra 1, the leftover 1 divided"},{"speaker":"Kim","startTime":1548.72,"endTime":1551.0,"body":"by 1/12 is 12."},{"speaker":"Kim","startTime":1552.29,"endTime":1558.23,"body":"So, if two-thirds divided by"},{"speaker":"Kim","startTime":1552.29,"endTime":1558.23,"body":"1/12 is 8. And 1 divided by 1/12"},{"speaker":"Kim","startTime":1558.26,"endTime":1563.39,"body":"is 12. Then, 8 and 12 is 20."},{"speaker":"Kim","startTime":1558.26,"endTime":1563.39,"body":"Twenty 1/12s."},{"speaker":"Pam","startTime":1563.66,"endTime":1566.96,"body":"There are twenty 1/12s in 1"},{"speaker":"Pam","startTime":1563.66,"endTime":1566.96,"body":"and 2/3."},{"speaker":"Kim","startTime":1567.2,"endTime":1567.62,"body":"Yeah."},{"speaker":"Pam","startTime":1567.86,"endTime":1570.74,"body":"Super thinking. And there's"},{"speaker":"Pam","startTime":1567.86,"endTime":1570.74,"body":"a few different ways that we"},{"speaker":"Pam","startTime":1570.74,"endTime":1573.47,"body":"could think about that, but I"},{"speaker":"Pam","startTime":1570.74,"endTime":1573.47,"body":"think at this point, I think"},{"speaker":"Pam","startTime":1573.47,"endTime":1577.04,"body":"we've done some nice fraction"},{"speaker":"Pam","startTime":1573.47,"endTime":1577.04,"body":"reasoning, fraction division"},{"speaker":"Pam","startTime":1577.04,"endTime":1580.58,"body":"reasoning. Teachers, I wonder if"},{"speaker":"Pam","startTime":1577.04,"endTime":1580.58,"body":"any of you, or listeners I"},{"speaker":"Pam","startTime":1580.58,"endTime":1583.04,"body":"wonder if any of you, are"},{"speaker":"Pam","startTime":1580.58,"endTime":1583.04,"body":"thinking, \"Whoa, I mean..."},{"speaker":"Pam","startTime":1583.25,"endTime":1586.13,"body":"That's a lot of thinking. Like,"},{"speaker":"Pam","startTime":1583.25,"endTime":1586.13,"body":"I got kids that don't even know"},{"speaker":"Pam","startTime":1586.13,"endTime":1590.15,"body":"their multiplication facts, and"},{"speaker":"Pam","startTime":1586.13,"endTime":1590.15,"body":"you want us to be...\" I hear"},{"speaker":"Pam","startTime":1590.15,"endTime":1594.59,"body":"you. I hear you. I acknowledge"},{"speaker":"Pam","startTime":1590.15,"endTime":1594.59,"body":"that the thinking that we just"},{"speaker":"Pam","startTime":1594.59,"endTime":1601.52,"body":"did was not trivial. Like, we"},{"speaker":"Pam","startTime":1594.59,"endTime":1601.52,"body":"were thinking. But in a big way,"},{"speaker":"Pam","startTime":1601.55,"endTime":1605.75,"body":"we were almost thinking less"},{"speaker":"Pam","startTime":1601.55,"endTime":1605.75,"body":"about fraction division, and we"},{"speaker":"Pam","startTime":1605.75,"endTime":1608.27,"body":"were thinking about the"},{"speaker":"Pam","startTime":1605.75,"endTime":1608.27,"body":"definition of unit fractions."},{"speaker":"Pam","startTime":1608.81,"endTime":1613.31,"body":"Like, as we're asking ourselves,"},{"speaker":"Pam","startTime":1608.81,"endTime":1613.31,"body":"\"How many 1/6 are in 2/3?\""},{"speaker":"Pam","startTime":1613.34,"endTime":1616.25,"body":"Two-thirds divided by one-sixth?"},{"speaker":"Pam","startTime":1613.34,"endTime":1616.25,"body":"If we're thinking about it"},{"speaker":"Pam","startTime":1616.25,"endTime":1619.52,"body":"quotitively, how many 1/6 are in"},{"speaker":"Pam","startTime":1616.25,"endTime":1619.52,"body":"2/3, we're asking ourselves,"},{"speaker":"Pam","startTime":1619.55,"endTime":1623.06,"body":"\"What's the relationship between"},{"speaker":"Pam","startTime":1619.55,"endTime":1623.06,"body":"one-sixth and one-third?\" And so"},{"speaker":"Pam","startTime":1623.06,"endTime":1624.77,"body":"then, therefore, what's the"},{"speaker":"Pam","startTime":1623.06,"endTime":1624.77,"body":"relationship between one-sixth"},{"speaker":"Pam","startTime":1624.77,"endTime":1630.05,"body":"and two-thirds? Like, we're"},{"speaker":"Pam","startTime":1624.77,"endTime":1630.05,"body":"really helping students think"},{"speaker":"Pam","startTime":1630.05,"endTime":1634.01,"body":"about fractions, the definition"},{"speaker":"Pam","startTime":1630.05,"endTime":1634.01,"body":"of fractions. What does it mean?"},{"speaker":"Pam","startTime":1634.01,"endTime":1637.19,"body":"What is the relationship between"},{"speaker":"Pam","startTime":1634.01,"endTime":1637.19,"body":"one-twelfth and one-sixth? And"},{"speaker":"Pam","startTime":1637.19,"endTime":1640.55,"body":"one-twelfth and one-third? And"},{"speaker":"Pam","startTime":1637.19,"endTime":1640.55,"body":"one-twelfth and two-thirds? The"},{"speaker":"Pam","startTime":1640.58,"endTime":1644.96,"body":"quotitive meaning of division"},{"speaker":"Pam","startTime":1640.58,"endTime":1644.96,"body":"can be super helpful to help the"},{"speaker":"Pam","startTime":1644.96,"endTime":1649.7,"body":"kids actually reason about what"},{"speaker":"Pam","startTime":1644.96,"endTime":1649.7,"body":"fractions mean. And we need"},{"speaker":"Pam","startTime":1649.73,"endTime":1654.95,"body":"that. In other words, you might"},{"speaker":"Pam","startTime":1649.73,"endTime":1654.95,"body":"be like \"Pam, in my section for"},{"speaker":"Pam","startTime":1654.95,"endTime":1658.04,"body":"fraction division, I got a day."},{"speaker":"Pam","startTime":1654.95,"endTime":1658.04,"body":"I got a day to say, 'Ours is not"},{"speaker":"Pam","startTime":1658.04,"endTime":1659.93,"body":"to reason why, just innvert and"},{"speaker":"Pam","startTime":1658.04,"endTime":1659.93,"body":"multiply.' I don't have this"},{"speaker":"Pam","startTime":1659.93,"endTime":1662.72,"body":"time to help kids reason about"},{"speaker":"Pam","startTime":1659.93,"endTime":1662.72,"body":"this.\" Well, then we get what"},{"speaker":"Pam","startTime":1662.72,"endTime":1665.63,"body":"we've gotten. Which is kids not"},{"speaker":"Pam","startTime":1662.72,"endTime":1665.63,"body":"reasoning about fractions, kids"},{"speaker":"Pam","startTime":1665.63,"endTime":1667.91,"body":"just memorizing a bunch of"},{"speaker":"Pam","startTime":1665.63,"endTime":1667.91,"body":"rules, and then mixing and"},{"speaker":"Pam","startTime":1667.91,"endTime":1670.97,"body":"matching the rules, and getting"},{"speaker":"Pam","startTime":1667.91,"endTime":1670.97,"body":"it all screwed up. And we get"},{"speaker":"Pam","startTime":1670.97,"endTime":1674.75,"body":"the mess we've had. What we need"},{"speaker":"Pam","startTime":1670.97,"endTime":1674.75,"body":"is kids to actually understand"},{"speaker":"Pam","startTime":1674.75,"endTime":1677.51,"body":"the meaning of fractions. So,"},{"speaker":"Pam","startTime":1674.75,"endTime":1677.51,"body":"I'm actually suggesting we could"},{"speaker":"Pam","startTime":1677.51,"endTime":1680.96,"body":"ask some of these questions that"},{"speaker":"Pam","startTime":1677.51,"endTime":1680.96,"body":"we asked today, and in last"},{"speaker":"Pam","startTime":1680.96,"endTime":1684.29,"body":"week's, and what we'll ask next"},{"speaker":"Pam","startTime":1680.96,"endTime":1684.29,"body":"week. We could ask some of these"},{"speaker":"Pam","startTime":1684.29,"endTime":1688.64,"body":"questions in grade 3. Like, as"},{"speaker":"Pam","startTime":1684.29,"endTime":1688.64,"body":"kids are thinking about the"},{"speaker":"Pam","startTime":1688.64,"endTime":1692.09,"body":"meaning of one-third, I could"},{"speaker":"Pam","startTime":1688.64,"endTime":1692.09,"body":"ask the question, 1 divided by"},{"speaker":"Pam","startTime":1692.09,"endTime":1695.06,"body":"1/3. Now, I probably wouldn't"},{"speaker":"Pam","startTime":1692.09,"endTime":1695.06,"body":"write it that way. I would say"},{"speaker":"Pam","startTime":1695.06,"endTime":1699.68,"body":"things like, \"Hey, how many 1/3"},{"speaker":"Pam","startTime":1695.06,"endTime":1699.68,"body":"are in 1?\" And third graders"},{"speaker":"Pam","startTime":1699.68,"endTime":1704.75,"body":"should say, \"Duh, 3.\" Right? And"},{"speaker":"Pam","startTime":1699.68,"endTime":1704.75,"body":"then, maybe I'll write it as 1"},{"speaker":"Pam","startTime":1704.75,"endTime":1707.69,"body":"divided by 1/3, but I want to"},{"speaker":"Pam","startTime":1704.75,"endTime":1707.69,"body":"like have them think, so that I"},{"speaker":"Pam","startTime":1707.69,"endTime":1710.03,"body":"might say, \"Well, how many"},{"speaker":"Pam","startTime":1707.69,"endTime":1710.03,"body":"one-thirds are in two-thirds?\""},{"speaker":"Pam","startTime":1710.42,"endTime":1713.21,"body":"Now, you might be like \"Pam,"},{"speaker":"Pam","startTime":1710.42,"endTime":1713.21,"body":"that's a fifth grade standard!"},{"speaker":"Pam","startTime":1713.21,"endTime":1718.16,"body":"That's fraction division!\" Or is"},{"speaker":"Pam","startTime":1713.21,"endTime":1718.16,"body":"it? Like, of course it is, but"},{"speaker":"Pam","startTime":1718.4,"endTime":1723.47,"body":"there are the meaning of"},{"speaker":"Pam","startTime":1718.4,"endTime":1723.47,"body":"fractions we can get at. We can"},{"speaker":"Pam","startTime":1723.47,"endTime":1726.59,"body":"help develop these relationships"},{"speaker":"Pam","startTime":1723.47,"endTime":1726.59,"body":"by asking questions like we did"},{"speaker":"Pam","startTime":1726.59,"endTime":1729.41,"body":"today in a quotitive kind of"},{"speaker":"Pam","startTime":1726.59,"endTime":1729.41,"body":"way...How many of the divisors"},{"speaker":"Pam","startTime":1729.41,"endTime":1732.59,"body":"are in the dividend?...to really"},{"speaker":"Pam","startTime":1729.41,"endTime":1732.59,"body":"help students reason about the"},{"speaker":"Pam","startTime":1732.59,"endTime":1736.31,"body":"relationships of fractions. And"},{"speaker":"Pam","startTime":1732.59,"endTime":1736.31,"body":"then, maybe we can develop"},{"speaker":"Pam","startTime":1736.31,"endTime":1740.51,"body":"everyone to think more and more"},{"speaker":"Pam","startTime":1736.31,"endTime":1740.51,"body":"like Kim, like mathematicians,"},{"speaker":"Pam","startTime":1740.51,"endTime":1745.16,"body":"like really reasoning about"},{"speaker":"Pam","startTime":1740.51,"endTime":1745.16,"body":"fractions. Anything else you"},{"speaker":"Pam","startTime":1745.16,"endTime":1745.85,"body":"want to say about that?"},{"speaker":"Kim","startTime":1746.63,"endTime":1747.44,"body":"I don't think so."},{"speaker":"Pam","startTime":1748.25,"endTime":1750.56,"body":"Like, I'm going to push a"},{"speaker":"Pam","startTime":1748.25,"endTime":1750.56,"body":"little bit on this, Kim. I'm"},{"speaker":"Pam","startTime":1750.56,"endTime":1753.77,"body":"wondering if you could tell me"},{"speaker":"Pam","startTime":1750.56,"endTime":1753.77,"body":"as we were doing this Problem"},{"speaker":"Pam","startTime":1753.77,"endTime":1758.21,"body":"String, how much division were"},{"speaker":"Pam","startTime":1753.77,"endTime":1758.21,"body":"you thinking about, and how much"},{"speaker":"Pam","startTime":1758.39,"endTime":1760.49,"body":"like relationships between"},{"speaker":"Pam","startTime":1758.39,"endTime":1760.49,"body":"fractions are you thinking"},{"speaker":"Pam","startTime":1760.49,"endTime":1761.3,"body":"about? Do you know what I mean?"},{"speaker":"Kim","startTime":1762.23,"endTime":1767.42,"body":"You know what, last week I"},{"speaker":"Kim","startTime":1762.23,"endTime":1767.42,"body":"think you mentioned that working"},{"speaker":"Kim","startTime":1767.42,"endTime":1772.1,"body":"with some of the strategies with"},{"speaker":"Kim","startTime":1767.42,"endTime":1772.1,"body":"whole numbers can be really"},{"speaker":"Kim","startTime":1772.1,"endTime":1775.16,"body":"useful. And I found myself"},{"speaker":"Kim","startTime":1772.1,"endTime":1775.16,"body":"thinking about that a little"},{"speaker":"Kim","startTime":1775.16,"endTime":1780.14,"body":"bit. That I know some"},{"speaker":"Kim","startTime":1775.16,"endTime":1780.14,"body":"relationships that now I'm just"},{"speaker":"Kim","startTime":1780.14,"endTime":1784.19,"body":"being asked to use those"},{"speaker":"Kim","startTime":1780.14,"endTime":1784.19,"body":"relationships with unit"},{"speaker":"Kim","startTime":1784.19,"endTime":1785.03,"body":"fractions."},{"speaker":"Pam","startTime":1785.24,"endTime":1785.9,"body":"Nice."},{"speaker":"Kim","startTime":1785.9,"endTime":1789.47,"body":"So, I'm drawing back on"},{"speaker":"Kim","startTime":1785.9,"endTime":1789.47,"body":"things that I know and have had"},{"speaker":"Kim","startTime":1789.65,"endTime":1794.42,"body":"experience with whole numbers."},{"speaker":"Kim","startTime":1789.65,"endTime":1794.42,"body":"So, if we have an opportunity to"},{"speaker":"Kim","startTime":1794.42,"endTime":1799.58,"body":"do that as well with students,"},{"speaker":"Kim","startTime":1794.42,"endTime":1799.58,"body":"then it doesn't feel quite so"},{"speaker":"Kim","startTime":1799.79,"endTime":1800.81,"body":"big a hurdle."},{"speaker":"Pam","startTime":1801.32,"endTime":1802.55,"body":"So overwhelming here."},{"speaker":"Kim","startTime":1802.58,"endTime":1803.51,"body":"Yes, yes."},{"speaker":"Pam","startTime":1803.54,"endTime":1807.02,"body":"Yeah, absolutely. That's an"},{"speaker":"Pam","startTime":1803.54,"endTime":1807.02,"body":"example I would say of kind of"},{"speaker":"Pam","startTime":1807.02,"endTime":1810.44,"body":"the finger thing that we've done"},{"speaker":"Pam","startTime":1807.02,"endTime":1810.44,"body":"before. Where we're students can"},{"speaker":"Pam","startTime":1810.44,"endTime":1813.77,"body":"be kind of all over the map, and"},{"speaker":"Pam","startTime":1810.44,"endTime":1813.77,"body":"if we do a Problem String like"},{"speaker":"Pam","startTime":1813.77,"endTime":1816.92,"body":"this, they should be able to"},{"speaker":"Pam","startTime":1813.77,"endTime":1816.92,"body":"access it kind of where they"},{"speaker":"Pam","startTime":1816.92,"endTime":1821.78,"body":"are. For example, I just talked"},{"speaker":"Pam","startTime":1816.92,"endTime":1821.78,"body":"about how a third grader could"},{"speaker":"Pam","startTime":1821.78,"endTime":1824.63,"body":"think about several of these"},{"speaker":"Pam","startTime":1821.78,"endTime":1824.63,"body":"problems just by using the"},{"speaker":"Pam","startTime":1824.63,"endTime":1828.11,"body":"definition of fractions, while"},{"speaker":"Pam","startTime":1824.63,"endTime":1828.11,"body":"Kim is simultaneously using"},{"speaker":"Pam","startTime":1828.11,"endTime":1832.04,"body":"these really nice multiplicative"},{"speaker":"Pam","startTime":1828.11,"endTime":1832.04,"body":"relationships in division that"},{"speaker":"Pam","startTime":1832.04,"endTime":1835.01,"body":"she's already developed with"},{"speaker":"Pam","startTime":1832.04,"endTime":1835.01,"body":"from whole number division."},{"speaker":"Kim","startTime":1835.43,"endTime":1835.79,"body":"Yeah."},{"speaker":"Pam","startTime":1836.18,"endTime":1839.51,"body":"That's a great example of"},{"speaker":"Pam","startTime":1836.18,"endTime":1839.51,"body":"if we mathematize with students,"},{"speaker":"Pam","startTime":1839.51,"endTime":1842.78,"body":"students can enter where they"},{"speaker":"Pam","startTime":1839.51,"endTime":1842.78,"body":"are, they all learn and grow,"},{"speaker":"Pam","startTime":1842.78,"endTime":1847.43,"body":"and we all think more and more"},{"speaker":"Pam","startTime":1842.78,"endTime":1847.43,"body":"like mathematicians. Nice."},{"speaker":"Pam","startTime":1847.46,"endTime":1851.48,"body":"Alright. So, ya'll, thanks for"},{"speaker":"Pam","startTime":1847.46,"endTime":1851.48,"body":"tuning in and teaching more and"},{"speaker":"Pam","startTime":1851.48,"endTime":1853.73,"body":"more real math. To find out more"},{"speaker":"Pam","startTime":1851.48,"endTime":1853.73,"body":"about the Math is"},{"speaker":"Pam","startTime":1853.76,"endTime":1857.33,"body":"Figure-Out-Able movement, visit"},{"speaker":"Pam","startTime":1853.76,"endTime":1857.33,"body":"mathisfigureoutable.com. Let's"},{"speaker":"Pam","startTime":1857.33,"endTime":1859.91,"body":"keep spreading the word that"},{"speaker":"Pam","startTime":1857.33,"endTime":1859.91,"body":"Math is Figure-Out-Able!"}]}