{"version":"1.0.0","segments":[{"speaker":"Pam","startTime":1.05,"endTime":4.29,"body":"Hey, fellow mathematicians!"},{"speaker":"Pam","startTime":1.05,"endTime":4.29,"body":"Welcome to the podcast where"},{"speaker":"Pam","startTime":4.29,"endTime":6.96,"body":"Math is Figure-Out-Able! I'm"},{"speaker":"Pam","startTime":4.29,"endTime":6.96,"body":"Pam."},{"speaker":"Kim","startTime":7.38,"endTime":8.07,"body":"And I'm Kim."},{"speaker":"Pam","startTime":8.4,"endTime":11.52,"body":"And you found a place where"},{"speaker":"Pam","startTime":8.4,"endTime":11.52,"body":"math is not about memorizing and"},{"speaker":"Pam","startTime":11.52,"endTime":17.76,"body":"mimicking, waiting to be told or"},{"speaker":"Pam","startTime":11.52,"endTime":17.76,"body":"shown what to do. But y'all it's"},{"speaker":"Pam","startTime":17.76,"endTime":18.0,"body":"about"},{"speaker":"Pam","startTime":18.0,"endTime":20.46,"body":"making sense of problems. I was"},{"speaker":"Pam","startTime":18.0,"endTime":20.46,"body":"going to say \"since making\"."},{"speaker":"Pam","startTime":20.49,"endTime":24.33,"body":"That will work too. Noticing"},{"speaker":"Pam","startTime":20.49,"endTime":24.33,"body":"patterns and reasoning using"},{"speaker":"Pam","startTime":24.36,"endTime":28.38,"body":"mathematical relationships. We"},{"speaker":"Pam","startTime":24.36,"endTime":28.38,"body":"can mentor students to think and"},{"speaker":"Pam","startTime":28.38,"endTime":32.34,"body":"reason like mathematicians. Not"},{"speaker":"Pam","startTime":28.38,"endTime":32.34,"body":"only are algorithms not"},{"speaker":"Pam","startTime":32.34,"endTime":35.49,"body":"particularly helpful in teaching"},{"speaker":"Pam","startTime":32.34,"endTime":35.49,"body":"mathematics, but rotely"},{"speaker":"Pam","startTime":35.49,"endTime":38.52,"body":"repeating steps actually keeps"},{"speaker":"Pam","startTime":35.49,"endTime":38.52,"body":"students from being the"},{"speaker":"Pam","startTime":38.52,"endTime":40.56,"body":"mathematicians they can be."},{"speaker":"Pam","startTime":38.52,"endTime":40.56,"body":"Woah!"},{"speaker":"Kim","startTime":41.19,"endTime":44.88,"body":"So, Pam, I was checking out"},{"speaker":"Kim","startTime":41.19,"endTime":44.88,"body":"podcast data the other day, and"},{"speaker":"Kim","startTime":44.88,"endTime":48.57,"body":"I saw that we got this really"},{"speaker":"Kim","startTime":44.88,"endTime":48.57,"body":"sweet comment that I hadn't seen"},{"speaker":"Kim","startTime":48.57,"endTime":51.27,"body":"before, and I don't know if you"},{"speaker":"Kim","startTime":48.57,"endTime":51.27,"body":"have. Can I share it before we"},{"speaker":"Kim","startTime":51.27,"endTime":51.81,"body":"get started today?"},{"speaker":"Pam","startTime":51.81,"endTime":53.37,"body":"Yeah, absolutely. I like"},{"speaker":"Pam","startTime":51.81,"endTime":53.37,"body":"sweet comments."},{"speaker":"Kim","startTime":53.37,"endTime":58.77,"body":"So, there is a new comment"},{"speaker":"Kim","startTime":53.37,"endTime":58.77,"body":"on the podcast that says, \"Thank"},{"speaker":"Kim","startTime":58.8,"endTime":63.09,"body":"you, Kim and Pam for helping me"},{"speaker":"Kim","startTime":58.8,"endTime":63.09,"body":"love doing Real Math and"},{"speaker":"Kim","startTime":63.09,"endTime":66.21,"body":"teaching math to my scholars."},{"speaker":"Kim","startTime":63.09,"endTime":66.21,"body":"Doing Real Math is the missing"},{"speaker":"Kim","startTime":66.21,"endTime":69.45,"body":"piece. As I begin to play with a"},{"speaker":"Kim","startTime":66.21,"endTime":69.45,"body":"relationship with numbers myself"},{"speaker":"Kim","startTime":69.45,"endTime":72.66,"body":"I'm becoming a better teacher."},{"speaker":"Kim","startTime":69.45,"endTime":72.66,"body":"Watching my scholars' eyes light"},{"speaker":"Kim","startTime":72.66,"endTime":76.05,"body":"up as things pop for them is why"},{"speaker":"Kim","startTime":72.66,"endTime":76.05,"body":"I teach. Keep on spreading the"},{"speaker":"Kim","startTime":76.05,"endTime":78.93,"body":"message that math is truly"},{"speaker":"Kim","startTime":76.05,"endTime":78.93,"body":"figure-out-able! We are"},{"speaker":"Kim","startTime":78.93,"endTime":79.5,"body":"listening!\""},{"speaker":"Pam","startTime":79.92,"endTime":80.37,"body":"Whoa!"},{"speaker":"Kim","startTime":80.43,"endTime":83.58,"body":"And that's from a listener"},{"speaker":"Kim","startTime":80.43,"endTime":83.58,"body":"called OneRedJeepGirl. So,"},{"speaker":"Kim","startTime":83.58,"endTime":84.78,"body":"thanks so much for listening."},{"speaker":"Pam","startTime":85.2,"endTime":87.93,"body":"Well, OneRedJeepGirl,"},{"speaker":"Pam","startTime":85.2,"endTime":87.93,"body":"you're amazing, and we sure"},{"speaker":"Pam","startTime":87.93,"endTime":90.81,"body":"appreciate you listening. And"},{"speaker":"Pam","startTime":87.93,"endTime":90.81,"body":"thanks for that feedback. That's"},{"speaker":"Pam","startTime":90.81,"endTime":94.65,"body":"awesome! What a great way to"},{"speaker":"Pam","startTime":90.81,"endTime":94.65,"body":"start the day. Nice. Nice. Yeah,"},{"speaker":"Pam","startTime":95.1,"endTime":99.81,"body":"scholars eyes lighting up is"},{"speaker":"Pam","startTime":95.1,"endTime":99.81,"body":"definitely the reason we teach,"},{"speaker":"Pam","startTime":99.81,"endTime":100.14,"body":"right?"},{"speaker":"Kim","startTime":100.41,"endTime":100.5,"body":"Yeah."},{"speaker":"Pam","startTime":100.98,"endTime":104.16,"body":"And if we can actually then"},{"speaker":"Pam","startTime":100.98,"endTime":104.16,"body":"teach Real Math, that is"},{"speaker":"Pam","startTime":104.16,"endTime":106.29,"body":"amazing. Super important."},{"speaker":"Pam","startTime":104.16,"endTime":106.29,"body":"Awesome."},{"speaker":"Kim","startTime":106.29,"endTime":106.86,"body":"Yeah, really cool."},{"speaker":"Kim","startTime":107.43,"endTime":110.22,"body":"So, today, we're going to kick"},{"speaker":"Kim","startTime":107.43,"endTime":110.22,"body":"off a short series about a model"},{"speaker":"Kim","startTime":110.22,"endTime":114.81,"body":"that we love and find so much"},{"speaker":"Kim","startTime":110.22,"endTime":114.81,"body":"value in. But we think it's"},{"speaker":"Kim","startTime":114.81,"endTime":118.14,"body":"gotten a little bit of a bad"},{"speaker":"Kim","startTime":114.81,"endTime":118.14,"body":"name as people have tried to"},{"speaker":"Kim","startTime":118.14,"endTime":121.56,"body":"make use of it. So, today's"},{"speaker":"Kim","startTime":118.14,"endTime":121.56,"body":"topic is all about the area"},{"speaker":"Kim","startTime":121.56,"endTime":122.01,"body":"model."},{"speaker":"Pam","startTime":122.34,"endTime":128.79,"body":"The area model. Yeah, so"},{"speaker":"Pam","startTime":122.34,"endTime":128.79,"body":"that shouldn't be as tricky as"},{"speaker":"Pam","startTime":128.79,"endTime":133.23,"body":"it is, but it's a little bit."},{"speaker":"Pam","startTime":128.79,"endTime":133.23,"body":"There's some subtle things"},{"speaker":"Pam","startTime":133.23,"endTime":137.61,"body":"happening that we would like to"},{"speaker":"Pam","startTime":133.23,"endTime":137.61,"body":"parse out today. So, let's start"},{"speaker":"Pam","startTime":137.61,"endTime":141.9,"body":"with what do we mean when we"},{"speaker":"Pam","startTime":137.61,"endTime":141.9,"body":"talk about the area model."},{"speaker":"Kim","startTime":142.17,"endTime":142.62,"body":"Yeah."},{"speaker":"Kim","startTime":142.68,"endTime":145.89,"body":"Well, and it's actually... You"},{"speaker":"Kim","startTime":142.68,"endTime":145.89,"body":"know, some people who haven't"},{"speaker":"Kim","startTime":145.92,"endTime":150.63,"body":"done a lot of work with it might"},{"speaker":"Kim","startTime":145.92,"endTime":150.63,"body":"be familiar with it because it's"},{"speaker":"Kim","startTime":150.63,"endTime":154.5,"body":"the model of choice that people"},{"speaker":"Kim","startTime":150.63,"endTime":154.5,"body":"complain about when they're on"},{"speaker":"Kim","startTime":154.5,"endTime":157.08,"body":"social media, and they're"},{"speaker":"Kim","startTime":154.5,"endTime":157.08,"body":"complaining about \"math these"},{"speaker":"Kim","startTime":157.08,"endTime":159.57,"body":"days\", and they are quoting"},{"speaker":"Kim","startTime":157.08,"endTime":159.57,"body":"\"math these days\", so you've"},{"speaker":"Kim","startTime":159.57,"endTime":163.92,"body":"seen it. It's a rectangle, but"},{"speaker":"Kim","startTime":159.57,"endTime":163.92,"body":"it could be a square depending"},{"speaker":"Kim","startTime":163.92,"endTime":166.5,"body":"on the dimensions. And it's what"},{"speaker":"Kim","startTime":163.92,"endTime":166.5,"body":"people sketch when they're"},{"speaker":"Kim","startTime":166.5,"endTime":171.21,"body":"solving a multiplication"},{"speaker":"Kim","startTime":166.5,"endTime":171.21,"body":"problem. So, if I were asked 18"},{"speaker":"Kim","startTime":171.27,"endTime":177.3,"body":"times 25, I would write 18 on"},{"speaker":"Kim","startTime":171.27,"endTime":177.3,"body":"one dimension of the rectangle"},{"speaker":"Kim","startTime":177.3,"endTime":180.18,"body":"and 25 on the other dimension of"},{"speaker":"Kim","startTime":177.3,"endTime":180.18,"body":"the rectangle. So, it would be a"},{"speaker":"Kim","startTime":180.18,"endTime":183.72,"body":"little bit longer. And then, I"},{"speaker":"Kim","startTime":180.18,"endTime":183.72,"body":"would consider cutting that"},{"speaker":"Kim","startTime":183.72,"endTime":187.8,"body":"problem up in different ways to"},{"speaker":"Kim","startTime":183.72,"endTime":187.8,"body":"solve the parts of that problem."},{"speaker":"Kim","startTime":187.8,"endTime":190.62,"body":"So, that representation is the"},{"speaker":"Kim","startTime":187.8,"endTime":190.62,"body":"area model."},{"speaker":"Pam","startTime":191.04,"endTime":194.16,"body":"Yeah, interestingly, you"},{"speaker":"Pam","startTime":191.04,"endTime":194.16,"body":"just really said that you're"},{"speaker":"Pam","startTime":194.16,"endTime":200.37,"body":"going to cut up that rectangle"},{"speaker":"Pam","startTime":194.16,"endTime":200.37,"body":"in intelligent ways, to solve"},{"speaker":"Pam","startTime":200.37,"endTime":203.13,"body":"parts of the problem, to then"},{"speaker":"Pam","startTime":200.37,"endTime":203.13,"body":"help you kind of solve the whole"},{"speaker":"Pam","startTime":203.13,"endTime":203.97,"body":"problem, right?"},{"speaker":"Kim","startTime":203.97,"endTime":204.0,"body":"Mmhmm."},{"speaker":"Pam","startTime":204.48,"endTime":208.23,"body":"So, you've just talked"},{"speaker":"Pam","startTime":204.48,"endTime":208.23,"body":"about labeling the length and"},{"speaker":"Pam","startTime":208.23,"endTime":212.94,"body":"the width of a rectangle, and by"},{"speaker":"Pam","startTime":208.23,"endTime":212.94,"body":"doing so you're actually then..."},{"speaker":"Pam","startTime":213.6,"endTime":215.94,"body":"To solve a multiplication"},{"speaker":"Pam","startTime":213.6,"endTime":215.94,"body":"problem. You're saying, \"If this"},{"speaker":"Pam","startTime":215.94,"endTime":218.61,"body":"is length by that width...\" then"},{"speaker":"Pam","startTime":215.94,"endTime":218.61,"body":"you're really sort of counting"},{"speaker":"Pam","startTime":218.61,"endTime":223.8,"body":"all of those unit squares. That"},{"speaker":"Pam","startTime":218.61,"endTime":223.8,"body":"if you have an 18 by 25, then"},{"speaker":"Pam","startTime":223.8,"endTime":226.5,"body":"you would have these little tiny"},{"speaker":"Pam","startTime":223.8,"endTime":226.5,"body":"1 by 1 squares, and you would"},{"speaker":"Pam","startTime":226.5,"endTime":231.15,"body":"have 18 by 25 of them. And as"},{"speaker":"Pam","startTime":226.5,"endTime":231.15,"body":"you're counting those little"},{"speaker":"Pam","startTime":231.15,"endTime":234.3,"body":"unit squares, that's the area of"},{"speaker":"Pam","startTime":231.15,"endTime":234.3,"body":"that rectangle, right? So, you"},{"speaker":"Pam","startTime":234.3,"endTime":237.18,"body":"have the length and the width of"},{"speaker":"Pam","startTime":234.3,"endTime":237.18,"body":"a rectangle, and all those unit"},{"speaker":"Pam","startTime":237.18,"endTime":240.63,"body":"squares. Added up together,"},{"speaker":"Pam","startTime":237.18,"endTime":240.63,"body":"that's the area. So, the"},{"speaker":"Pam","startTime":240.63,"endTime":244.44,"body":"dimensions of the rectangle are"},{"speaker":"Pam","startTime":240.63,"endTime":244.44,"body":"like the factors in a"},{"speaker":"Pam","startTime":244.44,"endTime":247.8,"body":"multiplication problem. And the"},{"speaker":"Pam","startTime":244.44,"endTime":247.8,"body":"area of the rectangle is like"},{"speaker":"Pam","startTime":247.8,"endTime":250.77,"body":"the product of that"},{"speaker":"Pam","startTime":247.8,"endTime":250.77,"body":"multiplication problem, so we"},{"speaker":"Pam","startTime":250.77,"endTime":254.85,"body":"have this correlation between"},{"speaker":"Pam","startTime":250.77,"endTime":254.85,"body":"factors and products, and"},{"speaker":"Pam","startTime":254.88,"endTime":261.33,"body":"dimensions and area, right?"},{"speaker":"Pam","startTime":254.88,"endTime":261.33,"body":"Okay, so, we've though seen"},{"speaker":"Pam","startTime":261.45,"endTime":266.7,"body":"people do some rote memorizable"},{"speaker":"Pam","startTime":261.45,"endTime":266.7,"body":"stuff with what they're calling"},{"speaker":"Pam","startTime":266.7,"endTime":271.95,"body":"an area model, but they're"},{"speaker":"Pam","startTime":266.7,"endTime":271.95,"body":"actually using it more as a"},{"speaker":"Pam","startTime":271.98,"endTime":277.44,"body":"procedure. So, for example, we"},{"speaker":"Pam","startTime":271.98,"endTime":277.44,"body":"see an 18 by 25. Someone's"},{"speaker":"Pam","startTime":277.44,"endTime":282.42,"body":"solving the problem 18 times 25,"},{"speaker":"Pam","startTime":277.44,"endTime":282.42,"body":"and they've drawn a square. And"},{"speaker":"Pam","startTime":282.45,"endTime":286.32,"body":"we are like, \"But hang on. The"},{"speaker":"Pam","startTime":282.45,"endTime":286.32,"body":"length of 18 should be...\" In"},{"speaker":"Pam","startTime":286.32,"endTime":288.39,"body":"fact, I just grabbed my pen. I"},{"speaker":"Pam","startTime":286.32,"endTime":288.39,"body":"don't know if you can hear me"},{"speaker":"Pam","startTime":288.39,"endTime":291.51,"body":"click it there. There, I'm"},{"speaker":"Pam","startTime":288.39,"endTime":291.51,"body":"clicking. Because I'm a pen"},{"speaker":"Pam","startTime":291.51,"endTime":293.16,"body":"person, Kim, not pencil."},{"speaker":"Kim","startTime":294.45,"endTime":295.2,"body":"You can be wrong."},{"speaker":"Pam","startTime":296.61,"endTime":300.9,"body":"I drew a length of 18. When"},{"speaker":"Pam","startTime":296.61,"endTime":300.9,"body":"I draw the other side of the"},{"speaker":"Pam","startTime":300.9,"endTime":304.29,"body":"rectangle as 25, If that's the"},{"speaker":"Pam","startTime":300.9,"endTime":304.29,"body":"problem I'm going to represent"},{"speaker":"Pam","startTime":304.38,"endTime":308.04,"body":"as the rectangle that's 18 by"},{"speaker":"Pam","startTime":304.38,"endTime":308.04,"body":"25, that 25 should be longer"},{"speaker":"Pam","startTime":308.04,"endTime":311.85,"body":"than the 18. Now, not like twice"},{"speaker":"Pam","startTime":308.04,"endTime":311.85,"body":"as long, right? Twice as long"},{"speaker":"Pam","startTime":311.85,"endTime":315.57,"body":"and be 36. It's not 36, it's"},{"speaker":"Pam","startTime":311.85,"endTime":315.57,"body":"only 25. But it's also not the"},{"speaker":"Pam","startTime":315.57,"endTime":319.17,"body":"same length as 18. It certainly"},{"speaker":"Pam","startTime":315.57,"endTime":319.17,"body":"shouldn't be shorter than 18."},{"speaker":"Pam","startTime":319.53,"endTime":323.4,"body":"The typical thing that we see"},{"speaker":"Pam","startTime":319.53,"endTime":323.4,"body":"that kind of is going awry is we"},{"speaker":"Pam","startTime":323.4,"endTime":326.73,"body":"see people drawing a square, not"},{"speaker":"Pam","startTime":323.4,"endTime":326.73,"body":"a rectangle. And in this case,"},{"speaker":"Pam","startTime":326.73,"endTime":329.76,"body":"it should be a rectangle because"},{"speaker":"Pam","startTime":326.73,"endTime":329.76,"body":"18 and 25 are not the same"},{"speaker":"Pam","startTime":330.33,"endTime":334.35,"body":"length. So, if I see someone"},{"speaker":"Pam","startTime":330.33,"endTime":334.35,"body":"solving a multiplication problem"},{"speaker":"Pam","startTime":334.35,"endTime":339.27,"body":"using a square when the"},{"speaker":"Pam","startTime":334.35,"endTime":339.27,"body":"dimensions aren't square, then"},{"speaker":"Pam","startTime":339.3,"endTime":342.69,"body":"instantly I have a little bit of"},{"speaker":"Pam","startTime":339.3,"endTime":342.69,"body":"a... What do I want to say? The"},{"speaker":"Pam","startTime":342.69,"endTime":345.03,"body":"hair raises on the back of my"},{"speaker":"Pam","startTime":342.69,"endTime":345.03,"body":"neck. It's a little bit like,"},{"speaker":"Pam","startTime":346.41,"endTime":348.36,"body":"\"Mmm...\"  I start to twitch just"},{"speaker":"Pam","startTime":346.41,"endTime":348.36,"body":"a little bit. I'm like, \"Umm,"},{"speaker":"Pam","startTime":348.72,"endTime":354.66,"body":"so...\" It appears to me, when"},{"speaker":"Pam","startTime":348.72,"endTime":354.66,"body":"people start that way, that then"},{"speaker":"Pam","startTime":354.66,"endTime":357.87,"body":"they're heading down a road of"},{"speaker":"Pam","startTime":354.66,"endTime":357.87,"body":"rote memorizable or what I might"},{"speaker":"Pam","startTime":357.87,"endTime":361.59,"body":"call fake mathing. It's not"},{"speaker":"Pam","startTime":357.87,"endTime":361.59,"body":"really fake math, but it's"},{"speaker":"Pam","startTime":361.62,"endTime":365.58,"body":"definitely fake mathing. I'm not"},{"speaker":"Pam","startTime":361.62,"endTime":365.58,"body":"doing the mathematizing that a"},{"speaker":"Pam","startTime":365.58,"endTime":368.7,"body":"mathematician would do. I might"},{"speaker":"Pam","startTime":365.58,"endTime":368.7,"body":"be using that square as more of"},{"speaker":"Pam","startTime":368.7,"endTime":373.2,"body":"a graphic organizer to keep"},{"speaker":"Pam","startTime":368.7,"endTime":373.2,"body":"track of steps, to keep track of"},{"speaker":"Pam","startTime":373.2,"endTime":374.16,"body":"a procedure."},{"speaker":"Kim","startTime":374.52,"endTime":374.64,"body":"Right."},{"speaker":"Pam","startTime":374.64,"endTime":377.25,"body":"So, I'm going to sort of"},{"speaker":"Pam","startTime":374.64,"endTime":377.25,"body":"talk about what it might look"},{"speaker":"Pam","startTime":377.25,"endTime":380.1,"body":"like because we're just... We're"},{"speaker":"Pam","startTime":377.25,"endTime":380.1,"body":"not visual here. We're just"},{"speaker":"Pam","startTime":380.1,"endTime":383.46,"body":"audio. So, that 18 by 25."},{"speaker":"Pam","startTime":380.1,"endTime":383.46,"body":"Somebody might draw a square,"},{"speaker":"Pam","startTime":383.46,"endTime":386.13,"body":"and so I just drew a square, and"},{"speaker":"Pam","startTime":383.46,"endTime":386.13,"body":"I put 18 on one side, and I put"},{"speaker":"Pam","startTime":386.13,"endTime":389.97,"body":"25 on one side. And then, they"},{"speaker":"Pam","startTime":386.13,"endTime":389.97,"body":"tend to cut that square evenly"},{"speaker":"Pam","startTime":390.0,"endTime":395.31,"body":"into 4 chunks. Again, if I'm"},{"speaker":"Pam","startTime":390.0,"endTime":395.31,"body":"cutting... Well, I'll let me"},{"speaker":"Pam","startTime":395.31,"endTime":398.52,"body":"keep going. If I cut it into 4"},{"speaker":"Pam","startTime":395.31,"endTime":398.52,"body":"chunks, then we often see that"},{"speaker":"Pam","startTime":398.52,"endTime":403.44,"body":"they label the first sort of cut"},{"speaker":"Pam","startTime":398.52,"endTime":403.44,"body":"on the 18 side. They'll label"},{"speaker":"Pam","startTime":403.44,"endTime":406.47,"body":"that 10. And then, the second"},{"speaker":"Pam","startTime":403.44,"endTime":406.47,"body":"cut, they'll label 8. Because"},{"speaker":"Pam","startTime":406.47,"endTime":410.85,"body":"they cut the 18 into place value"},{"speaker":"Pam","startTime":406.47,"endTime":410.85,"body":"parts. 10 and 8, 18. 10 and 8."},{"speaker":"Pam","startTime":411.3,"endTime":414.36,"body":"And then, for the 25, they'll"},{"speaker":"Pam","startTime":411.3,"endTime":414.36,"body":"cut the 25 into place value"},{"speaker":"Pam","startTime":414.36,"endTime":418.68,"body":"parts, 20 and 5. But there's a"},{"speaker":"Pam","startTime":414.36,"endTime":418.68,"body":"problem. If I've just cut that"},{"speaker":"Pam","startTime":418.68,"endTime":420.72,"body":"square. Remember, it shouldn't"},{"speaker":"Pam","startTime":418.68,"endTime":420.72,"body":"have been a square, should have"},{"speaker":"Pam","startTime":420.72,"endTime":423.45,"body":"been a rectangle. 25 is longer"},{"speaker":"Pam","startTime":420.72,"endTime":423.45,"body":"than 18. But they've drawn a"},{"speaker":"Pam","startTime":423.45,"endTime":427.44,"body":"square, and then they've cut the"},{"speaker":"Pam","startTime":423.45,"endTime":427.44,"body":"18 into 10, and then cut the 25"},{"speaker":"Pam","startTime":427.44,"endTime":431.46,"body":"into 20. Now, I have this other"},{"speaker":"Pam","startTime":427.44,"endTime":431.46,"body":"square because I've cut that big"},{"speaker":"Pam","startTime":431.46,"endTime":436.14,"body":"square into 4 squares. So, I"},{"speaker":"Pam","startTime":431.46,"endTime":436.14,"body":"have that top left square now"},{"speaker":"Pam","startTime":436.14,"endTime":440.91,"body":"labeled as a 10 by 20. Well, it"},{"speaker":"Pam","startTime":436.14,"endTime":440.91,"body":"shouldn't be a square if it's a"},{"speaker":"Pam","startTime":440.91,"endTime":444.27,"body":"10 by 20, right? Like it should"},{"speaker":"Pam","startTime":440.91,"endTime":444.27,"body":"be... If the one side is 10,"},{"speaker":"Pam","startTime":444.27,"endTime":446.61,"body":"then the other side should be"},{"speaker":"Pam","startTime":444.27,"endTime":446.61,"body":"exactly twice as long because"},{"speaker":"Pam","startTime":446.61,"endTime":451.08,"body":"that's 20. So, we now have lots"},{"speaker":"Pam","startTime":446.61,"endTime":451.08,"body":"of things that are mislabeled."},{"speaker":"Pam","startTime":451.08,"endTime":454.41,"body":"We're calling it an area model"},{"speaker":"Pam","startTime":451.08,"endTime":454.41,"body":"or an area diagram, but we're"},{"speaker":"Pam","startTime":454.41,"endTime":456.72,"body":"not really representing area at"},{"speaker":"Pam","startTime":454.41,"endTime":456.72,"body":"all."},{"speaker":"Kim","startTime":456.75,"endTime":456.96,"body":"Right."},{"speaker":"Pam","startTime":456.96,"endTime":460.95,"body":"What we're doing is we're,"},{"speaker":"Pam","startTime":456.96,"endTime":460.95,"body":"if we're doing it this way, we"},{"speaker":"Pam","startTime":460.95,"endTime":466.86,"body":"are chunking the multiplication"},{"speaker":"Pam","startTime":460.95,"endTime":466.86,"body":"problem into place value chunks,"},{"speaker":"Pam","startTime":467.16,"endTime":469.41,"body":"and then we're kind of saying"},{"speaker":"Pam","startTime":467.16,"endTime":469.41,"body":"\"Alright, so now I'm looking at"},{"speaker":"Pam","startTime":469.41,"endTime":471.99,"body":"this particular chunk, and I'm"},{"speaker":"Pam","startTime":469.41,"endTime":471.99,"body":"thinking that that's a 10 by"},{"speaker":"Pam","startTime":471.99,"endTime":474.33,"body":"20.\" But it's not really a 10 by"},{"speaker":"Pam","startTime":471.99,"endTime":474.33,"body":"20 because I haven't represented"},{"speaker":"Pam","startTime":474.33,"endTime":477.36,"body":"that way. But I'm thinking 10"},{"speaker":"Pam","startTime":474.33,"endTime":477.36,"body":"times 20. So, then, I think"},{"speaker":"Pam","startTime":477.36,"endTime":480.09,"body":"about 10 times 20, and I might"},{"speaker":"Pam","startTime":477.36,"endTime":480.09,"body":"fill that in with 200. And then,"},{"speaker":"Pam","startTime":480.09,"endTime":483.33,"body":"I'm looking at the one next to"},{"speaker":"Pam","startTime":480.09,"endTime":483.33,"body":"it. That will be a 10 times 5."},{"speaker":"Pam","startTime":483.33,"endTime":488.1,"body":"It should be a 10 by 5, which"},{"speaker":"Pam","startTime":483.33,"endTime":488.1,"body":"should be now twice as high as"},{"speaker":"Pam","startTime":488.1,"endTime":492.51,"body":"it is wide right? 10 by 5. But"},{"speaker":"Pam","startTime":488.1,"endTime":492.51,"body":"I've represented it as a square"},{"speaker":"Pam","startTime":492.51,"endTime":494.55,"body":"because I'm not thinking about"},{"speaker":"Pam","startTime":492.51,"endTime":494.55,"body":"area model. I'm used to using it"},{"speaker":"Pam","startTime":494.55,"endTime":497.94,"body":"as a way to keep track of the"},{"speaker":"Pam","startTime":494.55,"endTime":497.94,"body":"steps. So, then that looks like"},{"speaker":"Pam","startTime":497.97,"endTime":501.75,"body":"50. And then, I'm looking at the"},{"speaker":"Pam","startTime":497.97,"endTime":501.75,"body":"8 by 20. That will be 160. And"},{"speaker":"Pam","startTime":501.75,"endTime":504.96,"body":"then, I'm looking at 8 by 5, and"},{"speaker":"Pam","startTime":501.75,"endTime":504.96,"body":"that would be 40. So, basically,"},{"speaker":"Pam","startTime":504.96,"endTime":509.01,"body":"now I have a square that's split"},{"speaker":"Pam","startTime":504.96,"endTime":509.01,"body":"into 4 squares. And then, in"},{"speaker":"Pam","startTime":509.01,"endTime":512.01,"body":"each of those squares, I have a"},{"speaker":"Pam","startTime":509.01,"endTime":512.01,"body":"partial product. And that's the"},{"speaker":"Pam","startTime":512.01,"endTime":514.56,"body":"definition of what we mean by"},{"speaker":"Pam","startTime":512.01,"endTime":514.56,"body":"partial products. We've done"},{"speaker":"Pam","startTime":514.56,"endTime":517.05,"body":"part of the product. We're"},{"speaker":"Pam","startTime":514.56,"endTime":517.05,"body":"looking for the total product of"},{"speaker":"Pam","startTime":517.05,"endTime":519.6,"body":"18 by 25, but we have these"},{"speaker":"Pam","startTime":517.05,"endTime":519.6,"body":"partial products in each of"},{"speaker":"Pam","startTime":519.6,"endTime":522.63,"body":"these squares. And then, the"},{"speaker":"Pam","startTime":519.6,"endTime":522.63,"body":"kids add those up together. So,"},{"speaker":"Pam","startTime":522.66,"endTime":526.74,"body":"what you've done, listeners, if"},{"speaker":"Pam","startTime":522.66,"endTime":526.74,"body":"that's what you've been using"},{"speaker":"Pam","startTime":527.43,"endTime":529.98,"body":"and calling it an area model, if"},{"speaker":"Pam","startTime":527.43,"endTime":529.98,"body":"you've been using this square to"},{"speaker":"Pam","startTime":529.98,"endTime":533.34,"body":"find the product of factors,"},{"speaker":"Pam","startTime":529.98,"endTime":533.34,"body":"then you've kind of been using"},{"speaker":"Pam","startTime":533.34,"endTime":535.95,"body":"it as a graphic organizer."},{"speaker":"Pam","startTime":533.34,"endTime":535.95,"body":"You've said to yourself, \"I'm"},{"speaker":"Pam","startTime":535.95,"endTime":538.53,"body":"going to find these partial"},{"speaker":"Pam","startTime":535.95,"endTime":538.53,"body":"products and very specifically"},{"speaker":"Pam","startTime":538.56,"endTime":541.56,"body":"place value partial products,"},{"speaker":"Pam","startTime":538.56,"endTime":541.56,"body":"and I'm going to put it in this"},{"speaker":"Pam","startTime":541.56,"endTime":544.35,"body":"square to kind of keep track, so"},{"speaker":"Pam","startTime":541.56,"endTime":544.35,"body":"that I don't miss one of them.\""},{"speaker":"Pam","startTime":544.44,"endTime":546.72,"body":"I get all 4 of the partial"},{"speaker":"Pam","startTime":544.44,"endTime":546.72,"body":"products that I've split by"},{"speaker":"Pam","startTime":546.72,"endTime":549.3,"body":"place value, and then you add"},{"speaker":"Pam","startTime":546.72,"endTime":549.3,"body":"those up together, and you get a"},{"speaker":"Pam","startTime":549.3,"endTime":553.89,"body":"product. If we could just maybe"},{"speaker":"Pam","startTime":549.3,"endTime":553.89,"body":"agree, it's not an area model."},{"speaker":"Pam","startTime":554.04,"endTime":558.24,"body":"Could we agree that if that's"},{"speaker":"Pam","startTime":554.04,"endTime":558.24,"body":"what you've done, you've used a"},{"speaker":"Pam","startTime":558.24,"endTime":561.33,"body":"graphic organizer to make sure"},{"speaker":"Pam","startTime":558.24,"endTime":561.33,"body":"that you've gotten all of the"},{"speaker":"Pam","startTime":561.51,"endTime":564.03,"body":"numbers split into place value,"},{"speaker":"Pam","startTime":561.51,"endTime":564.03,"body":"and then you multiply those"},{"speaker":"Pam","startTime":564.03,"endTime":567.03,"body":"together, and you've added them"},{"speaker":"Pam","startTime":564.03,"endTime":567.03,"body":"up, but what it's not is an area"},{"speaker":"Pam","startTime":567.03,"endTime":570.78,"body":"model. It's not representing"},{"speaker":"Pam","startTime":567.03,"endTime":570.78,"body":"area because you drew a square."},{"speaker":"Pam","startTime":571.17,"endTime":575.58,"body":"And then, it's not a smart area"},{"speaker":"Pam","startTime":571.17,"endTime":575.58,"body":"model if when you cut it up, you"},{"speaker":"Pam","startTime":575.61,"endTime":579.21,"body":"always cut it in by place value."},{"speaker":"Pam","startTime":575.61,"endTime":579.21,"body":"If the way you split up the"},{"speaker":"Pam","startTime":579.21,"endTime":581.67,"body":"dimensions for 18 is always 10"},{"speaker":"Pam","startTime":579.21,"endTime":581.67,"body":"and 8, and the way you split it"},{"speaker":"Pam","startTime":581.67,"endTime":586.47,"body":"the 25 is always 20 and 5, then"},{"speaker":"Pam","startTime":581.67,"endTime":586.47,"body":"that's not a very clever way of"},{"speaker":"Pam","startTime":586.47,"endTime":590.88,"body":"finding partial products."},{"speaker":"Pam","startTime":586.47,"endTime":590.88,"body":"Especially for a problem like 18"},{"speaker":"Pam","startTime":590.88,"endTime":595.23,"body":"times 25. What could be a better"},{"speaker":"Pam","startTime":590.88,"endTime":595.23,"body":"way to do that? Well, Kim, I'm"},{"speaker":"Pam","startTime":595.23,"endTime":598.05,"body":"just going to ask you. I'm going"},{"speaker":"Pam","startTime":595.23,"endTime":598.05,"body":"to ask you. If I gave you 18"},{"speaker":"Pam","startTime":598.08,"endTime":602.73,"body":"times 25, what partial products"},{"speaker":"Pam","startTime":598.08,"endTime":602.73,"body":"might you be inclined to use?"},{"speaker":"Pam","startTime":602.79,"endTime":605.76,"body":"Would you just right now do 10"},{"speaker":"Pam","startTime":602.79,"endTime":605.76,"body":"and 8, and 20 and 5, and then"},{"speaker":"Pam","startTime":605.76,"endTime":606.57,"body":"find those 4?"},{"speaker":"Kim","startTime":606.57,"endTime":606.99,"body":"No, no, no."},{"speaker":"Pam","startTime":606.99,"endTime":607.68,"body":"What would you do?"},{"speaker":"Kim","startTime":608.07,"endTime":611.76,"body":"I think off the top of my"},{"speaker":"Kim","startTime":608.07,"endTime":611.76,"body":"head right now, I think do just"},{"speaker":"Kim","startTime":611.76,"endTime":614.82,"body":"split one of the numbers. So, I"},{"speaker":"Kim","startTime":611.76,"endTime":614.82,"body":"think I would just split the 18,"},{"speaker":"Kim","startTime":614.88,"endTime":621.6,"body":"and I would say 10 times 25. And"},{"speaker":"Kim","startTime":614.88,"endTime":621.6,"body":"then, 8 times 25. So, my area"},{"speaker":"Kim","startTime":621.6,"endTime":622.71,"body":"model would just have one cut."},{"speaker":"Pam","startTime":623.7,"endTime":626.76,"body":"And I just drew a 10 by"},{"speaker":"Pam","startTime":623.7,"endTime":626.76,"body":"something that's about 2 and a"},{"speaker":"Pam","startTime":626.76,"endTime":630.36,"body":"1/2 times wider. 10 by 25. And"},{"speaker":"Pam","startTime":626.76,"endTime":630.36,"body":"then, I tacked on the bottom of"},{"speaker":"Pam","startTime":630.36,"endTime":634.65,"body":"that an 8, which is shorter than"},{"speaker":"Pam","startTime":630.36,"endTime":634.65,"body":"the 10 by the same 25. So, I now"},{"speaker":"Pam","startTime":634.65,"endTime":637.44,"body":"have one rectangle that's an 18"},{"speaker":"Pam","startTime":634.65,"endTime":637.44,"body":"by 25 that actually looks like"},{"speaker":"Pam","startTime":637.44,"endTime":640.95,"body":"an 18 by 25. And like you said,"},{"speaker":"Pam","startTime":637.44,"endTime":640.95,"body":"it only has one cut. I only cut"},{"speaker":"Pam","startTime":640.95,"endTime":642.6,"body":"the 18 into 10 and 8, but Kim."},{"speaker":"Kim","startTime":642.6,"endTime":642.9,"body":"Yeah?"},{"speaker":"Kim","startTime":643.08,"endTime":646.315,"body":"You might know 10 times 25. I"},{"speaker":"Kim","startTime":643.08,"endTime":646.315,"body":"mean, that's. Okay. 10 times 10."},{"speaker":"Kim","startTime":646.367,"endTime":649.29,"body":"We can do that. That's... Go"},{"speaker":"Kim","startTime":646.367,"endTime":649.29,"body":"ahead. What is 10 times 25?"},{"speaker":"Kim","startTime":649.29,"endTime":649.74,"body":"Two hundred fifty."},{"speaker":"Pam","startTime":649.8,"endTime":652.47,"body":"That's 250. But you don't"},{"speaker":"Pam","startTime":649.8,"endTime":652.47,"body":"know 8 times 25? That's silly."},{"speaker":"Pam","startTime":652.5,"endTime":653.43,"body":"Like, you wouldn't know that."},{"speaker":"Kim","startTime":654.27,"endTime":654.66,"body":"Well,"},{"speaker":"Kim","startTime":654.66,"endTime":657.6,"body":"so I knew 8 quarters. But even"},{"speaker":"Kim","startTime":654.66,"endTime":657.6,"body":"if you didn't know 8 quarters,"},{"speaker":"Kim","startTime":657.6,"endTime":661.29,"body":"if you know ten 25's, then"},{"speaker":"Kim","startTime":657.6,"endTime":661.29,"body":"figuring eight 25's it's not so"},{"speaker":"Kim","startTime":661.29,"endTime":661.68,"body":"bad."},{"speaker":"Pam","startTime":661.86,"endTime":662.64,"body":"It's just 2 less."},{"speaker":"Kim","startTime":662.67,"endTime":663.63,"body":"Two less 25's. Yeah."},{"speaker":"Pam","startTime":663.99,"endTime":668.07,"body":"(unclear). Oh, and then 250"},{"speaker":"Pam","startTime":663.99,"endTime":668.07,"body":"minus 50, that's just 200. Cool."},{"speaker":"Pam","startTime":668.13,"endTime":670.32,"body":"Hey, tell me about 8 quarters"},{"speaker":"Pam","startTime":668.13,"endTime":670.32,"body":"because that we have listeners"},{"speaker":"Pam","startTime":670.32,"endTime":672.36,"body":"out there who don't think in"},{"speaker":"Pam","startTime":670.32,"endTime":672.36,"body":"terms of quarters. So, do"},{"speaker":"Pam","startTime":672.39,"endTime":672.51,"body":"(unclear)."},{"speaker":"Kim","startTime":673.2,"endTime":673.74,"body":"Yeah, so"},{"speaker":"Kim","startTime":673.74,"endTime":678.93,"body":"4 quarters is $1, so then 8"},{"speaker":"Kim","startTime":673.74,"endTime":678.93,"body":"quarters would be $2, which is"},{"speaker":"Kim","startTime":678.93,"endTime":679.95,"body":"200 cents."},{"speaker":"Pam","startTime":680.28,"endTime":682.86,"body":"Nice. So, 8 times 25 would"},{"speaker":"Pam","startTime":680.28,"endTime":682.86,"body":"be 200. And then, you could add"},{"speaker":"Pam","startTime":682.86,"endTime":686.76,"body":"that 250 and that 200 together"},{"speaker":"Pam","startTime":682.86,"endTime":686.76,"body":"to get 450. And  you're saying"},{"speaker":"Pam","startTime":686.76,"endTime":690.72,"body":"that's 18 times 25. And that"},{"speaker":"Pam","startTime":686.76,"endTime":690.72,"body":"would be a a smart partial"},{"speaker":"Pam","startTime":690.72,"endTime":693.06,"body":"product, not just a place value"},{"speaker":"Pam","startTime":690.72,"endTime":693.06,"body":"partial product, but like a"},{"speaker":"Pam","startTime":693.06,"endTime":694.98,"body":"clever partial product where"},{"speaker":"Pam","startTime":693.06,"endTime":694.98,"body":"you've really thought about"},{"speaker":"Pam","startTime":694.98,"endTime":701.16,"body":"those relationships. So, when"},{"speaker":"Pam","startTime":694.98,"endTime":701.16,"body":"you think that math is rote"},{"speaker":"Pam","startTime":701.16,"endTime":706.89,"body":"memorizable, then you might see"},{"speaker":"Pam","startTime":701.16,"endTime":706.89,"body":"someone saying, \"Use an area"},{"speaker":"Pam","startTime":706.89,"endTime":709.02,"body":"model.\" And you might even"},{"speaker":"Pam","startTime":706.89,"endTime":709.02,"body":"ignore the name. You might just"},{"speaker":"Pam","startTime":709.02,"endTime":710.76,"body":"like, \"Oh, what do you call"},{"speaker":"Pam","startTime":709.02,"endTime":710.76,"body":"that? You call it an area model."},{"speaker":"Pam","startTime":710.76,"endTime":712.65,"body":"I don't know why, but okay."},{"speaker":"Pam","startTime":710.76,"endTime":712.65,"body":"That's its name. It could be the"},{"speaker":"Pam","startTime":712.65,"endTime":715.35,"body":"George model. It could be"},{"speaker":"Pam","startTime":712.65,"endTime":715.35,"body":"the...\" Help me. Give me another"},{"speaker":"Pam","startTime":715.35,"endTime":718.02,"body":"name. \"The Maria model.\" Like,"},{"speaker":"Pam","startTime":715.35,"endTime":718.02,"body":"it could be whatever, right? It"},{"speaker":"Pam","startTime":718.02,"endTime":721.83,"body":"could just be a name that we've"},{"speaker":"Pam","startTime":718.02,"endTime":721.83,"body":"given. \"Oh, okay.\" So, if I come"},{"speaker":"Pam","startTime":721.83,"endTime":725.4,"body":"at this model from a..."},{"speaker":"Pam","startTime":721.83,"endTime":725.4,"body":"Especially if I come at it from"},{"speaker":"Pam","startTime":725.4,"endTime":728.43,"body":"a CRA perspective. But if I come"},{"speaker":"Pam","startTime":725.4,"endTime":728.43,"body":"at it from the perspective of,"},{"speaker":"Pam","startTime":728.43,"endTime":730.17,"body":"\"Oh, this is another new thing"},{"speaker":"Pam","startTime":728.43,"endTime":730.17,"body":"you want me to teach? I don't"},{"speaker":"Pam","startTime":730.17,"endTime":733.5,"body":"know why because math is rote"},{"speaker":"Pam","startTime":730.17,"endTime":733.5,"body":"memorizable, and I know kids"},{"speaker":"Pam","startTime":733.5,"endTime":736.35,"body":"just need the steps. All right,"},{"speaker":"Pam","startTime":733.5,"endTime":736.35,"body":"fine. You're telling me do this"},{"speaker":"Pam","startTime":736.35,"endTime":738.96,"body":"other thing. Okay, what? Let's"},{"speaker":"Pam","startTime":736.35,"endTime":738.96,"body":"see, it looks like what you're"},{"speaker":"Pam","startTime":738.96,"endTime":740.37,"body":"doing is you're drawing a"},{"speaker":"Pam","startTime":738.96,"endTime":740.37,"body":"square, and you're cutting"},{"speaker":"Pam","startTime":740.37,"endTime":743.79,"body":"things by place value. Oh, well,"},{"speaker":"Pam","startTime":740.37,"endTime":743.79,"body":"that's kind of interesting.\""},{"speaker":"Pam","startTime":743.82,"endTime":746.22,"body":"Then you're making me actually"},{"speaker":"Pam","startTime":743.82,"endTime":746.22,"body":"think about the place values."},{"speaker":"Pam","startTime":746.43,"endTime":749.16,"body":"Like, that 10 times 20. I had to"},{"speaker":"Pam","startTime":746.43,"endTime":749.16,"body":"think about 10 times 20 a little"},{"speaker":"Pam","startTime":749.16,"endTime":752.25,"body":"bit. I have to know something."},{"speaker":"Pam","startTime":749.16,"endTime":752.25,"body":"It's not just the digits that"},{"speaker":"Pam","startTime":752.25,"endTime":755.34,"body":"we're used to in the traditional"},{"speaker":"Pam","startTime":752.25,"endTime":755.34,"body":"algorithm. In the traditional"},{"speaker":"Pam","startTime":755.34,"endTime":758.46,"body":"multiplication algorithm, it's"},{"speaker":"Pam","startTime":755.34,"endTime":758.46,"body":"always just digits multiplying"},{"speaker":"Pam","startTime":758.64,"endTime":761.01,"body":"and that magic zero kind of"},{"speaker":"Pam","startTime":758.64,"endTime":761.01,"body":"takes care of the place value as"},{"speaker":"Pam","startTime":761.01,"endTime":762.48,"body":"you shift things over on the"},{"speaker":"Pam","startTime":761.01,"endTime":762.48,"body":"second line."},{"speaker":"Kim","startTime":762.48,"endTime":762.51,"body":"Mmhmm."},{"speaker":"Pam","startTime":762.84,"endTime":765.18,"body":"And so, the algorithms kind"},{"speaker":"Pam","startTime":762.84,"endTime":765.18,"body":"of taking care of that place"},{"speaker":"Pam","startTime":765.18,"endTime":768.51,"body":"value. So, you might, if you"},{"speaker":"Pam","startTime":765.18,"endTime":768.51,"body":"come at it from a math is rote"},{"speaker":"Pam","startTime":768.51,"endTime":771.15,"body":"memorizable perspective, you"},{"speaker":"Pam","startTime":768.51,"endTime":771.15,"body":"might look at this model that"},{"speaker":"Pam","startTime":771.15,"endTime":772.95,"body":"has a name. I don't know. The"},{"speaker":"Pam","startTime":771.15,"endTime":772.95,"body":"area. I don't know if that means"},{"speaker":"Pam","startTime":772.95,"endTime":775.59,"body":"anything. And you might be like,"},{"speaker":"Pam","startTime":772.95,"endTime":775.59,"body":"\"Oh, well, this is a way for the"},{"speaker":"Pam","startTime":775.59,"endTime":778.38,"body":"kids to actually have to think"},{"speaker":"Pam","startTime":775.59,"endTime":778.38,"body":"about the place values involved."},{"speaker":"Pam","startTime":778.44,"endTime":781.11,"body":"Huh. Okay. Alright. And then"},{"speaker":"Pam","startTime":778.44,"endTime":781.11,"body":"they add them up. I mean, that"},{"speaker":"Pam","startTime":781.11,"endTime":782.97,"body":"seems kind of less efficient"},{"speaker":"Pam","startTime":781.11,"endTime":782.97,"body":"than the traditional algorithm,"},{"speaker":"Pam","startTime":782.97,"endTime":784.95,"body":"but if you want me to teach it,"},{"speaker":"Pam","startTime":782.97,"endTime":784.95,"body":"I guess I can. 'Alright,"},{"speaker":"Pam","startTime":784.95,"endTime":787.05,"body":"everybody, here's how you do"},{"speaker":"Pam","startTime":784.95,"endTime":787.05,"body":"it.'\" And then you turn it into"},{"speaker":"Pam","startTime":787.05,"endTime":789.36,"body":"steps because that's what math"},{"speaker":"Pam","startTime":787.05,"endTime":789.36,"body":"is. If you're coming from that"},{"speaker":"Pam","startTime":789.39,"endTime":792.33,"body":"rote memorizing perspective."},{"speaker":"Pam","startTime":789.39,"endTime":792.33,"body":"Again, no blame here, right? I'm"},{"speaker":"Pam","startTime":792.33,"endTime":794.49,"body":"not blaming. Most of us were"},{"speaker":"Pam","startTime":792.33,"endTime":794.49,"body":"taught that that was the"},{"speaker":"Pam","startTime":794.49,"endTime":797.79,"body":"perspective, so I can completely"},{"speaker":"Pam","startTime":794.49,"endTime":797.79,"body":"understand that if that's your"},{"speaker":"Pam","startTime":797.79,"endTime":800.19,"body":"perspective, you would come upon"},{"speaker":"Pam","startTime":797.79,"endTime":800.19,"body":"this model, the George model,"},{"speaker":"Pam","startTime":800.19,"endTime":802.77,"body":"the Maria model, and you would"},{"speaker":"Pam","startTime":800.19,"endTime":802.77,"body":"say, \"Oh, okay. Well, now we're"},{"speaker":"Pam","startTime":802.77,"endTime":805.14,"body":"going to like do this every"},{"speaker":"Pam","startTime":802.77,"endTime":805.14,"body":"time. Okay. 'Students, here's"},{"speaker":"Pam","startTime":805.14,"endTime":808.32,"body":"what you do. Draw a square, cut"},{"speaker":"Pam","startTime":805.14,"endTime":808.32,"body":"the numbers by place value on"},{"speaker":"Pam","startTime":808.32,"endTime":811.29,"body":"each side. Now, do the"},{"speaker":"Pam","startTime":808.32,"endTime":811.29,"body":"multiplications in each of these"},{"speaker":"Pam","startTime":811.29,"endTime":813.33,"body":"bits. Now, add them together.'"},{"speaker":"Pam","startTime":811.29,"endTime":813.33,"body":"Woah! Okay, we've done that"},{"speaker":"Pam","startTime":813.33,"endTime":815.4,"body":"thing. Don't really know why we"},{"speaker":"Pam","startTime":813.33,"endTime":815.4,"body":"did that thing, except they kept"},{"speaker":"Pam","startTime":815.4,"endTime":818.85,"body":"the place values alive. Okay,"},{"speaker":"Pam","startTime":815.4,"endTime":818.85,"body":"fine.\" And can you see maybe"},{"speaker":"Pam","startTime":818.85,"endTime":820.98,"body":"then you made the connection"},{"speaker":"Pam","startTime":818.85,"endTime":820.98,"body":"between those chunks and how it"},{"speaker":"Pam","startTime":820.98,"endTime":822.51,"body":"looked on the traditional"},{"speaker":"Pam","startTime":820.98,"endTime":822.51,"body":"algorithm. And you might be"},{"speaker":"Pam","startTime":822.51,"endTime":824.61,"body":"like, \"Okay, I don't know why we"},{"speaker":"Pam","startTime":822.51,"endTime":824.61,"body":"had to do that, but alright,"},{"speaker":"Pam","startTime":824.61,"endTime":827.82,"body":"we're done,\" if you're coming at"},{"speaker":"Pam","startTime":824.61,"endTime":827.82,"body":"it from a rote memorizer"},{"speaker":"Pam","startTime":827.85,"endTime":830.04,"body":"perspective. But if you're"},{"speaker":"Pam","startTime":827.85,"endTime":830.04,"body":"coming at it from a Math is"},{"speaker":"Pam","startTime":830.04,"endTime":833.13,"body":"Figure-Out-Able perspective,"},{"speaker":"Pam","startTime":830.04,"endTime":833.13,"body":"what real mathematicians do,"},{"speaker":"Pam","startTime":833.13,"endTime":836.19,"body":"what people do when they're"},{"speaker":"Pam","startTime":833.13,"endTime":836.19,"body":"mathing, then you might be more"},{"speaker":"Pam","startTime":836.19,"endTime":840.15,"body":"like Kim. \"Oh, well, if I can"},{"speaker":"Pam","startTime":836.19,"endTime":840.15,"body":"think about an 18 by 25, then I"},{"speaker":"Pam","startTime":840.15,"endTime":844.32,"body":"can cut it in a way that I can"},{"speaker":"Pam","startTime":840.15,"endTime":844.32,"body":"then find those products in a"},{"speaker":"Pam","startTime":844.32,"endTime":847.11,"body":"more efficient, clever kind of"},{"speaker":"Pam","startTime":844.32,"endTime":847.11,"body":"way. I can use that model to"},{"speaker":"Pam","startTime":847.11,"endTime":851.58,"body":"help me think and reason about"},{"speaker":"Pam","startTime":847.11,"endTime":851.58,"body":"how I'm using the nice"},{"speaker":"Pam","startTime":851.58,"endTime":852.72,"body":"relationships to solve that"},{"speaker":"Pam","startTime":851.58,"endTime":852.72,"body":"problem.\""},{"speaker":"Kim","startTime":853.08,"endTime":857.85,"body":"Yeah. So, I'm thinking"},{"speaker":"Kim","startTime":853.08,"endTime":857.85,"body":"about when I was doing some"},{"speaker":"Kim","startTime":857.85,"endTime":863.7,"body":"coaching in my own school, which"},{"speaker":"Kim","startTime":857.85,"endTime":863.7,"body":"is always interesting. You know,"},{"speaker":"Kim","startTime":863.7,"endTime":866.52,"body":"I had done a lot of work in my"},{"speaker":"Kim","startTime":863.7,"endTime":866.52,"body":"classroom with area models, and"},{"speaker":"Kim","startTime":866.52,"endTime":869.94,"body":"I just assumed that other people"},{"speaker":"Kim","startTime":866.52,"endTime":869.94,"body":"thought about them in the same"},{"speaker":"Kim","startTime":869.94,"endTime":872.88,"body":"way that I did, which was a poor"},{"speaker":"Kim","startTime":869.94,"endTime":872.88,"body":"assumption, right? Very poor"},{"speaker":"Kim","startTime":872.88,"endTime":877.74,"body":"assumption. And I remember going"},{"speaker":"Kim","startTime":872.88,"endTime":877.74,"body":"into a classroom and seeing a"},{"speaker":"Kim","startTime":877.74,"endTime":881.52,"body":"teacher do exactly what you're"},{"speaker":"Kim","startTime":877.74,"endTime":881.52,"body":"describing, square and cutting"},{"speaker":"Kim","startTime":881.52,"endTime":883.98,"body":"up into chunks, and my"},{"speaker":"Kim","startTime":881.52,"endTime":883.98,"body":"favorite..."},{"speaker":"Pam","startTime":884.58,"endTime":886.26,"body":"Cutting it up into the same"},{"speaker":"Pam","startTime":884.58,"endTime":886.26,"body":"chunks, right?"},{"speaker":"Kim","startTime":886.26,"endTime":887.43,"body":"In chunks, same chunks,"},{"speaker":"Kim","startTime":886.26,"endTime":887.43,"body":"but..."},{"speaker":"Pam","startTime":887.0,"endTime":890.24,"body":"Four squares, a square cut"},{"speaker":"Pam","startTime":887.0,"endTime":890.24,"body":"into 4 squares. Mmhmm."},{"speaker":"Kim","startTime":890.25,"endTime":893.22,"body":"But the best is when you"},{"speaker":"Kim","startTime":890.25,"endTime":893.22,"body":"come across a problem where it's"},{"speaker":"Kim","startTime":893.22,"endTime":901.02,"body":"like 40 times 20, and kids are"},{"speaker":"Kim","startTime":893.22,"endTime":901.02,"body":"dutifully drawing a square,"},{"speaker":"Kim","startTime":901.05,"endTime":904.17,"body":"cutting into 4 chunks, and then"},{"speaker":"Kim","startTime":901.05,"endTime":904.17,"body":"they write the 4, 0 for the 40"},{"speaker":"Kim","startTime":904.17,"endTime":908.73,"body":"on one side and the 2, 0. Like,"},{"speaker":"Kim","startTime":904.17,"endTime":908.73,"body":"all the zeros, right? So,"},{"speaker":"Kim","startTime":908.73,"endTime":908.76,"body":"(unclear)."},{"speaker":"Pam","startTime":908.76,"endTime":911.04,"body":"Hey, I got one better for"},{"speaker":"Pam","startTime":908.76,"endTime":911.04,"body":"you. I got one better for you. I"},{"speaker":"Pam","startTime":911.04,"endTime":913.71,"body":"was at a campus. It was probably"},{"speaker":"Pam","startTime":911.04,"endTime":913.71,"body":"about the same time. And I saw a"},{"speaker":"Pam","startTime":913.71,"endTime":916.62,"body":"teacher, or I saw a kid really,"},{"speaker":"Pam","startTime":913.71,"endTime":916.62,"body":"supposed to multiply something"},{"speaker":"Pam","startTime":916.62,"endTime":921.39,"body":"like 5 times 14, drew a square"},{"speaker":"Pam","startTime":916.62,"endTime":921.39,"body":"and cut the square to 4 chunks."},{"speaker":"Pam","startTime":921.57,"endTime":926.49,"body":"On the 5 side wrote 0 and then"},{"speaker":"Pam","startTime":921.57,"endTime":926.49,"body":"5, and on the 14 wrote 10 and 4"},{"speaker":"Pam","startTime":926.49,"endTime":931.17,"body":"and then dutifully multiplied 0"},{"speaker":"Pam","startTime":926.49,"endTime":931.17,"body":"times 10, 0 times 4, 5 times 10,"},{"speaker":"Pam","startTime":931.17,"endTime":934.05,"body":"5 times 4. Like, dutifully"},{"speaker":"Pam","startTime":931.17,"endTime":934.05,"body":"multiplied. I was like, \"What?\""},{"speaker":"Pam","startTime":934.53,"endTime":937.62,"body":"It's so not like it could be."},{"speaker":"Pam","startTime":934.53,"endTime":937.62,"body":"The point is, listeners..."},{"speaker":"Pam","startTime":938.25,"endTime":942.27,"body":"Sorry, we're not trying to be"},{"speaker":"Pam","startTime":938.25,"endTime":942.27,"body":"awnry. We're trying to say, Ah,"},{"speaker":"Pam","startTime":942.42,"endTime":944.97,"body":"that's a misunderstanding that"},{"speaker":"Pam","startTime":942.42,"endTime":944.97,"body":"it's supposed to actually"},{"speaker":"Pam","startTime":944.97,"endTime":949.2,"body":"represent area. So, if it was 5"},{"speaker":"Pam","startTime":944.97,"endTime":949.2,"body":"by 14, it should be a length of"},{"speaker":"Pam","startTime":949.2,"endTime":953.34,"body":"5 by a longer length, like more"},{"speaker":"Pam","startTime":949.2,"endTime":953.34,"body":"than twice as long, almost three"},{"speaker":"Pam","startTime":953.34,"endTime":957.75,"body":"times as long 14. And then, it's"},{"speaker":"Pam","startTime":953.34,"endTime":957.75,"body":"not cut into 4 chunks, right?"},{"speaker":"Pam","startTime":957.75,"endTime":961.26,"body":"It's just a 5 by, and then you"},{"speaker":"Pam","startTime":957.75,"endTime":961.26,"body":"could maybe do 5 by 10. And 5 by"},{"speaker":"Pam","startTime":961.26,"endTime":961.8,"body":"4."},{"speaker":"Kim","startTime":961.83,"endTime":962.04,"body":"Yeah."},{"speaker":"Pam","startTime":962.07,"endTime":964.2,"body":"Like, those two chunks."},{"speaker":"Pam","startTime":962.07,"endTime":964.2,"body":"Sorry, I interrupted your story."},{"speaker":"Kim","startTime":964.32,"endTime":967.62,"body":"That's okay. No, it's fine."},{"speaker":"Kim","startTime":964.32,"endTime":967.62,"body":"You understand what I was saying"},{"speaker":"Kim","startTime":967.62,"endTime":970.23,"body":"because you have a similar"},{"speaker":"Kim","startTime":967.62,"endTime":970.23,"body":"scenario. So, before we move on,"},{"speaker":"Kim","startTime":970.23,"endTime":973.2,"body":"I'm just going to wrap up. You"},{"speaker":"Kim","startTime":970.23,"endTime":973.2,"body":"just said a whole lot, and so"},{"speaker":"Kim","startTime":973.2,"endTime":976.26,"body":"I'm going to wrap up. If we're"},{"speaker":"Kim","startTime":973.2,"endTime":976.26,"body":"talking about a graphic"},{"speaker":"Kim","startTime":976.26,"endTime":980.13,"body":"organizer versus area model. So,"},{"speaker":"Kim","startTime":976.26,"endTime":980.13,"body":"a graphic organizer is really"},{"speaker":"Kim","startTime":980.13,"endTime":983.16,"body":"only helpful if you're going to"},{"speaker":"Kim","startTime":980.13,"endTime":983.16,"body":"proceduralise the place value"},{"speaker":"Kim","startTime":983.16,"endTime":986.1,"body":"partial products. Like,"},{"speaker":"Kim","startTime":983.16,"endTime":986.1,"body":"that's... You might as well call"},{"speaker":"Kim","startTime":986.1,"endTime":988.68,"body":"it a graphic organizer at that"},{"speaker":"Kim","startTime":986.1,"endTime":988.68,"body":"point. But if you're talking"},{"speaker":"Kim","startTime":988.68,"endTime":989.43,"body":"about an (unclear)"},{"speaker":"Pam","startTime":989.7,"endTime":990.93,"body":"Please don't call it an"},{"speaker":"Pam","startTime":989.7,"endTime":990.93,"body":"area model."},{"speaker":"Kim","startTime":990.96,"endTime":991.11,"body":"Right."},{"speaker":"Pam","startTime":991.11,"endTime":993.24,"body":"Like, that's what it is. If"},{"speaker":"Pam","startTime":991.11,"endTime":993.24,"body":"you're like, \"Hey, every time"},{"speaker":"Pam","startTime":993.24,"endTime":996.3,"body":"you're going to see a problem,"},{"speaker":"Pam","startTime":993.24,"endTime":996.3,"body":"do this procedure, \"then fine,"},{"speaker":"Pam","startTime":996.51,"endTime":999.12,"body":"if that's your goal, but then"},{"speaker":"Pam","startTime":996.51,"endTime":999.12,"body":"call the graphic organizer."},{"speaker":"Pam","startTime":999.12,"endTime":999.96,"body":"Sorry, keep going."},{"speaker":"Kim","startTime":1002.33,"endTime":1004.61,"body":"But if you're going to call"},{"speaker":"Kim","startTime":1002.33,"endTime":1004.61,"body":"it an area model, and you're"},{"speaker":"Kim","startTime":1004.61,"endTime":1006.65,"body":"going to think about the area,"},{"speaker":"Kim","startTime":1004.61,"endTime":1006.65,"body":"and you're thinking and"},{"speaker":"Kim","startTime":1006.65,"endTime":1010.49,"body":"reasoning, you're probably not"},{"speaker":"Kim","startTime":1006.65,"endTime":1010.49,"body":"going to do place value chunks,"},{"speaker":"Kim","startTime":1010.55,"endTime":1013.22,"body":"and so there would be different"},{"speaker":"Kim","startTime":1010.55,"endTime":1013.22,"body":"cuts or chunks in your model."},{"speaker":"Kim","startTime":1013.22,"endTime":1015.29,"body":"And heavens, let's make it"},{"speaker":"Kim","startTime":1013.22,"endTime":1015.29,"body":"proportional."},{"speaker":"Pam","startTime":1015.9,"endTime":1019.5,"body":"Yes, please. Yeah, nice."},{"speaker":"Pam","startTime":1015.9,"endTime":1019.5,"body":"So, let's get clear on a few"},{"speaker":"Pam","startTime":1019.5,"endTime":1024.33,"body":"terms at the end of this podcast"},{"speaker":"Pam","startTime":1019.5,"endTime":1024.33,"body":"here. When... Nah, let's just go"},{"speaker":"Pam","startTime":1024.33,"endTime":1026.25,"body":"this way. I was going to do a"},{"speaker":"Pam","startTime":1024.33,"endTime":1026.25,"body":"whole history thing, and I"},{"speaker":"Pam","startTime":1026.25,"endTime":1029.85,"body":"won't. Let's get clear on some"},{"speaker":"Pam","startTime":1026.25,"endTime":1029.85,"body":"terms. So, if you have a"},{"speaker":"Pam","startTime":1029.85,"endTime":1038.25,"body":"discrete array of things. If I"},{"speaker":"Pam","startTime":1029.85,"endTime":1038.25,"body":"have a 4 by 5 array of marbles,"},{"speaker":"Pam","startTime":1038.49,"endTime":1044.22,"body":"like where I literally lineup 4"},{"speaker":"Pam","startTime":1038.49,"endTime":1044.22,"body":"rows by 5 columns of marbles,"},{"speaker":"Pam","startTime":1044.61,"endTime":1048.6,"body":"then that, the term for that is"},{"speaker":"Pam","startTime":1044.61,"endTime":1048.6,"body":"a \"discrete array\". It's an"},{"speaker":"Pam","startTime":1048.6,"endTime":1052.08,"body":"array of objects, and they're"},{"speaker":"Pam","startTime":1048.6,"endTime":1052.08,"body":"discrete because there's a"},{"speaker":"Pam","startTime":1052.08,"endTime":1054.39,"body":"marble, and a marble, and a"},{"speaker":"Pam","startTime":1052.08,"endTime":1054.39,"body":"marble. So, I could have a 4 by"},{"speaker":"Pam","startTime":1054.39,"endTime":1058.14,"body":"5 array of marbles. I could have"},{"speaker":"Pam","startTime":1054.39,"endTime":1058.14,"body":"a 4 by 5 array of post it notes."},{"speaker":"Pam","startTime":1058.14,"endTime":1062.46,"body":"I can have a 4 by 5 array of..."},{"speaker":"Pam","startTime":1058.14,"endTime":1062.46,"body":"Help me? What else? Peanut M\u0026M's"},{"speaker":"Pam","startTime":1062.46,"endTime":1064.98,"body":"That's on my desk over here. I"},{"speaker":"Pam","startTime":1062.46,"endTime":1064.98,"body":"could have a 4... Like, as soon"},{"speaker":"Pam","startTime":1064.98,"endTime":1067.95,"body":"as it's an object, that we call"},{"speaker":"Pam","startTime":1064.98,"endTime":1067.95,"body":"that discrete because it's not a"},{"speaker":"Pam","startTime":1067.95,"endTime":1070.98,"body":"measurement model. It's not a"},{"speaker":"Pam","startTime":1067.95,"endTime":1070.98,"body":"span of things. And so, I could"},{"speaker":"Pam","startTime":1070.98,"endTime":1073.74,"body":"sort of line those guys up, and"},{"speaker":"Pam","startTime":1070.98,"endTime":1073.74,"body":"that's a discrete array of"},{"speaker":"Pam","startTime":1073.74,"endTime":1077.94,"body":"things. Now, as soon as we take"},{"speaker":"Pam","startTime":1073.74,"endTime":1077.94,"body":"that discrete array, and we sort"},{"speaker":"Pam","startTime":1077.94,"endTime":1082.26,"body":"of flatten it out, and we"},{"speaker":"Pam","startTime":1077.94,"endTime":1082.26,"body":"actually are talking about area."},{"speaker":"Pam","startTime":1082.41,"endTime":1085.23,"body":"And maybe I should have left the"},{"speaker":"Pam","startTime":1082.41,"endTime":1085.23,"body":"post it notes for that. Like, if"},{"speaker":"Pam","startTime":1085.23,"endTime":1088.98,"body":"I had a 4 by 5 array of square"},{"speaker":"Pam","startTime":1085.23,"endTime":1088.98,"body":"posted notes. Which I actually"},{"speaker":"Pam","startTime":1088.98,"endTime":1091.56,"body":"have a square post it note right"},{"speaker":"Pam","startTime":1088.98,"endTime":1091.56,"body":"in front of me right here on my"},{"speaker":"Pam","startTime":1091.56,"endTime":1096.06,"body":"desk. If I had 4 of those all"},{"speaker":"Pam","startTime":1091.56,"endTime":1096.06,"body":"lined up next to each other by 5"},{"speaker":"Pam","startTime":1096.06,"endTime":1098.52,"body":"of them all lined up next to"},{"speaker":"Pam","startTime":1096.06,"endTime":1098.52,"body":"each other. I filled that in, so"},{"speaker":"Pam","startTime":1098.52,"endTime":1103.23,"body":"I had a 4 by 5 of these square"},{"speaker":"Pam","startTime":1098.52,"endTime":1103.23,"body":"units next to each other, then"},{"speaker":"Pam","startTime":1103.26,"endTime":1107.34,"body":"that we call a \"closed array\"."},{"speaker":"Pam","startTime":1103.26,"endTime":1107.34,"body":"That's a closed array because"},{"speaker":"Pam","startTime":1107.34,"endTime":1111.36,"body":"we've got all the grid marks."},{"speaker":"Pam","startTime":1107.34,"endTime":1111.36,"body":"So, if you look at grid paper,"},{"speaker":"Pam","startTime":1111.57,"endTime":1116.43,"body":"and you outline 4 rows by 5"},{"speaker":"Pam","startTime":1111.57,"endTime":1116.43,"body":"columns. You outline a rectangle"},{"speaker":"Pam","startTime":1116.43,"endTime":1118.95,"body":"like that, and you've got all"},{"speaker":"Pam","startTime":1116.43,"endTime":1118.95,"body":"the grid marks in the middle,"},{"speaker":"Pam","startTime":1119.22,"endTime":1122.73,"body":"then that is a closed array."},{"speaker":"Pam","startTime":1119.22,"endTime":1122.73,"body":"It's an area model with all the"},{"speaker":"Pam","startTime":1122.73,"endTime":1127.5,"body":"gridlines. A discrete array"},{"speaker":"Pam","startTime":1122.73,"endTime":1127.5,"body":"could be that same 4 by 5 on"},{"speaker":"Pam","startTime":1127.5,"endTime":1129.9,"body":"that grid paper but where I've"},{"speaker":"Pam","startTime":1127.5,"endTime":1129.9,"body":"put a marble in each of those"},{"speaker":"Pam","startTime":1129.93,"endTime":1132.78,"body":"squares. And then, I'm talking"},{"speaker":"Pam","startTime":1129.93,"endTime":1132.78,"body":"about the discrete array would"},{"speaker":"Pam","startTime":1132.78,"endTime":1135.36,"body":"be the marbles, not the"},{"speaker":"Pam","startTime":1132.78,"endTime":1135.36,"body":"gridlines underneath it. The"},{"speaker":"Pam","startTime":1135.36,"endTime":1139.44,"body":"gridlines underneath it would"},{"speaker":"Pam","startTime":1135.36,"endTime":1139.44,"body":"actually represent the area of"},{"speaker":"Pam","startTime":1139.44,"endTime":1144.96,"body":"that 4 by 5. Then, if we sort of"},{"speaker":"Pam","startTime":1139.44,"endTime":1144.96,"body":"lifted out of grid paper, and I"},{"speaker":"Pam","startTime":1144.96,"endTime":1149.76,"body":"draw that 4 by 5, so it's still"},{"speaker":"Pam","startTime":1144.96,"endTime":1149.76,"body":"4 by 5...it's not a square,"},{"speaker":"Pam","startTime":1149.76,"endTime":1154.08,"body":"should be a little bit longer"},{"speaker":"Pam","startTime":1149.76,"endTime":1154.08,"body":"than it is deep...but I don't"},{"speaker":"Pam","startTime":1154.08,"endTime":1157.41,"body":"put all the grid marks in there,"},{"speaker":"Pam","startTime":1154.08,"endTime":1157.41,"body":"then that's called an \"open"},{"speaker":"Pam","startTime":1157.41,"endTime":1161.97,"body":"array\". An open array is where"},{"speaker":"Pam","startTime":1157.41,"endTime":1161.97,"body":"we have well chosen grid lines."},{"speaker":"Pam","startTime":1162.24,"endTime":1166.62,"body":"So, for example, when Kim did 18"},{"speaker":"Pam","startTime":1162.24,"endTime":1166.62,"body":"by 25, and she split it into 10"},{"speaker":"Pam","startTime":1166.62,"endTime":1170.58,"body":"and 8 by 25. That's an open"},{"speaker":"Pam","startTime":1166.62,"endTime":1170.58,"body":"array because we have well"},{"speaker":"Pam","startTime":1170.58,"endTime":1174.33,"body":"chosen grid lines. We only have"},{"speaker":"Pam","startTime":1170.58,"endTime":1174.33,"body":"the grid lines we need. Now, you"},{"speaker":"Pam","startTime":1174.33,"endTime":1179.55,"body":"probably recognize that as a"},{"speaker":"Pam","startTime":1174.33,"endTime":1179.55,"body":"correlation between the open"},{"speaker":"Pam","startTime":1179.55,"endTime":1182.85,"body":"number line. We can have a"},{"speaker":"Pam","startTime":1179.55,"endTime":1182.85,"body":"closed number line. Well, in"},{"speaker":"Pam","startTime":1182.85,"endTime":1185.76,"body":"fact, let me even back up"},{"speaker":"Pam","startTime":1182.85,"endTime":1185.76,"body":"further than that. I can have a"},{"speaker":"Pam","startTime":1185.76,"endTime":1190.41,"body":"line of 10 marbles. I can line"},{"speaker":"Pam","startTime":1185.76,"endTime":1190.41,"body":"up 10 marbles, and I can count"},{"speaker":"Pam","startTime":1190.41,"endTime":1193.26,"body":"those 10 marbles. But as soon as"},{"speaker":"Pam","startTime":1190.41,"endTime":1193.26,"body":"I sort of flatten those out, and"},{"speaker":"Pam","startTime":1193.26,"endTime":1196.44,"body":"I make it more measurement. I"},{"speaker":"Pam","startTime":1193.26,"endTime":1196.44,"body":"make it the distance between"},{"speaker":"Pam","startTime":1196.44,"endTime":1199.59,"body":"tick marks. Now, I have a number"},{"speaker":"Pam","startTime":1196.44,"endTime":1199.59,"body":"line. And if I have all of the"},{"speaker":"Pam","startTime":1199.59,"endTime":1202.74,"body":"tick marks in between 0 and 10,"},{"speaker":"Pam","startTime":1199.59,"endTime":1202.74,"body":"and I'm counting the span"},{"speaker":"Pam","startTime":1202.74,"endTime":1205.53,"body":"between each of those, the"},{"speaker":"Pam","startTime":1202.74,"endTime":1205.53,"body":"measurement from each tick mark"},{"speaker":"Pam","startTime":1205.53,"endTime":1208.92,"body":"to the next one, but I have all"},{"speaker":"Pam","startTime":1205.53,"endTime":1208.92,"body":"of the tick marks, then that's"},{"speaker":"Pam","startTime":1208.92,"endTime":1212.91,"body":"called a closed number line."},{"speaker":"Pam","startTime":1208.92,"endTime":1212.91,"body":"When I have well chosen tick"},{"speaker":"Pam","startTime":1212.91,"endTime":1217.02,"body":"marks, say I'm going to add 8"},{"speaker":"Pam","startTime":1212.91,"endTime":1217.02,"body":"and 6. And so, then I just draw"},{"speaker":"Pam","startTime":1217.02,"endTime":1221.1,"body":"a number line, and I put the"},{"speaker":"Pam","startTime":1217.02,"endTime":1221.1,"body":"tick mark where 8 is, and then I"},{"speaker":"Pam","startTime":1221.1,"endTime":1225.0,"body":"do a hop to 10 and get to that"},{"speaker":"Pam","startTime":1221.1,"endTime":1225.0,"body":"friendly 10, and I put a tick"},{"speaker":"Pam","startTime":1225.0,"endTime":1228.09,"body":"mark where the 10 is, and then I"},{"speaker":"Pam","startTime":1225.0,"endTime":1228.09,"body":"add the rest of it on, the extra"},{"speaker":"Pam","startTime":1228.09,"endTime":1230.64,"body":"4. Because I'm doing 10 and 6."},{"speaker":"Pam","startTime":1228.09,"endTime":1230.64,"body":"So, I did 10 and 2, and then 4"},{"speaker":"Pam","startTime":1230.64,"endTime":1233.61,"body":"more. And I do that extra 4, and"},{"speaker":"Pam","startTime":1230.64,"endTime":1233.61,"body":"I have a tick mark. 10 and 4 is"},{"speaker":"Pam","startTime":1233.61,"endTime":1237.6,"body":"14. Those are well chosen tick"},{"speaker":"Pam","startTime":1233.61,"endTime":1237.6,"body":"marks. That's an open number"},{"speaker":"Pam","startTime":1237.6,"endTime":1242.25,"body":"line. So, just like I can have a"},{"speaker":"Pam","startTime":1237.6,"endTime":1242.25,"body":"bunch of discrete objects to a"},{"speaker":"Pam","startTime":1242.28,"endTime":1245.4,"body":"close number line where I have"},{"speaker":"Pam","startTime":1242.28,"endTime":1245.4,"body":"all the tick marks to an open"},{"speaker":"Pam","startTime":1245.4,"endTime":1248.79,"body":"number line where I have well"},{"speaker":"Pam","startTime":1245.4,"endTime":1248.79,"body":"chosen tick marks, similarly"},{"speaker":"Pam","startTime":1248.82,"endTime":1253.08,"body":"with area I can have a... Or"},{"speaker":"Pam","startTime":1248.82,"endTime":1253.08,"body":"maybe I should say with arrays,"},{"speaker":"Pam","startTime":1253.2,"endTime":1256.11,"body":"I can have a discrete array of"},{"speaker":"Pam","startTime":1253.2,"endTime":1256.11,"body":"objects where I have a number of"},{"speaker":"Pam","startTime":1256.11,"endTime":1259.2,"body":"rows by number of columns. But"},{"speaker":"Pam","startTime":1256.11,"endTime":1259.2,"body":"as soon as we flatten that out,"},{"speaker":"Pam","startTime":1259.2,"endTime":1262.56,"body":"we make it more of a span where"},{"speaker":"Pam","startTime":1259.2,"endTime":1262.56,"body":"I'm actually measuring the span"},{"speaker":"Pam","startTime":1262.56,"endTime":1265.08,"body":"of length by a span of length."},{"speaker":"Pam","startTime":1262.56,"endTime":1265.08,"body":"If you can see my hands right"},{"speaker":"Pam","startTime":1265.08,"endTime":1269.1,"body":"now every time I say \"span\" my"},{"speaker":"Pam","startTime":1265.08,"endTime":1269.1,"body":"hands are moving apart from each"},{"speaker":"Pam","startTime":1269.1,"endTime":1272.34,"body":"other. So, I'm measuring that"},{"speaker":"Pam","startTime":1269.1,"endTime":1272.34,"body":"distance from tick mark to tick"},{"speaker":"Pam","startTime":1272.34,"endTime":1275.1,"body":"marker or between the grid line"},{"speaker":"Pam","startTime":1272.34,"endTime":1275.1,"body":"to grid line. As soon as I'm"},{"speaker":"Pam","startTime":1275.1,"endTime":1278.4,"body":"measuring that distance from the"},{"speaker":"Pam","startTime":1275.1,"endTime":1278.4,"body":"grid lines that are measuring"},{"speaker":"Pam","startTime":1278.4,"endTime":1280.92,"body":"the rows and the distance that"},{"speaker":"Pam","startTime":1278.4,"endTime":1280.92,"body":"are on the grid lines that are"},{"speaker":"Pam","startTime":1280.92,"endTime":1284.34,"body":"measuring the columns, now we"},{"speaker":"Pam","startTime":1280.92,"endTime":1284.34,"body":"create that two dimensional"},{"speaker":"Pam","startTime":1284.34,"endTime":1287.79,"body":"measurement of that unit by unit"},{"speaker":"Pam","startTime":1284.34,"endTime":1287.79,"body":"square. That's area. That's"},{"speaker":"Pam","startTime":1287.79,"endTime":1290.49,"body":"where area comes from. So, we go"},{"speaker":"Pam","startTime":1287.79,"endTime":1290.49,"body":"from the discrete array of"},{"speaker":"Pam","startTime":1290.49,"endTime":1293.88,"body":"items, to a closed array where"},{"speaker":"Pam","startTime":1290.49,"endTime":1293.88,"body":"we have all of the grid lines,"},{"speaker":"Pam","startTime":1294.06,"endTime":1297.57,"body":"to an open array where we have"},{"speaker":"Pam","startTime":1294.06,"endTime":1297.57,"body":"well chosen grid lines."},{"speaker":"Kim","startTime":1297.71,"endTime":1298.16,"body":"Yeah."},{"speaker":"Pam","startTime":1298.94,"endTime":1301.4,"body":"Cool. So, super"},{"speaker":"Pam","startTime":1298.94,"endTime":1301.4,"body":"interesting. Kim, the other day,"},{"speaker":"Pam","startTime":1301.55,"endTime":1304.19,"body":"I was working on this with a"},{"speaker":"Pam","startTime":1301.55,"endTime":1304.19,"body":"group of participants, and one"},{"speaker":"Pam","startTime":1304.19,"endTime":1306.17,"body":"of the participants in the"},{"speaker":"Pam","startTime":1304.19,"endTime":1306.17,"body":"middle of a Problem String"},{"speaker":"Pam","startTime":1306.17,"endTime":1310.13,"body":"looked up and goes, \"Wait, wait."},{"speaker":"Pam","startTime":1306.17,"endTime":1310.13,"body":"So, if we do this with students,"},{"speaker":"Pam","startTime":1310.28,"endTime":1312.74,"body":"they're not just learning about"},{"speaker":"Pam","startTime":1310.28,"endTime":1312.74,"body":"multiplication, but they're"},{"speaker":"Pam","startTime":1312.74,"endTime":1314.18,"body":"actually learning about area.\""},{"speaker":"Kim","startTime":1314.96,"endTime":1317.39,"body":"Oh, that's great! What a"},{"speaker":"Kim","startTime":1314.96,"endTime":1317.39,"body":"good \"aha\" moment for them!"},{"speaker":"Pam","startTime":1317.42,"endTime":1319.31,"body":"Totally great \"aha\" moment!"},{"speaker":"Pam","startTime":1317.42,"endTime":1319.31,"body":"Because in that moment I was"},{"speaker":"Pam","startTime":1319.31,"endTime":1322.76,"body":"like, \"Yeah, and you know what"},{"speaker":"Pam","startTime":1319.31,"endTime":1322.76,"body":"that's why it's called the area"},{"speaker":"Pam","startTime":1322.76,"endTime":1326.36,"body":"model.\" And eyes lit up around"},{"speaker":"Pam","startTime":1322.76,"endTime":1326.36,"body":"the room, and they were like,"},{"speaker":"Pam","startTime":1326.99,"endTime":1329.72,"body":"\"Oh, that's why they call it an"},{"speaker":"Pam","startTime":1326.99,"endTime":1329.72,"body":"area model.\" And I was like,"},{"speaker":"Pam","startTime":1329.72,"endTime":1331.76,"body":"\"Yeah, it's not just a name.\""},{"speaker":"Pam","startTime":1329.72,"endTime":1331.76,"body":"It's not just a name of this"},{"speaker":"Pam","startTime":1332.18,"endTime":1335.21,"body":"procedure that we're doing at"},{"speaker":"Pam","startTime":1332.18,"endTime":1335.21,"body":"all. Like, it actually is"},{"speaker":"Pam","startTime":1335.24,"endTime":1338.72,"body":"intended to teach area and"},{"speaker":"Pam","startTime":1335.24,"endTime":1338.72,"body":"multiplication at the same time."},{"speaker":"Pam","startTime":1338.87,"endTime":1342.5,"body":"And it's one of those places"},{"speaker":"Pam","startTime":1338.87,"endTime":1342.5,"body":"where we can connect spatial"},{"speaker":"Pam","startTime":1342.5,"endTime":1347.69,"body":"reasoning and numeric reasoning"},{"speaker":"Pam","startTime":1342.5,"endTime":1347.69,"body":"at the same time. So, in our"},{"speaker":"Pam","startTime":1347.69,"endTime":1350.0,"body":"experience, Kim, there was a few"},{"speaker":"Pam","startTime":1347.69,"endTime":1350.0,"body":"things that worked and didn't"},{"speaker":"Pam","startTime":1350.0,"endTime":1353.24,"body":"work. I just want to share a"},{"speaker":"Pam","startTime":1350.0,"endTime":1353.24,"body":"couple of those. When we started"},{"speaker":"Pam","startTime":1353.27,"endTime":1355.91,"body":"helping teachers understand,"},{"speaker":"Pam","startTime":1353.27,"endTime":1355.91,"body":"really think and reason about"},{"speaker":"Pam","startTime":1355.91,"endTime":1360.65,"body":"multiplication, and we started"},{"speaker":"Pam","startTime":1355.91,"endTime":1360.65,"body":"using the area model, or maybe I"},{"speaker":"Pam","startTime":1360.65,"endTime":1363.92,"body":"would call it an open array, to"},{"speaker":"Pam","startTime":1360.65,"endTime":1363.92,"body":"help teachers and students"},{"speaker":"Pam","startTime":1363.92,"endTime":1367.34,"body":"reason about multiplication,"},{"speaker":"Pam","startTime":1363.92,"endTime":1367.34,"body":"what didn't really work so well"},{"speaker":"Pam","startTime":1367.79,"endTime":1372.59,"body":"is using the area model or"},{"speaker":"Pam","startTime":1367.79,"endTime":1372.59,"body":"rectangle as a tool for thinking"},{"speaker":"Pam","startTime":1372.59,"endTime":1376.01,"body":"about ugly problems. When the"},{"speaker":"Pam","startTime":1372.59,"endTime":1376.01,"body":"problems were ugly, the"},{"speaker":"Pam","startTime":1376.01,"endTime":1378.98,"body":"dimensions were... Like, one of"},{"speaker":"Pam","startTime":1376.01,"endTime":1378.98,"body":"the ones was way too long and"},{"speaker":"Pam","startTime":1378.98,"endTime":1382.28,"body":"way too short, and then cutting"},{"speaker":"Pam","startTime":1378.98,"endTime":1382.28,"body":"it up. And kids kind of got a"},{"speaker":"Pam","startTime":1382.28,"endTime":1384.59,"body":"little bit sometimes, and"},{"speaker":"Pam","startTime":1382.28,"endTime":1384.59,"body":"teachers too could get a little"},{"speaker":"Pam","startTime":1384.59,"endTime":1388.4,"body":"bit... What's the word I want?"},{"speaker":"Pam","startTime":1384.59,"endTime":1388.4,"body":"Stuck. Or kind of like fussing"},{"speaker":"Pam","startTime":1388.4,"endTime":1391.61,"body":"too much with making the"},{"speaker":"Pam","startTime":1388.4,"endTime":1391.61,"body":"rectangle look exactly right,"},{"speaker":"Pam","startTime":1391.61,"endTime":1393.68,"body":"and not just using it to help"},{"speaker":"Pam","startTime":1391.61,"endTime":1393.68,"body":"them think about the"},{"speaker":"Pam","startTime":1393.68,"endTime":1394.49,"body":"relationships."},{"speaker":"Kim","startTime":1394.64,"endTime":1395.09,"body":"Yeah."},{"speaker":"Pam","startTime":1395.51,"endTime":1399.5,"body":"Especially for division."},{"speaker":"Pam","startTime":1395.51,"endTime":1399.5,"body":"When we started using an area"},{"speaker":"Pam","startTime":1399.5,"endTime":1403.91,"body":"model or an open array to..."},{"speaker":"Pam","startTime":1399.5,"endTime":1403.91,"body":"Maybe I should have done the"},{"speaker":"Pam","startTime":1403.91,"endTime":1406.04,"body":"caveat this a different way. Let"},{"speaker":"Pam","startTime":1403.91,"endTime":1406.04,"body":"me tell you what worked well."},{"speaker":"Pam","startTime":1406.22,"endTime":1410.15,"body":"What worked well was to help"},{"speaker":"Pam","startTime":1406.22,"endTime":1410.15,"body":"kids reason about area, to help"},{"speaker":"Pam","startTime":1410.15,"endTime":1413.36,"body":"them understand that the span by"},{"speaker":"Pam","startTime":1410.15,"endTime":1413.36,"body":"that span created this two"},{"speaker":"Pam","startTime":1413.36,"endTime":1416.18,"body":"dimensional square unit, and"},{"speaker":"Pam","startTime":1413.36,"endTime":1416.18,"body":"that there was something about"},{"speaker":"Pam","startTime":1416.18,"endTime":1420.32,"body":"being able to measure the amount"},{"speaker":"Pam","startTime":1416.18,"endTime":1420.32,"body":"of carpet that you need by the"},{"speaker":"Pam","startTime":1420.32,"endTime":1422.87,"body":"amount of the square units that"},{"speaker":"Pam","startTime":1420.32,"endTime":1422.87,"body":"you could kind of lay out on the"},{"speaker":"Pam","startTime":1422.87,"endTime":1426.68,"body":"carpet. Building their spatial"},{"speaker":"Pam","startTime":1422.87,"endTime":1426.68,"body":"reasoning was great using the"},{"speaker":"Pam","startTime":1426.68,"endTime":1429.59,"body":"area model, using this open"},{"speaker":"Pam","startTime":1426.68,"endTime":1429.59,"body":"array. Making sense of which"},{"speaker":"Pam","startTime":1429.59,"endTime":1434.69,"body":"chunks to use, making sense of"},{"speaker":"Pam","startTime":1429.59,"endTime":1434.69,"body":"dimensions, and factors, and"},{"speaker":"Pam","startTime":1434.69,"endTime":1437.78,"body":"area, and product, making sense"},{"speaker":"Pam","startTime":1434.69,"endTime":1437.78,"body":"of all that, that spatial"},{"speaker":"Pam","startTime":1437.78,"endTime":1441.47,"body":"reasoning, that was brilliant."},{"speaker":"Pam","startTime":1437.78,"endTime":1441.47,"body":"What didn't work so well was"},{"speaker":"Pam","startTime":1441.47,"endTime":1445.22,"body":"then after that saying, \"Now use"},{"speaker":"Pam","startTime":1441.47,"endTime":1445.22,"body":"the area model as a tool to"},{"speaker":"Pam","startTime":1445.22,"endTime":1447.89,"body":"reason about these cranky"},{"speaker":"Pam","startTime":1445.22,"endTime":1447.89,"body":"problems.\" That didn't work as"},{"speaker":"Pam","startTime":1447.89,"endTime":1451.37,"body":"well. What we learned was there"},{"speaker":"Pam","startTime":1447.89,"endTime":1451.37,"body":"was a better tool to reason"},{"speaker":"Pam","startTime":1451.37,"endTime":1454.37,"body":"about the cranky problems, well"},{"speaker":"Pam","startTime":1451.37,"endTime":1454.37,"body":"and really to reason about"},{"speaker":"Pam","startTime":1454.37,"endTime":1456.8,"body":"multiplication, after we built"},{"speaker":"Pam","startTime":1454.37,"endTime":1456.8,"body":"spatial reasoning. So, we're not"},{"speaker":"Pam","startTime":1456.8,"endTime":1459.14,"body":"saying get rid of area model and"},{"speaker":"Pam","startTime":1456.8,"endTime":1459.14,"body":"get rid of the open array. We're"},{"speaker":"Pam","startTime":1459.14,"endTime":1461.24,"body":"not saying get rid of it at all."},{"speaker":"Pam","startTime":1459.14,"endTime":1461.24,"body":"We're saying, that's the place"},{"speaker":"Pam","startTime":1461.24,"endTime":1465.98,"body":"to begin and to build spatial"},{"speaker":"Pam","startTime":1461.24,"endTime":1465.98,"body":"reasoning. But as the tool that"},{"speaker":"Pam","startTime":1465.98,"endTime":1468.95,"body":"we found to actually compute"},{"speaker":"Pam","startTime":1465.98,"endTime":1468.95,"body":"with, to actually find those"},{"speaker":"Pam","startTime":1469.13,"endTime":1473.3,"body":"products, or if you're dividing"},{"speaker":"Pam","startTime":1469.13,"endTime":1473.3,"body":"to find that dividend... No, not"},{"speaker":"Pam","startTime":1473.3,"endTime":1475.28,"body":"find the dividend, find the"},{"speaker":"Pam","startTime":1473.3,"endTime":1475.28,"body":"quotient. I can get that word"},{"speaker":"Pam","startTime":1475.28,"endTime":1477.41,"body":"right. It was better to use a"},{"speaker":"Pam","startTime":1475.28,"endTime":1477.41,"body":"ratio table."},{"speaker":"Kim","startTime":1477.71,"endTime":1477.95,"body":"Yeah."},{"speaker":"Pam","startTime":1477.98,"endTime":1480.62,"body":"Ratio tables became the"},{"speaker":"Pam","startTime":1477.98,"endTime":1480.62,"body":"better tool with which to"},{"speaker":"Pam","startTime":1480.62,"endTime":1486.17,"body":"compute after, and maybe along"},{"speaker":"Pam","startTime":1480.62,"endTime":1486.17,"body":"with, at the same time as, we're"},{"speaker":"Pam","startTime":1486.17,"endTime":1489.23,"body":"building the sense of area, and"},{"speaker":"Pam","startTime":1486.17,"endTime":1489.23,"body":"the dimensions, and the size,"},{"speaker":"Pam","startTime":1489.23,"endTime":1491.9,"body":"and the magnitude, and the"},{"speaker":"Pam","startTime":1489.23,"endTime":1491.9,"body":"spatial sense with the area"},{"speaker":"Pam","startTime":1491.9,"endTime":1493.31,"body":"model. Did I just say any of"},{"speaker":"Pam","startTime":1491.9,"endTime":1493.31,"body":"that well?"},{"speaker":"Kim","startTime":1493.76,"endTime":1495.32,"body":"[Kim laughs] I followed"},{"speaker":"Kim","startTime":1493.76,"endTime":1495.32,"body":"you."},{"speaker":"Pam","startTime":1495.41,"endTime":1498.53,"body":"I feel like I was all over"},{"speaker":"Pam","startTime":1495.41,"endTime":1498.53,"body":"the place with that. So, maybe"},{"speaker":"Pam","startTime":1498.53,"endTime":1501.5,"body":"I'll do just a quick recap. So,"},{"speaker":"Pam","startTime":1498.53,"endTime":1501.5,"body":"teachers, do we want you to use"},{"speaker":"Pam","startTime":1501.5,"endTime":1505.4,"body":"the area model and open array?"},{"speaker":"Pam","startTime":1501.5,"endTime":1505.4,"body":"Absolutely. To build spatial"},{"speaker":"Pam","startTime":1505.4,"endTime":1509.33,"body":"sense, to help make sense of"},{"speaker":"Pam","startTime":1505.4,"endTime":1509.33,"body":"chunking products, and to"},{"speaker":"Pam","startTime":1509.33,"endTime":1512.69,"body":"connect dimensions to factors"},{"speaker":"Pam","startTime":1509.33,"endTime":1512.69,"body":"and area to products. We"},{"speaker":"Pam","startTime":1512.69,"endTime":1515.57,"body":"absolutely want you to do that."},{"speaker":"Pam","startTime":1512.69,"endTime":1515.57,"body":"But we also want you to"},{"speaker":"Pam","startTime":1515.57,"endTime":1518.54,"body":"introduce the ratio table and"},{"speaker":"Pam","startTime":1515.57,"endTime":1518.54,"body":"help build that model because"},{"speaker":"Pam","startTime":1518.54,"endTime":1522.68,"body":"that is going to become the tool"},{"speaker":"Pam","startTime":1518.54,"endTime":1522.68,"body":"that students will use as a tool"},{"speaker":"Pam","startTime":1522.95,"endTime":1523.73,"body":"for computing."},{"speaker":"Kim","startTime":1524.12,"endTime":1527.33,"body":"Yeah. And we have a whole"},{"speaker":"Kim","startTime":1524.12,"endTime":1527.33,"body":"series about the ratio table, so"},{"speaker":"Kim","startTime":1527.33,"endTime":1530.69,"body":"they can check that out, and"},{"speaker":"Kim","startTime":1527.33,"endTime":1530.69,"body":"we'll put the episodes in the"},{"speaker":"Kim","startTime":1530.69,"endTime":1534.62,"body":"show notes. But don't leave us"},{"speaker":"Kim","startTime":1530.69,"endTime":1534.62,"body":"now because we have more"},{"speaker":"Kim","startTime":1534.71,"endTime":1537.41,"body":"conversation to be had about the"},{"speaker":"Kim","startTime":1534.71,"endTime":1537.41,"body":"area model."},{"speaker":"Pam","startTime":1537.44,"endTime":1539.39,"body":"Ooh, and one other quick"},{"speaker":"Pam","startTime":1537.44,"endTime":1539.39,"body":"thing I want to mention. Sorry,"},{"speaker":"Pam","startTime":1539.39,"endTime":1539.63,"body":"sorry."},{"speaker":"Kim","startTime":1539.63,"endTime":1539.69,"body":"Yeah."},{"speaker":"Pam","startTime":1539.72,"endTime":1543.74,"body":"Is that another another"},{"speaker":"Pam","startTime":1539.72,"endTime":1543.74,"body":"good use of the area model...and"},{"speaker":"Pam","startTime":1543.86,"endTime":1545.45,"body":"maybe we'll talk about this more"},{"speaker":"Pam","startTime":1543.86,"endTime":1545.45,"body":"in the next episode, so I'll"},{"speaker":"Pam","startTime":1545.45,"endTime":1548.06,"body":"just mention it here...is making"},{"speaker":"Pam","startTime":1545.45,"endTime":1548.06,"body":"sense of the distributive"},{"speaker":"Pam","startTime":1548.06,"endTime":1551.87,"body":"property. That's a brilliant. We"},{"speaker":"Pam","startTime":1548.06,"endTime":1551.87,"body":"want to make sense of the"},{"speaker":"Pam","startTime":1551.87,"endTime":1555.41,"body":"distributive property using this"},{"speaker":"Pam","startTime":1551.87,"endTime":1555.41,"body":"area model more and more, and we"},{"speaker":"Pam","startTime":1555.41,"endTime":1556.97,"body":"will do that more in upcoming"},{"speaker":"Pam","startTime":1555.41,"endTime":1556.97,"body":"episodes."},{"speaker":"Kim","startTime":1557.09,"endTime":1561.05,"body":"Yeah. So, also, I don't"},{"speaker":"Kim","startTime":1557.09,"endTime":1561.05,"body":"know if you know this. You know"},{"speaker":"Kim","startTime":1561.05,"endTime":1565.52,"body":"this, Pam. But we have merch,"},{"speaker":"Kim","startTime":1561.05,"endTime":1565.52,"body":"and this month we just released"},{"speaker":"Kim","startTime":1565.55,"endTime":1570.44,"body":"a super cool shirt around area"},{"speaker":"Kim","startTime":1565.55,"endTime":1570.44,"body":"and perimeter that we think that"},{"speaker":"Kim","startTime":1570.44,"endTime":1572.39,"body":"you'll love. You can check that"},{"speaker":"Kim","startTime":1570.44,"endTime":1572.39,"body":"out at"},{"speaker":"Kim","startTime":1572.42,"endTime":1575.06,"body":"mathisfigureoutable.com/merchandise."},{"speaker":"Kim","startTime":1572.42,"endTime":1575.06,"body":"And..."},{"speaker":"Pam","startTime":1575.12,"endTime":1575.78,"body":"Merch! Yay!"},{"speaker":"Kim","startTime":1577.37,"endTime":1584.36,"body":"Yeah, we are almost at a 5"},{"speaker":"Kim","startTime":1577.37,"endTime":1584.36,"body":"out of 5 on Apple Podcast. So,"},{"speaker":"Kim","startTime":1584.36,"endTime":1587.9,"body":"would you please rate the"},{"speaker":"Kim","startTime":1584.36,"endTime":1587.9,"body":"podcast. It helps more listeners"},{"speaker":"Kim","startTime":1587.9,"endTime":1590.9,"body":"find the podcast, so we can"},{"speaker":"Kim","startTime":1587.9,"endTime":1590.9,"body":"spread the Math is"},{"speaker":"Kim","startTime":1590.9,"endTime":1593.87,"body":"Figure-Out-Able word and"},{"speaker":"Kim","startTime":1590.9,"endTime":1593.87,"body":"everybody can jump in on the"},{"speaker":"Kim","startTime":1593.87,"endTime":1594.23,"body":"movement."},{"speaker":"Pam","startTime":1594.53,"endTime":1597.29,"body":"Yes, please! Give us a"},{"speaker":"Pam","startTime":1594.53,"endTime":1597.29,"body":"rating on there, so more people"},{"speaker":"Pam","startTime":1597.29,"endTime":1600.86,"body":"can find the podcast. Ya'll,"},{"speaker":"Pam","startTime":1597.29,"endTime":1600.86,"body":"thank you for tuning in and"},{"speaker":"Pam","startTime":1600.86,"endTime":1603.56,"body":"teaching more and more Real"},{"speaker":"Pam","startTime":1600.86,"endTime":1603.56,"body":"Math. To find out more about the"},{"speaker":"Pam","startTime":1603.56,"endTime":1605.45,"body":"Math is Figure-Out-Able"},{"speaker":"Pam","startTime":1603.56,"endTime":1605.45,"body":"movement, visit"},{"speaker":"Pam","startTime":1605.93,"endTime":1609.32,"body":"mathisfigureoutable.com. Let's"},{"speaker":"Pam","startTime":1605.93,"endTime":1609.32,"body":"keep spreading the word that"},{"speaker":"Pam","startTime":1609.32,"endTime":1610.67,"body":"Math is Figure-Out-Able!"}]}