{"version":"1.0.0","segments":[{"speaker":"Pam","startTime":2.73,"endTime":6.06,"body":"Hey, fellow mathematicians."},{"speaker":"Pam","startTime":2.73,"endTime":6.06,"body":"Welcome to the podcast where"},{"speaker":"Pam","startTime":6.06,"endTime":7.74,"body":"Math is Figure-Out-Able!"},{"speaker":"Pam","startTime":7.95,"endTime":8.79,"body":"I'm Pam."},{"speaker":"Kim","startTime":9.15,"endTime":9.84,"body":"And I'm Kim."},{"speaker":"Pam","startTime":10.17,"endTime":13.47,"body":"And you found a place where"},{"speaker":"Pam","startTime":10.17,"endTime":13.47,"body":"math is not about memorizing and"},{"speaker":"Pam","startTime":13.47,"endTime":17.52,"body":"mimicking, waiting to be told or"},{"speaker":"Pam","startTime":13.47,"endTime":17.52,"body":"shown what to do. But, ya'll,"},{"speaker":"Pam","startTime":17.52,"endTime":21.06,"body":"it's about making sense of"},{"speaker":"Pam","startTime":17.52,"endTime":21.06,"body":"problems, noticing patterns. and"},{"speaker":"Pam","startTime":21.06,"endTime":25.32,"body":"reasoning using mathematical"},{"speaker":"Pam","startTime":21.06,"endTime":25.32,"body":"relationships. We can mentor"},{"speaker":"Pam","startTime":25.32,"endTime":29.97,"body":"mathematicians as we co-create"},{"speaker":"Pam","startTime":25.32,"endTime":29.97,"body":"meaning together. Not only are"},{"speaker":"Pam","startTime":29.97,"endTime":33.57,"body":"algorithms not particularly"},{"speaker":"Pam","startTime":29.97,"endTime":33.57,"body":"helpful in teaching mathematics,"},{"speaker":"Pam","startTime":33.84,"endTime":37.56,"body":"but rotely repeating steps"},{"speaker":"Pam","startTime":33.84,"endTime":37.56,"body":"actually keeps students from"},{"speaker":"Pam","startTime":37.56,"endTime":39.72,"body":"being the mathematicians they"},{"speaker":"Pam","startTime":37.56,"endTime":39.72,"body":"can be."},{"speaker":"Kim","startTime":40.86,"endTime":43.26,"body":"So, for the last two weeks,"},{"speaker":"Kim","startTime":40.86,"endTime":43.26,"body":"we've been talking about ratio"},{"speaker":"Kim","startTime":43.26,"endTime":47.25,"body":"tables and how powerful of a"},{"speaker":"Kim","startTime":43.26,"endTime":47.25,"body":"model they are. You may have"},{"speaker":"Kim","startTime":47.25,"endTime":50.61,"body":"noticed that both weeks we've"},{"speaker":"Kim","startTime":47.25,"endTime":50.61,"body":"done model building strings"},{"speaker":"Kim","startTime":50.61,"endTime":53.43,"body":"where we focus on a variety of"},{"speaker":"Kim","startTime":50.61,"endTime":53.43,"body":"strategies, kind of going in and"},{"speaker":"Kim","startTime":53.43,"endTime":56.7,"body":"out of the numbers. Sometimes we"},{"speaker":"Kim","startTime":53.43,"endTime":56.7,"body":"go a little bit over, and then"},{"speaker":"Kim","startTime":56.7,"endTime":60.96,"body":"back up. Sometimes we do 5 is"},{"speaker":"Kim","startTime":56.7,"endTime":60.96,"body":"half of 10. So, we're going to"},{"speaker":"Kim","startTime":60.96,"endTime":65.16,"body":"give another example today of a"},{"speaker":"Kim","startTime":60.96,"endTime":65.16,"body":"model building ratio table"},{"speaker":"Kim","startTime":65.16,"endTime":66.9,"body":"string. Also, don't forget to"},{"speaker":"Kim","startTime":65.16,"endTime":66.9,"body":"grab..."},{"speaker":"Pam","startTime":66.9,"endTime":69.15,"body":"Yeah, because that's what"},{"speaker":"Pam","startTime":66.9,"endTime":69.15,"body":"the series is about, right? Is"},{"speaker":"Pam","startTime":69.15,"endTime":69.78,"body":"the ratio table?"},{"speaker":"Kim","startTime":69.78,"endTime":69.84,"body":"Yeah."},{"speaker":"Pam","startTime":69.87,"endTime":72.81,"body":"Later, we'll talk more"},{"speaker":"Pam","startTime":69.87,"endTime":72.81,"body":"about strategy building, but for"},{"speaker":"Pam","startTime":72.81,"endTime":75.96,"body":"today, let's build that model"},{"speaker":"Pam","startTime":72.81,"endTime":75.96,"body":"some more. Sorry."},{"speaker":"Kim","startTime":75.96,"endTime":78.78,"body":"Yeah. That's okay. As we"},{"speaker":"Kim","startTime":75.96,"endTime":78.78,"body":"work through a Problem String,"},{"speaker":"Kim","startTime":78.84,"endTime":82.8,"body":"we'd love for you to grab a"},{"speaker":"Kim","startTime":78.84,"endTime":82.8,"body":"pencil and paper and practice"},{"speaker":"Kim","startTime":82.8,"endTime":87.15,"body":"your representation on a ratio"},{"speaker":"Kim","startTime":82.8,"endTime":87.15,"body":"table, and then post it to Pam's"},{"speaker":"Kim","startTime":87.15,"endTime":87.96,"body":"social media."},{"speaker":"Pam","startTime":88.62,"endTime":91.35,"body":"Yeah, then we can all share"},{"speaker":"Pam","startTime":88.62,"endTime":91.35,"body":"what it's looking like."},{"speaker":"Pam","startTime":91.35,"endTime":94.38,"body":"Especially if you do it with"},{"speaker":"Pam","startTime":91.35,"endTime":94.38,"body":"students. We really want to see"},{"speaker":"Pam","startTime":94.38,"endTime":97.5,"body":"what your board looks like, what"},{"speaker":"Pam","startTime":94.38,"endTime":97.5,"body":"students are thinking. Love to"},{"speaker":"Pam","startTime":97.5,"endTime":101.07,"body":"see how that's going. We'll all"},{"speaker":"Pam","startTime":97.5,"endTime":101.07,"body":"just keep mentoring each other"},{"speaker":"Pam","startTime":101.28,"endTime":103.32,"body":"as we do more and more Real"},{"speaker":"Pam","startTime":101.28,"endTime":103.32,"body":"Math."},{"speaker":"Pam","startTime":103.35,"endTime":106.8,"body":"Cool. So, Kim."},{"speaker":"Kim","startTime":107.04,"endTime":107.49,"body":"Yeah?"},{"speaker":"Pam","startTime":107.67,"endTime":109.32,"body":"I'm going to give you some"},{"speaker":"Pam","startTime":107.67,"endTime":109.32,"body":"problems today."},{"speaker":"Kim","startTime":109.74,"endTime":110.07,"body":"Okay."},{"speaker":"Pam","startTime":110.31,"endTime":114.69,"body":"I just was at a friend's"},{"speaker":"Pam","startTime":110.31,"endTime":114.69,"body":"house. And we had spaghetti. And"},{"speaker":"Pam","startTime":114.69,"endTime":120.12,"body":"I think there's like the perfect"},{"speaker":"Pam","startTime":114.69,"endTime":120.12,"body":"ratio of pasta to sauce. Yes?"},{"speaker":"Kim","startTime":120.12,"endTime":120.15,"body":"Mmhmm."},{"speaker":"Pam","startTime":120.51,"endTime":123.63,"body":"Like, I can't be drinking"},{"speaker":"Pam","startTime":120.51,"endTime":123.63,"body":"the sauce. That's too much"},{"speaker":"Pam","startTime":123.63,"endTime":124.02,"body":"sauce."},{"speaker":"Kim","startTime":124.02,"endTime":124.26,"body":"Yeah."},{"speaker":"Pam","startTime":124.38,"endTime":126.81,"body":"But it also... There's got"},{"speaker":"Pam","startTime":124.38,"endTime":126.81,"body":"to be enough sauce. Like, you"},{"speaker":"Pam","startTime":126.81,"endTime":130.8,"body":"have to. There's, like, this"},{"speaker":"Pam","startTime":126.81,"endTime":130.8,"body":"perfect. Well, I think that it's"},{"speaker":"Pam","startTime":130.8,"endTime":134.16,"body":"a perfect ratio. I have a big"},{"speaker":"Pam","startTime":130.8,"endTime":134.16,"body":"family. You know that. So, I"},{"speaker":"Pam","startTime":134.16,"endTime":137.67,"body":"make a lot of pasta, a lot of"},{"speaker":"Pam","startTime":134.16,"endTime":137.67,"body":"sauce, feed everybody. So, I"},{"speaker":"Pam","startTime":137.67,"endTime":142.5,"body":"think the perfect ratio is 8"},{"speaker":"Pam","startTime":137.67,"endTime":142.5,"body":"cups of pasta to 5 cups of"},{"speaker":"Pam","startTime":142.5,"endTime":145.62,"body":"sauce. Mmm, it's making me"},{"speaker":"Pam","startTime":142.5,"endTime":145.62,"body":"hungry right now."},{"speaker":"Kim","startTime":146.55,"endTime":147.48,"body":"Okay, 8 cups of pasta..."},{"speaker":"Pam","startTime":147.48,"endTime":151.11,"body":"Hey, by the way, do you"},{"speaker":"Pam","startTime":147.48,"endTime":151.11,"body":"prefer, like a red? Like, tomato"},{"speaker":"Pam","startTime":151.11,"endTime":153.93,"body":"sauce? Or do you prefer, like an"},{"speaker":"Pam","startTime":151.11,"endTime":153.93,"body":"Alfredo, white sauce?"},{"speaker":"Kim","startTime":154.44,"endTime":158.04,"body":"Well, the white sauce is"},{"speaker":"Kim","startTime":154.44,"endTime":158.04,"body":"not spaghetti. That's"},{"speaker":"Kim","startTime":158.04,"endTime":161.1,"body":"fettuccine. So, if you're saying"},{"speaker":"Kim","startTime":158.04,"endTime":161.1,"body":"spaghetti, it's red sauce."},{"speaker":"Pam","startTime":161.1,"endTime":164.52,"body":"Well, just pasta. Can I"},{"speaker":"Pam","startTime":161.1,"endTime":164.52,"body":"just do pasta? Just pasta. Any"},{"speaker":"Pam","startTime":164.52,"endTime":165.18,"body":"kind of pasta."},{"speaker":"Kim","startTime":166.8,"endTime":167.82,"body":"Ah. They're both good."},{"speaker":"Pam","startTime":167.88,"endTime":170.25,"body":"Somebody said \"past-ah\" the"},{"speaker":"Pam","startTime":167.88,"endTime":170.25,"body":"other day. It's not \"past-ah\","},{"speaker":"Pam","startTime":170.25,"endTime":171.09,"body":"right? It's pasta."},{"speaker":"Kim","startTime":171.12,"endTime":171.84,"body":"Pasta."},{"speaker":"Pam","startTime":171.96,"endTime":172.32,"body":"Pasta."},{"speaker":"Kim","startTime":172.32,"endTime":172.53,"body":"Alright."},{"speaker":"Pam","startTime":172.53,"endTime":175.23,"body":"Okay. Alright, so 8 to 5. I"},{"speaker":"Pam","startTime":172.53,"endTime":175.23,"body":"don't know."},{"speaker":"Kim","startTime":175.86,"endTime":177.45,"body":"Eight cups to 5 cups. Okay,"},{"speaker":"Kim","startTime":175.86,"endTime":177.45,"body":"I'm with you."},{"speaker":"Pam","startTime":177.45,"endTime":181.32,"body":"Eight cups to 5 cups. Okay."},{"speaker":"Pam","startTime":177.45,"endTime":181.32,"body":"Now, let's say that your family"},{"speaker":"Pam","startTime":181.32,"endTime":183.84,"body":"is coming over. And I don't"},{"speaker":"Pam","startTime":181.32,"endTime":183.84,"body":"know, maybe we have to have our"},{"speaker":"Pam","startTime":183.84,"endTime":185.94,"body":"neighbors over too. Lots of"},{"speaker":"Pam","startTime":183.84,"endTime":185.94,"body":"people are coming over, and so"},{"speaker":"Pam","startTime":185.97,"endTime":189.57,"body":"I'm thinking I'm going to make"},{"speaker":"Pam","startTime":185.97,"endTime":189.57,"body":"10 cups of sauce. If I make 10"},{"speaker":"Pam","startTime":189.57,"endTime":193.05,"body":"cups of sauce, how many cups of"},{"speaker":"Pam","startTime":189.57,"endTime":193.05,"body":"pasta, so that I keep the ratio?"},{"speaker":"Pam","startTime":193.86,"endTime":196.83,"body":"If I keep it really tasty, how"},{"speaker":"Pam","startTime":193.86,"endTime":196.83,"body":"many cups of pasta would we"},{"speaker":"Pam","startTime":196.83,"endTime":196.98,"body":"need?"},{"speaker":"Kim","startTime":196.98,"endTime":200.31,"body":"Yeah, I'm going to need 16."},{"speaker":"Kim","startTime":196.98,"endTime":200.31,"body":"You're going to need 16 cups of"},{"speaker":"Kim","startTime":200.31,"endTime":200.85,"body":"pasta."},{"speaker":"Pam","startTime":200.91,"endTime":201.63,"body":"Because?"},{"speaker":"Kim","startTime":201.84,"endTime":204.09,"body":"Well, you're doubling the"},{"speaker":"Kim","startTime":201.84,"endTime":204.09,"body":"amount of sauce, and so we need"},{"speaker":"Kim","startTime":204.09,"endTime":205.77,"body":"to double the amount of pasta."},{"speaker":"Pam","startTime":206.01,"endTime":210.06,"body":"Totally makes sense. But"},{"speaker":"Pam","startTime":206.01,"endTime":210.06,"body":"tonight, I'm just feeding my"},{"speaker":"Pam","startTime":210.06,"endTime":214.11,"body":"husband and myself. We're just"},{"speaker":"Pam","startTime":210.06,"endTime":214.11,"body":"barely empty nesters, and so I'm"},{"speaker":"Pam","startTime":214.11,"endTime":218.52,"body":"only going to make 1 cup of"},{"speaker":"Pam","startTime":214.11,"endTime":218.52,"body":"sauce. So, how many cups of"},{"speaker":"Pam","startTime":218.52,"endTime":221.37,"body":"pasta would be that yummy ratio?"},{"speaker":"Kim","startTime":225.36,"endTime":225.78,"body":"Hang on."},{"speaker":"Pam","startTime":226.47,"endTime":227.22,"body":"You still there, Kim?"},{"speaker":"Kim","startTime":227.28,"endTime":228.06,"body":"Yeah, I'm still here."},{"speaker":"Kim","startTime":228.27,"endTime":230.85,"body":"I'm recording on my ratio table,"},{"speaker":"Kim","startTime":228.27,"endTime":230.85,"body":"so that it can be."},{"speaker":"Pam","startTime":230.88,"endTime":233.37,"body":"Oh yeah, well done. Oh,"},{"speaker":"Pam","startTime":230.88,"endTime":233.37,"body":"yeah because we're going to post"},{"speaker":"Pam","startTime":233.37,"endTime":234.81,"body":"it, so everybody can see what it"},{"speaker":"Pam","startTime":233.37,"endTime":234.81,"body":"looks like."},{"speaker":"Kim","startTime":234.81,"endTime":237.72,"body":"So, you only need... You"},{"speaker":"Kim","startTime":234.81,"endTime":237.72,"body":"said you had 1 cup of sauce?"},{"speaker":"Pam","startTime":237.81,"endTime":240.21,"body":"Yeah, just 1 cup of sauce."},{"speaker":"Pam","startTime":237.81,"endTime":240.21,"body":"I got to make pasta. How much"},{"speaker":"Pam","startTime":240.21,"endTime":241.02,"body":"pasta should I make?"},{"speaker":"Kim","startTime":242.4,"endTime":245.1,"body":"Eight-fifths of a cup of"},{"speaker":"Kim","startTime":242.4,"endTime":245.1,"body":"pasta."},{"speaker":"Pam","startTime":245.1,"endTime":246.72,"body":"What? What does that even"},{"speaker":"Pam","startTime":245.1,"endTime":246.72,"body":"mean?"},{"speaker":"Kim","startTime":246.81,"endTime":249.78,"body":"One and 3/5 cups of pasta."},{"speaker":"Pam","startTime":251.82,"endTime":256.59,"body":"One and 3/5 cups. Like Kim,"},{"speaker":"Pam","startTime":251.82,"endTime":256.59,"body":"if I go into my cups right now,"},{"speaker":"Pam","startTime":256.59,"endTime":260.52,"body":"I don't think I'm going to find"},{"speaker":"Pam","startTime":256.59,"endTime":260.52,"body":"three-fifths of a cup. Is there"},{"speaker":"Pam","startTime":260.52,"endTime":263.43,"body":"any other relationship? I mean,"},{"speaker":"Pam","startTime":260.52,"endTime":263.43,"body":"I like it. I like it. By the"},{"speaker":"Pam","startTime":263.43,"endTime":265.02,"body":"way, how did you get"},{"speaker":"Pam","startTime":263.43,"endTime":265.02,"body":"eight-fifths? Can you say that"},{"speaker":"Pam","startTime":265.02,"endTime":265.38,"body":"first?"},{"speaker":"Kim","startTime":265.89,"endTime":272.1,"body":"So, I went from 5 cups of"},{"speaker":"Kim","startTime":265.89,"endTime":272.1,"body":"sauce to 1 cup of sauce by"},{"speaker":"Kim","startTime":272.1,"endTime":273.03,"body":"dividing by 5."},{"speaker":"Pam","startTime":273.3,"endTime":273.72,"body":"Okay."},{"speaker":"Kim","startTime":274.02,"endTime":278.28,"body":"And then, I went from 8"},{"speaker":"Kim","startTime":274.02,"endTime":278.28,"body":"cups of pasta, also divided by"},{"speaker":"Kim","startTime":278.28,"endTime":280.32,"body":"5, so the ratio would be the"},{"speaker":"Kim","startTime":278.28,"endTime":280.32,"body":"same."},{"speaker":"Pam","startTime":281.25,"endTime":283.5,"body":"So, that's how you got"},{"speaker":"Pam","startTime":281.25,"endTime":283.5,"body":"eight-fifths."},{"speaker":"Kim","startTime":283.53,"endTime":283.74,"body":"Yeah."},{"speaker":"Pam","startTime":283.74,"endTime":284.85,"body":"Eight divided by 5."},{"speaker":"Kim","startTime":285.0,"endTime":289.26,"body":"If you prefer, I could tell"},{"speaker":"Kim","startTime":285.0,"endTime":289.26,"body":"you it's 1.6 cups of pasta. I'm"},{"speaker":"Kim","startTime":289.26,"endTime":290.4,"body":"not sure if that's any better."},{"speaker":"Pam","startTime":290.52,"endTime":291.21,"body":"How did you get that?"},{"speaker":"Kim","startTime":291.75,"endTime":295.41,"body":"So, if I went from 10 cups,"},{"speaker":"Kim","startTime":291.75,"endTime":295.41,"body":"the previous 10 cups of sauce to"},{"speaker":"Kim","startTime":295.71,"endTime":300.15,"body":"get to 1 cup. So, then. I'm"},{"speaker":"Kim","startTime":295.71,"endTime":300.15,"body":"sorry, sauce. 10 cups of sauce"},{"speaker":"Kim","startTime":300.15,"endTime":301.05,"body":"to 1 cup of sauce."},{"speaker":"Pam","startTime":301.11,"endTime":303.48,"body":"And how are you doing that?"},{"speaker":"Pam","startTime":301.11,"endTime":303.48,"body":"10 to 1 is your?"},{"speaker":"Kim","startTime":303.54,"endTime":304.44,"body":"Divided by 10."},{"speaker":"Pam","startTime":304.53,"endTime":305.61,"body":"Okay, so divided by 10."},{"speaker":"Kim","startTime":305.94,"endTime":311.16,"body":"So, then, 16 cups of pasta"},{"speaker":"Kim","startTime":305.94,"endTime":311.16,"body":"divided by 10 to give you 1.6"},{"speaker":"Kim","startTime":312.21,"endTime":313.08,"body":"cups of pasta"},{"speaker":"Pam","startTime":313.62,"endTime":316.62,"body":"And call me crazy, but I"},{"speaker":"Pam","startTime":313.62,"endTime":316.62,"body":"think that's easier to measure."},{"speaker":"Pam","startTime":316.62,"endTime":319.29,"body":"Like, I would do 1 and a 1/2"},{"speaker":"Pam","startTime":316.62,"endTime":319.29,"body":"cups of pasta, and then just a"},{"speaker":"Pam","startTime":319.29,"endTime":323.52,"body":"little bit more to get 1.6, 1.5"},{"speaker":"Pam","startTime":319.29,"endTime":323.52,"body":"plus a little bit more. I don't"},{"speaker":"Pam","startTime":323.52,"endTime":323.58,"body":"know."},{"speaker":"Kim","startTime":323.61,"endTime":325.83,"body":"That's funny because I was"},{"speaker":"Kim","startTime":323.61,"endTime":325.83,"body":"actually intentionally leaving"},{"speaker":"Kim","startTime":325.83,"endTime":326.91,"body":"it in the fifths."},{"speaker":"Pam","startTime":327.33,"endTime":329.37,"body":"Well, so like, do you have"},{"speaker":"Pam","startTime":327.33,"endTime":329.37,"body":"a fifths cup measure?"},{"speaker":"Kim","startTime":330.69,"endTime":333.45,"body":"I feel like I do. Do I not?"},{"speaker":"Kim","startTime":330.69,"endTime":333.45,"body":"I don't cook much, Pam. Come on."},{"speaker":"Kim","startTime":334.71,"endTime":334.74,"body":"(unclear)"},{"speaker":"Pam","startTime":334.8,"endTime":337.62,"body":"I'm pretty sure you do not"},{"speaker":"Pam","startTime":334.8,"endTime":337.62,"body":"have a fifths cup measure."},{"speaker":"Pam","startTime":339.87,"endTime":342.12,"body":"Unless you're measuring in"},{"speaker":"Pam","startTime":339.87,"endTime":342.12,"body":"metric or something, but. Okay."},{"speaker":"Pam","startTime":342.15,"endTime":343.02,"body":"Alright. totally cool."},{"speaker":"Kim","startTime":343.05,"endTime":344.25,"body":"Clearly, I don't cook a"},{"speaker":"Kim","startTime":343.05,"endTime":344.25,"body":"lot."},{"speaker":"Pam","startTime":344.52,"endTime":347.37,"body":"Okay, how about 9 cups of"},{"speaker":"Pam","startTime":344.52,"endTime":347.37,"body":"sauce? If I've got 9 cups of"},{"speaker":"Pam","startTime":347.37,"endTime":349.2,"body":"sauce, how many cups of pasta do"},{"speaker":"Pam","startTime":347.37,"endTime":349.2,"body":"I need?"},{"speaker":"Kim","startTime":349.23,"endTime":353.16,"body":"Nine cups of sauce. Okay,"},{"speaker":"Kim","startTime":349.23,"endTime":353.16,"body":"so I'm going to go from 10 cups"},{"speaker":"Kim","startTime":353.19,"endTime":357.66,"body":"of sauce, minus 1 cup of sauce,"},{"speaker":"Kim","startTime":353.19,"endTime":357.66,"body":"to give me 9 cups of sauce."},{"speaker":"Pam","startTime":357.81,"endTime":358.23,"body":"Okay."},{"speaker":"Kim","startTime":358.29,"endTime":360.45,"body":"And here's where I'm happy"},{"speaker":"Kim","startTime":358.29,"endTime":360.45,"body":"to not be living in fraction"},{"speaker":"Kim","startTime":360.45,"endTime":364.38,"body":"land. So, I'm going to go 16"},{"speaker":"Kim","startTime":360.45,"endTime":364.38,"body":"cups of pasta that went with the"},{"speaker":"Kim","startTime":364.38,"endTime":371.22,"body":"10 cups of sauce, minus the 1.6"},{"speaker":"Kim","startTime":364.38,"endTime":371.22,"body":"cups of pasta."},{"speaker":"Pam","startTime":372.33,"endTime":372.36,"body":"Mmhmm."},{"speaker":"Kim","startTime":372.81,"endTime":377.28,"body":"So, that's going to be 14.4"},{"speaker":"Kim","startTime":372.81,"endTime":377.28,"body":"cups of pasta."},{"speaker":"Pam","startTime":377.61,"endTime":381.66,"body":"Nice, nice. So, 14.4 cups"},{"speaker":"Pam","startTime":377.61,"endTime":381.66,"body":"of pasta. 14 and almost a 1/2 a"},{"speaker":"Pam","startTime":381.66,"endTime":387.99,"body":"cup to 9 cups of sauce. And"},{"speaker":"Pam","startTime":381.66,"endTime":387.99,"body":"totally cool. Okay, but today I"},{"speaker":"Pam","startTime":387.99,"endTime":393.0,"body":"looked in my fridge, and I"},{"speaker":"Pam","startTime":387.99,"endTime":393.0,"body":"actually have 4 cups of pasta."},{"speaker":"Pam","startTime":393.39,"endTime":395.43,"body":"I'd like to know how much sauce"},{"speaker":"Pam","startTime":393.39,"endTime":395.43,"body":"I need to make."},{"speaker":"Kim","startTime":396.09,"endTime":398.82,"body":"Hmm. 4 cups. So..."},{"speaker":"Pam","startTime":399.33,"endTime":399.96,"body":"So, I think I just..."},{"speaker":"Kim","startTime":399.96,"endTime":400.74,"body":"Four cups of sauce?"},{"speaker":"Pam","startTime":400.86,"endTime":401.91,"body":"...flipped it a little bit,"},{"speaker":"Pam","startTime":400.86,"endTime":401.91,"body":"right?"},{"speaker":"Kim","startTime":401.97,"endTime":404.13,"body":"What did you say? Did you"},{"speaker":"Kim","startTime":401.97,"endTime":404.13,"body":"say 4 cups of pasta?"},{"speaker":"Pam","startTime":404.16,"endTime":405.21,"body":"Yeah, 4 cups of pasta."},{"speaker":"Kim","startTime":405.21,"endTime":409.65,"body":"Oh, okay. Alright. So, I"},{"speaker":"Kim","startTime":405.21,"endTime":409.65,"body":"only want 4 cups of pasta, which"},{"speaker":"Kim","startTime":409.65,"endTime":412.56,"body":"means I need 2 and a 1/2 cups of"},{"speaker":"Kim","startTime":409.65,"endTime":412.56,"body":"sauce. Because you told me when"},{"speaker":"Kim","startTime":412.56,"endTime":417.54,"body":"it's 8 cups of pasta, that's 5"},{"speaker":"Kim","startTime":412.56,"endTime":417.54,"body":"cups of sauce. So, now, I need"},{"speaker":"Kim","startTime":417.54,"endTime":419.76,"body":"half as much pasta and half as"},{"speaker":"Kim","startTime":417.54,"endTime":419.76,"body":"much sauce."},{"speaker":"Pam","startTime":419.91,"endTime":423.24,"body":"Cool. So, 4 cups of pasta,"},{"speaker":"Pam","startTime":419.91,"endTime":423.24,"body":"2 and a 1/2 cups of sauce. Nice."},{"speaker":"Pam","startTime":423.81,"endTime":427.92,"body":"But now I just have 2 cups of"},{"speaker":"Pam","startTime":423.81,"endTime":427.92,"body":"pasta. Two cups of pasta. How"},{"speaker":"Pam","startTime":427.92,"endTime":428.82,"body":"much sauce should I make?"},{"speaker":"Kim","startTime":431.01,"endTime":435.12,"body":"One point two five cups of"},{"speaker":"Kim","startTime":431.01,"endTime":435.12,"body":"sauce."},{"speaker":"Pam","startTime":435.21,"endTime":435.78,"body":"Because?"},{"speaker":"Kim","startTime":436.02,"endTime":440.13,"body":"Because we just talked"},{"speaker":"Kim","startTime":436.02,"endTime":440.13,"body":"about 4 cups of pasta was 2 and"},{"speaker":"Kim","startTime":440.13,"endTime":445.65,"body":"a 1/2 cups of sauce, so now I"},{"speaker":"Kim","startTime":440.13,"endTime":445.65,"body":"need half again. Half the pasta"},{"speaker":"Kim","startTime":445.65,"endTime":446.61,"body":"and half the sauce."},{"speaker":"Pam","startTime":446.7,"endTime":452.31,"body":"Cool. 1 cup of pasta, Kim."},{"speaker":"Pam","startTime":446.7,"endTime":452.31,"body":"Today, 1 cup of pasta. How much"},{"speaker":"Pam","startTime":452.34,"endTime":455.13,"body":"sauce? How many cups of sauce?"},{"speaker":"Kim","startTime":459.15,"endTime":473.55,"body":"That's going to be 0.625."},{"speaker":"Kim","startTime":459.15,"endTime":473.55,"body":"Is that right? Oh, yeah, 0.625."},{"speaker":"Kim","startTime":474.12,"endTime":478.14,"body":"You said... Wait, wait, tell me"},{"speaker":"Kim","startTime":474.12,"endTime":478.14,"body":"again. Did you say 0.25? You"},{"speaker":"Kim","startTime":478.14,"endTime":479.34,"body":"said 1 cup of pasta?"},{"speaker":"Pam","startTime":479.52,"endTime":480.48,"body":"1 cup of pasta."},{"speaker":"Kim","startTime":480.63,"endTime":484.68,"body":"Yeah. So, half the pasta,"},{"speaker":"Kim","startTime":480.63,"endTime":484.68,"body":"so I need to half the sauce."},{"speaker":"Pam","startTime":484.77,"endTime":486.33,"body":"Okay, what's half of?"},{"speaker":"Kim","startTime":486.51,"endTime":487.71,"body":"Half of $1.25?"},{"speaker":"Pam","startTime":488.01,"endTime":488.49,"body":"Half of $1.25."},{"speaker":"Kim","startTime":489.48,"endTime":490.32,"body":"Point six two five."},{"speaker":"Pam","startTime":490.89,"endTime":493.11,"body":"Point six two five. How are"},{"speaker":"Pam","startTime":490.89,"endTime":493.11,"body":"you thinking about that?"},{"speaker":"Kim","startTime":495.69,"endTime":497.94,"body":"Half of $1.00 is $0.50."},{"speaker":"Pam","startTime":498.48,"endTime":498.9,"body":"Okay."},{"speaker":"Kim","startTime":499.35,"endTime":505.44,"body":"And half of $0.25 is 12 and"},{"speaker":"Kim","startTime":499.35,"endTime":505.44,"body":"a 1/2 cents. So, that's 62 and a"},{"speaker":"Kim","startTime":505.44,"endTime":506.1,"body":"half cents."},{"speaker":"Pam","startTime":507.69,"endTime":511.29,"body":"Thanks for doing that out"},{"speaker":"Pam","startTime":507.69,"endTime":511.29,"body":"for me. I was thinking about"},{"speaker":"Pam","startTime":511.29,"endTime":512.43,"body":"half of $1.20"},{"speaker":"Kim","startTime":513.21,"endTime":514.08,"body":"Oh, that's nice."},{"speaker":"Pam","startTime":514.32,"endTime":517.26,"body":"That's $0.60, right? And"},{"speaker":"Pam","startTime":514.32,"endTime":517.26,"body":"then, I was getting stuck a"},{"speaker":"Pam","startTime":517.26,"endTime":519.39,"body":"little bit. Half of $0.05."},{"speaker":"Kim","startTime":519.6,"endTime":520.41,"body":"Yeah, it's weird."},{"speaker":"Pam","startTime":520.919,"endTime":524.939,"body":"Half of $0.05 is like, 2"},{"speaker":"Pam","startTime":520.919,"endTime":524.939,"body":"and a half cents. So, there's"},{"speaker":"Pam","startTime":524.939,"endTime":532.589,"body":"another 62 and a half. Cool. So,"},{"speaker":"Pam","startTime":524.939,"endTime":532.589,"body":"let's see. What if... Back to"},{"speaker":"Pam","startTime":532.589,"endTime":536.099,"body":"sauce. What if I... No, sorry."},{"speaker":"Pam","startTime":532.589,"endTime":536.099,"body":"Stay with pasta."},{"speaker":"Kim","startTime":536.46,"endTime":536.73,"body":"Okay."},{"speaker":"Pam","startTime":536.76,"endTime":540.33,"body":"What if I have 41.6 cups of"},{"speaker":"Pam","startTime":536.76,"endTime":540.33,"body":"pasta?"},{"speaker":"Kim","startTime":540.84,"endTime":541.8,"body":"Oh, goodness, 41.6."},{"speaker":"Pam","startTime":541.92,"endTime":542.76,"body":"Feed the neighborhood."},{"speaker":"Kim","startTime":543.18,"endTime":544.14,"body":"Feed the neighborhood."},{"speaker":"Kim","startTime":544.71,"endTime":553.5,"body":"Forty-one point six. Okay, bear"},{"speaker":"Kim","startTime":544.71,"endTime":553.5,"body":"with me. I'm going to go with..."},{"speaker":"Kim","startTime":554.04,"endTime":560.97,"body":"I knew 4 cups of pasta was going"},{"speaker":"Kim","startTime":554.04,"endTime":560.97,"body":"to go with 2 and a 1/2 cups of"},{"speaker":"Kim","startTime":560.97,"endTime":565.26,"body":"sauce. So, I actually wrote down"},{"speaker":"Kim","startTime":560.97,"endTime":565.26,"body":"41.6, but I'm going to erase it"},{"speaker":"Kim","startTime":565.26,"endTime":568.17,"body":"because I need room for 40 cups."},{"speaker":"Kim","startTime":565.26,"endTime":568.17,"body":"So, I'm writing in my ratio"},{"speaker":"Kim","startTime":568.17,"endTime":573.3,"body":"table 40 cups of pasta is going"},{"speaker":"Kim","startTime":568.17,"endTime":573.3,"body":"to go with 25 cups of sauce."},{"speaker":"Pam","startTime":573.33,"endTime":574.14,"body":"Oh, nice."},{"speaker":"Kim","startTime":574.2,"endTime":577.68,"body":"You said 41.6, right?"},{"speaker":"Pam","startTime":577.8,"endTime":578.34,"body":"Correct."},{"speaker":"Kim","startTime":579.15,"endTime":583.44,"body":"So, then, I'm looking back"},{"speaker":"Kim","startTime":579.15,"endTime":583.44,"body":"at the 16 cups of pasta goes"},{"speaker":"Kim","startTime":583.44,"endTime":586.83,"body":"with 10 cups of sauce, and I'm"},{"speaker":"Kim","startTime":583.44,"endTime":586.83,"body":"going to scale that down, and"},{"speaker":"Kim","startTime":586.83,"endTime":593.22,"body":"I'm over here writing 1.6 cups"},{"speaker":"Kim","startTime":586.83,"endTime":593.22,"body":"of pasta goes with 1 cup. And"},{"speaker":"Kim","startTime":593.22,"endTime":595.71,"body":"now, I'm going to put those two"},{"speaker":"Kim","startTime":593.22,"endTime":595.71,"body":"together, the ones I just told"},{"speaker":"Kim","startTime":595.71,"endTime":601.17,"body":"you, the 40 cups and the 1.6"},{"speaker":"Kim","startTime":595.71,"endTime":601.17,"body":"cups. And that is 26 cups of"},{"speaker":"Kim","startTime":601.17,"endTime":601.68,"body":"sauce."},{"speaker":"Pam","startTime":602.55,"endTime":602.67,"body":"Da-tah-dah."},{"speaker":"Kim","startTime":605.19,"endTime":605.97,"body":"That's alot of pasta."},{"speaker":"Pam","startTime":607.47,"endTime":611.28,"body":"And so, another way that"},{"speaker":"Pam","startTime":607.47,"endTime":611.28,"body":"I've heard students on the"},{"speaker":"Pam","startTime":611.28,"endTime":614.46,"body":"41.6...Nicely done, I liked how"},{"speaker":"Pam","startTime":611.28,"endTime":614.46,"body":"you went from the 4. That was"},{"speaker":"Pam","startTime":614.46,"endTime":617.04,"body":"very effective. Not sure I've"},{"speaker":"Pam","startTime":614.46,"endTime":617.04,"body":"ever had kids do that. It was"},{"speaker":"Pam","startTime":617.04,"endTime":621.9,"body":"nice though...is that they'll go"},{"speaker":"Pam","startTime":617.04,"endTime":621.9,"body":"from 8 to 40. So, you liked to"},{"speaker":"Pam","startTime":621.9,"endTime":624.39,"body":"40. They'll go from the 8 to 40"},{"speaker":"Pam","startTime":621.9,"endTime":624.39,"body":"by scaling times 5."},{"speaker":"Kim","startTime":625.17,"endTime":625.2,"body":"Mmhmm."},{"speaker":"Pam","startTime":625.38,"endTime":628.5,"body":"Five times 5 is the 25. And"},{"speaker":"Pam","startTime":625.38,"endTime":628.5,"body":"then, they'll add that 1.6."},{"speaker":"Pam","startTime":628.53,"endTime":634.02,"body":"Nice. And in a huge way, what we"},{"speaker":"Pam","startTime":628.53,"endTime":634.02,"body":"just did was reason very"},{"speaker":"Pam","startTime":634.02,"endTime":637.59,"body":"similarly to how we were"},{"speaker":"Pam","startTime":634.02,"endTime":637.59,"body":"reasoning multiplicatively with"},{"speaker":"Pam","startTime":637.59,"endTime":641.4,"body":"multiplication two weeks ago."},{"speaker":"Pam","startTime":637.59,"endTime":641.4,"body":"And multiplicatively with"},{"speaker":"Pam","startTime":641.4,"endTime":645.93,"body":"division in last week's episode."},{"speaker":"Pam","startTime":641.4,"endTime":645.93,"body":"And in today's episode, we're"},{"speaker":"Pam","startTime":645.93,"endTime":649.17,"body":"reasoning proportionally about a"},{"speaker":"Pam","startTime":645.93,"endTime":649.17,"body":"non-unit ratio."},{"speaker":"Kim","startTime":649.44,"endTime":649.8,"body":"Yeah."},{"speaker":"Pam","startTime":649.83,"endTime":652.89,"body":"So, two weeks ago, we"},{"speaker":"Pam","startTime":649.83,"endTime":652.89,"body":"reasoned about... Golly, what"},{"speaker":"Pam","startTime":652.89,"endTime":656.16,"body":"was it? One to 72. One box had"},{"speaker":"Pam","startTime":652.89,"endTime":656.16,"body":"72 smarties."},{"speaker":"Kim","startTime":656.34,"endTime":656.55,"body":"Yep."},{"speaker":"Pam","startTime":656.55,"endTime":659.67,"body":"And then, last week, we"},{"speaker":"Pam","startTime":656.55,"endTime":659.67,"body":"reasoned about 1 pack of water"},{"speaker":"Pam","startTime":659.67,"endTime":661.08,"body":"bottles had 12 water bottles."},{"speaker":"Kim","startTime":661.17,"endTime":661.5,"body":"Yep."},{"speaker":"Pam","startTime":661.86,"endTime":664.62,"body":"Those are the unit ratios"},{"speaker":"Pam","startTime":661.86,"endTime":664.62,"body":"because it's one to the thing."},{"speaker":"Pam","startTime":664.98,"endTime":671.52,"body":"And today, we're reasoning about"},{"speaker":"Pam","startTime":664.98,"endTime":671.52,"body":"non-unit ratios. Eight cups to 5"},{"speaker":"Pam","startTime":671.52,"endTime":675.66,"body":"cups, 8 to 5.That's a non-unit"},{"speaker":"Pam","startTime":671.52,"endTime":675.66,"body":"ratio, neither of those is 1."},{"speaker":"Pam","startTime":675.93,"endTime":679.05,"body":"And we can sort of reason in and"},{"speaker":"Pam","startTime":675.93,"endTime":679.05,"body":"out, multiplying and adding."},{"speaker":"Kim","startTime":679.32,"endTime":679.71,"body":"Yeah."},{"speaker":"Pam","startTime":679.74,"endTime":683.85,"body":"As long as we keep the"},{"speaker":"Pam","startTime":679.74,"endTime":683.85,"body":"ratio consistent. So, we've said"},{"speaker":"Pam","startTime":683.85,"endTime":687.39,"body":"one of the hallmarks, or the"},{"speaker":"Pam","startTime":683.85,"endTime":687.39,"body":"definition of a ratio table, is"},{"speaker":"Pam","startTime":687.39,"endTime":690.27,"body":"that the ratios are equivalent."},{"speaker":"Pam","startTime":687.39,"endTime":690.27,"body":"So, I'll just read a couple of"},{"speaker":"Pam","startTime":690.69,"endTime":701.55,"body":"ratios. We had 8 to 5; 16 to 10;"},{"speaker":"Pam","startTime":690.69,"endTime":701.55,"body":"1.6 to 1; 14.4 to 9; 4 to 2.5."},{"speaker":"Pam","startTime":701.58,"endTime":708.3,"body":"All of those ending with 41.6 to"},{"speaker":"Pam","startTime":701.58,"endTime":708.3,"body":"26. All of those are equivalent"},{"speaker":"Pam","startTime":708.3,"endTime":711.9,"body":"ratios. So, that last problem"},{"speaker":"Pam","startTime":708.3,"endTime":711.9,"body":"that I asked you, I can actually"},{"speaker":"Pam","startTime":711.9,"endTime":717.27,"body":"write as I could write the ratio"},{"speaker":"Pam","startTime":711.9,"endTime":717.27,"body":"of 8 to 5 is equivalent to. And"},{"speaker":"Pam","startTime":717.51,"endTime":722.04,"body":"we didn't know the 26, right?"},{"speaker":"Pam","startTime":717.51,"endTime":722.04,"body":"So, 8 to 5 is equivalent to 41.6"},{"speaker":"Pam","startTime":722.34,"endTime":726.63,"body":"to x, or whatever. And if I"},{"speaker":"Pam","startTime":722.34,"endTime":726.63,"body":"write that as a proportion, that"},{"speaker":"Pam","startTime":726.63,"endTime":734.13,"body":"could look like 8 over 41.6, or"},{"speaker":"Pam","startTime":726.63,"endTime":734.13,"body":"8 to 41.6, equals 5 to x. 5 over"},{"speaker":"Pam","startTime":734.13,"endTime":738.72,"body":"x. And that problem could be"},{"speaker":"Pam","startTime":734.13,"endTime":738.72,"body":"solved with cross multiply and"},{"speaker":"Pam","startTime":738.72,"endTime":742.95,"body":"divide. Bleh. That would be what"},{"speaker":"Pam","startTime":738.72,"endTime":742.95,"body":"41.6 times 5, and then divide"},{"speaker":"Pam","startTime":742.95,"endTime":748.47,"body":"that by 8? Or, we could reason"},{"speaker":"Pam","startTime":742.95,"endTime":748.47,"body":"proportionally like you did to"},{"speaker":"Pam","startTime":748.47,"endTime":751.71,"body":"solve that problem, and at the"},{"speaker":"Pam","startTime":748.47,"endTime":751.71,"body":"same time, build proportional"},{"speaker":"Pam","startTime":751.71,"endTime":752.04,"body":"reasoning."},{"speaker":"Kim","startTime":752.04,"endTime":752.1,"body":"Yeah."},{"speaker":"Pam","startTime":752.13,"endTime":755.85,"body":"Students actually get"},{"speaker":"Pam","startTime":752.13,"endTime":755.85,"body":"better, and their brains think"},{"speaker":"Pam","startTime":755.85,"endTime":760.2,"body":"more sophisticatedly, if we help"},{"speaker":"Pam","startTime":755.85,"endTime":760.2,"body":"them grapple with the"},{"speaker":"Pam","startTime":760.2,"endTime":763.74,"body":"relationships, not just give"},{"speaker":"Pam","startTime":760.2,"endTime":763.74,"body":"them ways to solve problems that"},{"speaker":"Pam","startTime":763.74,"endTime":765.63,"body":"use less sophisticated"},{"speaker":"Pam","startTime":763.74,"endTime":765.63,"body":"reasoning."},{"speaker":"Kim","startTime":765.9,"endTime":769.62,"body":"Yeah, so when Cooper, my"},{"speaker":"Kim","startTime":765.9,"endTime":769.62,"body":"younger, was in elementary"},{"speaker":"Kim","startTime":769.62,"endTime":774.27,"body":"school, you would sometimes put"},{"speaker":"Kim","startTime":769.62,"endTime":774.27,"body":"MathStratChat problems that were"},{"speaker":"Kim","startTime":774.27,"endTime":779.94,"body":"about solving proportions. And"},{"speaker":"Kim","startTime":774.27,"endTime":779.94,"body":"he loves to participate, right?"},{"speaker":"Kim","startTime":779.94,"endTime":783.96,"body":"And so, when we would post those"},{"speaker":"Kim","startTime":779.94,"endTime":783.96,"body":"problems, he would be like,"},{"speaker":"Kim","startTime":783.96,"endTime":783.99,"body":"\"Oh...awesome...\""},{"speaker":"Pam","startTime":784.02,"endTime":786.99,"body":"Oh, sadness."},{"speaker":"Kim","startTime":786.99,"endTime":790.11,"body":"And he would be a little"},{"speaker":"Kim","startTime":786.99,"endTime":790.11,"body":"sad. But when I said to him,"},{"speaker":"Kim","startTime":790.23,"endTime":794.31,"body":"\"Oh, this is about scaling on a"},{"speaker":"Kim","startTime":790.23,"endTime":794.31,"body":"ratio table.\" He was like, \"Oh,"},{"speaker":"Kim","startTime":794.34,"endTime":799.23,"body":"I could do that!\" And it was"},{"speaker":"Kim","startTime":794.34,"endTime":799.23,"body":"like he knew what he could think"},{"speaker":"Kim","startTime":799.23,"endTime":802.2,"body":"about because he was used to"},{"speaker":"Kim","startTime":799.23,"endTime":802.2,"body":"scaling up and down in a ratio"},{"speaker":"Kim","startTime":802.2,"endTime":805.62,"body":"table. And all he had to know"},{"speaker":"Kim","startTime":802.2,"endTime":805.62,"body":"was, \"I'm getting from 8 to"},{"speaker":"Kim","startTime":805.65,"endTime":810.42,"body":"41.6? I can do that.\" And it's a"},{"speaker":"Kim","startTime":805.65,"endTime":810.42,"body":"nice introduction using a model"},{"speaker":"Kim","startTime":810.42,"endTime":814.2,"body":"that he has made sense of to"},{"speaker":"Kim","startTime":810.42,"endTime":814.2,"body":"introduce things that he hasn't"},{"speaker":"Kim","startTime":814.2,"endTime":816.93,"body":"even really tackled in school"},{"speaker":"Kim","startTime":814.2,"endTime":816.93,"body":"yet. I love that."},{"speaker":"Pam","startTime":816.93,"endTime":819.03,"body":"Yeah. That's super, super"},{"speaker":"Pam","startTime":816.93,"endTime":819.03,"body":"cool."},{"speaker":"Kim","startTime":819.03,"endTime":819.09,"body":"Yeah."},{"speaker":"Pam","startTime":819.54,"endTime":822.39,"body":"And I was just talking to"},{"speaker":"Pam","startTime":819.54,"endTime":822.39,"body":"our colleague Kristin Frang this"},{"speaker":"Pam","startTime":822.39,"endTime":827.4,"body":"morning. And we were talking"},{"speaker":"Pam","startTime":822.39,"endTime":827.4,"body":"about properties. And, Tad"},{"speaker":"Pam","startTime":827.73,"endTime":831.0,"body":"Watanabe has been sort of poking"},{"speaker":"Pam","startTime":827.73,"endTime":831.0,"body":"me on Twitter a little bit about"},{"speaker":"Pam","startTime":831.0,"endTime":834.42,"body":"properties. And so, eventually,"},{"speaker":"Pam","startTime":831.0,"endTime":834.42,"body":"we would definitely want to pull"},{"speaker":"Pam","startTime":834.42,"endTime":836.97,"body":"out that...you just mentioned"},{"speaker":"Pam","startTime":834.42,"endTime":836.97,"body":"scaling on a ratio table...that"},{"speaker":"Pam","startTime":837.42,"endTime":840.99,"body":"as we are scaling, that is an"},{"speaker":"Pam","startTime":837.42,"endTime":840.99,"body":"application of the associative"},{"speaker":"Pam","startTime":840.99,"endTime":845.1,"body":"property. That we're thinking"},{"speaker":"Pam","startTime":840.99,"endTime":845.1,"body":"about taking ,it's a"},{"speaker":"Pam","startTime":845.1,"endTime":848.1,"body":"multiplicative relationship. And"},{"speaker":"Pam","startTime":845.1,"endTime":848.1,"body":"we're thinking about as we"},{"speaker":"Pam","startTime":848.1,"endTime":852.96,"body":"scale, we're associating those"},{"speaker":"Pam","startTime":848.1,"endTime":852.96,"body":"factors together. And as we"},{"speaker":"Pam","startTime":852.96,"endTime":858.3,"body":"chunk things together. Like, if"},{"speaker":"Pam","startTime":852.96,"endTime":858.3,"body":"you take the 8 cups of pasta..."},{"speaker":"Pam","startTime":858.33,"endTime":861.39,"body":"Let me think on this one. If we"},{"speaker":"Pam","startTime":858.33,"endTime":861.39,"body":"took like 4 cups of pasta, and 2"},{"speaker":"Pam","startTime":861.39,"endTime":864.33,"body":"cups of pasta, and added it"},{"speaker":"Pam","startTime":861.39,"endTime":864.33,"body":"together to get 6 cups of pasta."},{"speaker":"Kim","startTime":864.36,"endTime":864.72,"body":"Yep."},{"speaker":"Pam","startTime":864.75,"endTime":867.18,"body":"And so, we took the"},{"speaker":"Pam","startTime":864.75,"endTime":867.18,"body":"corresponding cups of sauce and"},{"speaker":"Pam","startTime":867.18,"endTime":869.97,"body":"added it together. That's more"},{"speaker":"Pam","startTime":867.18,"endTime":869.97,"body":"an application of the"},{"speaker":"Pam","startTime":869.97,"endTime":871.02,"body":"distributive property."},{"speaker":"Kim","startTime":871.02,"endTime":871.08,"body":"Yeah."},{"speaker":"Pam","startTime":871.11,"endTime":874.44,"body":"We sort of chunk the chunks"},{"speaker":"Pam","startTime":871.11,"endTime":874.44,"body":"together. And so, yes. We"},{"speaker":"Pam","startTime":874.44,"endTime":879.66,"body":"definitely eventually want to"},{"speaker":"Pam","startTime":874.44,"endTime":879.66,"body":"get to discussing properties and"},{"speaker":"Pam","startTime":879.66,"endTime":882.93,"body":"the basis of how all this works."},{"speaker":"Pam","startTime":879.66,"endTime":882.93,"body":"So, teachers, we definitely need"},{"speaker":"Pam","startTime":882.93,"endTime":885.54,"body":"you to sort of go that"},{"speaker":"Pam","startTime":882.93,"endTime":885.54,"body":"direction, but the starting"},{"speaker":"Pam","startTime":885.54,"endTime":889.14,"body":"point is to ask good questions"},{"speaker":"Pam","startTime":885.54,"endTime":889.14,"body":"like the questions in a Problem"},{"speaker":"Pam","startTime":889.14,"endTime":893.58,"body":"String, represent, pull out the"},{"speaker":"Pam","startTime":889.14,"endTime":893.58,"body":"thinking of students, represent"},{"speaker":"Pam","startTime":893.58,"endTime":897.54,"body":"that thinking, make it visible,"},{"speaker":"Pam","startTime":893.58,"endTime":897.54,"body":"and help this tool become a"},{"speaker":"Pam","startTime":897.54,"endTime":900.66,"body":"tool, this ratio table become a"},{"speaker":"Pam","startTime":897.54,"endTime":900.66,"body":"tool for students to think and"},{"speaker":"Pam","startTime":900.66,"endTime":904.23,"body":"reason with. And then, we can"},{"speaker":"Pam","startTime":900.66,"endTime":904.23,"body":"dive a little bit deeper into"},{"speaker":"Pam","startTime":904.38,"endTime":906.06,"body":"the properties and what they're"},{"speaker":"Pam","startTime":904.38,"endTime":906.06,"body":"based on."},{"speaker":"Kim","startTime":906.96,"endTime":907.23,"body":"Yeah."},{"speaker":"Pam","startTime":907.68,"endTime":910.41,"body":"Super cool. We love the"},{"speaker":"Pam","startTime":907.68,"endTime":910.41,"body":"ratio table. Hey, let me mention"},{"speaker":"Pam","startTime":910.41,"endTime":914.55,"body":"one other thing. This week, the"},{"speaker":"Pam","startTime":910.41,"endTime":914.55,"body":"previous week, and the week"},{"speaker":"Pam","startTime":914.55,"endTime":916.95,"body":"previous to that. So, three"},{"speaker":"Pam","startTime":914.55,"endTime":916.95,"body":"episodes in a row, we've been"},{"speaker":"Pam","startTime":916.95,"endTime":920.76,"body":"talking about ratio tables. The"},{"speaker":"Pam","startTime":916.95,"endTime":920.76,"body":"strings that we have done, the"},{"speaker":"Pam","startTime":920.76,"endTime":923.67,"body":"Problem Strings that we've done"},{"speaker":"Pam","startTime":920.76,"endTime":923.67,"body":"in all of these three weeks have"},{"speaker":"Pam","startTime":924.12,"endTime":927.75,"body":"been model building strings."},{"speaker":"Kim","startTime":927.84,"endTime":928.08,"body":"Right."},{"speaker":"Pam","startTime":928.11,"endTime":931.83,"body":"We also at some point need"},{"speaker":"Pam","startTime":928.11,"endTime":931.83,"body":"to talk about what strategy"},{"speaker":"Pam","startTime":931.83,"endTime":935.76,"body":"building strings look like"},{"speaker":"Pam","startTime":931.83,"endTime":935.76,"body":"because it's not just about all"},{"speaker":"Pam","startTime":935.76,"endTime":937.89,"body":"the different ways. You'll"},{"speaker":"Pam","startTime":935.76,"endTime":937.89,"body":"notice that when Kim would solve"},{"speaker":"Pam","startTime":937.89,"endTime":939.96,"body":"it, I would say, \"Ooh, and I can"},{"speaker":"Pam","startTime":937.89,"endTime":939.96,"body":"also think about it like this.\""},{"speaker":"Pam","startTime":939.96,"endTime":942.45,"body":"Or last week, when I was solving"},{"speaker":"Pam","startTime":939.96,"endTime":942.45,"body":"it, Kim would say, \"Ooh, and I"},{"speaker":"Pam","startTime":942.45,"endTime":946.5,"body":"could also think about it like"},{"speaker":"Pam","startTime":942.45,"endTime":946.5,"body":"that.\" When you're doing a model"},{"speaker":"Pam","startTime":946.5,"endTime":949.98,"body":"building string, we want to"},{"speaker":"Pam","startTime":946.5,"endTime":949.98,"body":"share and represent multiple"},{"speaker":"Pam","startTime":949.98,"endTime":952.95,"body":"strategies because we want to go"},{"speaker":"Pam","startTime":949.98,"endTime":952.95,"body":"in and out of the model, and we"},{"speaker":"Pam","startTime":952.95,"endTime":957.45,"body":"want to strengthen the sense of"},{"speaker":"Pam","startTime":952.95,"endTime":957.45,"body":"the model. But then, we want to"},{"speaker":"Pam","startTime":957.45,"endTime":960.87,"body":"also help students develop"},{"speaker":"Pam","startTime":957.45,"endTime":960.87,"body":"certain strategies using that"},{"speaker":"Pam","startTime":960.87,"endTime":966.42,"body":"model. And let's do that in a"},{"speaker":"Pam","startTime":960.87,"endTime":966.42,"body":"future episode. So, stay tuned"},{"speaker":"Pam","startTime":966.6,"endTime":970.77,"body":"for what a strategy building"},{"speaker":"Pam","startTime":966.6,"endTime":970.77,"body":"string could look like as"},{"speaker":"Pam","startTime":970.77,"endTime":973.41,"body":"students use the tool of a ratio"},{"speaker":"Pam","startTime":970.77,"endTime":973.41,"body":"table to solve problems."},{"speaker":"Kim","startTime":974.31,"endTime":977.55,"body":"So, you can check out what"},{"speaker":"Kim","startTime":974.31,"endTime":977.55,"body":"we did to record our thinking on"},{"speaker":"Kim","startTime":977.55,"endTime":980.58,"body":"a ratio table and share your"},{"speaker":"Kim","startTime":977.55,"endTime":980.58,"body":"thinking with us as well on"},{"speaker":"Kim","startTime":980.58,"endTime":981.33,"body":"social media."},{"speaker":"Pam","startTime":981.81,"endTime":984.63,"body":"Love to see what's going on"},{"speaker":"Pam","startTime":981.81,"endTime":984.63,"body":"as you're doing these Problem"},{"speaker":"Pam","startTime":984.63,"endTime":985.56,"body":"Strings with your students."},{"speaker":"Kim","startTime":985.68,"endTime":986.01,"body":"Yeah."},{"speaker":"Pam","startTime":986.16,"endTime":989.25,"body":"Hey, y'all, thanks for"},{"speaker":"Pam","startTime":986.16,"endTime":989.25,"body":"tuning in and teaching more and"},{"speaker":"Pam","startTime":989.25,"endTime":991.95,"body":"more real math! To find out more"},{"speaker":"Pam","startTime":989.25,"endTime":991.95,"body":"about the Math is"},{"speaker":"Pam","startTime":991.98,"endTime":996.03,"body":"Figure-Out-Able movement, visit"},{"speaker":"Pam","startTime":991.98,"endTime":996.03,"body":"mathisfigureoutable.com. Let's"},{"speaker":"Pam","startTime":996.03,"endTime":998.94,"body":"keep spreading the word that"},{"speaker":"Pam","startTime":996.03,"endTime":998.94,"body":"Math is Figure-Out-Able!"}]}