{"version":"1.0.0","segments":[{"speaker":"Pam Harris","startTime":1.17,"endTime":3.51,"body":"Hey fellow"},{"speaker":"Pam Harris","startTime":1.17,"endTime":3.51,"body":"mathematicians. Welcome to the"},{"speaker":"Pam Harris","startTime":3.51,"endTime":7.35,"body":"podcast where Math is"},{"speaker":"Pam Harris","startTime":3.51,"endTime":7.35,"body":"Figure-Out-Able. I'm Pam."},{"speaker":"Kim Montague","startTime":7.59,"endTime":8.25,"body":"And I'm Kim."},{"speaker":"Pam Harris","startTime":8.67,"endTime":10.92,"body":"And you found a"},{"speaker":"Pam Harris","startTime":8.67,"endTime":10.92,"body":"place where math is not about"},{"speaker":"Pam Harris","startTime":10.92,"endTime":13.98,"body":"memorizing and mimicking,"},{"speaker":"Pam Harris","startTime":10.92,"endTime":13.98,"body":"waiting to be told or shown what"},{"speaker":"Pam Harris","startTime":13.98,"endTime":17.55,"body":"to do. But it's about making"},{"speaker":"Pam Harris","startTime":13.98,"endTime":17.55,"body":"sense of problems, noticing"},{"speaker":"Pam Harris","startTime":17.55,"endTime":21.24,"body":"patterns and reasoning using"},{"speaker":"Pam Harris","startTime":17.55,"endTime":21.24,"body":"mathematical relationships. We"},{"speaker":"Pam Harris","startTime":21.24,"endTime":25.89,"body":"can mentor students to think and"},{"speaker":"Pam Harris","startTime":21.24,"endTime":25.89,"body":"reason like mathematicians, not"},{"speaker":"Pam Harris","startTime":25.89,"endTime":29.37,"body":"only our algorithms and step by"},{"speaker":"Pam Harris","startTime":25.89,"endTime":29.37,"body":"step procedures, not"},{"speaker":"Pam Harris","startTime":29.37,"endTime":32.58,"body":"particularly helpful in teaching"},{"speaker":"Pam Harris","startTime":29.37,"endTime":32.58,"body":"mathematics. But rotely"},{"speaker":"Pam Harris","startTime":32.61,"endTime":36.63,"body":"repeating those steps actually"},{"speaker":"Pam Harris","startTime":32.61,"endTime":36.63,"body":"keep students from being the"},{"speaker":"Pam Harris","startTime":36.63,"endTime":38.1,"body":"mathematicians they can be."},{"speaker":"Kim Montague","startTime":38.88,"endTime":41.28,"body":"So we get some"},{"speaker":"Kim Montague","startTime":38.88,"endTime":41.28,"body":"great ideas from all over the"},{"speaker":"Kim Montague","startTime":41.28,"endTime":44.73,"body":"place about what to chat about"},{"speaker":"Kim Montague","startTime":41.28,"endTime":44.73,"body":"on the podcast. Right? And so"},{"speaker":"Kim Montague","startTime":44.76,"endTime":47.28,"body":"this week, we thought we would"},{"speaker":"Kim Montague","startTime":44.76,"endTime":47.28,"body":"talk about a tweet that we"},{"speaker":"Kim Montague","startTime":47.28,"endTime":50.76,"body":"actually saw quite a while back,"},{"speaker":"Kim Montague","startTime":47.28,"endTime":50.76,"body":"but it's popped up in"},{"speaker":"Kim Montague","startTime":50.76,"endTime":55.38,"body":"conversation between us several"},{"speaker":"Kim Montague","startTime":50.76,"endTime":55.38,"body":"times, as we talk about"},{"speaker":"Kim Montague","startTime":55.38,"endTime":59.31,"body":"subtraction. So Pam, we've"},{"speaker":"Kim Montague","startTime":55.38,"endTime":59.31,"body":"actually joked about this a few"},{"speaker":"Kim Montague","startTime":59.31,"endTime":63.27,"body":"times, because sometimes as we"},{"speaker":"Kim Montague","startTime":59.31,"endTime":63.27,"body":"talk about this particular type"},{"speaker":"Kim Montague","startTime":63.27,"endTime":66.21,"body":"of problem, one of us will go,"},{"speaker":"Kim Montague","startTime":63.27,"endTime":66.21,"body":"it's this right?"},{"speaker":"Pam Harris","startTime":67.35,"endTime":71.01,"body":"Yeah, let's be"},{"speaker":"Pam Harris","startTime":67.35,"endTime":71.01,"body":"clear, it's usually me. It's"},{"speaker":"Pam Harris","startTime":71.01,"endTime":74.61,"body":"usually me going, \"Hey, is that,"},{"speaker":"Pam Harris","startTime":71.01,"endTime":74.61,"body":"is that...\" and we'll tell you,"},{"speaker":"Pam Harris","startTime":74.64,"endTime":77.91,"body":"we actually have a name that"},{"speaker":"Pam Harris","startTime":74.64,"endTime":77.91,"body":"we've tossed around, but we"},{"speaker":"Pam Harris","startTime":77.91,"endTime":81.72,"body":"don't want to give it away right"},{"speaker":"Pam Harris","startTime":77.91,"endTime":81.72,"body":"now. So, David Marain, I hope I"},{"speaker":"Pam Harris","startTime":81.72,"endTime":84.78,"body":"am saying your last name"},{"speaker":"Pam Harris","startTime":81.72,"endTime":84.78,"body":"correctly, David, is a guy that"},{"speaker":"Pam Harris","startTime":84.9,"endTime":87.57,"body":"I've gone back and forth on"},{"speaker":"Pam Harris","startTime":84.9,"endTime":87.57,"body":"Twitter with and post some"},{"speaker":"Pam Harris","startTime":87.57,"endTime":92.1,"body":"excellent questions. So"},{"speaker":"Pam Harris","startTime":87.57,"endTime":92.1,"body":"@dmarain, feel free to follow"},{"speaker":"Pam Harris","startTime":92.1,"endTime":95.19,"body":"him. He's got some good things"},{"speaker":"Pam Harris","startTime":92.1,"endTime":95.19,"body":"that he posts. But quite a while"},{"speaker":"Pam Harris","startTime":95.19,"endTime":100.02,"body":"ago, he posted, \"Children learn"},{"speaker":"Pam Harris","startTime":95.19,"endTime":100.02,"body":"at an early age that counting a"},{"speaker":"Pam Harris","startTime":100.02,"endTime":103.83,"body":"number of objects starts from"},{"speaker":"Pam Harris","startTime":100.02,"endTime":103.83,"body":"one and the last number you say"},{"speaker":"Pam Harris","startTime":103.83,"endTime":108.45,"body":"is how many. However, both"},{"speaker":"Pam Harris","startTime":103.83,"endTime":108.45,"body":"children and adults fall into"},{"speaker":"Pam Harris","startTime":108.45,"endTime":112.41,"body":"the 'off by one trap', when"},{"speaker":"Pam Harris","startTime":108.45,"endTime":112.41,"body":"presented with a problem, like"},{"speaker":"Pam Harris","startTime":112.56,"endTime":116.31,"body":"how many whole numbers are there"},{"speaker":"Pam Harris","startTime":112.56,"endTime":116.31,"body":"from 13 through 23? With the"},{"speaker":"Pam Harris","startTime":116.31,"endTime":121.5,"body":"instinctive response being 10."},{"speaker":"Pam Harris","startTime":116.31,"endTime":121.5,"body":"What are some of your favorite"},{"speaker":"Pam Harris","startTime":121.5,"endTime":124.05,"body":"ways to convey the concept?\""},{"speaker":"Pam Harris","startTime":121.5,"endTime":124.05,"body":"Now, you may or may not have"},{"speaker":"Pam Harris","startTime":124.05,"endTime":126.63,"body":"caught that. I read that kind of"},{"speaker":"Pam Harris","startTime":124.05,"endTime":126.63,"body":"fast, and I didn't really stop"},{"speaker":"Pam Harris","startTime":126.63,"endTime":130.02,"body":"and explain or anything. But"},{"speaker":"Pam Harris","startTime":126.63,"endTime":130.02,"body":"when I read that tweet, it was"},{"speaker":"Pam Harris","startTime":130.02,"endTime":131.76,"body":"one of those times where I was"},{"speaker":"Pam Harris","startTime":130.02,"endTime":131.76,"body":"like, \"Kim, Kim, look,"},{"speaker":"Pam Harris","startTime":131.76,"endTime":133.92,"body":"somebody's talking about it!\""},{"speaker":"Pam Harris","startTime":131.76,"endTime":133.92,"body":"this thing that we keep, you"},{"speaker":"Pam Harris","startTime":133.92,"endTime":137.76,"body":"know, come up between us and"},{"speaker":"Pam Harris","startTime":133.92,"endTime":137.76,"body":"everything. And so he asked,"},{"speaker":"Pam Harris","startTime":137.76,"endTime":139.92,"body":"\"What are some of the favorite"},{"speaker":"Pam Harris","startTime":137.76,"endTime":139.92,"body":"ways to convey the concept?\""},{"speaker":"Pam Harris","startTime":139.95,"endTime":144.81,"body":"Wow, listeners, I'm gonna"},{"speaker":"Pam Harris","startTime":139.95,"endTime":144.81,"body":"probably write a Problem String,"},{"speaker":"Pam Harris","startTime":144.84,"endTime":147.81,"body":"like chances are, if you asked"},{"speaker":"Pam Harris","startTime":144.84,"endTime":147.81,"body":"me for a way to convey the"},{"speaker":"Pam Harris","startTime":147.81,"endTime":150.81,"body":"concept, chances are high, I'm"},{"speaker":"Pam Harris","startTime":147.81,"endTime":150.81,"body":"going to write a Problem String"},{"speaker":"Pam Harris","startTime":150.81,"endTime":154.53,"body":"to do that. And so I did. So"},{"speaker":"Pam Harris","startTime":150.81,"endTime":154.53,"body":"let's do a Problem String today."},{"speaker":"Pam Harris","startTime":154.56,"endTime":156.78,"body":"Again, don't feel like you have"},{"speaker":"Pam Harris","startTime":154.56,"endTime":156.78,"body":"to go listen to that, again, to"},{"speaker":"Pam Harris","startTime":156.78,"endTime":158.61,"body":"understand what it is because"},{"speaker":"Pam Harris","startTime":156.78,"endTime":158.61,"body":"we're going to do a Problem"},{"speaker":"Pam Harris","startTime":158.61,"endTime":161.7,"body":"String. And by the end of it, I"},{"speaker":"Pam Harris","startTime":158.61,"endTime":161.7,"body":"think you'll understand what"},{"speaker":"Pam Harris","startTime":161.7,"endTime":165.24,"body":"David was talking about. Yeah."},{"speaker":"Pam Harris","startTime":161.7,"endTime":165.24,"body":"So usually in the podcast, when"},{"speaker":"Pam Harris","startTime":165.24,"endTime":168.54,"body":"we do a Problem String, I'll ask"},{"speaker":"Pam Harris","startTime":165.24,"endTime":168.54,"body":"the questions. And then Kim will"},{"speaker":"Pam Harris","startTime":168.54,"endTime":171.42,"body":"talk about her thinking. And"},{"speaker":"Pam Harris","startTime":168.54,"endTime":171.42,"body":"we'll sort of, you know, kind of"},{"speaker":"Pam Harris","startTime":171.42,"endTime":174.69,"body":"go back and forth and discuss"},{"speaker":"Pam Harris","startTime":171.42,"endTime":174.69,"body":"how she's, what her strategy is,"},{"speaker":"Pam Harris","startTime":174.69,"endTime":179.4,"body":"or vice versa. But that won't"},{"speaker":"Pam Harris","startTime":174.69,"endTime":179.4,"body":"work so well today, because both"},{"speaker":"Pam Harris","startTime":179.4,"endTime":182.73,"body":"Kim and I have constructed a"},{"speaker":"Pam Harris","startTime":179.4,"endTime":182.73,"body":"strategy for this, for these"},{"speaker":"Pam Harris","startTime":182.73,"endTime":186.54,"body":"problems. It won't be super"},{"speaker":"Pam Harris","startTime":182.73,"endTime":186.54,"body":"helpful to just tell you that."},{"speaker":"Pam Harris","startTime":186.54,"endTime":190.2,"body":"We want to help construct that"},{"speaker":"Pam Harris","startTime":186.54,"endTime":190.2,"body":"strategy. Here's the string."},{"speaker":"Pam Harris","startTime":190.23,"endTime":196.32,"body":"Kim, first problem is you are on"},{"speaker":"Pam Harris","startTime":190.23,"endTime":196.32,"body":"page 17 in the booklet. There"},{"speaker":"Pam Harris","startTime":196.32,"endTime":200.67,"body":"are 23 pages in this small"},{"speaker":"Pam Harris","startTime":196.32,"endTime":200.67,"body":"booklet. How many pages do you"},{"speaker":"Pam Harris","startTime":200.67,"endTime":201.51,"body":"have left to read?"},{"speaker":"Kim Montague","startTime":202.98,"endTime":206.19,"body":"Okay, so I would"},{"speaker":"Kim Montague","startTime":202.98,"endTime":206.19,"body":"expect that some students would"},{"speaker":"Kim Montague","startTime":206.19,"endTime":210.93,"body":"think about that like a"},{"speaker":"Kim Montague","startTime":206.19,"endTime":210.93,"body":"subtraction problem and say 23"},{"speaker":"Kim Montague","startTime":211.38,"endTime":214.32,"body":"minus 17. And then, you know,"},{"speaker":"Kim Montague","startTime":211.38,"endTime":214.32,"body":"they could solve it a couple of"},{"speaker":"Kim Montague","startTime":214.32,"endTime":217.59,"body":"different ways. So they might"},{"speaker":"Kim Montague","startTime":214.32,"endTime":217.59,"body":"start with 23 on the number"},{"speaker":"Kim Montague","startTime":217.59,"endTime":222.87,"body":"line. And you know, I like Over,"},{"speaker":"Kim Montague","startTime":217.59,"endTime":222.87,"body":"so they might subtract 20 to get"},{"speaker":"Kim Montague","startTime":222.87,"endTime":226.86,"body":"to three, and then realize they"},{"speaker":"Kim Montague","startTime":222.87,"endTime":226.86,"body":"removed too much. So then they"},{"speaker":"Kim Montague","startTime":226.86,"endTime":230.1,"body":"add three back on to get six,"},{"speaker":"Kim Montague","startTime":226.86,"endTime":230.1,"body":"six pages."},{"speaker":"Kim Montague","startTime":232.68,"endTime":238.29,"body":"Somebody else might say. \"What"},{"speaker":"Kim Montague","startTime":232.68,"endTime":238.29,"body":"is the distance between 17 and"},{"speaker":"Kim Montague","startTime":238.29,"endTime":244.11,"body":"23?\" And so I have to read six"},{"speaker":"Kim Montague","startTime":238.29,"endTime":244.11,"body":"pages, because that's the kind"},{"speaker":"Kim Montague","startTime":244.11,"endTime":246.84,"body":"of the gap between 17 and 23."},{"speaker":"Pam Harris","startTime":247.14,"endTime":250.44,"body":"So you think 17 up"},{"speaker":"Pam Harris","startTime":247.14,"endTime":250.44,"body":"to 20? Twenty up to 23? That's"},{"speaker":"Pam Harris","startTime":250.44,"endTime":254.1,"body":"the two threes and that's six."},{"speaker":"Pam Harris","startTime":250.44,"endTime":254.1,"body":"That's kind of, and the context"},{"speaker":"Pam Harris","startTime":254.1,"endTime":257.1,"body":"kind of calls for that kind of"},{"speaker":"Pam Harris","startTime":254.1,"endTime":257.1,"body":"looking between 17 and 23. Cool."},{"speaker":"Pam Harris","startTime":257.85,"endTime":261.3,"body":"So as a teacher, we would"},{"speaker":"Pam Harris","startTime":257.85,"endTime":261.3,"body":"probably represent one or at"},{"speaker":"Pam Harris","startTime":261.3,"endTime":265.02,"body":"least the distance one, maybe"},{"speaker":"Pam Harris","startTime":261.3,"endTime":265.02,"body":"the removal one, but we would"},{"speaker":"Pam Harris","startTime":265.02,"endTime":267.12,"body":"expect students to kind of be"},{"speaker":"Pam Harris","startTime":265.02,"endTime":267.12,"body":"thinking about one of those two,"},{"speaker":"Pam Harris","startTime":267.45,"endTime":271.59,"body":"and we'd say, \"Great.\" Okay,"},{"speaker":"Pam Harris","startTime":267.45,"endTime":271.59,"body":"next question. There are some"},{"speaker":"Pam Harris","startTime":271.62,"endTime":276.51,"body":"parking spots in the senior"},{"speaker":"Pam Harris","startTime":271.62,"endTime":276.51,"body":"parking lot left to paint. So I"},{"speaker":"Pam Harris","startTime":276.51,"endTime":279.03,"body":"don't know if you guys have that"},{"speaker":"Pam Harris","startTime":276.51,"endTime":279.03,"body":"at your school. But sometimes"},{"speaker":"Pam Harris","startTime":279.03,"endTime":284.61,"body":"schools will like allow senior"},{"speaker":"Pam Harris","startTime":279.03,"endTime":284.61,"body":"students to 'rent' a parking"},{"speaker":"Pam Harris","startTime":284.61,"endTime":287.55,"body":"spot for the year and they can"},{"speaker":"Pam Harris","startTime":284.61,"endTime":287.55,"body":"go paint it and make it their"},{"speaker":"Pam Harris","startTime":287.55,"endTime":291.3,"body":"own or whatever. So there are"},{"speaker":"Pam Harris","startTime":287.55,"endTime":291.3,"body":"some parking spots left to paint"},{"speaker":"Pam Harris","startTime":291.33,"endTime":295.89,"body":"in the parking lot. How many"},{"speaker":"Pam Harris","startTime":291.33,"endTime":295.89,"body":"more kids can choose a spot if"},{"speaker":"Pam Harris","startTime":295.92,"endTime":298.95,"body":"spots 17 through 23 are open?"},{"speaker":"Kim Montague","startTime":299.61,"endTime":302.19,"body":"Hmm. What should I"},{"speaker":"Kim Montague","startTime":299.61,"endTime":302.19,"body":"expect students to do?"},{"speaker":"Pam Harris","startTime":302.49,"endTime":302.64,"body":"Umhum."},{"speaker":"Kim Montague","startTime":303.27,"endTime":308.01,"body":"I would expect"},{"speaker":"Kim Montague","startTime":303.27,"endTime":308.01,"body":"that many students will count by"},{"speaker":"Kim Montague","startTime":308.01,"endTime":313.23,"body":"ones and say, \"17, 18, 19, 20,"},{"speaker":"Kim Montague","startTime":308.01,"endTime":313.23,"body":"21, 22, 23.\""},{"speaker":"Pam Harris","startTime":313.68,"endTime":316.53,"body":"And when you just"},{"speaker":"Pam Harris","startTime":313.68,"endTime":316.53,"body":"counted that, how many did you"},{"speaker":"Pam Harris","startTime":316.53,"endTime":316.86,"body":"get?"},{"speaker":"Kim Montague","startTime":317.31,"endTime":318.33,"body":"Seven spots."},{"speaker":"Pam Harris","startTime":319.14,"endTime":322.29,"body":"But I thought 23"},{"speaker":"Pam Harris","startTime":319.14,"endTime":322.29,"body":"minus 17 was six. Didn't we just"},{"speaker":"Pam Harris","startTime":322.29,"endTime":326.04,"body":"decide that the distance between"},{"speaker":"Pam Harris","startTime":322.29,"endTime":326.04,"body":"17 and 23 was six?"},{"speaker":"Kim Montague","startTime":326.1,"endTime":326.58,"body":"Yeah."},{"speaker":"Pam Harris","startTime":327.33,"endTime":329.76,"body":"But you just got"},{"speaker":"Pam Harris","startTime":327.33,"endTime":329.76,"body":"seven. There's seven spots."},{"speaker":"Kim Montague","startTime":330.06,"endTime":330.48,"body":"Yep."},{"speaker":"Pam Harris","startTime":331.05,"endTime":334.02,"body":"That's interesting."},{"speaker":"Pam Harris","startTime":331.05,"endTime":334.02,"body":"And that's literally what I"},{"speaker":"Pam Harris","startTime":334.02,"endTime":338.1,"body":"would say in class. I would be"},{"speaker":"Pam Harris","startTime":334.02,"endTime":338.1,"body":"like, \"That's interesting. Wait,"},{"speaker":"Pam Harris","startTime":338.1,"endTime":341.16,"body":"what?\" And I might ask students,"},{"speaker":"Pam Harris","startTime":338.1,"endTime":341.16,"body":"\"How are you making sense of"},{"speaker":"Pam Harris","startTime":341.16,"endTime":343.71,"body":"that?\" But I don't want to kill"},{"speaker":"Pam Harris","startTime":341.16,"endTime":343.71,"body":"it too much in this first, these"},{"speaker":"Pam Harris","startTime":343.71,"endTime":346.8,"body":"first two problems. But I do"},{"speaker":"Pam Harris","startTime":343.71,"endTime":346.8,"body":"want to encourage students, you"},{"speaker":"Pam Harris","startTime":346.8,"endTime":350.1,"body":"know, \"How are you making sense"},{"speaker":"Pam Harris","startTime":346.8,"endTime":350.1,"body":"of the fact that both of these"},{"speaker":"Pam Harris","startTime":350.1,"endTime":354.69,"body":"problems have a 17 to 23 in"},{"speaker":"Pam Harris","startTime":350.1,"endTime":354.69,"body":"them? And for one of them we got"},{"speaker":"Pam Harris","startTime":354.72,"endTime":357.18,"body":"the answer six, and for one of"},{"speaker":"Pam Harris","startTime":354.72,"endTime":357.18,"body":"them, we get the answer seven.\""},{"speaker":"Pam Harris","startTime":358.05,"endTime":362.94,"body":"Next question. What's the"},{"speaker":"Pam Harris","startTime":358.05,"endTime":362.94,"body":"distance between the eight"},{"speaker":"Pam Harris","startTime":362.94,"endTime":367.14,"body":"centimeter mark and the 13"},{"speaker":"Pam Harris","startTime":362.94,"endTime":367.14,"body":"centimeter mark? Now, ideally, I"},{"speaker":"Pam Harris","startTime":367.14,"endTime":370.53,"body":"would maybe show a picture where"},{"speaker":"Pam Harris","startTime":367.14,"endTime":370.53,"body":"I would have like, we call it"},{"speaker":"Pam Harris","startTime":370.53,"endTime":373.23,"body":"the broken ruler problem, where"},{"speaker":"Pam Harris","startTime":370.53,"endTime":373.23,"body":"you kind of see like this"},{"speaker":"Pam Harris","startTime":373.23,"endTime":375.54,"body":"jaggedy edge where you don't see"},{"speaker":"Pam Harris","startTime":373.23,"endTime":375.54,"body":"the rest of the ruler, and you"},{"speaker":"Pam Harris","startTime":375.54,"endTime":378.24,"body":"kind of see maybe the seven"},{"speaker":"Pam Harris","startTime":375.54,"endTime":378.24,"body":"centimeter mark and eight"},{"speaker":"Pam Harris","startTime":378.24,"endTime":381.63,"body":"centimeter mark, and then 9, 10,"},{"speaker":"Pam Harris","startTime":378.24,"endTime":381.63,"body":"11, 12, 13 centimeter mark,"},{"speaker":"Pam Harris","startTime":381.63,"endTime":385.38,"body":"maybe the 14 centimeter mark. So"},{"speaker":"Pam Harris","startTime":381.63,"endTime":385.38,"body":"if I'm asking between eight and"},{"speaker":"Pam Harris","startTime":385.41,"endTime":389.13,"body":"13, I might have a centimeter on"},{"speaker":"Pam Harris","startTime":385.41,"endTime":389.13,"body":"either side. And I might then"},{"speaker":"Pam Harris","startTime":389.67,"endTime":394.47,"body":"draw a line on top of the ruler"},{"speaker":"Pam Harris","startTime":389.67,"endTime":394.47,"body":"that kind of shows I'm looking"},{"speaker":"Pam Harris","startTime":394.47,"endTime":397.68,"body":"between eight and 13, the eight"},{"speaker":"Pam Harris","startTime":394.47,"endTime":397.68,"body":"centimeter mark and 13"},{"speaker":"Pam Harris","startTime":397.68,"endTime":400.56,"body":"centimeter mark. So the question"},{"speaker":"Pam Harris","startTime":397.68,"endTime":400.56,"body":"would be, what is the distance"},{"speaker":"Pam Harris","startTime":400.56,"endTime":402.69,"body":"between the eight centimeter"},{"speaker":"Pam Harris","startTime":400.56,"endTime":402.69,"body":"mark and the 13 centimeter mark?"},{"speaker":"Pam Harris","startTime":402.72,"endTime":406.47,"body":"This is a typical question that"},{"speaker":"Pam Harris","startTime":402.72,"endTime":406.47,"body":"showed up on the NAEP exam. It's"},{"speaker":"Pam Harris","startTime":406.47,"endTime":410.1,"body":"one of the things that we talk"},{"speaker":"Pam Harris","startTime":406.47,"endTime":410.1,"body":"about a NAEP exam, we call the"},{"speaker":"Pam Harris","startTime":410.1,"endTime":413.01,"body":"broken ruler question. So Kim,"},{"speaker":"Pam Harris","startTime":410.1,"endTime":413.01,"body":"what would you expect students"},{"speaker":"Pam Harris","startTime":413.01,"endTime":414.06,"body":"to do with that question?"},{"speaker":"Kim Montague","startTime":414.63,"endTime":417.54,"body":"It was also a very"},{"speaker":"Kim Montague","startTime":414.63,"endTime":417.54,"body":"common question in third grade"},{"speaker":"Kim Montague","startTime":417.96,"endTime":422.82,"body":"state exams for Texas, years"},{"speaker":"Kim Montague","startTime":417.96,"endTime":422.82,"body":"back. So between, I would think"},{"speaker":"Kim Montague","startTime":422.82,"endTime":426.27,"body":"many students would say, \"Okay,"},{"speaker":"Kim Montague","startTime":422.82,"endTime":426.27,"body":"between eight and 13, I might"},{"speaker":"Kim Montague","startTime":426.27,"endTime":429.9,"body":"figure out between eight and 10"},{"speaker":"Kim Montague","startTime":426.27,"endTime":429.9,"body":"will be two centimeters. And"},{"speaker":"Kim Montague","startTime":429.9,"endTime":432.78,"body":"between 10 and three would be"},{"speaker":"Kim Montague","startTime":429.9,"endTime":432.78,"body":"three more centimeters..."},{"speaker":"Pam Harris","startTime":432.78,"endTime":437.28,"body":"Ten and 13. You said"},{"speaker":"Pam Harris","startTime":432.78,"endTime":437.28,"body":"10 and three. Between 10 and 13."},{"speaker":"Kim Montague","startTime":440.4,"endTime":442.35,"body":"So the total"},{"speaker":"Kim Montague","startTime":440.4,"endTime":442.35,"body":"distance between eight and 13,"},{"speaker":"Kim Montague","startTime":442.35,"endTime":443.49,"body":"would be five centimeters."},{"speaker":"Pam Harris","startTime":443.52,"endTime":445.17,"body":"Those five"},{"speaker":"Pam Harris","startTime":443.52,"endTime":445.17,"body":"centimeters. Yeah. And"},{"speaker":"Pam Harris","startTime":445.2,"endTime":447.06,"body":"hopefully, you know, like, you"},{"speaker":"Pam Harris","startTime":445.2,"endTime":447.06,"body":"can picture that. We would"},{"speaker":"Pam Harris","startTime":447.06,"endTime":449.04,"body":"probably draw an open number"},{"speaker":"Pam Harris","startTime":447.06,"endTime":449.04,"body":"line on the board and maybe do"},{"speaker":"Pam Harris","startTime":449.04,"endTime":452.73,"body":"those jumps, the 8 to 10 and the"},{"speaker":"Pam Harris","startTime":449.04,"endTime":452.73,"body":"10 to 13. Cool. All right. Next"},{"speaker":"Pam Harris","startTime":452.73,"endTime":456.48,"body":"question. How many mile markers,"},{"speaker":"Pam Harris","startTime":452.73,"endTime":456.48,"body":"so we're driving down the road,"},{"speaker":"Pam Harris","startTime":456.48,"endTime":459.6,"body":"and there's these mile markers."},{"speaker":"Pam Harris","startTime":456.48,"endTime":459.6,"body":"How many mile markers, those are"},{"speaker":"Pam Harris","startTime":459.6,"endTime":463.92,"body":"signs. So I'm aware that we have"},{"speaker":"Pam Harris","startTime":459.6,"endTime":463.92,"body":"international listeners and so"},{"speaker":"Pam Harris","startTime":463.95,"endTime":469.11,"body":"like signs that every mile on"},{"speaker":"Pam Harris","startTime":463.95,"endTime":469.11,"body":"highways often will have markers"},{"speaker":"Pam Harris","startTime":469.11,"endTime":471.81,"body":"of how many miles you are from"},{"speaker":"Pam Harris","startTime":469.11,"endTime":471.81,"body":"the beginning of that whatever"},{"speaker":"Pam Harris","startTime":471.81,"endTime":476.07,"body":"the beginning is, often it's the"},{"speaker":"Pam Harris","startTime":471.81,"endTime":476.07,"body":"state line. So how many mile"},{"speaker":"Pam Harris","startTime":476.07,"endTime":481.05,"body":"markers do you need to replace,"},{"speaker":"Pam Harris","startTime":476.07,"endTime":481.05,"body":"if mile markers eight through 13"},{"speaker":"Pam Harris","startTime":481.08,"endTime":482.49,"body":"got blown over in the storm?"},{"speaker":"Kim Montague","startTime":482.64,"endTime":486.57,"body":"Yeah. So again, I"},{"speaker":"Kim Montague","startTime":482.64,"endTime":486.57,"body":"would expect that many students"},{"speaker":"Kim Montague","startTime":487.38,"endTime":491.46,"body":"would think about each one of"},{"speaker":"Kim Montague","startTime":487.38,"endTime":491.46,"body":"those individually."},{"speaker":"Pam Harris","startTime":491.82,"endTime":492.27,"body":"Okay."},{"speaker":"Kim Montague","startTime":492.63,"endTime":497.16,"body":"And so they might"},{"speaker":"Kim Montague","startTime":492.63,"endTime":497.16,"body":"say, \"Eight, 9,10, 11, 12, 13."},{"speaker":"Kim Montague","startTime":497.19,"endTime":499.62,"body":"So that's six mile markers.\""},{"speaker":"Pam Harris","startTime":500.88,"endTime":504.33,"body":"Because you have to"},{"speaker":"Pam Harris","startTime":500.88,"endTime":504.33,"body":"replace mile marker eight. You"},{"speaker":"Pam Harris","startTime":504.33,"endTime":507.3,"body":"have to replace my marker 9, 10."},{"speaker":"Pam Harris","startTime":504.33,"endTime":507.3,"body":"So when you were like saying,"},{"speaker":"Pam Harris","startTime":507.66,"endTime":509.79,"body":"like you said, counting by ones"},{"speaker":"Pam Harris","startTime":507.66,"endTime":509.79,"body":"are actually counting each of"},{"speaker":"Pam Harris","startTime":509.79,"endTime":513.42,"body":"those mile markers. So you're"},{"speaker":"Pam Harris","startTime":509.79,"endTime":513.42,"body":"saying that even though we had"},{"speaker":"Pam Harris","startTime":514.17,"endTime":517.71,"body":"eight and 13 in both of those"},{"speaker":"Pam Harris","startTime":514.17,"endTime":517.71,"body":"questions that the distance"},{"speaker":"Pam Harris","startTime":517.71,"endTime":519.9,"body":"between the eight centimeter"},{"speaker":"Pam Harris","startTime":517.71,"endTime":519.9,"body":"mark and the 13 centimeter mark"},{"speaker":"Pam Harris","startTime":519.9,"endTime":524.25,"body":"was five, but when it was the"},{"speaker":"Pam Harris","startTime":519.9,"endTime":524.25,"body":"eight mile marker to the 13 mile"},{"speaker":"Pam Harris","startTime":524.25,"endTime":525.93,"body":"marker, then we had to replace"},{"speaker":"Pam Harris","startTime":524.25,"endTime":525.93,"body":"six?"},{"speaker":"Kim Montague","startTime":527.52,"endTime":528.12,"body":"Yeah."},{"speaker":"Pam Harris","startTime":528.42,"endTime":532.08,"body":"Like why do we have"},{"speaker":"Pam Harris","startTime":528.42,"endTime":532.08,"body":"five one time and six another"},{"speaker":"Pam Harris","startTime":532.08,"endTime":536.82,"body":"time? That's confusing. I have"},{"speaker":"Pam Harris","startTime":532.08,"endTime":536.82,"body":"one more question. How many"},{"speaker":"Pam Harris","startTime":536.82,"endTime":541.77,"body":"fence posts do you need to"},{"speaker":"Pam Harris","startTime":536.82,"endTime":541.77,"body":"paint, if you're painting fence"},{"speaker":"Pam Harris","startTime":541.77,"endTime":545.76,"body":"post number 34 through fence"},{"speaker":"Pam Harris","startTime":541.77,"endTime":545.76,"body":"post number fourty."},{"speaker":"Kim Montague","startTime":546.42,"endTime":548.64,"body":"Okay, so this is"},{"speaker":"Kim Montague","startTime":546.42,"endTime":548.64,"body":"going to be one like the one you"},{"speaker":"Kim Montague","startTime":548.64,"endTime":554.13,"body":"just asked me where I have to"},{"speaker":"Kim Montague","startTime":548.64,"endTime":554.13,"body":"consider that I'm painting the"},{"speaker":"Kim Montague","startTime":554.16,"endTime":556.47,"body":"34th fencepost."},{"speaker":"Pam Harris","startTime":556.65,"endTime":557.1,"body":"Okay."},{"speaker":"Kim Montague","startTime":557.64,"endTime":562.23,"body":"So, I'm gonna"},{"speaker":"Kim Montague","startTime":557.64,"endTime":562.23,"body":"paint each one of those 35, 36,"},{"speaker":"Kim Montague","startTime":562.23,"endTime":568.89,"body":"37, 38, 39, 40. What did I just"},{"speaker":"Kim Montague","startTime":562.23,"endTime":568.89,"body":"say, 34, 35, 36, 37, 38, 39, 40."},{"speaker":"Kim Montague","startTime":568.89,"endTime":573.78,"body":"I was like wait, why did I get 6"},{"speaker":"Kim Montague","startTime":568.89,"endTime":573.78,"body":"not 7. That's weird. So there's"},{"speaker":"Kim Montague","startTime":573.78,"endTime":576.12,"body":"gonna be seven fence posts."},{"speaker":"Pam Harris","startTime":576.15,"endTime":578.55,"body":"So when you"},{"speaker":"Pam Harris","startTime":576.15,"endTime":578.55,"body":"recounted you got seven?"},{"speaker":"Kim Montague","startTime":578.58,"endTime":578.94,"body":"Yeah."},{"speaker":"Pam Harris","startTime":579.93,"endTime":583.02,"body":"Even though 40 minus"},{"speaker":"Pam Harris","startTime":579.93,"endTime":583.02,"body":"34 is clearly six."},{"speaker":"Kim Montague","startTime":583.05,"endTime":583.44,"body":"Yeah."},{"speaker":"Pam Harris","startTime":583.86,"endTime":586.5,"body":"Thirty four plus six"},{"speaker":"Pam Harris","startTime":583.86,"endTime":586.5,"body":"is clearly 40. But you're saying"},{"speaker":"Pam Harris","startTime":586.5,"endTime":590.91,"body":"the answer is seven. So,"},{"speaker":"Pam Harris","startTime":586.5,"endTime":590.91,"body":"listeners, you might want to"},{"speaker":"Pam Harris","startTime":590.91,"endTime":593.58,"body":"actually like draw the fence"},{"speaker":"Pam Harris","startTime":590.91,"endTime":593.58,"body":"posts, like countless fence"},{"speaker":"Pam Harris","startTime":593.58,"endTime":597.78,"body":"posts, are there really seven"},{"speaker":"Pam Harris","startTime":593.58,"endTime":597.78,"body":"fence posts. Okay, okay. Hey,"},{"speaker":"Pam Harris","startTime":597.78,"endTime":601.17,"body":"what's the distance, how much"},{"speaker":"Pam Harris","startTime":597.78,"endTime":601.17,"body":"wire do I need to put how many"},{"speaker":"Pam Harris","startTime":601.17,"endTime":604.5,"body":"feet of wire if they're a foot"},{"speaker":"Pam Harris","startTime":601.17,"endTime":604.5,"body":"apart, that's dumb a meter"},{"speaker":"Pam Harris","startTime":604.5,"endTime":604.92,"body":"apart."},{"speaker":"Pam Harris","startTime":607.2,"endTime":610.11,"body":"I don't know how much fence"},{"speaker":"Pam Harris","startTime":607.2,"endTime":610.11,"body":"posts or how much wire you need,"},{"speaker":"Pam Harris","startTime":610.11,"endTime":614.91,"body":"but the distance between them"},{"speaker":"Pam Harris","startTime":610.11,"endTime":614.91,"body":"from 34 to 40 is six."},{"speaker":"Pam Harris","startTime":615.3,"endTime":618.72,"body":"The distance between the six,"},{"speaker":"Pam Harris","startTime":615.3,"endTime":618.72,"body":"whatever that unit is. So if the"},{"speaker":"Pam Harris","startTime":618.72,"endTime":621.48,"body":"fence posts are, say this is a"},{"speaker":"Pam Harris","startTime":618.72,"endTime":621.48,"body":"really skinny fence, I don't"},{"speaker":"Pam Harris","startTime":621.48,"endTime":625.65,"body":"know, the fence posts are very"},{"speaker":"Pam Harris","startTime":621.48,"endTime":625.65,"body":"close together. So 34 to 40 is"},{"speaker":"Pam Harris","startTime":625.65,"endTime":634.08,"body":"6. But if I'm painting fence"},{"speaker":"Pam Harris","startTime":625.65,"endTime":634.08,"body":"posts, 34 to 47, fence posts,"},{"speaker":"Pam Harris","startTime":634.2,"endTime":636.72,"body":"and we call this fence post"},{"speaker":"Pam Harris","startTime":634.2,"endTime":636.72,"body":"problem. At least I do, I don't"},{"speaker":"Pam Harris","startTime":636.72,"endTime":641.22,"body":"know why. And so I wanted to end"},{"speaker":"Pam Harris","startTime":636.72,"endTime":641.22,"body":"this string with fence posts, so"},{"speaker":"Pam Harris","startTime":641.22,"endTime":644.46,"body":"that I could start calling it"},{"speaker":"Pam Harris","startTime":641.22,"endTime":644.46,"body":"the fence post problem. This is"},{"speaker":"Pam Harris","startTime":644.46,"endTime":647.28,"body":"what Kim and I will refer to,"},{"speaker":"Pam Harris","startTime":644.46,"endTime":647.28,"body":"we'll get to some sort of"},{"speaker":"Pam Harris","startTime":647.52,"endTime":650.4,"body":"problem in lots of different"},{"speaker":"Pam Harris","startTime":647.52,"endTime":650.4,"body":"contexts, lots of different"},{"speaker":"Pam Harris","startTime":650.4,"endTime":653.25,"body":"situations, higher math, lower"},{"speaker":"Pam Harris","startTime":650.4,"endTime":653.25,"body":"math, you know, like all over"},{"speaker":"Pam Harris","startTime":653.25,"endTime":655.47,"body":"the place where all of a sudden,"},{"speaker":"Pam Harris","startTime":653.25,"endTime":655.47,"body":"I'll go, \"Ah, this is a"},{"speaker":"Pam Harris","startTime":655.47,"endTime":659.37,"body":"fencepost problem.\" Where all of"},{"speaker":"Pam Harris","startTime":655.47,"endTime":659.37,"body":"a sudden, I realize it's not"},{"speaker":"Pam Harris","startTime":659.37,"endTime":666.18,"body":"just a distance between problem."},{"speaker":"Pam Harris","startTime":659.37,"endTime":666.18,"body":"But it's a fence post problem. I"},{"speaker":"Pam Harris","startTime":666.18,"endTime":670.44,"body":"can't just look at how far apart"},{"speaker":"Pam Harris","startTime":666.18,"endTime":670.44,"body":"the posts are, I have to"},{"speaker":"Pam Harris","startTime":670.59,"endTime":677.13,"body":"actually count the posts. So a"},{"speaker":"Pam Harris","startTime":670.59,"endTime":677.13,"body":"big takeaway, a big question I"},{"speaker":"Pam Harris","startTime":677.13,"endTime":682.35,"body":"would ask students is, \"Are you"},{"speaker":"Pam Harris","startTime":677.13,"endTime":682.35,"body":"counting objects? Or are you"},{"speaker":"Pam Harris","startTime":682.35,"endTime":687.99,"body":"finding the distance between"},{"speaker":"Pam Harris","startTime":682.35,"endTime":687.99,"body":"objects?\" And this is a... go"},{"speaker":"Pam Harris","startTime":687.99,"endTime":688.2,"body":"ahead."},{"speaker":"Kim Montague","startTime":688.23,"endTime":694.53,"body":"Well, I was gonna"},{"speaker":"Kim Montague","startTime":688.23,"endTime":694.53,"body":"say I'm struck by how this is"},{"speaker":"Kim Montague","startTime":694.53,"endTime":700.2,"body":"exactly the scenario or the"},{"speaker":"Kim Montague","startTime":694.53,"endTime":700.2,"body":"situation, why it's so important"},{"speaker":"Kim Montague","startTime":700.2,"endTime":703.02,"body":"that we don't have kids just"},{"speaker":"Kim Montague","startTime":700.2,"endTime":703.02,"body":"pluck numbers out of a problem."},{"speaker":"Kim Montague","startTime":703.5,"endTime":711.72,"body":"Because clearly the context of"},{"speaker":"Kim Montague","startTime":703.5,"endTime":711.72,"body":"the situation is changing your"},{"speaker":"Kim Montague","startTime":711.72,"endTime":712.62,"body":"solution."},{"speaker":"Pam Harris","startTime":713.01,"endTime":715.44,"body":"Yeah, well, that's a"},{"speaker":"Pam Harris","startTime":713.01,"endTime":715.44,"body":"really good point. Because we"},{"speaker":"Pam Harris","startTime":715.44,"endTime":718.62,"body":"might have kids look at a"},{"speaker":"Pam Harris","startTime":715.44,"endTime":718.62,"body":"problem and go, it's clearly"},{"speaker":"Pam Harris","startTime":718.62,"endTime":723.45,"body":"subtraction, grab the, pick some"},{"speaker":"Pam Harris","startTime":718.62,"endTime":723.45,"body":"numbers, grab the 34 and the 40."},{"speaker":"Pam Harris","startTime":723.48,"endTime":726.57,"body":"Bam, it's six. Right? It"},{"speaker":"Pam Harris","startTime":723.48,"endTime":726.57,"body":"depends, right? It depends on"},{"speaker":"Pam Harris","startTime":726.57,"endTime":728.76,"body":"the context in what you're"},{"speaker":"Pam Harris","startTime":726.57,"endTime":728.76,"body":"asking. Oh, that's, that's well"},{"speaker":"Pam Harris","startTime":728.76,"endTime":732.45,"body":"said. Kim, we may have just"},{"speaker":"Pam Harris","startTime":728.76,"endTime":732.45,"body":"given high stakes test writers a"},{"speaker":"Pam Harris","startTime":732.45,"endTime":736.68,"body":"way to trick kids. Not trick, no"},{"speaker":"Pam Harris","startTime":732.45,"endTime":736.68,"body":"trick, right, because high"},{"speaker":"Pam Harris","startTime":736.68,"endTime":739.86,"body":"stakes test writers do it, do it"},{"speaker":"Pam Harris","startTime":736.68,"endTime":739.86,"body":"because then that will help"},{"speaker":"Pam Harris","startTime":739.86,"endTime":742.38,"body":"encourage teachers to go, \"Oh,"},{"speaker":"Pam Harris","startTime":739.86,"endTime":742.38,"body":"we actually have to help"},{"speaker":"Pam Harris","startTime":742.38,"endTime":746.4,"body":"students understand what's"},{"speaker":"Pam Harris","startTime":742.38,"endTime":746.4,"body":"happening. Not just pluck the"},{"speaker":"Pam Harris","startTime":746.4,"endTime":749.28,"body":"numbers, throw in an operation"},{"speaker":"Pam Harris","startTime":746.4,"endTime":749.28,"body":"that make sense and go from"},{"speaker":"Pam Harris","startTime":749.28,"endTime":752.97,"body":"there.\" Yeah. And I want to pay"},{"speaker":"Pam Harris","startTime":749.28,"endTime":752.97,"body":"homage a little bit to Cathy"},{"speaker":"Pam Harris","startTime":752.97,"endTime":756.57,"body":"Fosnot, because she's one of the"},{"speaker":"Pam Harris","startTime":752.97,"endTime":756.57,"body":"people that helped me begin to"},{"speaker":"Pam Harris","startTime":756.57,"endTime":760.41,"body":"make sense of this. Like, I'm,"},{"speaker":"Pam Harris","startTime":756.57,"endTime":760.41,"body":"I'll be clear, I'm a little"},{"speaker":"Pam Harris","startTime":760.41,"endTime":766.38,"body":"embarrassed how long it took me"},{"speaker":"Pam Harris","startTime":760.41,"endTime":766.38,"body":"to be willing to do enough post"},{"speaker":"Pam Harris","startTime":766.38,"endTime":769.77,"body":"problems to make sense of what"},{"speaker":"Pam Harris","startTime":766.38,"endTime":769.77,"body":"was happening to come up with a"},{"speaker":"Pam Harris","startTime":769.77,"endTime":773.46,"body":"strategy. Kim, I was, I'm not"},{"speaker":"Pam Harris","startTime":769.77,"endTime":773.46,"body":"gonna tell you how old, but it"},{"speaker":"Pam Harris","startTime":773.46,"endTime":778.02,"body":"was quite a while that when I"},{"speaker":"Pam Harris","startTime":773.46,"endTime":778.02,"body":"realized it was a fence post"},{"speaker":"Pam Harris","startTime":778.02,"endTime":779.64,"body":"problem, I would literally"},{"speaker":"Pam Harris","startTime":778.02,"endTime":779.64,"body":"count."},{"speaker":"Pam Harris","startTime":780.18,"endTime":780.57,"body":"Yeah."},{"speaker":"Pam Harris","startTime":780.9,"endTime":785.13,"body":"That's the only strategy I had"},{"speaker":"Pam Harris","startTime":780.9,"endTime":785.13,"body":"was to count. And I want to hear"},{"speaker":"Pam Harris","startTime":785.13,"endTime":789.69,"body":"from you what your strategy is"},{"speaker":"Pam Harris","startTime":785.13,"endTime":789.69,"body":"in just a second. But first, I"},{"speaker":"Pam Harris","startTime":789.69,"endTime":794.13,"body":"want to pay homage to Cathy"},{"speaker":"Pam Harris","startTime":789.69,"endTime":794.13,"body":"Fosnot. So she has a replacement"},{"speaker":"Pam Harris","startTime":794.13,"endTime":798.45,"body":"unit. In her Addition,"},{"speaker":"Pam Harris","startTime":794.13,"endTime":798.45,"body":"Subtraction collection of units,"},{"speaker":"Pam Harris","startTime":798.81,"endTime":802.11,"body":"that is called Measuring For the"},{"speaker":"Pam Harris","startTime":798.81,"endTime":802.11,"body":"Art Show. And in Measuring For"},{"speaker":"Pam Harris","startTime":802.11,"endTime":805.77,"body":"the Art Show, she has this"},{"speaker":"Pam Harris","startTime":802.11,"endTime":805.77,"body":"amazing task for kids to do,"},{"speaker":"Pam Harris","startTime":805.98,"endTime":811.32,"body":"where they measure strips of"},{"speaker":"Pam Harris","startTime":805.98,"endTime":811.32,"body":"paper so that they can label"},{"speaker":"Pam Harris","startTime":811.32,"endTime":815.34,"body":"their artwork. And it's at one"},{"speaker":"Pam Harris","startTime":811.32,"endTime":815.34,"body":"point, they have this brilliant"},{"speaker":"Pam Harris","startTime":815.34,"endTime":818.73,"body":"conversation and some video that"},{"speaker":"Pam Harris","startTime":815.34,"endTime":818.73,"body":"I saw of students doing this"},{"speaker":"Pam Harris","startTime":818.73,"endTime":822.69,"body":"task, video she produced the"},{"speaker":"Pam Harris","startTime":818.73,"endTime":822.69,"body":"students in this task, where the"},{"speaker":"Pam Harris","startTime":822.69,"endTime":831.6,"body":"question is, where would you put"},{"speaker":"Pam Harris","startTime":822.69,"endTime":831.6,"body":"if the paper was 66 cubes long,"},{"speaker":"Pam Harris","startTime":831.69,"endTime":838.02,"body":"66 units long, where would you"},{"speaker":"Pam Harris","startTime":831.69,"endTime":838.02,"body":"put 66? And she's able to use"},{"speaker":"Pam Harris","startTime":838.02,"endTime":842.16,"body":"the idea of well, if we want to"},{"speaker":"Pam Harris","startTime":838.02,"endTime":842.16,"body":"make the paper 66 cubes long,"},{"speaker":"Pam Harris","startTime":842.49,"endTime":848.49,"body":"then the 66 has to go at the"},{"speaker":"Pam Harris","startTime":842.49,"endTime":848.49,"body":"edge of the 66th cube. You're"},{"speaker":"Pam Harris","startTime":848.49,"endTime":852.96,"body":"not counting cubes, it wouldn't"},{"speaker":"Pam Harris","startTime":848.49,"endTime":852.96,"body":"be in the middle of the 66th"},{"speaker":"Pam Harris","startTime":852.96,"endTime":856.71,"body":"cube that might be like if"},{"speaker":"Pam Harris","startTime":852.96,"endTime":856.71,"body":"you're labeling, here's cube 66."},{"speaker":"Pam Harris","startTime":857.16,"endTime":862.14,"body":"So we're not counting cubes."},{"speaker":"Pam Harris","startTime":857.16,"endTime":862.14,"body":"We're measuring a span of"},{"speaker":"Pam Harris","startTime":862.14,"endTime":865.02,"body":"distance. And I may not have"},{"speaker":"Pam Harris","startTime":862.14,"endTime":865.02,"body":"just given that enough credit."},{"speaker":"Pam Harris","startTime":865.02,"endTime":869.37,"body":"But if you're building the open"},{"speaker":"Pam Harris","startTime":865.02,"endTime":869.37,"body":"number line as a model, I highly"},{"speaker":"Pam Harris","startTime":869.37,"endTime":873.03,"body":"recommend considering that. I"},{"speaker":"Pam Harris","startTime":869.37,"endTime":873.03,"body":"think, Kim, we did an episode"},{"speaker":"Pam Harris","startTime":873.69,"endTime":876.27,"body":"where we talked about, yeah,"},{"speaker":"Pam Harris","startTime":873.69,"endTime":876.27,"body":"with Measuring For the Art Show."},{"speaker":"Pam Harris","startTime":876.27,"endTime":880.23,"body":"So so we'll put that episode in"},{"speaker":"Pam Harris","startTime":876.27,"endTime":880.23,"body":"the show notes. So you go check"},{"speaker":"Pam Harris","startTime":880.23,"endTime":882.84,"body":"that out where we talk more"},{"speaker":"Pam Harris","startTime":880.23,"endTime":882.84,"body":"about that. But it is a big"},{"speaker":"Pam Harris","startTime":882.84,"endTime":888.0,"body":"deal. Because what do kids do"},{"speaker":"Pam Harris","startTime":882.84,"endTime":888.0,"body":"initially? The very first thing"},{"speaker":"Pam Harris","startTime":888.0,"endTime":891.21,"body":"kids do when we're teaching them"},{"speaker":"Pam Harris","startTime":888.0,"endTime":891.21,"body":"to count is they count the fence"},{"speaker":"Pam Harris","startTime":891.21,"endTime":896.13,"body":"posts. And I would then take"},{"speaker":"Pam Harris","startTime":891.21,"endTime":896.13,"body":"that to a ruler, they count the"},{"speaker":"Pam Harris","startTime":896.13,"endTime":902.13,"body":"tick marks. So if we say, if we"},{"speaker":"Pam Harris","startTime":896.13,"endTime":902.13,"body":"just throw a ruler at well, let"},{"speaker":"Pam Harris","startTime":902.13,"endTime":905.73,"body":"me start, let me backup. So if"},{"speaker":"Pam Harris","startTime":902.13,"endTime":905.73,"body":"we give kids hey, I got five"},{"speaker":"Pam Harris","startTime":905.73,"endTime":908.97,"body":"puppies, show me five puppies,"},{"speaker":"Pam Harris","startTime":905.73,"endTime":908.97,"body":"they're gonna literally grab"},{"speaker":"Pam Harris","startTime":908.97,"endTime":913.2,"body":"five counters, they're gonna put"},{"speaker":"Pam Harris","startTime":908.97,"endTime":913.2,"body":"five fingers up, they're gonna"},{"speaker":"Pam Harris","startTime":913.2,"endTime":916.92,"body":"move five beads on a number"},{"speaker":"Pam Harris","startTime":913.2,"endTime":916.92,"body":"rack. They're counting the fence"},{"speaker":"Pam Harris","startTime":916.92,"endTime":924.18,"body":"posts. But then when we say what"},{"speaker":"Pam Harris","startTime":916.92,"endTime":924.18,"body":"is five minus three? Now they"},{"speaker":"Pam Harris","startTime":924.18,"endTime":928.29,"body":"have to think about the distance"},{"speaker":"Pam Harris","startTime":924.18,"endTime":928.29,"body":"between five and three. And"},{"speaker":"Pam Harris","startTime":928.32,"endTime":931.74,"body":"that's one of the reasons why a"},{"speaker":"Pam Harris","startTime":928.32,"endTime":931.74,"body":"ruler can be so difficult for"},{"speaker":"Pam Harris","startTime":931.74,"endTime":934.32,"body":"kids is because they have to"},{"speaker":"Pam Harris","startTime":931.74,"endTime":934.32,"body":"make sense of am I counting the"},{"speaker":"Pam Harris","startTime":934.32,"endTime":939.42,"body":"tick marks? Or am I looking at"},{"speaker":"Pam Harris","startTime":934.32,"endTime":939.42,"body":"the span between the tick marks?"},{"speaker":"Pam Harris","startTime":939.42,"endTime":941.58,"body":"It's one of the reasons why"},{"speaker":"Pam Harris","startTime":939.42,"endTime":941.58,"body":"measurements can be so difficult"},{"speaker":"Pam Harris","startTime":941.58,"endTime":945.48,"body":"for kids. And we have to give"},{"speaker":"Pam Harris","startTime":941.58,"endTime":945.48,"body":"them experience making sense of"},{"speaker":"Pam Harris","startTime":945.48,"endTime":949.83,"body":"the difference between the tick"},{"speaker":"Pam Harris","startTime":945.48,"endTime":949.83,"body":"marks. And the span between the"},{"speaker":"Pam Harris","startTime":949.83,"endTime":953.49,"body":"tick marks. It's a huge deal"},{"speaker":"Pam Harris","startTime":949.83,"endTime":953.49,"body":"when we are moving to the open"},{"speaker":"Pam Harris","startTime":953.49,"endTime":957.12,"body":"number line. That's me pausing"},{"speaker":"Pam Harris","startTime":953.49,"endTime":957.12,"body":"in case you wanted to say"},{"speaker":"Pam Harris","startTime":957.12,"endTime":957.51,"body":"anything."},{"speaker":"Kim Montague","startTime":957.93,"endTime":959.91,"body":"No, I was thinking"},{"speaker":"Kim Montague","startTime":957.93,"endTime":959.91,"body":"if there is anything I wanted to"},{"speaker":"Kim Montague","startTime":959.91,"endTime":961.95,"body":"say. But I don't think anything"},{"speaker":"Kim Montague","startTime":959.91,"endTime":961.95,"body":"I want to add."},{"speaker":"Pam Harris","startTime":962.55,"endTime":965.61,"body":"No problem. So"},{"speaker":"Pam Harris","startTime":962.55,"endTime":965.61,"body":"listeners, Kim and I were"},{"speaker":"Pam Harris","startTime":965.61,"endTime":967.11,"body":"talking and she's like,"},{"speaker":"Pam Harris","startTime":965.61,"endTime":967.11,"body":"\"Sometimes I don't feel like"},{"speaker":"Pam Harris","startTime":967.11,"endTime":968.88,"body":"interrupting you, Pam.\" And I"},{"speaker":"Pam Harris","startTime":967.11,"endTime":968.88,"body":"was like, \"Oh, then I'll pause"},{"speaker":"Pam Harris","startTime":968.88,"endTime":969.33,"body":"more often.\""},{"speaker":"Pam Harris","startTime":969.36,"endTime":973.98,"body":"She's like, \"We'll just pause"},{"speaker":"Pam Harris","startTime":969.36,"endTime":973.98,"body":"and let me hang there.\" Okay, I"},{"speaker":"Pam Harris","startTime":973.98,"endTime":976.68,"body":"don't know. [laughs]"},{"speaker":"Kim Montague","startTime":976.68,"endTime":977.16,"body":"[laughs] I'll jump"},{"speaker":"Kim Montague","startTime":976.68,"endTime":977.16,"body":"in."},{"speaker":"Pam Harris","startTime":979.44,"endTime":981.75,"body":"So I was actually"},{"speaker":"Pam Harris","startTime":979.44,"endTime":981.75,"body":"talking about this with one of"},{"speaker":"Pam Harris","startTime":981.75,"endTime":985.89,"body":"my sons the other day, and he"},{"speaker":"Pam Harris","startTime":981.75,"endTime":985.89,"body":"said, \"Oh, yeah, like, this is a"},{"speaker":"Pam Harris","startTime":985.89,"endTime":989.07,"body":"thing in computer science.\" And"},{"speaker":"Pam Harris","startTime":985.89,"endTime":989.07,"body":"I was like, \"Tell me more.\" And"},{"speaker":"Pam Harris","startTime":989.07,"endTime":992.25,"body":"he goes, \"Oh, it's often that"},{"speaker":"Pam Harris","startTime":989.07,"endTime":992.25,"body":"will have strings in computer"},{"speaker":"Pam Harris","startTime":992.25,"endTime":995.31,"body":"science.\" A string is like a"},{"speaker":"Pam Harris","startTime":992.25,"endTime":995.31,"body":"list of characters. So it could"},{"speaker":"Pam Harris","startTime":995.31,"endTime":999.27,"body":"be numbers. It could be letters,"},{"speaker":"Pam Harris","startTime":995.31,"endTime":999.27,"body":"it could be words, but you know,"},{"speaker":"Pam Harris","startTime":999.3,"endTime":1003.62,"body":"it could be names. So you have"},{"speaker":"Pam Harris","startTime":999.3,"endTime":1003.62,"body":"this list of characters, and"},{"speaker":"Pam Harris","startTime":1003.62,"endTime":1006.59,"body":"then there are times you need to"},{"speaker":"Pam Harris","startTime":1003.62,"endTime":1006.59,"body":"do things with those. And you"},{"speaker":"Pam Harris","startTime":1006.59,"endTime":1010.88,"body":"have to decide, are you going to"},{"speaker":"Pam Harris","startTime":1006.59,"endTime":1010.88,"body":"be inclusive? In other words,"},{"speaker":"Pam Harris","startTime":1010.88,"endTime":1015.05,"body":"are you counting fence posts? Or"},{"speaker":"Pam Harris","startTime":1010.88,"endTime":1015.05,"body":"exclusive where, no, you're"},{"speaker":"Pam Harris","startTime":1015.05,"endTime":1018.98,"body":"leaving out that first fence"},{"speaker":"Pam Harris","startTime":1015.05,"endTime":1018.98,"body":"post? And you're just looking at"},{"speaker":"Pam Harris","startTime":1018.98,"endTime":1021.65,"body":"the span or the distance between"},{"speaker":"Pam Harris","startTime":1018.98,"endTime":1021.65,"body":"them. And you have to make sense"},{"speaker":"Pam Harris","startTime":1021.65,"endTime":1023.54,"body":"of that. And it was interesting"},{"speaker":"Pam Harris","startTime":1021.65,"endTime":1023.54,"body":"for me that that's kind of where"},{"speaker":"Pam Harris","startTime":1023.54,"endTime":1026.18,"body":"it came up for him was in"},{"speaker":"Pam Harris","startTime":1023.54,"endTime":1026.18,"body":"computer science. All of a"},{"speaker":"Pam Harris","startTime":1026.18,"endTime":1029.96,"body":"sudden, he had to make sense. Do"},{"speaker":"Pam Harris","startTime":1026.18,"endTime":1029.96,"body":"I, what do I mean? Do I mean the"},{"speaker":"Pam Harris","startTime":1029.96,"endTime":1033.44,"body":"span between the fence posts or"},{"speaker":"Pam Harris","startTime":1029.96,"endTime":1033.44,"body":"the tick marks? Or do I mean"},{"speaker":"Pam Harris","startTime":1033.44,"endTime":1036.89,"body":"that no, no, no, I actually have"},{"speaker":"Pam Harris","startTime":1033.44,"endTime":1036.89,"body":"to count that first fence post"},{"speaker":"Pam Harris","startTime":1036.92,"endTime":1040.52,"body":"as well. And so he said, like,"},{"speaker":"Pam Harris","startTime":1036.92,"endTime":1040.52,"body":"sometimes you'll have to order"},{"speaker":"Pam Harris","startTime":1040.52,"endTime":1044.66,"body":"lists, or edit lists and string"},{"speaker":"Pam Harris","startTime":1040.52,"endTime":1044.66,"body":"and you have to know the number"},{"speaker":"Pam Harris","startTime":1044.66,"endTime":1048.56,"body":"of objects, not the distance"},{"speaker":"Pam Harris","startTime":1044.66,"endTime":1048.56,"body":"between them. And so that's a"},{"speaker":"Pam Harris","startTime":1048.56,"endTime":1052.49,"body":"huge, that's a specific"},{"speaker":"Pam Harris","startTime":1048.56,"endTime":1052.49,"body":"instance. But then Kim, you were"},{"speaker":"Pam Harris","startTime":1052.49,"endTime":1054.41,"body":"like, oh, but Pam, it shows up"},{"speaker":"Pam Harris","startTime":1052.49,"endTime":1054.41,"body":"everywhere."},{"speaker":"Kim Montague","startTime":1054.86,"endTime":1057.14,"body":"Yeah, I think it"},{"speaker":"Kim Montague","startTime":1054.86,"endTime":1057.14,"body":"shows up in our daily life more"},{"speaker":"Kim Montague","startTime":1057.14,"endTime":1059.54,"body":"than we probably realize. And"},{"speaker":"Kim Montague","startTime":1057.14,"endTime":1059.54,"body":"now that we're mentioning what"},{"speaker":"Kim Montague","startTime":1059.54,"endTime":1062.51,"body":"we call fence post problems. I"},{"speaker":"Kim Montague","startTime":1059.54,"endTime":1062.51,"body":"think listeners will probably be"},{"speaker":"Kim Montague","startTime":1062.51,"endTime":1065.87,"body":"able to go, \"Oh, wait, that that"},{"speaker":"Kim Montague","startTime":1062.51,"endTime":1065.87,"body":"is a fence post problem.\" And"},{"speaker":"Kim Montague","startTime":1065.9,"endTime":1070.61,"body":"I'm wondering if people might"},{"speaker":"Kim Montague","startTime":1065.9,"endTime":1070.61,"body":"find themselves kind of"},{"speaker":"Kim Montague","startTime":1070.61,"endTime":1073.46,"body":"reverting back and counting in"},{"speaker":"Kim Montague","startTime":1070.61,"endTime":1073.46,"body":"those situations?"},{"speaker":"Pam Harris","startTime":1073.49,"endTime":1074.57,"body":"I mean, I did."},{"speaker":"Kim Montague","startTime":1074.57,"endTime":1074.84,"body":"Yeah."},{"speaker":"Pam Harris","startTime":1074.84,"endTime":1076.07,"body":"I did so often."},{"speaker":"Kim Montague","startTime":1076.07,"endTime":1078.23,"body":"Yeah, because it's"},{"speaker":"Kim Montague","startTime":1076.07,"endTime":1078.23,"body":"just so it's just like a little"},{"speaker":"Kim Montague","startTime":1078.23,"endTime":1082.7,"body":"twist on a subtraction problem"},{"speaker":"Kim Montague","startTime":1078.23,"endTime":1082.7,"body":"that maybe shakes you up a"},{"speaker":"Kim Montague","startTime":1082.7,"endTime":1083.0,"body":"little bit."},{"speaker":"Pam Harris","startTime":1083.51,"endTime":1086.51,"body":"Oh, and I got really"},{"speaker":"Pam Harris","startTime":1083.51,"endTime":1086.51,"body":"clear that if I, once I realized"},{"speaker":"Pam Harris","startTime":1086.51,"endTime":1089.18,"body":"it was a fencepost problem, if I"},{"speaker":"Pam Harris","startTime":1086.51,"endTime":1089.18,"body":"didn't count, I was getting it"},{"speaker":"Pam Harris","startTime":1089.18,"endTime":1091.76,"body":"wrong. And I was trying to get"},{"speaker":"Pam Harris","startTime":1089.18,"endTime":1091.76,"body":"it wrong. And so I was like, I'm"},{"speaker":"Pam Harris","startTime":1091.76,"endTime":1094.97,"body":"just gonna count. Then I know,"},{"speaker":"Pam Harris","startTime":1091.76,"endTime":1094.97,"body":"I'm right. And what I didn't do"},{"speaker":"Pam Harris","startTime":1095.57,"endTime":1100.19,"body":"was take the time to compare."},{"speaker":"Pam Harris","startTime":1095.57,"endTime":1100.19,"body":"What I didn't do was take the"},{"speaker":"Pam Harris","startTime":1100.19,"endTime":1102.86,"body":"time to compare. So let's look"},{"speaker":"Pam Harris","startTime":1100.19,"endTime":1102.86,"body":"back at the problem string that"},{"speaker":"Pam Harris","startTime":1102.86,"endTime":1106.61,"body":"we just did a minute ago. So I"},{"speaker":"Pam Harris","startTime":1102.86,"endTime":1106.61,"body":"said, \"We're on page 17. There's"},{"speaker":"Pam Harris","startTime":1106.64,"endTime":1109.61,"body":"23 pages in the book.\" You said,"},{"speaker":"Pam Harris","startTime":1106.64,"endTime":1109.61,"body":"how many pages were there left"},{"speaker":"Pam Harris","startTime":1109.61,"endTime":1109.91,"body":"to read?"},{"speaker":"Kim Montague","startTime":1110.09,"endTime":1110.69,"body":"Six."},{"speaker":"Pam Harris","startTime":1110.75,"endTime":1114.86,"body":"Six. So that's like"},{"speaker":"Pam Harris","startTime":1110.75,"endTime":1114.86,"body":"23 minus 17. Yeah? Then I said,"},{"speaker":"Pam Harris","startTime":1114.89,"endTime":1118.16,"body":"\"Okay, but they're senior"},{"speaker":"Pam Harris","startTime":1114.89,"endTime":1118.16,"body":"parking spots, number of parking"},{"speaker":"Pam Harris","startTime":1118.16,"endTime":1121.31,"body":"spots 17 through 23.\" And you"},{"speaker":"Pam Harris","startTime":1118.16,"endTime":1121.31,"body":"said the answer was?"},{"speaker":"Kim Montague","startTime":1122.06,"endTime":1122.6,"body":"Seven."},{"speaker":"Pam Harris","startTime":1122.75,"endTime":1126.08,"body":"Seven. So if you're"},{"speaker":"Pam Harris","startTime":1122.75,"endTime":1126.08,"body":"just subtracting and looking at"},{"speaker":"Pam Harris","startTime":1126.08,"endTime":1130.4,"body":"span, the answer was six. If"},{"speaker":"Pam Harris","startTime":1126.08,"endTime":1130.4,"body":"you're counting objects,"},{"speaker":"Pam Harris","startTime":1130.4,"endTime":1135.44,"body":"counting spots, the answer was"},{"speaker":"Pam Harris","startTime":1130.4,"endTime":1135.44,"body":"seven. Is it always one off?"},{"speaker":"Kim Montague","startTime":1138.14,"endTime":1139.37,"body":"You wanting me to"},{"speaker":"Kim Montague","startTime":1138.14,"endTime":1139.37,"body":"say something?"},{"speaker":"Pam Harris","startTime":1139.43,"endTime":1140.33,"body":"I kind of am, yeah."},{"speaker":"Kim Montague","startTime":1140.36,"endTime":1145.4,"body":"Okay. Yeah. So"},{"speaker":"Kim Montague","startTime":1140.36,"endTime":1145.4,"body":"yeah, it's one because, and I"},{"speaker":"Kim Montague","startTime":1145.4,"endTime":1151.91,"body":"don't know when I generalize"},{"speaker":"Kim Montague","startTime":1145.4,"endTime":1151.91,"body":"this, but I think about it like,"},{"speaker":"Kim Montague","startTime":1152.0,"endTime":1156.32,"body":"it's the distance plus one. And"},{"speaker":"Kim Montague","startTime":1152.0,"endTime":1156.32,"body":"so I'm going to go to your fence"},{"speaker":"Kim Montague","startTime":1156.32,"endTime":1158.69,"body":"post, I'm going to jump ahead to"},{"speaker":"Kim Montague","startTime":1156.32,"endTime":1158.69,"body":"your fence post problem and give"},{"speaker":"Kim Montague","startTime":1159.05,"endTime":1163.43,"body":"kind of a picture in that"},{"speaker":"Kim Montague","startTime":1159.05,"endTime":1163.43,"body":"context. So if I'm standing at"},{"speaker":"Kim Montague","startTime":1163.43,"endTime":1166.19,"body":"the first fence post, or the"},{"speaker":"Kim Montague","startTime":1163.43,"endTime":1166.19,"body":"17th, or whatever number you"},{"speaker":"Kim Montague","startTime":1166.19,"endTime":1169.85,"body":"gave us, then you can think"},{"speaker":"Kim Montague","startTime":1166.19,"endTime":1169.85,"body":"about the span of it, like the"},{"speaker":"Kim Montague","startTime":1169.85,"endTime":1173.51,"body":"space and the fence posts, this"},{"speaker":"Kim Montague","startTime":1169.85,"endTime":1173.51,"body":"space and the fence posts, the"},{"speaker":"Kim Montague","startTime":1173.51,"endTime":1176.0,"body":"space and the fence posts and"},{"speaker":"Kim Montague","startTime":1173.51,"endTime":1176.0,"body":"keep doing that till you get to"},{"speaker":"Kim Montague","startTime":1176.0,"endTime":1179.69,"body":"the last fence posts. So there's"},{"speaker":"Kim Montague","startTime":1176.0,"endTime":1179.69,"body":"that kind of span. But then"},{"speaker":"Kim Montague","startTime":1179.69,"endTime":1183.35,"body":"you've got to remember to come"},{"speaker":"Kim Montague","startTime":1179.69,"endTime":1183.35,"body":"back and pick up that first"},{"speaker":"Kim Montague","startTime":1183.35,"endTime":1186.59,"body":"fence posts. So you can think"},{"speaker":"Kim Montague","startTime":1183.35,"endTime":1186.59,"body":"about it like the span or the"},{"speaker":"Kim Montague","startTime":1186.59,"endTime":1191.24,"body":"distance between them. But oh,"},{"speaker":"Kim Montague","startTime":1186.59,"endTime":1191.24,"body":"yeah, don't forget that first"},{"speaker":"Kim Montague","startTime":1191.24,"endTime":1191.51,"body":"one."},{"speaker":"Pam Harris","startTime":1192.47,"endTime":1194.72,"body":"And the reason you"},{"speaker":"Pam Harris","startTime":1192.47,"endTime":1194.72,"body":"can think about it, this is span"},{"speaker":"Pam Harris","startTime":1194.72,"endTime":1197.15,"body":"or distance because as you said,"},{"speaker":"Pam Harris","startTime":1194.72,"endTime":1197.15,"body":"as you're walking down the fence"},{"speaker":"Pam Harris","startTime":1197.15,"endTime":1199.04,"body":"plus and I'm gonna actually use"},{"speaker":"Pam Harris","startTime":1197.15,"endTime":1199.04,"body":"the numbers we used in the"},{"speaker":"Pam Harris","startTime":1199.04,"endTime":1204.32,"body":"string so 34 to 40. So if I"},{"speaker":"Pam Harris","startTime":1199.04,"endTime":1204.32,"body":"start at the 34th fence post,"},{"speaker":"Pam Harris","startTime":1204.32,"endTime":1206.75,"body":"but I'm not counting it, because"},{"speaker":"Pam Harris","startTime":1204.32,"endTime":1206.75,"body":"I'm thinking about distance,"},{"speaker":"Pam Harris","startTime":1207.14,"endTime":1212.72,"body":"then I'm going to count that"},{"speaker":"Pam Harris","startTime":1207.14,"endTime":1212.72,"body":"span from 34 to 35. That's also"},{"speaker":"Pam Harris","startTime":1212.72,"endTime":1217.01,"body":"equivalent to counting the 35th"},{"speaker":"Pam Harris","startTime":1212.72,"endTime":1217.01,"body":"fence post. Then I count the"},{"speaker":"Pam Harris","startTime":1217.01,"endTime":1222.17,"body":"span from 35 to 36. That's like"},{"speaker":"Pam Harris","startTime":1217.01,"endTime":1222.17,"body":"I've grabbed the 36th fence"},{"speaker":"Pam Harris","startTime":1222.17,"endTime":1228.17,"body":"post, 36 to 37. So as I count"},{"speaker":"Pam Harris","startTime":1222.17,"endTime":1228.17,"body":"each of the spans, I'm also kind"},{"speaker":"Pam Harris","startTime":1228.17,"endTime":1233.09,"body":"of grabbing the fence posts that"},{"speaker":"Pam Harris","startTime":1228.17,"endTime":1233.09,"body":"goes with it. But I've missed"},{"speaker":"Pam Harris","startTime":1233.12,"endTime":1237.17,"body":"the first fence post if I do it"},{"speaker":"Pam Harris","startTime":1233.12,"endTime":1237.17,"body":"that way. So you're saying I can"},{"speaker":"Pam Harris","startTime":1237.17,"endTime":1239.81,"body":"just count the number of spans"},{"speaker":"Pam Harris","startTime":1237.17,"endTime":1239.81,"body":"because that's equal to the"},{"speaker":"Pam Harris","startTime":1239.81,"endTime":1242.57,"body":"number of fence posts. But then"},{"speaker":"Pam Harris","startTime":1239.81,"endTime":1242.57,"body":"I'm going to add one more,"},{"speaker":"Pam Harris","startTime":1242.57,"endTime":1244.37,"body":"because I would have missed the"},{"speaker":"Pam Harris","startTime":1242.57,"endTime":1244.37,"body":"first fence post."},{"speaker":"Kim Montague","startTime":1244.37,"endTime":1244.79,"body":"Yeah."},{"speaker":"Pam Harris","startTime":1245.0,"endTime":1250.94,"body":"So y'all, we can"},{"speaker":"Pam Harris","startTime":1245.0,"endTime":1250.94,"body":"help students realize that in"},{"speaker":"Pam Harris","startTime":1250.94,"endTime":1253.52,"body":"fence post problems, we got to"},{"speaker":"Pam Harris","startTime":1250.94,"endTime":1253.52,"body":"go back and grab that first"},{"speaker":"Pam Harris","startTime":1253.52,"endTime":1257.78,"body":"fence post. So if I would have"},{"speaker":"Pam Harris","startTime":1253.52,"endTime":1257.78,"body":"asked you, Kim, a question like,"},{"speaker":"Pam Harris","startTime":1258.68,"endTime":1260.87,"body":"how many mile markers do you"},{"speaker":"Pam Harris","startTime":1258.68,"endTime":1260.87,"body":"need to replace between eight"},{"speaker":"Pam Harris","startTime":1260.87,"endTime":1262.73,"body":"and 13? What would you really"},{"speaker":"Pam Harris","startTime":1260.87,"endTime":1262.73,"body":"have done?"},{"speaker":"Kim Montague","startTime":1263.39,"endTime":1264.89,"body":"I would have"},{"speaker":"Kim Montague","startTime":1263.39,"endTime":1264.89,"body":"thought about the distance"},{"speaker":"Kim Montague","startTime":1264.89,"endTime":1270.83,"body":"between eight and 13, which is"},{"speaker":"Kim Montague","startTime":1264.89,"endTime":1270.83,"body":"five and then added one more. So"},{"speaker":"Kim Montague","startTime":1270.83,"endTime":1271.64,"body":"it's six."},{"speaker":"Pam Harris","startTime":1271.79,"endTime":1275.27,"body":"Bam if it was six."},{"speaker":"Pam Harris","startTime":1271.79,"endTime":1275.27,"body":"That's your strategy. Listeners,"},{"speaker":"Pam Harris","startTime":1275.27,"endTime":1280.07,"body":"I wonder what your strategy is?"},{"speaker":"Pam Harris","startTime":1275.27,"endTime":1280.07,"body":"Hey, y'all, thanks for tuning in"},{"speaker":"Pam Harris","startTime":1280.1,"endTime":1283.01,"body":"and teaching more and more Real"},{"speaker":"Pam Harris","startTime":1280.1,"endTime":1283.01,"body":"Math. To find out more about the"},{"speaker":"Pam Harris","startTime":1283.01,"endTime":1285.56,"body":"math is Figure-Out-Able movement"},{"speaker":"Pam Harris","startTime":1283.01,"endTime":1285.56,"body":"visit mathisFigureOutAble.com."},{"speaker":"Pam Harris","startTime":1287.0,"endTime":1290.21,"body":"Let's keep spreading the word"},{"speaker":"Pam Harris","startTime":1287.0,"endTime":1290.21,"body":"that Math is Figure-Out-Able."}]}