{"version":"1.0.0","segments":[{"speaker":"Pam","startTime":0.87,"endTime":4.17,"body":"Hey, fellow mathematicians!"},{"speaker":"Pam","startTime":0.87,"endTime":4.17,"body":"Welcome to the podcast where"},{"speaker":"Pam","startTime":4.17,"endTime":6.81,"body":"Math is Figure-Out-Able. I'm"},{"speaker":"Pam","startTime":4.17,"endTime":6.81,"body":"Pam."},{"speaker":"Kim","startTime":7.11,"endTime":7.83,"body":"And I'm Kim."},{"speaker":"Pam","startTime":8.07,"endTime":11.64,"body":"And you found a place where"},{"speaker":"Pam","startTime":8.07,"endTime":11.64,"body":"math is not about memorizing and"},{"speaker":"Pam","startTime":11.64,"endTime":14.61,"body":"mimicking, waiting to be told or"},{"speaker":"Pam","startTime":11.64,"endTime":14.61,"body":"shown what to do. But it's about"},{"speaker":"Pam","startTime":14.61,"endTime":18.12,"body":"making sense of problems,"},{"speaker":"Pam","startTime":14.61,"endTime":18.12,"body":"noticing patterns, and reasoning"},{"speaker":"Pam","startTime":18.12,"endTime":21.18,"body":"using mathematical"},{"speaker":"Pam","startTime":18.12,"endTime":21.18,"body":"relationships. We can mentor"},{"speaker":"Pam","startTime":21.18,"endTime":25.32,"body":"students to think and reason"},{"speaker":"Pam","startTime":21.18,"endTime":25.32,"body":"like mathematicians. Not only"},{"speaker":"Pam","startTime":25.32,"endTime":29.19,"body":"are algorithms really not"},{"speaker":"Pam","startTime":25.32,"endTime":29.19,"body":"helpful in teaching mathematics,"},{"speaker":"Pam","startTime":29.34,"endTime":32.85,"body":"but rotely repeating steps"},{"speaker":"Pam","startTime":29.34,"endTime":32.85,"body":"actually keep students from"},{"speaker":"Pam","startTime":32.85,"endTime":34.77,"body":"being the mathematicians they"},{"speaker":"Pam","startTime":32.85,"endTime":34.77,"body":"can be."},{"speaker":"Kim","startTime":35.79,"endTime":38.94,"body":"So, in the last two"},{"speaker":"Kim","startTime":35.79,"endTime":38.94,"body":"episodes, we've been answering"},{"speaker":"Kim","startTime":38.94,"endTime":42.45,"body":"your question from a follower of"},{"speaker":"Kim","startTime":38.94,"endTime":42.45,"body":"our Math is Figure-Out-Able,"},{"speaker":"Kim","startTime":42.72,"endTime":45.93,"body":"teacher Facebook group, and"},{"speaker":"Kim","startTime":42.72,"endTime":45.93,"body":"we've been diving into fraction"},{"speaker":"Kim","startTime":45.93,"endTime":49.5,"body":"division. So, today, we're going"},{"speaker":"Kim","startTime":45.93,"endTime":49.5,"body":"to hopefully finish and continue"},{"speaker":"Kim","startTime":49.5,"endTime":51.51,"body":"to answer Beth's question."},{"speaker":"Pam","startTime":51.63,"endTime":53.88,"body":"So, I'm going to be honest."},{"speaker":"Pam","startTime":51.63,"endTime":53.88,"body":"It might be our last episode"},{"speaker":"Pam","startTime":53.88,"endTime":56.16,"body":"that we do on fraction division"},{"speaker":"Pam","startTime":53.88,"endTime":56.16,"body":"for a minute because we have"},{"speaker":"Pam","startTime":56.16,"endTime":57.84,"body":"some other things we're going to"},{"speaker":"Pam","startTime":56.16,"endTime":57.84,"body":"do. I don't know that we're"},{"speaker":"Pam","startTime":57.84,"endTime":59.94,"body":"going to finish fraction"},{"speaker":"Pam","startTime":57.84,"endTime":59.94,"body":"division today, but I think"},{"speaker":"Pam","startTime":59.94,"endTime":62.37,"body":"we'll give you some really good"},{"speaker":"Pam","startTime":59.94,"endTime":62.37,"body":"things to think about and"},{"speaker":"Pam","startTime":62.37,"endTime":67.86,"body":"continue your journey, at least"},{"speaker":"Pam","startTime":62.37,"endTime":67.86,"body":"about thinking quotitively about"},{"speaker":"Pam","startTime":67.86,"endTime":68.94,"body":"fraction division."},{"speaker":"Kim","startTime":68.94,"endTime":69.12,"body":"Yeah."},{"speaker":"Pam","startTime":69.12,"endTime":74.22,"body":"So, what about fractions"},{"speaker":"Pam","startTime":69.12,"endTime":74.22,"body":"divided by fractions, especially"},{"speaker":"Pam","startTime":74.22,"endTime":77.37,"body":"fractions where their"},{"speaker":"Pam","startTime":74.22,"endTime":77.37,"body":"denominators are not factors of"},{"speaker":"Pam","startTime":77.37,"endTime":81.81,"body":"each other? I say that because"},{"speaker":"Pam","startTime":77.37,"endTime":81.81,"body":"in last week's episode, we did a"},{"speaker":"Pam","startTime":81.81,"endTime":84.66,"body":"bunch of fraction problems,"},{"speaker":"Pam","startTime":81.81,"endTime":84.66,"body":"fraction division problems,"},{"speaker":"Pam","startTime":85.11,"endTime":89.28,"body":"things like thirds divided by"},{"speaker":"Pam","startTime":85.11,"endTime":89.28,"body":"sixths, and thirds divided by"},{"speaker":"Pam","startTime":89.28,"endTime":94.08,"body":"twelfths. And so thirds and"},{"speaker":"Pam","startTime":89.28,"endTime":94.08,"body":"sixths. 3 and 6, and 3 and 12, 4"},{"speaker":"Pam","startTime":94.08,"endTime":95.79,"body":"and 12. Those are all related."},{"speaker":"Kim","startTime":96.03,"endTime":96.33,"body":"Right."},{"speaker":"Pam","startTime":96.33,"endTime":99.81,"body":"Their factors of each"},{"speaker":"Pam","startTime":96.33,"endTime":99.81,"body":"other. And so, there's maybe"},{"speaker":"Pam","startTime":99.81,"endTime":102.21,"body":"some different thinking that"},{"speaker":"Pam","startTime":99.81,"endTime":102.21,"body":"happens. And so today, we kind"},{"speaker":"Pam","startTime":102.21,"endTime":105.21,"body":"of wanted to dive in. What if"},{"speaker":"Pam","startTime":102.21,"endTime":105.21,"body":"the fractions are not quite as"},{"speaker":"Pam","startTime":105.21,"endTime":109.02,"body":"nice? And let's do it. Are you"},{"speaker":"Pam","startTime":105.21,"endTime":109.02,"body":"ready, Kim?"},{"speaker":"Kim","startTime":109.41,"endTime":110.07,"body":"Yep."},{"speaker":"Pam","startTime":110.52,"endTime":113.67,"body":"Alright. So, your first"},{"speaker":"Pam","startTime":110.52,"endTime":113.67,"body":"problem today... I'm getting my"},{"speaker":"Pam","startTime":113.67,"endTime":115.35,"body":"pen out? Do you have your pencil"},{"speaker":"Pam","startTime":113.67,"endTime":115.35,"body":"out?"},{"speaker":"Kim","startTime":115.53,"endTime":118.05,"body":"I do, of course. (unclear)"},{"speaker":"Kim","startTime":115.53,"endTime":118.05,"body":"eraser?"},{"speaker":"Pam","startTime":118.41,"endTime":120.09,"body":"Yeah, I have no eraser"},{"speaker":"Pam","startTime":118.41,"endTime":120.09,"body":"because I have a pen. I have a"},{"speaker":"Pam","startTime":120.09,"endTime":123.09,"body":"gel pen today. Let's see if it"},{"speaker":"Pam","startTime":120.09,"endTime":123.09,"body":"smears on my... Actually, I have"},{"speaker":"Pam","startTime":123.09,"endTime":125.28,"body":"a really nice gel pen. I don't"},{"speaker":"Pam","startTime":123.09,"endTime":125.28,"body":"think this one smears. Anyway,"},{"speaker":"Pam","startTime":125.31,"endTime":130.38,"body":"moving on. What is 3 divided by"},{"speaker":"Pam","startTime":125.31,"endTime":130.38,"body":"2? And I know we said fraction"},{"speaker":"Pam","startTime":130.38,"endTime":132.27,"body":"division, but bear with me."},{"speaker":"Pam","startTime":130.38,"endTime":132.27,"body":"What's 3 divided by 2?"},{"speaker":"Kim","startTime":133.53,"endTime":135.06,"body":"One and a 1/2."},{"speaker":"Pam","startTime":135.51,"endTime":138.84,"body":"Okay, and I was going to"},{"speaker":"Pam","startTime":135.51,"endTime":138.84,"body":"write 1.5 until you said 1 and a"},{"speaker":"Pam","startTime":138.84,"endTime":141.15,"body":"1/2, and then, I wrote 1 and the"},{"speaker":"Pam","startTime":138.84,"endTime":141.15,"body":"fraction 1/2. But it could be"},{"speaker":"Pam","startTime":141.15,"endTime":144.72,"body":"either, right? 1.5, 1 and a 1/2."},{"speaker":"Pam","startTime":141.15,"endTime":144.72,"body":"How do you know?"},{"speaker":"Kim","startTime":145.38,"endTime":151.89,"body":"Because I can think about"},{"speaker":"Kim","startTime":145.38,"endTime":151.89,"body":"it like I can fit 2 into 3, one"},{"speaker":"Kim","startTime":151.89,"endTime":157.14,"body":"time. Like, there's room for 2."},{"speaker":"Kim","startTime":151.89,"endTime":157.14,"body":"But then, I can only fit"},{"speaker":"Kim","startTime":158.52,"endTime":163.56,"body":"2 into 3, one-half again. So,"},{"speaker":"Kim","startTime":158.52,"endTime":163.56,"body":"there's already one and a half"},{"speaker":"Kim","startTime":163.56,"endTime":164.55,"body":"2s in 3. Yeah,"},{"speaker":"Pam","startTime":164.58,"endTime":166.47,"body":"One and a half 2s in 3. So,"},{"speaker":"Pam","startTime":164.58,"endTime":166.47,"body":"you're really thinking"},{"speaker":"Pam","startTime":166.47,"endTime":168.72,"body":"quotitively, which I kind of"},{"speaker":"Pam","startTime":166.47,"endTime":168.72,"body":"asked you to."},{"speaker":"Kim","startTime":168.9,"endTime":169.14,"body":"Yeah."},{"speaker":"Pam","startTime":169.14,"endTime":171.69,"body":"How many 2s are in 3? And"},{"speaker":"Pam","startTime":169.14,"endTime":171.69,"body":"you're like, \"Well, I can fit a"},{"speaker":"Pam","startTime":171.69,"endTime":172.86,"body":"whole 2 in 3.\""},{"speaker":"Kim","startTime":172.98,"endTime":173.46,"body":"Yep."},{"speaker":"Pam","startTime":173.61,"endTime":175.77,"body":"And I've only got 1"},{"speaker":"Pam","startTime":173.61,"endTime":175.77,"body":"leftover. And how many 2s are in"},{"speaker":"Pam","startTime":175.77,"endTime":179.13,"body":"that 1 leftover? Just a half."},{"speaker":"Pam","startTime":175.77,"endTime":179.13,"body":"Cool. Okay, so you can think"},{"speaker":"Pam","startTime":179.13,"endTime":182.55,"body":"about 3 divided by 2 is 1 and a"},{"speaker":"Pam","startTime":179.13,"endTime":182.55,"body":"1/2. Listeners, if you've never"},{"speaker":"Pam","startTime":182.55,"endTime":187.02,"body":"thought about something like"},{"speaker":"Pam","startTime":182.55,"endTime":187.02,"body":"that, 3 divided by 2,"},{"speaker":"Pam","startTime":187.05,"endTime":189.81,"body":"quotitively. If you've never"},{"speaker":"Pam","startTime":187.05,"endTime":189.81,"body":"thought about, \"How many 2s can"},{"speaker":"Pam","startTime":189.81,"endTime":192.54,"body":"I fit into 3.\" You might want to"},{"speaker":"Pam","startTime":189.81,"endTime":192.54,"body":"pause the podcast and think"},{"speaker":"Pam","startTime":192.54,"endTime":195.81,"body":"about that maybe a little bit"},{"speaker":"Pam","startTime":192.54,"endTime":195.81,"body":"more before we go on. Maybe."},{"speaker":"Pam","startTime":197.16,"endTime":199.92,"body":"Maybe think about how many."},{"speaker":"Pam","startTime":197.16,"endTime":199.92,"body":"Like, if I said, \"5 divided by"},{"speaker":"Pam","startTime":199.92,"endTime":203.52,"body":"2,\" you might think \"how many 2s"},{"speaker":"Pam","startTime":199.92,"endTime":203.52,"body":"are in 5?\" Kind of see if you"},{"speaker":"Pam","startTime":203.52,"endTime":205.47,"body":"can kind of make some"},{"speaker":"Pam","startTime":203.52,"endTime":205.47,"body":"generalizations about that."},{"speaker":"Pam","startTime":205.5,"endTime":211.38,"body":"Okay, so next problem. What"},{"speaker":"Pam","startTime":205.5,"endTime":211.38,"body":"about three-sixths divided by"},{"speaker":"Pam","startTime":211.41,"endTime":214.41,"body":"one-sixth. Three-sixth divided"},{"speaker":"Pam","startTime":211.41,"endTime":214.41,"body":"by one-sixth? What do you got?"},{"speaker":"Kim","startTime":215.85,"endTime":216.48,"body":"Three."},{"speaker":"Pam","startTime":216.93,"endTime":217.29,"body":"Because?"},{"speaker":"Kim","startTime":217.29,"endTime":223.14,"body":"Because there's one-sixth,"},{"speaker":"Kim","startTime":217.29,"endTime":223.14,"body":"three times in three-sixths."},{"speaker":"Pam","startTime":223.32,"endTime":226.77,"body":"Cool. And so, I might could"},{"speaker":"Pam","startTime":223.32,"endTime":226.77,"body":"draw. In fact, I should have"},{"speaker":"Pam","startTime":227.28,"endTime":230.7,"body":"maybe talked about 3 divided by"},{"speaker":"Pam","startTime":227.28,"endTime":230.7,"body":"2. I might have had 3 candy"},{"speaker":"Pam","startTime":230.7,"endTime":234.84,"body":"bars. And in this case, I'm"},{"speaker":"Pam","startTime":230.7,"endTime":234.84,"body":"going to say, \"If I wanted to"},{"speaker":"Pam","startTime":234.84,"endTime":238.5,"body":"share that with 2 people...\" No."},{"speaker":"Pam","startTime":234.84,"endTime":238.5,"body":"That's not how I want to say"},{"speaker":"Pam","startTime":238.5,"endTime":238.98,"body":"that. Nope,"},{"speaker":"Kim","startTime":239.01,"endTime":239.22,"body":"Yeah."},{"speaker":"Pam","startTime":239.22,"endTime":243.27,"body":"Nope, nope. I want to say"},{"speaker":"Pam","startTime":239.22,"endTime":243.27,"body":"if, \"I'm going to give...\" No."},{"speaker":"Pam","startTime":243.72,"endTime":247.44,"body":"How would I say that? I hadn't"},{"speaker":"Pam","startTime":243.72,"endTime":247.44,"body":"thought about a model for this"},{"speaker":"Pam","startTime":247.44,"endTime":250.29,"body":"one Kim ahead of time, and"},{"speaker":"Pam","startTime":247.44,"endTime":250.29,"body":"that's not... That wasn't smart"},{"speaker":"Pam","startTime":250.29,"endTime":250.83,"body":"on my part."},{"speaker":"Kim","startTime":253.59,"endTime":259.44,"body":"Well, I was just thinking"},{"speaker":"Kim","startTime":253.59,"endTime":259.44,"body":"about like of a 1 size candy bar"},{"speaker":"Kim","startTime":259.47,"endTime":263.85,"body":"is 3 pieces long. and another"},{"speaker":"Kim","startTime":259.47,"endTime":263.85,"body":"size candy bars 2 pieces long."},{"speaker":"Kim","startTime":263.85,"endTime":266.67,"body":"How many of the 2 piece candy"},{"speaker":"Kim","startTime":263.85,"endTime":266.67,"body":"bars would fit in the 3 piece"},{"speaker":"Kim","startTime":266.67,"endTime":271.56,"body":"candy bar? You know like, 3 bars"},{"speaker":"Kim","startTime":266.67,"endTime":271.56,"body":"long. If it's an extra large"},{"speaker":"Kim","startTime":271.56,"endTime":272.16,"body":"candy bar."},{"speaker":"Pam","startTime":273.63,"endTime":275.46,"body":"The pieces would have to be"},{"speaker":"Pam","startTime":273.63,"endTime":275.46,"body":"the same size, right?"},{"speaker":"Kim","startTime":275.46,"endTime":275.7,"body":"Yeah."},{"speaker":"Pam","startTime":276.03,"endTime":279.45,"body":"So, how many 2 piece candy"},{"speaker":"Pam","startTime":276.03,"endTime":279.45,"body":"bars can fit in a 3 piece candy"},{"speaker":"Pam","startTime":279.45,"endTime":279.69,"body":"bar?"},{"speaker":"Kim","startTime":279.72,"endTime":280.17,"body":"Yeah, (unclear)."},{"speaker":"Pam","startTime":280.41,"endTime":283.53,"body":"That's perfect. Perfect."},{"speaker":"Pam","startTime":280.41,"endTime":283.53,"body":"Nicely done. Cool. Alright, so"},{"speaker":"Pam","startTime":283.53,"endTime":287.64,"body":"we've got 3 divided by 2 is 1"},{"speaker":"Pam","startTime":283.53,"endTime":287.64,"body":"and a 1/2. 3/6 divided by 1/6 is"},{"speaker":"Pam","startTime":287.64,"endTime":291.75,"body":"3. What's three-sixths divided"},{"speaker":"Pam","startTime":287.64,"endTime":291.75,"body":"by two-sixths?"},{"speaker":"Kim","startTime":293.85,"endTime":297.63,"body":"Oh, you just asked me"},{"speaker":"Kim","startTime":293.85,"endTime":297.63,"body":"three-sixths divided by"},{"speaker":"Kim","startTime":297.63,"endTime":302.91,"body":"one-sixth, and that was three."},{"speaker":"Kim","startTime":297.63,"endTime":302.91,"body":"But now the pieces are twice as"},{"speaker":"Kim","startTime":302.91,"endTime":306.03,"body":"big, so there's going to be half"},{"speaker":"Kim","startTime":302.91,"endTime":306.03,"body":"as many of them. So, it's going"},{"speaker":"Kim","startTime":306.03,"endTime":306.93,"body":"to be 1 and a 1/2."},{"speaker":"Pam","startTime":307.71,"endTime":312.84,"body":"Because half of 3 is 1 and"},{"speaker":"Pam","startTime":307.71,"endTime":312.84,"body":"a 1/2. So, you kind of used the"},{"speaker":"Pam","startTime":312.84,"endTime":317.88,"body":"relationship with the problem"},{"speaker":"Pam","startTime":312.84,"endTime":317.88,"body":"before. So, if I say 3/6 divided"},{"speaker":"Pam","startTime":317.88,"endTime":322.53,"body":"by 1/6 is 3, then three-sixths"},{"speaker":"Pam","startTime":317.88,"endTime":322.53,"body":"divided by something twice as"},{"speaker":"Pam","startTime":322.53,"endTime":325.98,"body":"big has to be half as... The"},{"speaker":"Pam","startTime":322.53,"endTime":325.98,"body":"answer's half as much?"},{"speaker":"Kim","startTime":326.01,"endTime":326.52,"body":"Yeah."},{"speaker":"Pam","startTime":326.76,"endTime":328.56,"body":"So, 3/6 divided by 2/6 is 1"},{"speaker":"Pam","startTime":326.76,"endTime":328.56,"body":"and a 1/2?"},{"speaker":"Kim","startTime":328.56,"endTime":328.8,"body":"Mmhmm."},{"speaker":"Pam","startTime":329.94,"endTime":331.23,"body":"Can I say that in a"},{"speaker":"Pam","startTime":329.94,"endTime":331.23,"body":"slightly different way?"},{"speaker":"Kim","startTime":331.65,"endTime":331.86,"body":"Sure."},{"speaker":"Pam","startTime":331.89,"endTime":337.5,"body":"If 3/6 divided by 1/6. How"},{"speaker":"Pam","startTime":331.89,"endTime":337.5,"body":"many 1/6 are in 3/6? Is 3. Then,"},{"speaker":"Pam","startTime":337.53,"endTime":341.85,"body":"when I asked 3/6 divided by 2/6,"},{"speaker":"Pam","startTime":337.53,"endTime":341.85,"body":"how many 2/6, how many something"},{"speaker":"Pam","startTime":341.85,"endTime":346.17,"body":"twice as big are in the same"},{"speaker":"Pam","startTime":341.85,"endTime":346.17,"body":"total? That would have to be"},{"speaker":"Pam","startTime":346.17,"endTime":347.61,"body":"half as many. 1 and a 1/2."},{"speaker":"Kim","startTime":347.61,"endTime":347.73,"body":"Yeah."},{"speaker":"Kim","startTime":347.73,"endTime":352.17,"body":"So, I actually was just thinking"},{"speaker":"Kim","startTime":347.73,"endTime":352.17,"body":"while you were talking about how"},{"speaker":"Kim","startTime":352.26,"endTime":355.59,"body":"I thought about the first"},{"speaker":"Kim","startTime":352.26,"endTime":355.59,"body":"problem. Like, how many 2s are"},{"speaker":"Kim","startTime":355.59,"endTime":356.16,"body":"in 3?"},{"speaker":"Pam","startTime":356.76,"endTime":356.79,"body":"Mmhmm."},{"speaker":"Kim","startTime":357.03,"endTime":359.31,"body":"And so, for this problem,"},{"speaker":"Kim","startTime":357.03,"endTime":359.31,"body":"you could think about how many"},{"speaker":"Kim","startTime":359.34,"endTime":362.49,"body":"two-sixths fit inside"},{"speaker":"Kim","startTime":359.34,"endTime":362.49,"body":"three-sixth?"},{"speaker":"Kim","startTime":364.11,"endTime":370.59,"body":"So, there's going to be one 2/6"},{"speaker":"Kim","startTime":364.11,"endTime":370.59,"body":"inside that 3/6. But I can only"},{"speaker":"Kim","startTime":370.59,"endTime":375.15,"body":"fit half of the two-sixths the"},{"speaker":"Kim","startTime":370.59,"endTime":375.15,"body":"second time."},{"speaker":"Pam","startTime":375.39,"endTime":377.07,"body":"Like, in the leftover ones?"},{"speaker":"Kim","startTime":377.1,"endTime":377.94,"body":"In the leftover. Mmhmm."},{"speaker":"Pam","startTime":380.1,"endTime":383.1,"body":"So, that's interesting."},{"speaker":"Pam","startTime":380.1,"endTime":383.1,"body":"What I'm hearing you say is."},{"speaker":"Pam","startTime":383.13,"endTime":386.79,"body":"I've given you three problems."},{"speaker":"Pam","startTime":383.13,"endTime":386.79,"body":"To do the third problem, first"},{"speaker":"Pam","startTime":386.79,"endTime":388.62,"body":"you thought about the second"},{"speaker":"Pam","startTime":386.79,"endTime":388.62,"body":"problem to help you."},{"speaker":"Kim","startTime":388.98,"endTime":389.7,"body":"Yeah."},{"speaker":"Pam","startTime":389.82,"endTime":392.37,"body":"But then you also said,"},{"speaker":"Pam","startTime":389.82,"endTime":392.37,"body":"\"But I can also think about the"},{"speaker":"Pam","startTime":392.37,"endTime":393.69,"body":"first problem to help me.\""},{"speaker":"Kim","startTime":393.69,"endTime":394.11,"body":"Yep."},{"speaker":"Pam","startTime":394.2,"endTime":396.96,"body":"So, listeners, this might"},{"speaker":"Pam","startTime":394.2,"endTime":396.96,"body":"be. If you've never actually"},{"speaker":"Pam","startTime":396.96,"endTime":398.58,"body":"pulled out a pen and pencil"},{"speaker":"Pam","startTime":396.96,"endTime":398.58,"body":"while you're listening to the"},{"speaker":"Pam","startTime":398.58,"endTime":402.45,"body":"podcast, this one might be one"},{"speaker":"Pam","startTime":398.58,"endTime":402.45,"body":"that you want to. Yeah."},{"speaker":"Kim","startTime":402.96,"endTime":403.65,"body":"(unclear). Pull over on the"},{"speaker":"Kim","startTime":402.96,"endTime":403.65,"body":"side of the road."},{"speaker":"Pam","startTime":404.31,"endTime":407.13,"body":"So, if we can just focus on"},{"speaker":"Pam","startTime":404.31,"endTime":407.13,"body":"how you use the first problem."},{"speaker":"Pam","startTime":407.16,"endTime":409.92,"body":"It's almost like I hear you"},{"speaker":"Pam","startTime":407.16,"endTime":409.92,"body":"saying...the first problem you"},{"speaker":"Pam","startTime":409.92,"endTime":411.69,"body":"thought about 3 divided by"},{"speaker":"Pam","startTime":409.92,"endTime":411.69,"body":"2....you thought about how many"},{"speaker":"Pam","startTime":411.72,"endTime":416.19,"body":"2s are in 3. And the third"},{"speaker":"Pam","startTime":411.72,"endTime":416.19,"body":"problem, three-sixths divided by"},{"speaker":"Pam","startTime":416.19,"endTime":419.13,"body":"two-sixths, you thought about"},{"speaker":"Pam","startTime":416.19,"endTime":419.13,"body":"how many two-sixths are in"},{"speaker":"Pam","startTime":419.16,"endTime":422.97,"body":"three-sixths. It's almost like"},{"speaker":"Pam","startTime":419.16,"endTime":422.97,"body":"you were thinking about how many"},{"speaker":"Pam","startTime":423.3,"endTime":426.36,"body":"two-somethings could fit into"},{"speaker":"Pam","startTime":423.3,"endTime":426.36,"body":"three-somethings."},{"speaker":"Kim","startTime":426.54,"endTime":426.57,"body":"Mmhmm."},{"speaker":"Pam","startTime":427.32,"endTime":430.26,"body":"And in the first problem,"},{"speaker":"Pam","startTime":427.32,"endTime":430.26,"body":"you were like 2 wholes. How many"},{"speaker":"Pam","startTime":430.26,"endTime":433.56,"body":"2 wholes could fit into 3 holes?"},{"speaker":"Pam","startTime":430.26,"endTime":433.56,"body":"And then, the third problem you"},{"speaker":"Pam","startTime":433.56,"endTime":437.49,"body":"thought, how many two 1/6 could"},{"speaker":"Pam","startTime":433.56,"endTime":437.49,"body":"fit into three 1/6? And both"},{"speaker":"Pam","startTime":437.49,"endTime":439.17,"body":"times the answer was 1 and a"},{"speaker":"Pam","startTime":437.49,"endTime":439.17,"body":"1/2."},{"speaker":"Kim","startTime":439.68,"endTime":440.07,"body":"Yep."},{"speaker":"Pam","startTime":440.46,"endTime":443.79,"body":"1 and a 1/2 of those 2"},{"speaker":"Pam","startTime":440.46,"endTime":443.79,"body":"whatevers could fit into those 3"},{"speaker":"Pam","startTime":443.79,"endTime":448.95,"body":"whatever's. Interesting. Okay,"},{"speaker":"Pam","startTime":443.79,"endTime":448.95,"body":"next problem. Three-fifths"},{"speaker":"Pam","startTime":448.98,"endTime":450.24,"body":"divided by one-fifth?"},{"speaker":"Kim","startTime":452.52,"endTime":455.49,"body":"Three 1/5s."},{"speaker":"Pam","startTime":456.15,"endTime":457.59,"body":"Fit into 3/5s."},{"speaker":"Kim","startTime":458.25,"endTime":459.24,"body":"Fit into three-fifths."},{"speaker":"Pam","startTime":459.36,"endTime":459.99,"body":"Okay, (unclear)."},{"speaker":"Kim","startTime":460.77,"endTime":461.73,"body":"Did I say that wrong?"},{"speaker":"Pam","startTime":461.94,"endTime":463.92,"body":"No, you said it, right."},{"speaker":"Pam","startTime":461.94,"endTime":463.92,"body":"It's just depending on how"},{"speaker":"Pam","startTime":463.92,"endTime":467.31,"body":"you're... Yeah, okay. So, 3/5"},{"speaker":"Pam","startTime":463.92,"endTime":467.31,"body":"divided by 1/5 is 3. Cool. Next"},{"speaker":"Pam","startTime":467.31,"endTime":469.71,"body":"problem. Three-fifths divided by"},{"speaker":"Pam","startTime":467.31,"endTime":469.71,"body":"two-fifths?"},{"speaker":"Kim","startTime":471.69,"endTime":475.47,"body":"So two-fifths can fit"},{"speaker":"Kim","startTime":471.69,"endTime":475.47,"body":"inside of three-fifths, one"},{"speaker":"Kim","startTime":475.47,"endTime":480.96,"body":"time, and then half again. So,"},{"speaker":"Kim","startTime":475.47,"endTime":480.96,"body":"it's going to be 1 and a 1/2."},{"speaker":"Pam","startTime":481.65,"endTime":482.07,"body":"Again."},{"speaker":"Kim","startTime":482.07,"endTime":484.17,"body":"Oh, and that was like the"},{"speaker":"Kim","startTime":482.07,"endTime":484.17,"body":"first problem, Pam."},{"speaker":"Pam","startTime":484.5,"endTime":485.07,"body":"Say more."},{"speaker":"Kim","startTime":485.07,"endTime":488.28,"body":"You said 3 of something,"},{"speaker":"Kim","startTime":485.07,"endTime":488.28,"body":"divided by 2 of something. It"},{"speaker":"Kim","startTime":488.28,"endTime":489.99,"body":"has been 1 and a 1/2. So, three"},{"speaker":"Kim","startTime":488.28,"endTime":489.99,"body":"1/5s divided by two 1/5s is"},{"speaker":"Kim","startTime":490.02,"endTime":499.83,"body":"still going to be 1 and a 1/2."},{"speaker":"Pam","startTime":500.7,"endTime":506.19,"body":"Still 1 and a 1/2. So, I"},{"speaker":"Pam","startTime":500.7,"endTime":506.19,"body":"wonder... Like, I'm adding a"},{"speaker":"Pam","startTime":506.19,"endTime":509.97,"body":"problem late in the game here."},{"speaker":"Pam","startTime":506.19,"endTime":509.97,"body":"So, if I said something like"},{"speaker":"Pam","startTime":510.21,"endTime":513.78,"body":"three-sevenths divided by"},{"speaker":"Pam","startTime":510.21,"endTime":513.78,"body":"two-sevenths?"},{"speaker":"Kim","startTime":514.26,"endTime":514.8,"body":"Yeah."},{"speaker":"Pam","startTime":515.25,"endTime":516.66,"body":"You think it still might"},{"speaker":"Pam","startTime":515.25,"endTime":516.66,"body":"be?"},{"speaker":"Kim","startTime":516.809,"endTime":517.589,"body":"One and a 1/2."},{"speaker":"Pam","startTime":517.77,"endTime":518.43,"body":"One and a 1/2?"},{"speaker":"Kim","startTime":519.059,"endTime":519.299,"body":"Yep."},{"speaker":"Pam","startTime":519.33,"endTime":526.32,"body":"What if it was 3/29 divided"},{"speaker":"Pam","startTime":519.33,"endTime":526.32,"body":"by 2/29?"},{"speaker":"Kim","startTime":526.5,"endTime":526.95,"body":"Yep."},{"speaker":"Pam","startTime":527.16,"endTime":527.91,"body":"Still 1 and a half?"},{"speaker":"Kim","startTime":527.91,"endTime":529.08,"body":"Still 1 and a 1/2. Yep."},{"speaker":"Pam","startTime":529.14,"endTime":533.4,"body":"Because 2 whatevers can fit"},{"speaker":"Pam","startTime":529.14,"endTime":533.4,"body":"1 and a 1/2 times into 3"},{"speaker":"Pam","startTime":533.4,"endTime":534.09,"body":"whatever's."},{"speaker":"Kim","startTime":534.12,"endTime":534.66,"body":"Yeah."},{"speaker":"Pam","startTime":534.69,"endTime":536.01,"body":"Whatever they are."},{"speaker":"Pam","startTime":534.69,"endTime":536.01,"body":"Interesting."},{"speaker":"Kim","startTime":536.07,"endTime":536.34,"body":"Yep."},{"speaker":"Pam","startTime":536.52,"endTime":540.27,"body":"Alright, next next problem"},{"speaker":"Pam","startTime":536.52,"endTime":540.27,"body":"of the string. 10 divided by 9."},{"speaker":"Kim","startTime":542.67,"endTime":546.18,"body":"Well, you're asking me to"},{"speaker":"Kim","startTime":542.67,"endTime":546.18,"body":"think quotitively, so 9 can fit"},{"speaker":"Kim","startTime":546.18,"endTime":550.56,"body":"into 10, one time. And then..."},{"speaker":"Pam","startTime":550.65,"endTime":551.82,"body":"But there's some stuff"},{"speaker":"Pam","startTime":550.65,"endTime":551.82,"body":"leftover."},{"speaker":"Kim","startTime":551.85,"endTime":554.49,"body":"There's some stuff"},{"speaker":"Kim","startTime":551.85,"endTime":554.49,"body":"leftover. And 9 can fit into the"},{"speaker":"Kim","startTime":554.49,"endTime":560.76,"body":"stuff leftover only 1/9. So, 1"},{"speaker":"Kim","startTime":554.49,"endTime":560.76,"body":"and 1/9."},{"speaker":"Pam","startTime":562.29,"endTime":564.63,"body":"You're saying 10 divided by"},{"speaker":"Pam","startTime":562.29,"endTime":564.63,"body":"9 is 1 and 1/9?"},{"speaker":"Kim","startTime":564.84,"endTime":565.44,"body":"Yeah."},{"speaker":"Pam","startTime":566.67,"endTime":568.26,"body":"Say that... Why again?"},{"speaker":"Kim","startTime":569.67,"endTime":571.86,"body":"Because 9 can fit..."},{"speaker":"Pam","startTime":572.04,"endTime":574.11,"body":"How many 9s are in 10?"},{"speaker":"Pam","startTime":572.04,"endTime":574.11,"body":"You're thinking about how many"},{"speaker":"Pam","startTime":574.11,"endTime":575.13,"body":"9s are in 10. Sorry to"},{"speaker":"Pam","startTime":574.11,"endTime":575.13,"body":"interrupt."},{"speaker":"Kim","startTime":575.43,"endTime":578.82,"body":"Yeah. That's okay. So, 9"},{"speaker":"Kim","startTime":575.43,"endTime":578.82,"body":"can fit into 10, one full time."},{"speaker":"Pam","startTime":580.59,"endTime":581.73,"body":"And then there's what"},{"speaker":"Pam","startTime":580.59,"endTime":581.73,"body":"leftover?"},{"speaker":"Kim","startTime":581.94,"endTime":584.1,"body":"There's a tenth leftover."},{"speaker":"Pam","startTime":585.39,"endTime":589.56,"body":"I think there's one"},{"speaker":"Pam","startTime":585.39,"endTime":589.56,"body":"leftover, yeah? A tenth of 10 is"},{"speaker":"Pam","startTime":589.56,"endTime":589.92,"body":"1."},{"speaker":"Kim","startTime":590.37,"endTime":591.09,"body":"Sorry."},{"speaker":"Kim","startTime":595.05,"endTime":597.84,"body":"So, it can fit into 10, one"},{"speaker":"Kim","startTime":595.05,"endTime":597.84,"body":"time, and then there's 1"},{"speaker":"Kim","startTime":597.84,"endTime":601.86,"body":"leftover. And then, 9 can only"},{"speaker":"Kim","startTime":597.84,"endTime":601.86,"body":"fit into that 1 leftover, 1/9"},{"speaker":"Kim","startTime":601.86,"endTime":602.52,"body":"(unclear)."},{"speaker":"Pam","startTime":605.04,"endTime":605.76,"body":"Yeah."},{"speaker":"Kim","startTime":605.79,"endTime":608.61,"body":"It can't fit the whole"},{"speaker":"Kim","startTime":605.79,"endTime":608.61,"body":"time. It's just one-ninth."},{"speaker":"Pam","startTime":608.61,"endTime":610.26,"body":"We can only get one-ninth."},{"speaker":"Pam","startTime":608.61,"endTime":610.26,"body":"Yeah."},{"speaker":"Kim","startTime":610.26,"endTime":610.44,"body":"Yeah."},{"speaker":"Pam","startTime":610.47,"endTime":613.86,"body":"There's only... Yeah."},{"speaker":"Pam","startTime":610.47,"endTime":613.86,"body":"That's crazy kind of reasoning,"},{"speaker":"Pam","startTime":613.86,"endTime":617.67,"body":"right? That's interesting. So, I"},{"speaker":"Pam","startTime":613.86,"endTime":617.67,"body":"have on my paper written 10"},{"speaker":"Pam","startTime":617.73,"endTime":621.66,"body":"\"division sign\" 9, \"equals\" 1"},{"speaker":"Pam","startTime":617.73,"endTime":621.66,"body":"and 1/9."},{"speaker":"Kim","startTime":621.9,"endTime":622.23,"body":"Yes."},{"speaker":"Pam","startTime":622.23,"endTime":626.13,"body":"I also want to remind us"},{"speaker":"Pam","startTime":622.23,"endTime":626.13,"body":"that sometimes we can write 10"},{"speaker":"Pam","startTime":626.13,"endTime":629.25,"body":"divided by 9 as 10 \"fraction"},{"speaker":"Pam","startTime":626.13,"endTime":629.25,"body":"bar\" 9."},{"speaker":"Kim","startTime":629.76,"endTime":630.12,"body":"Yeah."},{"speaker":"Pam","startTime":630.15,"endTime":631.41,"body":"10/9."},{"speaker":"Kim","startTime":631.59,"endTime":631.95,"body":"Yep."},{"speaker":"Pam","startTime":632.01,"endTime":635.49,"body":"And is 10/9 equivalent to 1"},{"speaker":"Pam","startTime":632.01,"endTime":635.49,"body":"and 1/9? Like, you just reason"},{"speaker":"Pam","startTime":635.52,"endTime":636.12,"body":"quotitively."},{"speaker":"Kim","startTime":636.33,"endTime":636.99,"body":"Yes."},{"speaker":"Pam","startTime":637.08,"endTime":639.09,"body":"Oh, sure enough, sure"},{"speaker":"Pam","startTime":637.08,"endTime":639.09,"body":"enough. So, a couple different"},{"speaker":"Pam","startTime":639.09,"endTime":641.1,"body":"connections that we can make."},{"speaker":"Pam","startTime":639.09,"endTime":641.1,"body":"Now, I kind of forced you to"},{"speaker":"Pam","startTime":641.1,"endTime":643.62,"body":"think quotitively, and you were"},{"speaker":"Pam","startTime":641.1,"endTime":643.62,"body":"like, \"Alright, I can think"},{"speaker":"Pam","startTime":643.62,"endTime":647.01,"body":"about how many 9s fit into 10.\""},{"speaker":"Pam","startTime":643.62,"endTime":647.01,"body":"And well done doing that. But we"},{"speaker":"Pam","startTime":647.01,"endTime":650.01,"body":"can also sort of... That"},{"speaker":"Pam","startTime":647.01,"endTime":650.01,"body":"connection between division and"},{"speaker":"Pam","startTime":650.01,"endTime":655.71,"body":"fractions, we can think about 10"},{"speaker":"Pam","startTime":650.01,"endTime":655.71,"body":"divided by 9 as 10/9. Cool. Nice"},{"speaker":"Pam","startTime":655.71,"endTime":658.95,"body":"thinking. Alright, ready? Next"},{"speaker":"Pam","startTime":655.71,"endTime":658.95,"body":"problem. Ten-twelfths. So, the"},{"speaker":"Pam","startTime":658.95,"endTime":663.96,"body":"fraction ten-twelfths divided by"},{"speaker":"Pam","startTime":658.95,"endTime":663.96,"body":"nine-twelfths. Ten-twelfths"},{"speaker":"Pam","startTime":663.96,"endTime":664.89,"body":"divided by nine-twelfths."},{"speaker":"Kim","startTime":666.33,"endTime":670.23,"body":"Nine-twelfths fits inside"},{"speaker":"Kim","startTime":666.33,"endTime":670.23,"body":"10/12, one time."},{"speaker":"Pam","startTime":671.43,"endTime":672.42,"body":"With some stuff leftover."},{"speaker":"Kim","startTime":672.6,"endTime":681.03,"body":"With some stuff over. And"},{"speaker":"Kim","startTime":672.6,"endTime":681.03,"body":"there's a twelfth leftover. And"},{"speaker":"Kim","startTime":681.48,"endTime":687.69,"body":"nine-twelfths can fit into"},{"speaker":"Kim","startTime":681.48,"endTime":687.69,"body":"one-twelfth, a ninth."},{"speaker":"Pam","startTime":689.13,"endTime":690.42,"body":"Like, it really doesn't"},{"speaker":"Pam","startTime":689.13,"endTime":690.42,"body":"fit, right. (unclear)."},{"speaker":"Kim","startTime":690.51,"endTime":693.39,"body":"It doesn't fit. It can only"},{"speaker":"Kim","startTime":690.51,"endTime":693.39,"body":"fit (unclear)."},{"speaker":"Pam","startTime":693.39,"endTime":693.42,"body":"(unclear)."},{"speaker":"Kim","startTime":693.99,"endTime":695.43,"body":"But you know what would"},{"speaker":"Kim","startTime":693.99,"endTime":695.43,"body":"have been like a little bit"},{"speaker":"Kim","startTime":695.43,"endTime":696.18,"body":"easier for me?"},{"speaker":"Pam","startTime":696.18,"endTime":697.38,"body":"Okay, mmhmm, go ahead."},{"speaker":"Kim","startTime":697.98,"endTime":700.17,"body":"If I had thought about the"},{"speaker":"Kim","startTime":697.98,"endTime":700.17,"body":"problem before."},{"speaker":"Pam","startTime":700.71,"endTime":700.74,"body":"Mmhmm?"},{"speaker":"Kim","startTime":700.77,"endTime":703.02,"body":"And what we kind of just"},{"speaker":"Kim","startTime":700.77,"endTime":703.02,"body":"talked about."},{"speaker":"Pam","startTime":703.08,"endTime":703.62,"body":"Yeah?"},{"speaker":"Kim","startTime":703.8,"endTime":709.62,"body":"And 10/12. The thing is the"},{"speaker":"Kim","startTime":703.8,"endTime":709.62,"body":"twelfths. So, 10 something,"},{"speaker":"Kim","startTime":709.71,"endTime":715.44,"body":"10/12, divided by 9 something,"},{"speaker":"Kim","startTime":709.71,"endTime":715.44,"body":"9/12 is going to be the same."},{"speaker":"Kim","startTime":715.47,"endTime":720.66,"body":"It's an equivalent answer to 10"},{"speaker":"Kim","startTime":715.47,"endTime":720.66,"body":"divided by 9. So, it's still 1"},{"speaker":"Kim","startTime":720.66,"endTime":720.87,"body":"and 1/9."},{"speaker":"Pam","startTime":721.95,"endTime":726.99,"body":"So, you're saying 10/12"},{"speaker":"Pam","startTime":721.95,"endTime":726.99,"body":"divided by 9/12 is equivalent to"},{"speaker":"Pam","startTime":726.99,"endTime":728.01,"body":"10 divided by 9?"},{"speaker":"Kim","startTime":729.12,"endTime":729.15,"body":"Mmhmm."},{"speaker":"Pam","startTime":729.81,"endTime":732.93,"body":"Because it's almost like 10"},{"speaker":"Pam","startTime":729.81,"endTime":732.93,"body":"things divided by 9 things?"},{"speaker":"Kim","startTime":733.02,"endTime":733.41,"body":"Yep."},{"speaker":"Pam","startTime":733.44,"endTime":736.56,"body":"It's 10 divided by 9, which"},{"speaker":"Pam","startTime":733.44,"endTime":736.56,"body":"is 1 and 1/9 or 10/9."},{"speaker":"Kim","startTime":736.74,"endTime":737.22,"body":"Yep."},{"speaker":"Pam","startTime":738.12,"endTime":741.12,"body":"Fascinating. Okay. Okay."},{"speaker":"Pam","startTime":738.12,"endTime":741.12,"body":"So, similar to what we were"},{"speaker":"Pam","startTime":741.12,"endTime":744.72,"body":"doing before. If we can kind of"},{"speaker":"Pam","startTime":741.12,"endTime":744.72,"body":"think about 10/9, 10 divided by"},{"speaker":"Pam","startTime":744.72,"endTime":747.27,"body":"9, we can think about 10"},{"speaker":"Pam","startTime":744.72,"endTime":747.27,"body":"anythings divided by 9"},{"speaker":"Pam","startTime":747.27,"endTime":750.63,"body":"anythings. There's still going"},{"speaker":"Pam","startTime":747.27,"endTime":750.63,"body":"to be equivalent to 10/9."},{"speaker":"Kim","startTime":751.02,"endTime":751.44,"body":"Yep."},{"speaker":"Pam","startTime":751.65,"endTime":754.98,"body":"Cool. Alright. Next"},{"speaker":"Pam","startTime":751.65,"endTime":754.98,"body":"problem. How about five-sixths"},{"speaker":"Pam","startTime":755.73,"endTime":758.85,"body":"divided by three-fourths? Now,"},{"speaker":"Pam","startTime":755.73,"endTime":758.85,"body":"this isn't related to anything"},{"speaker":"Pam","startTime":758.85,"endTime":761.79,"body":"we've done, so just random"},{"speaker":"Pam","startTime":758.85,"endTime":761.79,"body":"problem. Five-sixths divided by."},{"speaker":"Kim","startTime":761.82,"endTime":763.92,"body":"Well, I'm glad I've been"},{"speaker":"Kim","startTime":761.82,"endTime":763.92,"body":"writing the problems down"},{"speaker":"Kim","startTime":764.25,"endTime":765.0,"body":"because."},{"speaker":"Pam","startTime":765.21,"endTime":767.46,"body":"So, listeners, you might"},{"speaker":"Pam","startTime":765.21,"endTime":767.46,"body":"want to actually take the advice"},{"speaker":"Pam","startTime":767.46,"endTime":768.9,"body":"we have, (unclear) writing stuff"},{"speaker":"Pam","startTime":767.46,"endTime":768.9,"body":"down."},{"speaker":"Kim","startTime":769.53,"endTime":774.36,"body":"So, I'm comparing the"},{"speaker":"Kim","startTime":769.53,"endTime":774.36,"body":"problem you just gave me and the"},{"speaker":"Kim","startTime":774.36,"endTime":783.09,"body":"problem prior to that. So,"},{"speaker":"Kim","startTime":774.36,"endTime":783.09,"body":"five-sixths is equivalent to"},{"speaker":"Kim","startTime":783.09,"endTime":786.63,"body":"ten-twelfths from the previous"},{"speaker":"Kim","startTime":783.09,"endTime":786.63,"body":"problem."},{"speaker":"Pam","startTime":786.63,"endTime":786.72,"body":"Okay."},{"speaker":"Kim","startTime":786.9,"endTime":791.34,"body":"And three-fourths is"},{"speaker":"Kim","startTime":786.9,"endTime":791.34,"body":"equivalent to the nine-twelfths"},{"speaker":"Kim","startTime":791.37,"endTime":792.51,"body":"in the previous problem."},{"speaker":"Pam","startTime":792.69,"endTime":793.23,"body":"Okay."},{"speaker":"Kim","startTime":793.98,"endTime":796.86,"body":"So, the answer is going to"},{"speaker":"Kim","startTime":793.98,"endTime":796.86,"body":"be the same. 1 and 1/9."},{"speaker":"Pam","startTime":797.34,"endTime":801.69,"body":"Or, 10/9. So, Kim, what did"},{"speaker":"Pam","startTime":797.34,"endTime":801.69,"body":"you think, though? Like, when"},{"speaker":"Pam","startTime":801.69,"endTime":804.6,"body":"you saw five- sixths divided by"},{"speaker":"Pam","startTime":801.69,"endTime":804.6,"body":"three-fourths, is there a first"},{"speaker":"Pam","startTime":804.6,"endTime":807.03,"body":"thought that you thought, \"Okay,"},{"speaker":"Pam","startTime":804.6,"endTime":807.03,"body":"how many three-fourths are"},{"speaker":"Pam","startTime":807.03,"endTime":809.37,"body":"in...\" Or did you just go, \"It's"},{"speaker":"Pam","startTime":807.03,"endTime":809.37,"body":"a Problem String. I'm going to"},{"speaker":"Pam","startTime":809.37,"endTime":810.18,"body":"see if they're equivalent.\""},{"speaker":"Kim","startTime":810.18,"endTime":812.4,"body":"I totally did. I'm not"},{"speaker":"Kim","startTime":810.18,"endTime":812.4,"body":"going to lie. I totally did. I"},{"speaker":"Kim","startTime":812.4,"endTime":814.17,"body":"was like, \"There's got to be"},{"speaker":"Kim","startTime":812.4,"endTime":814.17,"body":"something here because that"},{"speaker":"Kim","startTime":814.17,"endTime":815.52,"body":"problem is funky.\""},{"speaker":"Pam","startTime":815.7,"endTime":818.73,"body":"Well, so when you said that"},{"speaker":"Pam","startTime":815.7,"endTime":818.73,"body":"problem is funky, then I"},{"speaker":"Pam","startTime":818.73,"endTime":821.28,"body":"actually want to pause that"},{"speaker":"Pam","startTime":818.73,"endTime":821.28,"body":"brief second because I think you"},{"speaker":"Pam","startTime":821.28,"endTime":825.39,"body":"really quickly were like, \"That"},{"speaker":"Pam","startTime":821.28,"endTime":825.39,"body":"problem is funky. It's a Problem"},{"speaker":"Pam","startTime":825.39,"endTime":827.22,"body":"String. I'm going to look for a"},{"speaker":"Pam","startTime":825.39,"endTime":827.22,"body":"pattern. I'm going to look for"},{"speaker":"Pam","startTime":827.22,"endTime":827.82,"body":"something.\""},{"speaker":"Kim","startTime":828.03,"endTime":828.24,"body":"Yeah."},{"speaker":"Pam","startTime":828.24,"endTime":830.16,"body":"And I think we could"},{"speaker":"Pam","startTime":828.24,"endTime":830.16,"body":"potentially kind of skip over"},{"speaker":"Pam","startTime":830.16,"endTime":833.34,"body":"the fact that you actually"},{"speaker":"Pam","startTime":830.16,"endTime":833.34,"body":"considered five-sixth divided by"},{"speaker":"Pam","startTime":833.37,"endTime":836.91,"body":"three-fourths first. Like,"},{"speaker":"Pam","startTime":833.37,"endTime":836.91,"body":"mathematicians consider that."},{"speaker":"Pam","startTime":836.91,"endTime":837.99,"body":"You don't just look to"},{"speaker":"Pam","startTime":836.91,"endTime":837.99,"body":"(unclear)."},{"speaker":"Kim","startTime":838.11,"endTime":840.9,"body":"Oh, yeah, yeah. I looked at"},{"speaker":"Kim","startTime":838.11,"endTime":840.9,"body":"it. And I thought about it. And"},{"speaker":"Kim","startTime":840.9,"endTime":842.37,"body":"I was like, \"Ugh.\""},{"speaker":"Pam","startTime":842.79,"endTime":844.71,"body":"And then, you said to"},{"speaker":"Pam","startTime":842.79,"endTime":844.71,"body":"yourself, \"What else do I know?\""},{"speaker":"Pam","startTime":844.83,"endTime":848.61,"body":"Oh, great mathematical thinking."},{"speaker":"Pam","startTime":844.83,"endTime":848.61,"body":"And you're like, \"Hey, sweet!"},{"speaker":"Pam","startTime":848.61,"endTime":850.98,"body":"It's equivalent to the one"},{"speaker":"Pam","startTime":848.61,"endTime":850.98,"body":"before, and so the answer is"},{"speaker":"Pam","startTime":850.98,"endTime":851.58,"body":"going to be equivalent.\""},{"speaker":"Kim","startTime":851.91,"endTime":852.45,"body":"Yeah."},{"speaker":"Pam","startTime":852.87,"endTime":856.05,"body":"Let's maybe parse out a"},{"speaker":"Pam","startTime":852.87,"endTime":856.05,"body":"little bit. Five-sixths divided"},{"speaker":"Pam","startTime":856.05,"endTime":859.32,"body":"by three-fourths? You could"},{"speaker":"Pam","startTime":856.05,"endTime":859.32,"body":"think about how many"},{"speaker":"Pam","startTime":859.35,"endTime":862.77,"body":"three-fourths are in"},{"speaker":"Pam","startTime":859.35,"endTime":862.77,"body":"five-sixths. And then, that's"},{"speaker":"Pam","startTime":862.77,"endTime":866.79,"body":"like. Wow, like fourths and"},{"speaker":"Pam","startTime":862.77,"endTime":866.79,"body":"sixths. And those are not"},{"speaker":"Pam","startTime":867.0,"endTime":868.56,"body":"delightfully related."},{"speaker":"Kim","startTime":868.62,"endTime":868.86,"body":"Right."},{"speaker":"Pam","startTime":868.86,"endTime":871.8,"body":"(unclear) in a super, you"},{"speaker":"Pam","startTime":868.86,"endTime":871.8,"body":"know like, \"If I just cut them"},{"speaker":"Pam","startTime":871.8,"endTime":875.01,"body":"in half, I get the other one,\""},{"speaker":"Pam","startTime":871.8,"endTime":875.01,"body":"or whatever. So, then, you kind"},{"speaker":"Pam","startTime":875.01,"endTime":878.22,"body":"of said to yourself, \"Since"},{"speaker":"Pam","startTime":875.01,"endTime":878.22,"body":"they're not, I wonder what else"},{"speaker":"Pam","startTime":878.22,"endTime":882.51,"body":"I know.\" And yeah, the problem"},{"speaker":"Pam","startTime":878.22,"endTime":882.51,"body":"before was just sitting there."},{"speaker":"Pam","startTime":882.72,"endTime":885.48,"body":"But in a way, the problem before"},{"speaker":"Pam","startTime":882.72,"endTime":885.48,"body":"when you said, \"What else do I"},{"speaker":"Pam","startTime":885.48,"endTime":888.0,"body":"know?\" you kind of found a"},{"speaker":"Pam","startTime":885.48,"endTime":888.0,"body":"problem that had the same sort"},{"speaker":"Pam","startTime":888.0,"endTime":888.96,"body":"of pieces."},{"speaker":"Kim","startTime":889.98,"endTime":890.01,"body":"Mmhmm."},{"speaker":"Pam","startTime":890.04,"endTime":892.68,"body":"Like, often when we add and"},{"speaker":"Pam","startTime":890.04,"endTime":892.68,"body":"subtract fractions, we say to"},{"speaker":"Pam","startTime":892.68,"endTime":894.93,"body":"ourselves, \"Oh, I can't really"},{"speaker":"Pam","startTime":892.68,"endTime":894.93,"body":"add sixths and fourths, so let"},{"speaker":"Pam","startTime":894.93,"endTime":897.75,"body":"me find equivalent fractions"},{"speaker":"Pam","startTime":894.93,"endTime":897.75,"body":"that have the same kind of"},{"speaker":"Pam","startTime":897.75,"endTime":900.39,"body":"pieces.\" Maybe twelfths. And"},{"speaker":"Pam","startTime":897.75,"endTime":900.39,"body":"then, \"Hey, I could add them"},{"speaker":"Pam","startTime":900.39,"endTime":903.48,"body":"together.\" It's almost like this"},{"speaker":"Pam","startTime":900.39,"endTime":903.48,"body":"time you said to yourself, \"I"},{"speaker":"Pam","startTime":903.48,"endTime":905.76,"body":"wonder if I could find the same"},{"speaker":"Pam","startTime":903.48,"endTime":905.76,"body":"number of pieces, so that I"},{"speaker":"Pam","startTime":905.76,"endTime":909.72,"body":"could divide?\" I don't know that"},{"speaker":"Pam","startTime":905.76,"endTime":909.72,"body":"we typically have done that,"},{"speaker":"Pam","startTime":910.41,"endTime":911.94,"body":"teachers. I wonder, you know"},{"speaker":"Pam","startTime":910.41,"endTime":911.94,"body":"like, when you said,"},{"speaker":"Pam","startTime":911.94,"endTime":914.46,"body":"\"Five-sixths divided"},{"speaker":"Pam","startTime":911.94,"endTime":914.46,"body":"three-fourths... Hey, but they"},{"speaker":"Pam","startTime":914.46,"endTime":917.37,"body":"both can turn into twelfths. And"},{"speaker":"Pam","startTime":914.46,"endTime":917.37,"body":"if I can turn them both into"},{"speaker":"Pam","startTime":917.37,"endTime":920.19,"body":"twelfths, then I could just"},{"speaker":"Pam","startTime":917.37,"endTime":920.19,"body":"think about the twelfths.\""},{"speaker":"Kim","startTime":920.46,"endTime":923.1,"body":"Yeah. So, I think there's"},{"speaker":"Kim","startTime":920.46,"endTime":923.1,"body":"two things that happened too"},{"speaker":"Kim","startTime":923.1,"endTime":926.94,"body":"that I'm aware of that I want"},{"speaker":"Kim","startTime":923.1,"endTime":926.94,"body":"for our students. Like, in this"},{"speaker":"Kim","startTime":926.94,"endTime":930.57,"body":"moment is, One, what I was going"},{"speaker":"Kim","startTime":926.94,"endTime":930.57,"body":"to say to you is, I think this"},{"speaker":"Kim","startTime":930.57,"endTime":935.43,"body":"is the funkiest problem that"},{"speaker":"Kim","startTime":930.57,"endTime":935.43,"body":"we've done in the last couple of"},{"speaker":"Kim","startTime":936.75,"endTime":937.56,"body":"episodes."},{"speaker":"Pam","startTime":937.59,"endTime":938.01,"body":"Yeah."},{"speaker":"Kim","startTime":938.34,"endTime":943.62,"body":"And I want for kids to"},{"speaker":"Kim","startTime":938.34,"endTime":943.62,"body":"think about the fact that there"},{"speaker":"Kim","startTime":943.62,"endTime":948.36,"body":"are kind of different... I don't"},{"speaker":"Kim","startTime":943.62,"endTime":948.36,"body":"want to say \"levels of"},{"speaker":"Kim","startTime":948.36,"endTime":951.99,"body":"problems\", but like, some are a"},{"speaker":"Kim","startTime":948.36,"endTime":951.99,"body":"little funkier than others. And"},{"speaker":"Kim","startTime":951.99,"endTime":955.08,"body":"so like, I want them to be a"},{"speaker":"Kim","startTime":951.99,"endTime":955.08,"body":"little bit more discerning"},{"speaker":"Kim","startTime":955.11,"endTime":961.08,"body":"about, \"I have this variety of"},{"speaker":"Kim","startTime":955.11,"endTime":961.08,"body":"strategies, and this problem is"},{"speaker":"Kim","startTime":961.08,"endTime":963.42,"body":"one that I might have to think"},{"speaker":"Kim","startTime":961.08,"endTime":963.42,"body":"about a little bit differently.\""},{"speaker":"Kim","startTime":963.45,"endTime":966.87,"body":"But also, I know, you just gave"},{"speaker":"Kim","startTime":963.45,"endTime":966.87,"body":"me the ten-twelves divided by"},{"speaker":"Kim","startTime":966.87,"endTime":969.96,"body":"nine-twelfths, but I looked at"},{"speaker":"Kim","startTime":966.87,"endTime":969.96,"body":"it and was like, \"Oh, those are"},{"speaker":"Kim","startTime":969.96,"endTime":973.83,"body":"equivalent,\" so I had to know"},{"speaker":"Kim","startTime":969.96,"endTime":973.83,"body":"that those were equivalent to be"},{"speaker":"Kim","startTime":973.83,"endTime":975.15,"body":"able to make use of it."},{"speaker":"Pam","startTime":975.69,"endTime":978.15,"body":"Absolutely. Hey, one other"},{"speaker":"Pam","startTime":975.69,"endTime":978.15,"body":"thing that we should probably"},{"speaker":"Pam","startTime":978.15,"endTime":981.09,"body":"mention is, in this Problem"},{"speaker":"Pam","startTime":978.15,"endTime":981.09,"body":"String if I was doing it with"},{"speaker":"Pam","startTime":981.09,"endTime":984.87,"body":"students and not Kim, I think"},{"speaker":"Pam","startTime":981.09,"endTime":984.87,"body":"that I... Well, I guess I could"},{"speaker":"Pam","startTime":984.87,"endTime":986.82,"body":"have done it with you too. But I"},{"speaker":"Pam","startTime":984.87,"endTime":986.82,"body":"might have said, \"Hey, let's"},{"speaker":"Pam","startTime":986.82,"endTime":988.95,"body":"actually talk about five-sixths"},{"speaker":"Pam","startTime":986.82,"endTime":988.95,"body":"and three-fourths. How do they"},{"speaker":"Pam","startTime":988.95,"endTime":991.74,"body":"relate? If I'm asking how many"},{"speaker":"Pam","startTime":988.95,"endTime":991.74,"body":"three-fourths fit into"},{"speaker":"Pam","startTime":991.74,"endTime":994.32,"body":"five-sixths, am I going to have"},{"speaker":"Pam","startTime":991.74,"endTime":994.32,"body":"a lot of three-fourths and"},{"speaker":"Pam","startTime":994.35,"endTime":996.99,"body":"five-sixths? Am I going to"},{"speaker":"Pam","startTime":994.35,"endTime":996.99,"body":"have... Is the answer a"},{"speaker":"Pam","startTime":996.99,"endTime":1000.68,"body":"fraction? Three-fourths doesn't"},{"speaker":"Pam","startTime":996.99,"endTime":1000.68,"body":"fit? Is three-fourths less than"},{"speaker":"Pam","startTime":1000.89,"endTime":1004.58,"body":"five-sixths? Like, how do those"},{"speaker":"Pam","startTime":1000.89,"endTime":1004.58,"body":"relate?\" And, Kim, how would you"},{"speaker":"Pam","startTime":1004.58,"endTime":1005.87,"body":"answer that? How do those"},{"speaker":"Pam","startTime":1004.58,"endTime":1005.87,"body":"relate?"},{"speaker":"Kim","startTime":1006.98,"endTime":1009.05,"body":"You know, the first thing"},{"speaker":"Kim","startTime":1006.98,"endTime":1009.05,"body":"I'm thinking about..."},{"speaker":"Pam","startTime":1009.92,"endTime":1011.81,"body":"(unclear). I was just going"},{"speaker":"Pam","startTime":1009.92,"endTime":1011.81,"body":"to say just relative size. But"},{"speaker":"Pam","startTime":1011.81,"endTime":1013.16,"body":"go ahead. What was the first"},{"speaker":"Pam","startTime":1011.81,"endTime":1013.16,"body":"thing you were thinking?"},{"speaker":"Kim","startTime":1013.16,"endTime":1017.69,"body":"Well, so I know that I know"},{"speaker":"Kim","startTime":1013.16,"endTime":1017.69,"body":"a lot about three-fourths, and"},{"speaker":"Kim","startTime":1017.69,"endTime":1023.18,"body":"so I was actually thinking about"},{"speaker":"Kim","startTime":1017.69,"endTime":1023.18,"body":"what's 3/4 of 6 to see if 5/6 is"},{"speaker":"Kim","startTime":1023.18,"endTime":1025.16,"body":"more than 3/4 or less than 3/4."},{"speaker":"Pam","startTime":1025.16,"endTime":1028.73,"body":"[Pam laughs] Okay. Alright."},{"speaker":"Pam","startTime":1025.16,"endTime":1028.73,"body":"Let's go there in a minute. Can"},{"speaker":"Pam","startTime":1028.73,"endTime":1029.87,"body":"we slow that down a little bit?"},{"speaker":"Kim","startTime":1029.9,"endTime":1030.29,"body":"[Kim laughs] Sorry."},{"speaker":"Pam","startTime":1030.41,"endTime":1034.61,"body":"I want to slow you down"},{"speaker":"Pam","startTime":1030.41,"endTime":1034.61,"body":"just a handful. So, if we were"},{"speaker":"Pam","startTime":1034.61,"endTime":1037.64,"body":"just to compare five-sixths and"},{"speaker":"Pam","startTime":1034.61,"endTime":1037.64,"body":"three-fourths, which one's"},{"speaker":"Pam","startTime":1037.64,"endTime":1038.09,"body":"bigger?"},{"speaker":"Kim","startTime":1039.47,"endTime":1040.13,"body":"Five-sixths."},{"speaker":"Pam","startTime":1040.28,"endTime":1040.85,"body":"Five-sixths."},{"speaker":"Kim","startTime":1040.97,"endTime":1044.63,"body":"But I had to know that"},{"speaker":"Kim","startTime":1040.97,"endTime":1044.63,"body":"because I had to think about"},{"speaker":"Kim","startTime":1044.63,"endTime":1046.13,"body":"what I know about three-fourths."},{"speaker":"Pam","startTime":1047.03,"endTime":1050.03,"body":"Sure, sure. And in that"},{"speaker":"Pam","startTime":1047.03,"endTime":1050.03,"body":"way, we would want to do some"},{"speaker":"Pam","startTime":1050.03,"endTime":1053.51,"body":"work with students. Five-sixths"},{"speaker":"Pam","startTime":1050.03,"endTime":1053.51,"body":"is just one unit fraction away"},{"speaker":"Pam","startTime":1053.51,"endTime":1056.69,"body":"from six-sixths. It's just"},{"speaker":"Pam","startTime":1053.51,"endTime":1056.69,"body":"one-sixth away from six-sixths."},{"speaker":"Pam","startTime":1056.93,"endTime":1060.83,"body":"And three-fourths is just one"},{"speaker":"Pam","startTime":1056.93,"endTime":1060.83,"body":"unit fraction, one-fourth away"},{"speaker":"Pam","startTime":1060.83,"endTime":1064.34,"body":"from four-fourths. And so, I can"},{"speaker":"Pam","startTime":1060.83,"endTime":1064.34,"body":"think about what's bigger?"},{"speaker":"Pam","startTime":1064.37,"endTime":1068.06,"body":"One-fourth or one-sixth? And"},{"speaker":"Pam","startTime":1064.37,"endTime":1068.06,"body":"that can help me think about"},{"speaker":"Pam","startTime":1068.06,"endTime":1072.38,"body":"what's closer to 1. Since"},{"speaker":"Pam","startTime":1068.06,"endTime":1072.38,"body":"one-sixth is smaller than"},{"speaker":"Pam","startTime":1072.38,"endTime":1077.09,"body":"one-fourth, five-sixths is"},{"speaker":"Pam","startTime":1072.38,"endTime":1077.09,"body":"closer to 1 than three-fourths."},{"speaker":"Pam","startTime":1077.3,"endTime":1079.52,"body":"And so, now, I have this"},{"speaker":"Pam","startTime":1077.3,"endTime":1079.52,"body":"comparison. Three-fourths is"},{"speaker":"Pam","startTime":1079.52,"endTime":1082.37,"body":"smaller than five-sixths. So,"},{"speaker":"Pam","startTime":1079.52,"endTime":1082.37,"body":"when I ask \"How many"},{"speaker":"Pam","startTime":1082.4,"endTime":1086.33,"body":"three-fourths are in"},{"speaker":"Pam","startTime":1082.4,"endTime":1086.33,"body":"five-sixths?\" I should get an"},{"speaker":"Pam","startTime":1086.33,"endTime":1090.35,"body":"answer of \"Well, at least one."},{"speaker":"Pam","startTime":1086.33,"endTime":1090.35,"body":"One and some extra.\" Right?"},{"speaker":"Kim","startTime":1091.46,"endTime":1091.49,"body":"Mmhmm."},{"speaker":"Pam","startTime":1091.52,"endTime":1092.9,"body":"Did I say that right? Okay,"},{"speaker":"Pam","startTime":1091.52,"endTime":1092.9,"body":"cool."},{"speaker":"Kim","startTime":1092.93,"endTime":1093.41,"body":"Yeah."},{"speaker":"Pam","startTime":1093.5,"endTime":1095.93,"body":"Then, I could go to what"},{"speaker":"Pam","startTime":1093.5,"endTime":1095.93,"body":"you were talking about that"},{"speaker":"Pam","startTime":1095.93,"endTime":1095.96,"body":"(unclear)."},{"speaker":"Kim","startTime":1095.99,"endTime":1098.39,"body":"Well, I think I compared as"},{"speaker":"Kim","startTime":1095.99,"endTime":1098.39,"body":"well. I just compared it in a"},{"speaker":"Kim","startTime":1098.39,"endTime":1101.36,"body":"different way than you did. I"},{"speaker":"Kim","startTime":1098.39,"endTime":1101.36,"body":"think it's the same. Like, we"},{"speaker":"Kim","startTime":1101.36,"endTime":1103.31,"body":"were both seeking to compare."},{"speaker":"Pam","startTime":1103.97,"endTime":1110.0,"body":"Oh, interesting. What is"},{"speaker":"Pam","startTime":1103.97,"endTime":1110.0,"body":"3/4 of 6? I think your way is"},{"speaker":"Pam","startTime":1110.0,"endTime":1112.19,"body":"more multiplicative. I'll just"},{"speaker":"Pam","startTime":1110.0,"endTime":1112.19,"body":"say that. Mine was less"},{"speaker":"Pam","startTime":1112.19,"endTime":1114.95,"body":"multiplicative. Mine was more"},{"speaker":"Pam","startTime":1112.19,"endTime":1114.95,"body":"based on the definition of"},{"speaker":"Pam","startTime":1114.95,"endTime":1117.92,"body":"fractions, and I think yours was"},{"speaker":"Pam","startTime":1114.95,"endTime":1117.92,"body":"a bit more multiplicative. So,"},{"speaker":"Pam","startTime":1117.92,"endTime":1120.26,"body":"you said three-fourths of six."},{"speaker":"Pam","startTime":1117.92,"endTime":1120.26,"body":"Why would you ask three-fourths"},{"speaker":"Pam","startTime":1120.26,"endTime":1120.74,"body":"of six?"},{"speaker":"Kim","startTime":1121.58,"endTime":1126.38,"body":"Because I know I have five,"},{"speaker":"Kim","startTime":1121.58,"endTime":1126.38,"body":"1/6s, and I want to know if"},{"speaker":"Kim","startTime":1126.38,"endTime":1130.64,"body":"that's more than three-fourths"},{"speaker":"Kim","startTime":1126.38,"endTime":1130.64,"body":"or less than three-fourths. So,"},{"speaker":"Kim","startTime":1130.64,"endTime":1135.92,"body":"I thought about what is 3/4 of"},{"speaker":"Kim","startTime":1130.64,"endTime":1135.92,"body":"6, and I know that it's 4 and a"},{"speaker":"Kim","startTime":1135.92,"endTime":1142.91,"body":"1/2. So, if four and a half of 6"},{"speaker":"Kim","startTime":1135.92,"endTime":1142.91,"body":"is 3/4 than 5/6 is going to be"},{"speaker":"Kim","startTime":1143.51,"endTime":1144.89,"body":"more than 3/4."},{"speaker":"Pam","startTime":1144.95,"endTime":1147.71,"body":"I love it. That's brilliant"},{"speaker":"Pam","startTime":1144.95,"endTime":1147.71,"body":"thinking. Well done. Alright,"},{"speaker":"Pam","startTime":1147.71,"endTime":1148.13,"body":"cool."},{"speaker":"Kim","startTime":1148.25,"endTime":1148.97,"body":"Moving on."},{"speaker":"Pam","startTime":1149.09,"endTime":1152.12,"body":"So, the upshot of this"},{"speaker":"Pam","startTime":1149.09,"endTime":1152.12,"body":"problem is, we can look at a"},{"speaker":"Pam","startTime":1152.12,"endTime":1155.0,"body":"cranky problem like five-sixths"},{"speaker":"Pam","startTime":1152.12,"endTime":1155.0,"body":"divided by three-fourths, and we"},{"speaker":"Pam","startTime":1155.0,"endTime":1157.85,"body":"can say to ourselves, \"I wonder"},{"speaker":"Pam","startTime":1155.0,"endTime":1157.85,"body":"if we can find the same kind of"},{"speaker":"Pam","startTime":1157.85,"endTime":1161.51,"body":"pieces, and then deal with that"},{"speaker":"Pam","startTime":1157.85,"endTime":1161.51,"body":"problem.\" So, you said, \"Yeah, I"},{"speaker":"Pam","startTime":1161.51,"endTime":1163.28,"body":"know ten-twelfths divided by"},{"speaker":"Pam","startTime":1161.51,"endTime":1163.28,"body":"nine-twelfths. Bam! I can think"},{"speaker":"Pam","startTime":1163.28,"endTime":1165.08,"body":"about that like 10 divided by"},{"speaker":"Pam","startTime":1163.28,"endTime":1165.08,"body":"9.\" Woah!"},{"speaker":"Kim","startTime":1165.08,"endTime":1165.56,"body":"Yep."},{"speaker":"Pam","startTime":1165.62,"endTime":1167.48,"body":"Cool. Last problem set."},{"speaker":"Kim","startTime":1168.11,"endTime":1168.38,"body":"Okay."},{"speaker":"Pam","startTime":1168.38,"endTime":1170.6,"body":"9 divided by 4. What's 9"},{"speaker":"Pam","startTime":1168.38,"endTime":1170.6,"body":"divided by 4?"},{"speaker":"Kim","startTime":1173.24,"endTime":1175.61,"body":"I just took a deep breath"},{"speaker":"Kim","startTime":1173.24,"endTime":1175.61,"body":"(unclear) a lot of talking."},{"speaker":"Kim","startTime":1175.82,"endTime":1177.08,"body":"Okay, so I know..."},{"speaker":"Pam","startTime":1177.11,"endTime":1177.8,"body":"A lot of thinking."},{"speaker":"Kim","startTime":1178.16,"endTime":1184.25,"body":"Yeah. So, I'm going to say"},{"speaker":"Kim","startTime":1178.16,"endTime":1184.25,"body":"that that is... I can fit two 4s"},{"speaker":"Kim","startTime":1184.37,"endTime":1192.59,"body":"in 9. Two 4s in 9. So, then I'm"},{"speaker":"Kim","startTime":1184.37,"endTime":1192.59,"body":"going to say 2 and a 1/4."},{"speaker":"Pam","startTime":1194.15,"endTime":1198.65,"body":"2 and 1/4. Because two 4s"},{"speaker":"Pam","startTime":1194.15,"endTime":1198.65,"body":"is 8, so you've got 1 leftover."},{"speaker":"Kim","startTime":1199.04,"endTime":1199.37,"body":"Yep."},{"speaker":"Pam","startTime":1199.4,"endTime":1202.19,"body":"And then, you're thinking"},{"speaker":"Pam","startTime":1199.4,"endTime":1202.19,"body":"about how many 4s are in 1?"},{"speaker":"Kim","startTime":1202.49,"endTime":1202.97,"body":"Yep."},{"speaker":"Pam","startTime":1203.18,"endTime":1204.83,"body":"And you're like, \"That's a"},{"speaker":"Pam","startTime":1203.18,"endTime":1204.83,"body":"fourth, one-fourth.\""},{"speaker":"Kim","startTime":1204.86,"endTime":1205.34,"body":"Yep."},{"speaker":"Pam","startTime":1205.73,"endTime":1209.15,"body":"Okay, cool. So, 9 divided"},{"speaker":"Pam","startTime":1205.73,"endTime":1209.15,"body":"by 4 is 2 and a 1/4. Could I"},{"speaker":"Pam","startTime":1209.15,"endTime":1212.63,"body":"also remind you that we can"},{"speaker":"Pam","startTime":1209.15,"endTime":1212.63,"body":"think about that as 9/4?"},{"speaker":"Kim","startTime":1212.66,"endTime":1213.2,"body":"Yep."},{"speaker":"Pam","startTime":1213.56,"endTime":1217.31,"body":"So, 9 divided by 4 is 9/4,"},{"speaker":"Pam","startTime":1213.56,"endTime":1217.31,"body":"2 and a 1/4. Those are all"},{"speaker":"Pam","startTime":1217.31,"endTime":1218.75,"body":"equivalent. We want all that"},{"speaker":"Pam","startTime":1217.31,"endTime":1218.75,"body":"going on."},{"speaker":"Kim","startTime":1218.75,"endTime":1218.84,"body":"Yep."},{"speaker":"Pam","startTime":1218.84,"endTime":1222.38,"body":"Cool. Next question. What's"},{"speaker":"Pam","startTime":1218.84,"endTime":1222.38,"body":"nine-twelfths divided by"},{"speaker":"Pam","startTime":1222.38,"endTime":1223.58,"body":"four-twelfths."},{"speaker":"Kim","startTime":1225.14,"endTime":1231.02,"body":"That's 9. It's similar to 9"},{"speaker":"Kim","startTime":1225.14,"endTime":1231.02,"body":"divided by 4. So, it's still"},{"speaker":"Kim","startTime":1231.02,"endTime":1232.07,"body":"going to be 2 and a 1/4."},{"speaker":"Pam","startTime":1233.57,"endTime":1234.26,"body":"Because?"},{"speaker":"Kim","startTime":1235.91,"endTime":1243.26,"body":"Because I have 9 somethings"},{"speaker":"Kim","startTime":1235.91,"endTime":1243.26,"body":"divided by 4 somethings, so"},{"speaker":"Kim","startTime":1243.26,"endTime":1246.95,"body":"that's the same as 9 divided by"},{"speaker":"Kim","startTime":1243.26,"endTime":1246.95,"body":"4. I could fit four 1/12s into"},{"speaker":"Kim","startTime":1246.95,"endTime":1250.82,"body":"nine-twelfths, twice. And a"},{"speaker":"Kim","startTime":1246.95,"endTime":1250.82,"body":"fourth again."},{"speaker":"Pam","startTime":1251.6,"endTime":1256.55,"body":"Another fourth leftover."},{"speaker":"Pam","startTime":1251.6,"endTime":1256.55,"body":"Cool. So, similarly, if I know"},{"speaker":"Pam","startTime":1256.55,"endTime":1260.03,"body":"something about 9 divided by 4,"},{"speaker":"Pam","startTime":1256.55,"endTime":1260.03,"body":"then I can reason about 9"},{"speaker":"Pam","startTime":1260.03,"endTime":1263.66,"body":"anythings divided by 4"},{"speaker":"Pam","startTime":1260.03,"endTime":1263.66,"body":"anythings, would also have that"},{"speaker":"Pam","startTime":1263.66,"endTime":1269.45,"body":"equivalent 9/4 solution. Nice."},{"speaker":"Pam","startTime":1263.66,"endTime":1269.45,"body":"Last problem. Three-fourths"},{"speaker":"Pam","startTime":1269.69,"endTime":1273.59,"body":"divided by one-third. How many"},{"speaker":"Pam","startTime":1269.69,"endTime":1273.59,"body":"one-thirds are in three-fourths?"},{"speaker":"Kim","startTime":1274.64,"endTime":1275.42,"body":"That's nice."},{"speaker":"Pam","startTime":1277.49,"endTime":1277.64,"body":"[Pam laughs]."},{"speaker":"Kim","startTime":1277.67,"endTime":1279.98,"body":"No, it really is because"},{"speaker":"Kim","startTime":1277.67,"endTime":1279.98,"body":"I'm thinking about how I"},{"speaker":"Kim","startTime":1280.31,"endTime":1284.81,"body":"could...I can scale both those"},{"speaker":"Kim","startTime":1280.31,"endTime":1284.81,"body":"up, and I could use twelfths. I"},{"speaker":"Kim","startTime":1284.81,"endTime":1286.97,"body":"could use a couple of different"},{"speaker":"Kim","startTime":1284.81,"endTime":1286.97,"body":"things, but I'm going to go with"},{"speaker":"Kim","startTime":1286.97,"endTime":1292.28,"body":"twelfths. And if I scale the"},{"speaker":"Kim","startTime":1286.97,"endTime":1292.28,"body":"three-fourths, that would be"},{"speaker":"Kim","startTime":1292.28,"endTime":1296.48,"body":"equivalent to nine-twelfths. And"},{"speaker":"Kim","startTime":1292.28,"endTime":1296.48,"body":"if I scale the one-third to"},{"speaker":"Kim","startTime":1296.48,"endTime":1298.79,"body":"twelfth, that would be"},{"speaker":"Kim","startTime":1296.48,"endTime":1298.79,"body":"four-twelfths. And then, I land"},{"speaker":"Kim","startTime":1298.79,"endTime":1303.08,"body":"back in the same place where"},{"speaker":"Kim","startTime":1298.79,"endTime":1303.08,"body":"it's 9/12 divided by 4/12, or 9"},{"speaker":"Kim","startTime":1303.08,"endTime":1305.3,"body":"divided by 4, which is 2 and a"},{"speaker":"Kim","startTime":1303.08,"endTime":1305.3,"body":"1/4."},{"speaker":"Pam","startTime":1305.87,"endTime":1309.38,"body":"And so, you're saying the"},{"speaker":"Pam","startTime":1305.87,"endTime":1309.38,"body":"answer to 3/4 divided by 1/3 is"},{"speaker":"Pam","startTime":1309.38,"endTime":1311.93,"body":"2 and a 1/4 because it's"},{"speaker":"Pam","startTime":1309.38,"endTime":1311.93,"body":"equivalent to the two problems"},{"speaker":"Pam","startTime":1311.93,"endTime":1312.56,"body":"that we did before?"},{"speaker":"Kim","startTime":1312.59,"endTime":1312.95,"body":"Yeah."},{"speaker":"Pam","startTime":1313.55,"endTime":1314.42,"body":"Or 9/4. Either one."},{"speaker":"Kim","startTime":1315.02,"endTime":1317.06,"body":"I'm going to go looking for"},{"speaker":"Kim","startTime":1315.02,"endTime":1317.06,"body":"problems like these."},{"speaker":"Pam","startTime":1318.47,"endTime":1325.55,"body":"Nice. So, ya'll, fraction"},{"speaker":"Pam","startTime":1318.47,"endTime":1325.55,"body":"division is figure-out-able, and"},{"speaker":"Pam","startTime":1325.58,"endTime":1330.65,"body":"we want to spend time helping"},{"speaker":"Pam","startTime":1325.58,"endTime":1330.65,"body":"students reason about fractions,"},{"speaker":"Pam","startTime":1330.65,"endTime":1334.49,"body":"reason about partitive and"},{"speaker":"Pam","startTime":1330.65,"endTime":1334.49,"body":"quotitive. And we've only been"},{"speaker":"Pam","startTime":1334.49,"endTime":1336.92,"body":"kind of focusing on quotitive"},{"speaker":"Pam","startTime":1334.49,"endTime":1336.92,"body":"division. We will do more"},{"speaker":"Pam","startTime":1336.92,"endTime":1339.38,"body":"episodes later where we focus on"},{"speaker":"Pam","startTime":1336.92,"endTime":1339.38,"body":"partitive division for"},{"speaker":"Pam","startTime":1339.38,"endTime":1343.22,"body":"fractions. But I wanted to kind"},{"speaker":"Pam","startTime":1339.38,"endTime":1343.22,"body":"of think about this Problem"},{"speaker":"Pam","startTime":1343.22,"endTime":1345.2,"body":"String that we did today, and I"},{"speaker":"Pam","startTime":1343.22,"endTime":1345.2,"body":"want to take a slightly"},{"speaker":"Pam","startTime":1345.2,"endTime":1348.47,"body":"different what we just kind of"},{"speaker":"Pam","startTime":1345.2,"endTime":1348.47,"body":"ended with. If I have fractions"},{"speaker":"Pam","startTime":1348.47,"endTime":1351.5,"body":"that are kind of gnarly like"},{"speaker":"Pam","startTime":1348.47,"endTime":1351.5,"body":"five-sixths divided by"},{"speaker":"Pam","startTime":1351.5,"endTime":1355.07,"body":"three-fourths or three-fourths"},{"speaker":"Pam","startTime":1351.5,"endTime":1355.07,"body":"divided by one-third. We said to"},{"speaker":"Pam","startTime":1355.07,"endTime":1358.19,"body":"ourselves, \"Mmm, I wonder if I"},{"speaker":"Pam","startTime":1355.07,"endTime":1358.19,"body":"could find equivalent, if I"},{"speaker":"Pam","startTime":1358.19,"endTime":1361.37,"body":"create an equivalent problem"},{"speaker":"Pam","startTime":1358.19,"endTime":1361.37,"body":"where I could think about the"},{"speaker":"Pam","startTime":1361.4,"endTime":1365.57,"body":"same denominator, same kind of"},{"speaker":"Pam","startTime":1361.4,"endTime":1365.57,"body":"pieces. Then, I could kind of"},{"speaker":"Pam","startTime":1365.57,"endTime":1367.55,"body":"reason about it.\" Like that last"},{"speaker":"Pam","startTime":1365.57,"endTime":1367.55,"body":"one. Three-fourths divided by"},{"speaker":"Pam","startTime":1367.55,"endTime":1370.16,"body":"one-third. Bam! I can think"},{"speaker":"Pam","startTime":1367.55,"endTime":1370.16,"body":"about that as equivalent to"},{"speaker":"Pam","startTime":1370.19,"endTime":1372.35,"body":"nine-twelfths divided by"},{"speaker":"Pam","startTime":1370.19,"endTime":1372.35,"body":"four-twelfths. Oh. Well, that's"},{"speaker":"Pam","startTime":1372.35,"endTime":1375.5,"body":"equivalent to 9 divided by 4"},{"speaker":"Pam","startTime":1372.35,"endTime":1375.5,"body":"anything. 9 anythings divided by"},{"speaker":"Pam","startTime":1375.5,"endTime":1377.75,"body":"four anythings. And so, we just"},{"speaker":"Pam","startTime":1375.5,"endTime":1377.75,"body":"sort of think about that. If I"},{"speaker":"Pam","startTime":1377.75,"endTime":1381.26,"body":"could just maybe leave you with,"},{"speaker":"Pam","startTime":1377.75,"endTime":1381.26,"body":"what we just did was thinking"},{"speaker":"Pam","startTime":1381.26,"endTime":1384.35,"body":"about finding common"},{"speaker":"Pam","startTime":1381.26,"endTime":1384.35,"body":"denominators in order to divide."},{"speaker":"Pam","startTime":1385.01,"endTime":1389.84,"body":"But what we didn't do was tell"},{"speaker":"Pam","startTime":1385.01,"endTime":1389.84,"body":"kids that, \"Hey, when you"},{"speaker":"Pam","startTime":1389.84,"endTime":1392.75,"body":"divide, find common"},{"speaker":"Pam","startTime":1389.84,"endTime":1392.75,"body":"denominators.\" It's not a rule"},{"speaker":"Pam","startTime":1392.75,"endTime":1395.6,"body":"that we're telling kids. It's"},{"speaker":"Pam","startTime":1392.75,"endTime":1395.6,"body":"relationships we're developing"},{"speaker":"Pam","startTime":1395.6,"endTime":1398.3,"body":"as we actually reason through"},{"speaker":"Pam","startTime":1395.6,"endTime":1398.3,"body":"the math. And you might be like,"},{"speaker":"Pam","startTime":1398.57,"endTime":1401.54,"body":"\"Pam, why do we want to stress"},{"speaker":"Pam","startTime":1398.57,"endTime":1401.54,"body":"kids out? Can't we just tell"},{"speaker":"Pam","startTime":1401.54,"endTime":1405.89,"body":"them what to do and let them do"},{"speaker":"Pam","startTime":1401.54,"endTime":1405.89,"body":"it? It's so much easier.\" Well,"},{"speaker":"Pam","startTime":1406.13,"endTime":1409.82,"body":"what's your goal? If your goal"},{"speaker":"Pam","startTime":1406.13,"endTime":1409.82,"body":"is to get answers in the easiest"},{"speaker":"Pam","startTime":1409.82,"endTime":1415.19,"body":"way possible, why are you not"},{"speaker":"Pam","startTime":1409.82,"endTime":1415.19,"body":"just using ChatGPT, or Google,"},{"speaker":"Pam","startTime":1415.22,"endTime":1419.48,"body":"or a calculator, or... Like, if"},{"speaker":"Pam","startTime":1415.22,"endTime":1419.48,"body":"your goal is to get the answers"},{"speaker":"Pam","startTime":1419.48,"endTime":1424.31,"body":"the easiest way possible, then"},{"speaker":"Pam","startTime":1419.48,"endTime":1424.31,"body":"go for it. But if your goal is"},{"speaker":"Pam","startTime":1424.31,"endTime":1427.46,"body":"to develop reasoners and"},{"speaker":"Pam","startTime":1424.31,"endTime":1427.46,"body":"mathematicians and help kids"},{"speaker":"Pam","startTime":1427.46,"endTime":1430.22,"body":"think more and more"},{"speaker":"Pam","startTime":1427.46,"endTime":1430.22,"body":"sophisticatedly, then division"},{"speaker":"Pam","startTime":1430.22,"endTime":1434.72,"body":"of fractions is figure-out-able."},{"speaker":"Pam","startTime":1430.22,"endTime":1434.72,"body":"Y'all thanks for tuning in and"},{"speaker":"Pam","startTime":1434.72,"endTime":1437.81,"body":"teaching more and more Real"},{"speaker":"Pam","startTime":1434.72,"endTime":1437.81,"body":"Math. To find out more about the"},{"speaker":"Pam","startTime":1437.81,"endTime":1439.43,"body":"Math is Figure-Out-Able"},{"speaker":"Pam","startTime":1437.81,"endTime":1439.43,"body":"movement, visit"},{"speaker":"Pam","startTime":1439.88,"endTime":1443.75,"body":"mathisfigureoutable.com. Thanks"},{"speaker":"Pam","startTime":1439.88,"endTime":1443.75,"body":"for joining us, and let's keep"},{"speaker":"Pam","startTime":1443.75,"endTime":1446.27,"body":"spreading the word that Math is"},{"speaker":"Pam","startTime":1443.75,"endTime":1446.27,"body":"Figure-Out-Able!"}]}