{"version":"1.0.0","segments":[{"speaker":"Pam","startTime":1.02,"endTime":4.32,"body":"Hey, fellow mathematicians!"},{"speaker":"Pam","startTime":1.02,"endTime":4.32,"body":"Welcome to the podcast where"},{"speaker":"Pam","startTime":4.32,"endTime":6.99,"body":"Math is Figure-Out-Able. I'm"},{"speaker":"Pam","startTime":4.32,"endTime":6.99,"body":"Pam."},{"speaker":"Kim","startTime":7.32,"endTime":8.07,"body":"And I'm Kim."},{"speaker":"Pam","startTime":8.37,"endTime":11.64,"body":"And you found a place where"},{"speaker":"Pam","startTime":8.37,"endTime":11.64,"body":"math is not about memorizing and"},{"speaker":"Pam","startTime":11.64,"endTime":15.09,"body":"mimicking, waiting to be told or"},{"speaker":"Pam","startTime":11.64,"endTime":15.09,"body":"shown what to do. But it's about"},{"speaker":"Pam","startTime":15.09,"endTime":18.51,"body":"making sense of problems,"},{"speaker":"Pam","startTime":15.09,"endTime":18.51,"body":"noticing patterns, and reasoning"},{"speaker":"Pam","startTime":18.51,"endTime":21.66,"body":"using mathematical"},{"speaker":"Pam","startTime":18.51,"endTime":21.66,"body":"relationships. We can mentor"},{"speaker":"Pam","startTime":21.66,"endTime":25.86,"body":"mathematicians as we co-create"},{"speaker":"Pam","startTime":21.66,"endTime":25.86,"body":"meaning together. Not only are"},{"speaker":"Pam","startTime":25.86,"endTime":29.37,"body":"algorithms not particularly"},{"speaker":"Pam","startTime":25.86,"endTime":29.37,"body":"helpful in teaching mathematics,"},{"speaker":"Pam","startTime":29.76,"endTime":33.24,"body":"but rotely repeating steps"},{"speaker":"Pam","startTime":29.76,"endTime":33.24,"body":"actually keep students from"},{"speaker":"Pam","startTime":33.24,"endTime":35.25,"body":"being the mathematicians they"},{"speaker":"Pam","startTime":33.24,"endTime":35.25,"body":"can be."},{"speaker":"Kim","startTime":35.76,"endTime":38.01,"body":"So, in the last three"},{"speaker":"Kim","startTime":35.76,"endTime":38.01,"body":"episodes, we've been talking"},{"speaker":"Kim","startTime":38.01,"endTime":41.64,"body":"about one of our very favorite"},{"speaker":"Kim","startTime":38.01,"endTime":41.64,"body":"mathematical models, which is"},{"speaker":"Kim","startTime":41.67,"endTime":47.07,"body":"the ratio table. Yeah, in"},{"speaker":"Kim","startTime":41.67,"endTime":47.07,"body":"Episode 129, we discussed using"},{"speaker":"Kim","startTime":47.07,"endTime":50.94,"body":"a ratio table to think about"},{"speaker":"Kim","startTime":47.07,"endTime":50.94,"body":"multiplication. In Episode 130,"},{"speaker":"Kim","startTime":50.97,"endTime":54.45,"body":"it was all about division with"},{"speaker":"Kim","startTime":50.97,"endTime":54.45,"body":"ratio tables. And then, last"},{"speaker":"Kim","startTime":54.45,"endTime":59.04,"body":"week in Episode 131, we had fun"},{"speaker":"Kim","startTime":54.45,"endTime":59.04,"body":"reasoning proportionally about"},{"speaker":"Kim","startTime":59.04,"endTime":63.12,"body":"solving proportions. In this"},{"speaker":"Kim","startTime":59.04,"endTime":63.12,"body":"episode, we're going to continue"},{"speaker":"Kim","startTime":63.12,"endTime":66.24,"body":"our series on the ratio table"},{"speaker":"Kim","startTime":63.12,"endTime":66.24,"body":"model by extending the work to"},{"speaker":"Kim","startTime":66.24,"endTime":68.37,"body":"equivalent ratios and fractions"},{"speaker":"Pam","startTime":69.75,"endTime":73.26,"body":"Now, if you teach younger"},{"speaker":"Pam","startTime":69.75,"endTime":73.26,"body":"subjects than that, you're still"},{"speaker":"Pam","startTime":73.26,"endTime":76.41,"body":"going to want to listen to today"},{"speaker":"Pam","startTime":73.26,"endTime":76.41,"body":"because it's going to impact how"},{"speaker":"Pam","startTime":76.41,"endTime":80.7,"body":"you and why you use ratio tables"},{"speaker":"Pam","startTime":76.41,"endTime":80.7,"body":"with younger stuff like"},{"speaker":"Pam","startTime":80.7,"endTime":83.88,"body":"multiplication, division. And"},{"speaker":"Pam","startTime":80.7,"endTime":83.88,"body":"really, if you're teaching"},{"speaker":"Pam","startTime":83.88,"endTime":86.07,"body":"multiplication, division, you"},{"speaker":"Pam","startTime":83.88,"endTime":86.07,"body":"are teaching some fraction"},{"speaker":"Pam","startTime":86.07,"endTime":89.4,"body":"stuff, so this is going to be"},{"speaker":"Pam","startTime":86.07,"endTime":89.4,"body":"super helpful to kind of see"},{"speaker":"Pam","startTime":89.4,"endTime":94.2,"body":"that extension and how it"},{"speaker":"Pam","startTime":89.4,"endTime":94.2,"body":"relates to all the things. And"},{"speaker":"Pam","startTime":94.2,"endTime":98.22,"body":"it has been super fun to see the"},{"speaker":"Pam","startTime":94.2,"endTime":98.22,"body":"number of people on social media"},{"speaker":"Pam","startTime":98.22,"endTime":102.3,"body":"who are getting so excited about"},{"speaker":"Pam","startTime":98.22,"endTime":102.3,"body":"using ratio tables because A,"},{"speaker":"Pam","startTime":102.3,"endTime":106.59,"body":"it's super cool. And B, I think"},{"speaker":"Pam","startTime":102.3,"endTime":106.59,"body":"it's a relatively unknown model"},{"speaker":"Pam","startTime":106.59,"endTime":110.61,"body":"for many of us. And so, it's"},{"speaker":"Pam","startTime":106.59,"endTime":110.61,"body":"been really... I mean, for me,"},{"speaker":"Pam","startTime":110.61,"endTime":114.9,"body":"it's been life changing to use"},{"speaker":"Pam","startTime":110.61,"endTime":114.9,"body":"ratio tables. So, check it out."},{"speaker":"Pam","startTime":115.26,"endTime":119.55,"body":"A colleague of mine, dear friend"},{"speaker":"Pam","startTime":115.26,"endTime":119.55,"body":"Karen Camp, who falls and does"},{"speaker":"Pam","startTime":119.55,"endTime":123.21,"body":"all the things, used four"},{"speaker":"Pam","startTime":119.55,"endTime":123.21,"body":"strategies this last week for"},{"speaker":"Pam","startTime":123.24,"endTime":126.42,"body":"MathStratChat. It was super,"},{"speaker":"Pam","startTime":123.24,"endTime":126.42,"body":"super cool. And in one tweet,"},{"speaker":"Pam","startTime":126.42,"endTime":129.54,"body":"she got four strategies. And"},{"speaker":"Pam","startTime":126.42,"endTime":129.54,"body":"then, she followed up with"},{"speaker":"Pam","startTime":129.54,"endTime":132.99,"body":"another tweet and in the second"},{"speaker":"Pam","startTime":129.54,"endTime":132.99,"body":"tweet... It's like she couldn't"},{"speaker":"Pam","startTime":132.99,"endTime":136.14,"body":"fit all of them in one tweet."},{"speaker":"Pam","startTime":132.99,"endTime":136.14,"body":"So, four strategies to solve the"},{"speaker":"Pam","startTime":136.14,"endTime":137.73,"body":"MathStratChat problem in the"},{"speaker":"Pam","startTime":136.14,"endTime":137.73,"body":"first tweet. And then, the"},{"speaker":"Pam","startTime":137.73,"endTime":145.98,"body":"second tweet, she said, \"Also"},{"speaker":"Pam","startTime":137.73,"endTime":145.98,"body":"ratio table!\" And then, in"},{"speaker":"Pam","startTime":145.98,"endTime":149.73,"body":"parentheses, she said, \"Listen"},{"speaker":"Pam","startTime":145.98,"endTime":149.73,"body":"to this week's podcast\" with a"},{"speaker":"Pam","startTime":149.73,"endTime":153.42,"body":"winky smiley face. Woah, sweet!"},{"speaker":"Pam","startTime":149.73,"endTime":153.42,"body":"Hey, Karen, thanks for listening"},{"speaker":"Pam","startTime":153.42,"endTime":157.53,"body":"to the podcast, and I love that"},{"speaker":"Pam","startTime":153.42,"endTime":157.53,"body":"it encouraged you to use a ratio"},{"speaker":"Pam","startTime":157.53,"endTime":162.51,"body":"table to solve a problem. Right"},{"speaker":"Pam","startTime":157.53,"endTime":162.51,"body":"after that, another colleague"},{"speaker":"Pam","startTime":162.51,"endTime":167.55,"body":"and dear friend, Ray O'Brien or"},{"speaker":"Pam","startTime":162.51,"endTime":167.55,"body":"@pimathman on Twitter. He"},{"speaker":"Pam","startTime":167.55,"endTime":171.27,"body":"tweeted, \"Was I supposed to use"},{"speaker":"Pam","startTime":167.55,"endTime":171.27,"body":"ratio tables?\" That was sort of"},{"speaker":"Pam","startTime":171.27,"endTime":174.21,"body":"his answer to Karen's, you know,"},{"speaker":"Pam","startTime":171.27,"endTime":174.21,"body":"\"I used ratio table!\" Then he's"},{"speaker":"Pam","startTime":174.21,"endTime":177.54,"body":"like, \"Was I supposed to use"},{"speaker":"Pam","startTime":174.21,"endTime":177.54,"body":"ratio tables?\" So, you might be"},{"speaker":"Pam","startTime":177.54,"endTime":183.15,"body":"interested in how I responded to"},{"speaker":"Pam","startTime":177.54,"endTime":183.15,"body":"Ray. And @pimathman, thanks for"},{"speaker":"Pam","startTime":183.15,"endTime":187.53,"body":"your question. So, I responded."},{"speaker":"Pam","startTime":183.15,"endTime":187.53,"body":"I know people hate it when you"},{"speaker":"Pam","startTime":187.53,"endTime":189.18,"body":"answer a question with a"},{"speaker":"Pam","startTime":187.53,"endTime":189.18,"body":"question, but that's exactly"},{"speaker":"Pam","startTime":189.18,"endTime":192.18,"body":"what I did. I said, \"I would"},{"speaker":"Pam","startTime":189.18,"endTime":192.18,"body":"answer that question with a"},{"speaker":"Pam","startTime":192.18,"endTime":197.67,"body":"question. Could you use a ratio"},{"speaker":"Pam","startTime":192.18,"endTime":197.67,"body":"table if you wanted to? If the"},{"speaker":"Pam","startTime":197.67,"endTime":204.27,"body":"answer is yes, and you chose not"},{"speaker":"Pam","startTime":197.67,"endTime":204.27,"body":"to, okay. No problem. However,"},{"speaker":"Pam","startTime":204.51,"endTime":209.49,"body":"if the answer is no. In other"},{"speaker":"Pam","startTime":204.51,"endTime":209.49,"body":"words, no you couldn't use the"},{"speaker":"Pam","startTime":209.49,"endTime":211.41,"body":"ratio table if you wanted to"},{"speaker":"Pam","startTime":209.49,"endTime":211.41,"body":"because you don't know what it"},{"speaker":"Pam","startTime":211.41,"endTime":213.54,"body":"is, you don't know how to use"},{"speaker":"Pam","startTime":211.41,"endTime":213.54,"body":"it, or you don't know what to"},{"speaker":"Pam","startTime":213.54,"endTime":217.59,"body":"do. If your answer is no...\" I'm"},{"speaker":"Pam","startTime":213.54,"endTime":217.59,"body":"adding a little more in here, by"},{"speaker":"Pam","startTime":217.59,"endTime":220.2,"body":"the way than what was in the"},{"speaker":"Pam","startTime":217.59,"endTime":220.2,"body":"tweet but \"If your answer is no,"},{"speaker":"Pam","startTime":220.23,"endTime":224.67,"body":"then I'd wish for you to own the"},{"speaker":"Pam","startTime":220.23,"endTime":224.67,"body":"coolness of ratio tables, so"},{"speaker":"Pam","startTime":224.67,"endTime":229.8,"body":"that you would have the choice."},{"speaker":"Pam","startTime":224.67,"endTime":229.8,"body":"Empowerment is about choice.\""},{"speaker":"Kim","startTime":229.86,"endTime":230.22,"body":"Yeah."},{"speaker":"Pam","startTime":230.25,"endTime":234.0,"body":"Okay, so that's the end of"},{"speaker":"Pam","startTime":230.25,"endTime":234.0,"body":"that tweet. And Ray responded,"},{"speaker":"Pam","startTime":234.42,"endTime":237.87,"body":"\"I can use the ratio table. I do"},{"speaker":"Pam","startTime":234.42,"endTime":237.87,"body":"like them. Practically, when I"},{"speaker":"Pam","startTime":237.87,"endTime":239.97,"body":"see the question on my phone, I"},{"speaker":"Pam","startTime":237.87,"endTime":239.97,"body":"want to solve the problem"},{"speaker":"Pam","startTime":239.97,"endTime":243.24,"body":"mentally. So, if I was on an"},{"speaker":"Pam","startTime":239.97,"endTime":243.24,"body":"iPad, I might be more likely to"},{"speaker":"Pam","startTime":243.24,"endTime":245.46,"body":"use the ratio table. I'm not"},{"speaker":"Pam","startTime":243.24,"endTime":245.46,"body":"gonna get out a piece of paper"},{"speaker":"Pam","startTime":245.46,"endTime":246.51,"body":"and pencil, but that's me.\""},{"speaker":"Kim","startTime":246.72,"endTime":247.05,"body":"Sure."},{"speaker":"Pam","startTime":247.08,"endTime":252.36,"body":"Ah, so that's a huge,"},{"speaker":"Pam","startTime":247.08,"endTime":252.36,"body":"interesting answer because what"},{"speaker":"Pam","startTime":252.36,"endTime":255.66,"body":"Ray is saying is, \"Yeah, yeah,"},{"speaker":"Pam","startTime":252.36,"endTime":255.66,"body":"yeah. Yeah, I own that"},{"speaker":"Pam","startTime":255.66,"endTime":260.43,"body":"representation. I could put my"},{"speaker":"Pam","startTime":255.66,"endTime":260.43,"body":"thinking. I could make it"},{"speaker":"Pam","startTime":260.43,"endTime":264.36,"body":"visible in a ratio table. I"},{"speaker":"Pam","startTime":260.43,"endTime":264.36,"body":"could use the relationships that"},{"speaker":"Pam","startTime":264.36,"endTime":267.24,"body":"I'm thinking about, and I could"},{"speaker":"Pam","startTime":264.36,"endTime":267.24,"body":"put them in a ratio table. But"},{"speaker":"Pam","startTime":267.24,"endTime":269.1,"body":"then, I'd have to get out of"},{"speaker":"Pam","startTime":267.24,"endTime":269.1,"body":"paper and pencil, and I don't"},{"speaker":"Pam","startTime":269.1,"endTime":271.89,"body":"want to do that, so I'm going to"},{"speaker":"Pam","startTime":269.1,"endTime":271.89,"body":"record my thinking in a"},{"speaker":"Pam","startTime":271.89,"endTime":274.95,"body":"different way because I'm on"},{"speaker":"Pam","startTime":271.89,"endTime":274.95,"body":"Twitter, and I'm responding to"},{"speaker":"Pam","startTime":274.98,"endTime":279.09,"body":"MathStratChat in that way.\" That"},{"speaker":"Pam","startTime":274.98,"endTime":279.09,"body":"is a completely. Way to go, Ray!"},{"speaker":"Pam","startTime":279.12,"endTime":283.47,"body":"Woah! Absolutely no, don't give"},{"speaker":"Pam","startTime":279.12,"endTime":283.47,"body":"me a ratio table. Because it's"},{"speaker":"Pam","startTime":283.47,"endTime":287.88,"body":"the thinking. It's the strategy"},{"speaker":"Pam","startTime":283.47,"endTime":287.88,"body":"that we're interested in. Not"},{"speaker":"Pam","startTime":287.91,"endTime":295.02,"body":"the model. The model is a model."},{"speaker":"Pam","startTime":287.91,"endTime":295.02,"body":"And on MathStratChat, it's math"},{"speaker":"Pam","startTime":295.05,"endTime":298.35,"body":"strategy chat. We're interested"},{"speaker":"Pam","startTime":295.05,"endTime":298.35,"body":"to talk about the strategies."},{"speaker":"Pam","startTime":298.89,"endTime":303.12,"body":"So, then, why bring up ratio"},{"speaker":"Pam","startTime":298.89,"endTime":303.12,"body":"tables? Because it's such a"},{"speaker":"Pam","startTime":303.12,"endTime":309.6,"body":"powerful model that we can use"},{"speaker":"Pam","startTime":303.12,"endTime":309.6,"body":"to make the strategies visible."},{"speaker":"Pam","startTime":310.11,"endTime":314.67,"body":"And as we do that, that model"},{"speaker":"Pam","startTime":310.11,"endTime":314.67,"body":"can then become a tool with"},{"speaker":"Pam","startTime":314.67,"endTime":319.5,"body":"which we actually think we use"},{"speaker":"Pam","startTime":314.67,"endTime":319.5,"body":"it as a tool, not just to record"},{"speaker":"Pam","startTime":319.5,"endTime":322.95,"body":"our thinking, but actually kind"},{"speaker":"Pam","startTime":319.5,"endTime":322.95,"body":"of as a tool in order to think."},{"speaker":"Pam","startTime":322.95,"endTime":326.7,"body":"It can kind of nudge us to go,"},{"speaker":"Pam","startTime":322.95,"endTime":326.7,"body":"\"Oh, well, if I've used that"},{"speaker":"Pam","startTime":326.7,"endTime":329.25,"body":"relationship, ooh, and it"},{"speaker":"Pam","startTime":326.7,"endTime":329.25,"body":"can...\" We can see other"},{"speaker":"Pam","startTime":329.25,"endTime":334.2,"body":"relationships can appear. It can"},{"speaker":"Pam","startTime":329.25,"endTime":334.2,"body":"be a helpful tool in solving"},{"speaker":"Pam","startTime":334.2,"endTime":334.8,"body":"problems. So."},{"speaker":"Kim","startTime":334.83,"endTime":336.45,"body":"Yeah. Yeah, so."},{"speaker":"Pam","startTime":336.45,"endTime":336.48,"body":"(unclear)."},{"speaker":"Kim","startTime":336.87,"endTime":337.32,"body":"Go ahead."},{"speaker":"Pam","startTime":337.32,"endTime":337.35,"body":"(laughs)."},{"speaker":"Pam","startTime":339.48,"endTime":343.26,"body":"So, if you are asking yourself,"},{"speaker":"Pam","startTime":339.48,"endTime":343.26,"body":"\"Should I be using a ratio"},{"speaker":"Pam","startTime":343.26,"endTime":347.97,"body":"table?\" The more important"},{"speaker":"Pam","startTime":343.26,"endTime":347.97,"body":"question is, do you own ratio"},{"speaker":"Pam","startTime":347.97,"endTime":348.54,"body":"tables."},{"speaker":"Kim","startTime":348.69,"endTime":348.99,"body":"Yeah."},{"speaker":"Pam","startTime":348.99,"endTime":351.54,"body":"And if you do, then it's"},{"speaker":"Pam","startTime":348.99,"endTime":351.54,"body":"your choice. You can use it or"},{"speaker":"Pam","startTime":351.54,"endTime":357.84,"body":"not. If you don't, man join in,"},{"speaker":"Pam","startTime":351.54,"endTime":357.84,"body":"dive in, and let us help you"},{"speaker":"Pam","startTime":358.17,"endTime":361.08,"body":"learn how to use ratio tables,"},{"speaker":"Pam","startTime":358.17,"endTime":361.08,"body":"so that then you have the"},{"speaker":"Pam","startTime":361.08,"endTime":365.73,"body":"choice, then you're empowered to"},{"speaker":"Pam","startTime":361.08,"endTime":365.73,"body":"do what works best in that"},{"speaker":"Pam","startTime":365.73,"endTime":369.63,"body":"problem. Whatever tool you're"},{"speaker":"Pam","startTime":365.73,"endTime":369.63,"body":"going to use best to help you"},{"speaker":"Pam","startTime":369.63,"endTime":373.14,"body":"with whatever strategy you're"},{"speaker":"Pam","startTime":369.63,"endTime":373.14,"body":"using, then you're empowered to"},{"speaker":"Pam","startTime":373.14,"endTime":374.7,"body":"do that. Do you remember what"},{"speaker":"Pam","startTime":373.14,"endTime":374.7,"body":"you were going to say?"},{"speaker":"Kim","startTime":374.73,"endTime":376.29,"body":"Yeah, I do actually. That's"},{"speaker":"Kim","startTime":374.73,"endTime":376.29,"body":"rare."},{"speaker":"Pam","startTime":376.29,"endTime":376.8,"body":"Yay!"},{"speaker":"Kim","startTime":377.55,"endTime":382.74,"body":"You know, you and I look at"},{"speaker":"Kim","startTime":377.55,"endTime":382.74,"body":"the comments that people make"},{"speaker":"Kim","startTime":382.74,"endTime":385.5,"body":"for MathStratChat, right, and we"},{"speaker":"Kim","startTime":382.74,"endTime":385.5,"body":"like to talk about them and kind"},{"speaker":"Kim","startTime":385.5,"endTime":388.14,"body":"of one of our favorite things to"},{"speaker":"Kim","startTime":385.5,"endTime":388.14,"body":"do is share pictures of what"},{"speaker":"Kim","startTime":388.14,"endTime":392.58,"body":"people are doing. But sometimes"},{"speaker":"Kim","startTime":388.14,"endTime":392.58,"body":"I wonder if people scroll"},{"speaker":"Kim","startTime":392.58,"endTime":396.21,"body":"through MathStratChat and see"},{"speaker":"Kim","startTime":392.58,"endTime":396.21,"body":"other people's thinking on ratio"},{"speaker":"Kim","startTime":396.21,"endTime":399.03,"body":"tables and just keep scrolling,"},{"speaker":"Kim","startTime":396.21,"endTime":399.03,"body":"thinking that they're all the"},{"speaker":"Kim","startTime":399.03,"endTime":402.75,"body":"same, that everything that's on"},{"speaker":"Kim","startTime":399.03,"endTime":402.75,"body":"a ratio table is one strategy,"},{"speaker":"Kim","startTime":402.75,"endTime":405.78,"body":"which is the ratio table"},{"speaker":"Kim","startTime":402.75,"endTime":405.78,"body":"strategy. Which is not a"},{"speaker":"Kim","startTime":405.78,"endTime":409.05,"body":"strategy, right? In reality,"},{"speaker":"Kim","startTime":405.78,"endTime":409.05,"body":"they would have to look really"},{"speaker":"Kim","startTime":409.05,"endTime":412.35,"body":"carefully at what people are"},{"speaker":"Kim","startTime":409.05,"endTime":412.35,"body":"putting in the ratio table to"},{"speaker":"Kim","startTime":412.35,"endTime":414.21,"body":"understand their thinking about"},{"speaker":"Kim","startTime":412.35,"endTime":414.21,"body":"the problem."},{"speaker":"Pam","startTime":414.54,"endTime":418.26,"body":"Oh, that is so well said."},{"speaker":"Pam","startTime":414.54,"endTime":418.26,"body":"It's almost like the comparison"},{"speaker":"Pam","startTime":418.26,"endTime":421.89,"body":"could be that you could look at"},{"speaker":"Pam","startTime":418.26,"endTime":421.89,"body":"an open array, a rectangular"},{"speaker":"Pam","startTime":421.89,"endTime":425.58,"body":"area model, and you might. If"},{"speaker":"Pam","startTime":421.89,"endTime":425.58,"body":"the only thing you've ever seen"},{"speaker":"Pam","startTime":425.94,"endTime":430.65,"body":"on that area model is place"},{"speaker":"Pam","startTime":425.94,"endTime":430.65,"body":"value, partial products, or"},{"speaker":"Pam","startTime":430.65,"endTime":434.04,"body":"somebody's always splitting the"},{"speaker":"Pam","startTime":430.65,"endTime":434.04,"body":"numbers into the 10s and 1s, and"},{"speaker":"Pam","startTime":434.04,"endTime":436.65,"body":"10s and 1s, and then they're"},{"speaker":"Pam","startTime":434.04,"endTime":436.65,"body":"multiplying all those parts. If"},{"speaker":"Pam","startTime":436.65,"endTime":441.09,"body":"that's the only thing you've"},{"speaker":"Pam","startTime":436.65,"endTime":441.09,"body":"ever seen on an area model"},{"speaker":"Pam","startTime":441.09,"endTime":444.48,"body":"rectangle, then you might be"},{"speaker":"Pam","startTime":441.09,"endTime":444.48,"body":"like, \"Oh, they did an array,\""},{"speaker":"Pam","startTime":445.02,"endTime":448.92,"body":"without realizing they might"},{"speaker":"Pam","startTime":445.02,"endTime":448.92,"body":"have cut the pieces very"},{"speaker":"Pam","startTime":448.92,"endTime":452.43,"body":"strategically. And they might"},{"speaker":"Pam","startTime":448.92,"endTime":452.43,"body":"have used very clever partial"},{"speaker":"Pam","startTime":452.43,"endTime":456.45,"body":"products. And that's what's"},{"speaker":"Pam","startTime":452.43,"endTime":456.45,"body":"worth looking at. It's the way"},{"speaker":"Pam","startTime":456.45,"endTime":461.49,"body":"they cut the area up. Similarly,"},{"speaker":"Pam","startTime":456.45,"endTime":461.49,"body":"what you're saying is in a ratio"},{"speaker":"Pam","startTime":461.49,"endTime":464.04,"body":"table, it depends on what"},{"speaker":"Pam","startTime":461.49,"endTime":464.04,"body":"relationships you use in the"},{"speaker":"Pam","startTime":464.04,"endTime":468.75,"body":"ratio table that's the strategy."},{"speaker":"Pam","startTime":464.04,"endTime":468.75,"body":"So, yeah, we would encourage you"},{"speaker":"Pam","startTime":468.75,"endTime":472.44,"body":"that as you look at"},{"speaker":"Pam","startTime":468.75,"endTime":472.44,"body":"MathStratChat, or ratio tables"},{"speaker":"Pam","startTime":472.44,"endTime":476.52,"body":"anywhere else that you dive into"},{"speaker":"Pam","startTime":472.44,"endTime":476.52,"body":"what are the relationships that"},{"speaker":"Pam","startTime":476.52,"endTime":481.26,"body":"are being showcased that are"},{"speaker":"Pam","startTime":476.52,"endTime":481.26,"body":"being mentally... What's the"},{"speaker":"Pam","startTime":481.26,"endTime":484.89,"body":"word I want? The connections"},{"speaker":"Pam","startTime":481.26,"endTime":484.89,"body":"that are being made. That's"},{"speaker":"Pam","startTime":484.89,"endTime":488.4,"body":"what's cool to look at in a"},{"speaker":"Pam","startTime":484.89,"endTime":488.4,"body":"ratio table, not just \"Oh, that"},{"speaker":"Pam","startTime":488.4,"endTime":492.12,"body":"person did a ratio table. Click."},{"speaker":"Pam","startTime":488.4,"endTime":492.12,"body":"Let me go see if somebody did"},{"speaker":"Pam","startTime":492.12,"endTime":494.88,"body":"something different.\" No, no."},{"speaker":"Pam","startTime":492.12,"endTime":494.88,"body":"Like, it's what they did in a"},{"speaker":"Pam","startTime":494.88,"endTime":500.01,"body":"ratio table is super important."},{"speaker":"Pam","startTime":494.88,"endTime":500.01,"body":"Yeah. Yeah. Nicely said. And one"},{"speaker":"Pam","startTime":500.01,"endTime":503.4,"body":"of those places that's super"},{"speaker":"Pam","startTime":500.01,"endTime":503.4,"body":"cool that we can do with ratio"},{"speaker":"Pam","startTime":503.4,"endTime":508.38,"body":"tables is fraction equivalence."},{"speaker":"Pam","startTime":503.4,"endTime":508.38,"body":"And you might be like \"Pam"},{"speaker":"Pam","startTime":508.44,"endTime":511.74,"body":"fraction equivalence. That's so"},{"speaker":"Pam","startTime":508.44,"endTime":511.74,"body":"easy. All you do is you write"},{"speaker":"Pam","startTime":511.74,"endTime":514.14,"body":"down... Like, to find an"},{"speaker":"Pam","startTime":511.74,"endTime":514.14,"body":"equivalent fraction, there's"},{"speaker":"Pam","startTime":514.14,"endTime":517.26,"body":"this rule, there's this"},{"speaker":"Pam","startTime":514.14,"endTime":517.26,"body":"procedure that you can do. You"},{"speaker":"Pam","startTime":517.26,"endTime":520.29,"body":"just write down the fraction.\""},{"speaker":"Pam","startTime":517.26,"endTime":520.29,"body":"Like, I just wrote down. I don't"},{"speaker":"Pam","startTime":520.29,"endTime":523.86,"body":"know. Why not? Five-sevenths"},{"speaker":"Pam","startTime":520.29,"endTime":523.86,"body":"because it is, and say you"},{"speaker":"Pam","startTime":523.86,"endTime":527.79,"body":"wanted to make it equivalent to"},{"speaker":"Pam","startTime":523.86,"endTime":527.79,"body":"something with 21s. And so, I've"},{"speaker":"Pam","startTime":527.79,"endTime":531.57,"body":"got the fraction five-sevenths"},{"speaker":"Pam","startTime":527.79,"endTime":531.57,"body":"equal. And then, I have the"},{"speaker":"Pam","startTime":531.57,"endTime":535.14,"body":"fraction bar. And then, in the"},{"speaker":"Pam","startTime":531.57,"endTime":535.14,"body":"denominator, I have 21 because"},{"speaker":"Pam","startTime":535.14,"endTime":537.84,"body":"I'm going to try to create"},{"speaker":"Pam","startTime":535.14,"endTime":537.84,"body":"equivalent fraction. And you"},{"speaker":"Pam","startTime":537.84,"endTime":542.7,"body":"might have memorized. I did as a"},{"speaker":"Pam","startTime":537.84,"endTime":542.7,"body":"student. 7 goes into 21 how many"},{"speaker":"Pam","startTime":542.7,"endTime":544.86,"body":"times? And then, you take that"},{"speaker":"Pam","startTime":542.7,"endTime":544.86,"body":"number, and you multiply it by"},{"speaker":"Pam","startTime":544.86,"endTime":547.23,"body":"the 5, and then you get the"},{"speaker":"Pam","startTime":544.86,"endTime":547.23,"body":"other numerator. And you might"},{"speaker":"Pam","startTime":547.23,"endTime":549.57,"body":"be like, \"Yeah, Pam, that's what"},{"speaker":"Pam","startTime":547.23,"endTime":549.57,"body":"you do to find the equivalent"},{"speaker":"Pam","startTime":549.57,"endTime":553.86,"body":"fraction.\" Well, that might be a"},{"speaker":"Pam","startTime":549.57,"endTime":553.86,"body":"set of steps, that might be a"},{"speaker":"Pam","startTime":553.86,"endTime":556.8,"body":"procedure or an algorithm to"},{"speaker":"Pam","startTime":553.86,"endTime":556.8,"body":"find equivalent fractions, but"},{"speaker":"Pam","startTime":556.8,"endTime":560.61,"body":"what it's not is demonstrating"},{"speaker":"Pam","startTime":556.8,"endTime":560.61,"body":"understanding equivalent"},{"speaker":"Pam","startTime":560.61,"endTime":565.77,"body":"fractions. It's not using what"},{"speaker":"Pam","startTime":560.61,"endTime":565.77,"body":"you know about equivalence and"},{"speaker":"Pam","startTime":565.77,"endTime":568.65,"body":"building equivalence at the same"},{"speaker":"Pam","startTime":565.77,"endTime":568.65,"body":"time to find an equivalent"},{"speaker":"Pam","startTime":568.65,"endTime":572.58,"body":"fraction. I will never forget."},{"speaker":"Pam","startTime":568.65,"endTime":572.58,"body":"Kim, you remember Garland"},{"speaker":"Pam","startTime":572.58,"endTime":573.24,"body":"Linkenhoger?"},{"speaker":"Kim","startTime":573.45,"endTime":574.41,"body":"Oh, yeah, yeah."},{"speaker":"Pam","startTime":574.41,"endTime":577.56,"body":"So, dear friend of ours,"},{"speaker":"Pam","startTime":574.41,"endTime":577.56,"body":"who we have not seen lately for."},{"speaker":"Pam","startTime":577.56,"endTime":580.2,"body":"Come on, Garland. We have to"},{"speaker":"Pam","startTime":577.56,"endTime":580.2,"body":"figure out how to meet up with"},{"speaker":"Pam","startTime":580.2,"endTime":583.89,"body":"her at some point. Wonderful,"},{"speaker":"Pam","startTime":580.2,"endTime":583.89,"body":"wonderful lady who taught us a"},{"speaker":"Pam","startTime":583.89,"endTime":587.31,"body":"ton. We worked really early in"},{"speaker":"Pam","startTime":583.89,"endTime":587.31,"body":"when you and I were working"},{"speaker":"Pam","startTime":587.31,"endTime":588.45,"body":"together at the school you were"},{"speaker":"Pam","startTime":587.31,"endTime":588.45,"body":"teaching."},{"speaker":"Kim","startTime":588.45,"endTime":588.51,"body":"Yeah."},{"speaker":"Pam","startTime":589.41,"endTime":592.71,"body":"She she said one day. So,"},{"speaker":"Pam","startTime":589.41,"endTime":592.71,"body":"this is super early in my"},{"speaker":"Pam","startTime":592.71,"endTime":597.27,"body":"journey in learning that Math is"},{"speaker":"Pam","startTime":592.71,"endTime":597.27,"body":"Figure-Out-Able and that more"},{"speaker":"Pam","startTime":597.27,"endTime":599.52,"body":"than I ever knew was"},{"speaker":"Pam","startTime":597.27,"endTime":599.52,"body":"figure-out-able. So, I'm diving"},{"speaker":"Pam","startTime":599.52,"endTime":602.25,"body":"into the research. I'm diving"},{"speaker":"Pam","startTime":599.52,"endTime":602.25,"body":"into my kids classrooms. I'm"},{"speaker":"Pam","startTime":602.25,"endTime":606.54,"body":"working with Garland. And she"},{"speaker":"Pam","startTime":602.25,"endTime":606.54,"body":"said one day to me. I'll never"},{"speaker":"Pam","startTime":606.54,"endTime":610.98,"body":"forget. She looked at me and she"},{"speaker":"Pam","startTime":606.54,"endTime":610.98,"body":"goes, \"Pam, if you really"},{"speaker":"Pam","startTime":610.98,"endTime":614.79,"body":"understand fraction equivalence,"},{"speaker":"Pam","startTime":610.98,"endTime":614.79,"body":"you don't have to have any rules"},{"speaker":"Pam","startTime":614.82,"endTime":619.35,"body":"for fraction operations.\" And I"},{"speaker":"Pam","startTime":614.82,"endTime":619.35,"body":"said, \"I'm sorry, what?\" She"},{"speaker":"Pam","startTime":619.35,"endTime":623.22,"body":"said, \"Like, all the rules to do"},{"speaker":"Pam","startTime":619.35,"endTime":623.22,"body":"fraction operations. You don't"},{"speaker":"Pam","startTime":623.22,"endTime":626.19,"body":"have to know any of those if you"},{"speaker":"Pam","startTime":623.22,"endTime":626.19,"body":"actually understand fraction"},{"speaker":"Pam","startTime":626.19,"endTime":631.68,"body":"equivalence.\" That idea was so"},{"speaker":"Pam","startTime":626.19,"endTime":631.68,"body":"new to me, and so... Like,"},{"speaker":"Pam","startTime":631.68,"endTime":635.1,"body":"fractions, to me we're all about"},{"speaker":"Pam","startTime":631.68,"endTime":635.1,"body":"which rule to do when. Don't"},{"speaker":"Pam","startTime":635.1,"endTime":638.19,"body":"look down on me, listeners. Not"},{"speaker":"Pam","startTime":635.1,"endTime":638.19,"body":"right now. Don't be like, \"Pam,"},{"speaker":"Pam","startTime":638.19,"endTime":640.11,"body":"really? That's what you think.\""},{"speaker":"Pam","startTime":638.19,"endTime":640.11,"body":"Yes, that is what I thought"},{"speaker":"Pam","startTime":640.11,"endTime":642.6,"body":"because that's what I was"},{"speaker":"Pam","startTime":640.11,"endTime":642.6,"body":"taught. And if the rest of you"},{"speaker":"Pam","startTime":642.6,"endTime":644.73,"body":"are like, \"Yeah, that's what we"},{"speaker":"Pam","startTime":642.6,"endTime":644.73,"body":"were taught,\" yeah, that's what"},{"speaker":"Pam","startTime":644.73,"endTime":649.23,"body":"we were taught! So, if that's"},{"speaker":"Pam","startTime":644.73,"endTime":649.23,"body":"your sort of focus of when you"},{"speaker":"Pam","startTime":649.23,"endTime":652.05,"body":"think of fractions and addition,"},{"speaker":"Pam","startTime":649.23,"endTime":652.05,"body":"subtraction, multiplication,"},{"speaker":"Pam","startTime":652.05,"endTime":654.03,"body":"division, and you're like,"},{"speaker":"Pam","startTime":652.05,"endTime":654.03,"body":"\"Yeah, which rule, and if I"},{"speaker":"Pam","startTime":654.03,"endTime":656.79,"body":"remember which rule to do, and"},{"speaker":"Pam","startTime":654.03,"endTime":656.79,"body":"the steps, and the rule,\" I'm"},{"speaker":"Pam","startTime":656.79,"endTime":659.46,"body":"going to invite you to consider"},{"speaker":"Pam","startTime":656.79,"endTime":659.46,"body":"if you actually understand"},{"speaker":"Pam","startTime":659.46,"endTime":664.05,"body":"fraction equivalence. We don't"},{"speaker":"Pam","startTime":659.46,"endTime":664.05,"body":"need rules to operate with"},{"speaker":"Pam","startTime":664.05,"endTime":668.28,"body":"fractions. So, it's important"},{"speaker":"Pam","startTime":664.05,"endTime":668.28,"body":"that students actually have this"},{"speaker":"Pam","startTime":668.28,"endTime":672.36,"body":"feel and sense and"},{"speaker":"Pam","startTime":668.28,"endTime":672.36,"body":"understanding, not just this"},{"speaker":"Pam","startTime":672.54,"endTime":674.76,"body":"sort of vague conceptual"},{"speaker":"Pam","startTime":672.54,"endTime":674.76,"body":"understanding, so then we can"},{"speaker":"Pam","startTime":674.76,"endTime":677.46,"body":"learn the rule. No, no, no, no."},{"speaker":"Pam","startTime":674.76,"endTime":677.46,"body":"It's like actually really"},{"speaker":"Pam","startTime":677.46,"endTime":681.93,"body":"feeling fraction equivalence. In"},{"speaker":"Pam","startTime":677.46,"endTime":681.93,"body":"fact, do you remember? Kim, I"},{"speaker":"Pam","startTime":681.93,"endTime":685.2,"body":"came home from that day talking"},{"speaker":"Pam","startTime":681.93,"endTime":685.2,"body":"with Garland, and I said"},{"speaker":"Pam","startTime":685.2,"endTime":687.54,"body":"something to my personal kid."},{"speaker":"Pam","startTime":685.2,"endTime":687.54,"body":"And those of you who listen to"},{"speaker":"Pam","startTime":687.54,"endTime":691.05,"body":"podcasts for a while know that I"},{"speaker":"Pam","startTime":687.54,"endTime":691.05,"body":"was hugely influenced by my"},{"speaker":"Pam","startTime":691.05,"endTime":694.62,"body":"oldest son, the way that he just"},{"speaker":"Pam","startTime":691.05,"endTime":694.62,"body":"kind of naturally mathematized"},{"speaker":"Pam","startTime":694.95,"endTime":699.54,"body":"was really the impetus. It was"},{"speaker":"Pam","startTime":694.95,"endTime":699.54,"body":"my inspiration for diving into"},{"speaker":"Pam","startTime":699.54,"endTime":702.57,"body":"all the math and all the things."},{"speaker":"Pam","startTime":699.54,"endTime":702.57,"body":"And I went home to him, and I"},{"speaker":"Pam","startTime":702.57,"endTime":705.51,"body":"said something like, \"I can't"},{"speaker":"Pam","startTime":702.57,"endTime":705.51,"body":"believe she said that. Like"},{"speaker":"Pam","startTime":705.51,"endTime":710.25,"body":"what? Cameron, what do you know"},{"speaker":"Pam","startTime":705.51,"endTime":710.25,"body":"about fraction equivalence?\" I"},{"speaker":"Pam","startTime":710.25,"endTime":712.17,"body":"was just super, super curious."},{"speaker":"Pam","startTime":710.25,"endTime":712.17,"body":"Because remember, he's my"},{"speaker":"Pam","startTime":712.17,"endTime":714.39,"body":"inspiration. So, I'm like, \"What"},{"speaker":"Pam","startTime":712.17,"endTime":714.39,"body":"do you? What do you mean? What."},{"speaker":"Pam","startTime":714.51,"endTime":717.18,"body":"Tell me about fraction"},{"speaker":"Pam","startTime":714.51,"endTime":717.18,"body":"equivalence.\" And he looked at"},{"speaker":"Pam","startTime":717.18,"endTime":720.3,"body":"me, kind of cocked his head,"},{"speaker":"Pam","startTime":717.18,"endTime":720.3,"body":"closed one eye just slightly,"},{"speaker":"Pam","startTime":720.54,"endTime":727.92,"body":"and he goes, \"Well, it's like,"},{"speaker":"Pam","startTime":720.54,"endTime":727.92,"body":"if you cut the pieces in half,"},{"speaker":"Pam","startTime":728.34,"endTime":730.95,"body":"you would need to have twice as"},{"speaker":"Pam","startTime":728.34,"endTime":730.95,"body":"many to have the same amount of"},{"speaker":"Pam","startTime":730.95,"endTime":737.25,"body":"pizza. And I was like, \"Say that"},{"speaker":"Pam","startTime":730.95,"endTime":737.25,"body":"again.\" Like, he really had"},{"speaker":"Pam","startTime":737.25,"endTime":741.45,"body":"thought about the fact that if"},{"speaker":"Pam","startTime":737.25,"endTime":741.45,"body":"you'd cut the pizza into 7"},{"speaker":"Pam","startTime":741.6,"endTime":748.17,"body":"pieces, so you had sevenths."},{"speaker":"Pam","startTime":741.6,"endTime":748.17,"body":"One-seventh of a pizza was one"},{"speaker":"Pam","startTime":748.17,"endTime":752.55,"body":"of those slices. If you cut them"},{"speaker":"Pam","startTime":748.17,"endTime":752.55,"body":"all in half, then you'd have"},{"speaker":"Pam","startTime":752.55,"endTime":756.6,"body":"twice as many pieces, right? But"},{"speaker":"Pam","startTime":752.55,"endTime":756.6,"body":"now you'd have fourteenths. And"},{"speaker":"Pam","startTime":756.63,"endTime":760.71,"body":"so, you'd have to take twice as"},{"speaker":"Pam","startTime":756.63,"endTime":760.71,"body":"many. If I took 1 piece, and I"},{"speaker":"Pam","startTime":760.71,"endTime":763.05,"body":"had one-seventh, and now I've"},{"speaker":"Pam","startTime":760.71,"endTime":763.05,"body":"cut them all in half, I would"},{"speaker":"Pam","startTime":763.05,"endTime":765.54,"body":"have to take two of those"},{"speaker":"Pam","startTime":763.05,"endTime":765.54,"body":"fourteenths in order to have the"},{"speaker":"Pam","startTime":765.54,"endTime":768.09,"body":"same amount of pizza as the"},{"speaker":"Pam","startTime":765.54,"endTime":768.09,"body":"one-seventh."},{"speaker":"Kim","startTime":768.12,"endTime":768.54,"body":"Mmhmm."},{"speaker":"Pam","startTime":769.32,"endTime":771.72,"body":"And you might like, \"Well,"},{"speaker":"Pam","startTime":769.32,"endTime":771.72,"body":"that's trivial, Pam.\" No, no. So"},{"speaker":"Pam","startTime":771.72,"endTime":774.45,"body":"not trivial. Like, that's a"},{"speaker":"Pam","startTime":771.72,"endTime":774.45,"body":"generalization that he was"},{"speaker":"Pam","startTime":774.45,"endTime":778.65,"body":"making. That just was starting"},{"speaker":"Pam","startTime":774.45,"endTime":778.65,"body":"him in this idea that if you cut"},{"speaker":"Pam","startTime":778.65,"endTime":783.12,"body":"the pieces into even number of"},{"speaker":"Pam","startTime":778.65,"endTime":783.12,"body":"shares, and you make a smaller"},{"speaker":"Pam","startTime":783.12,"endTime":788.19,"body":"fraction, then you got to scale"},{"speaker":"Pam","startTime":783.12,"endTime":788.19,"body":"up that many kinds of that many."},{"speaker":"Pam","startTime":788.25,"endTime":790.32,"body":"Boy, I'm saying this to"},{"speaker":"Pam","startTime":788.25,"endTime":790.32,"body":"(unclear). So, that's why he"},{"speaker":"Pam","startTime":790.32,"endTime":792.78,"body":"said it in halves, right? It was"},{"speaker":"Pam","startTime":790.32,"endTime":792.78,"body":"so much easier just to say, if"},{"speaker":"Pam","startTime":792.78,"endTime":795.93,"body":"you cut it in half, you have to"},{"speaker":"Pam","startTime":792.78,"endTime":795.93,"body":"twice many pieces in order to"},{"speaker":"Pam","startTime":795.93,"endTime":798.9,"body":"have the same amount of pizza."},{"speaker":"Pam","startTime":795.93,"endTime":798.9,"body":"That idea, that sense of"},{"speaker":"Pam","startTime":798.9,"endTime":802.95,"body":"fraction equivalence is super"},{"speaker":"Pam","startTime":798.9,"endTime":802.95,"body":"important. And we can help that"},{"speaker":"Pam","startTime":802.95,"endTime":808.23,"body":"happen with fractions, and"},{"speaker":"Pam","startTime":802.95,"endTime":808.23,"body":"ratios, and with ratio tables."},{"speaker":"Pam","startTime":808.23,"endTime":813.03,"body":"Ratio tables can be this model"},{"speaker":"Pam","startTime":808.23,"endTime":813.03,"body":"that can be one of the helps in"},{"speaker":"Pam","startTime":813.03,"endTime":813.72,"body":"making that happen."},{"speaker":"Kim","startTime":814.47,"endTime":818.4,"body":"Yeah, so we're talking"},{"speaker":"Kim","startTime":814.47,"endTime":818.4,"body":"about ratio tables today. And"},{"speaker":"Kim","startTime":818.43,"endTime":821.61,"body":"so, let me give you a problem."},{"speaker":"Kim","startTime":818.43,"endTime":821.61,"body":"And will you describe for us how"},{"speaker":"Kim","startTime":821.61,"endTime":824.91,"body":"you would use a ratio table to"},{"speaker":"Kim","startTime":821.61,"endTime":824.91,"body":"solve a problem?"},{"speaker":"Pam","startTime":825.09,"endTime":825.84,"body":"Do it. Let's do it."},{"speaker":"Kim","startTime":825.84,"endTime":828.99,"body":"Okay. So, I'm going to give"},{"speaker":"Kim","startTime":825.84,"endTime":828.99,"body":"you three-fourths plus your"},{"speaker":"Kim","startTime":829.02,"endTime":831.0,"body":"five-sevenths that you were just"},{"speaker":"Kim","startTime":829.02,"endTime":831.0,"body":"talking about. You were talking"},{"speaker":"Kim","startTime":831.0,"endTime":833.43,"body":"about sevenths. Three-fourths"},{"speaker":"Kim","startTime":831.0,"endTime":833.43,"body":"plus five-sevenths."},{"speaker":"Pam","startTime":833.88,"endTime":836.52,"body":"Okay, so to actually use a"},{"speaker":"Pam","startTime":833.88,"endTime":836.52,"body":"ratio table to solve this"},{"speaker":"Pam","startTime":836.52,"endTime":840.12,"body":"problem, I need to back up just"},{"speaker":"Pam","startTime":836.52,"endTime":840.12,"body":"a hair to say it's definitely"},{"speaker":"Pam","startTime":840.12,"endTime":842.7,"body":"not the first thing that I'm"},{"speaker":"Pam","startTime":840.12,"endTime":842.7,"body":"doing to build fraction"},{"speaker":"Pam","startTime":842.7,"endTime":847.74,"body":"understanding. So, we're going"},{"speaker":"Pam","startTime":842.7,"endTime":847.74,"body":"to do all of the things and to"},{"speaker":"Pam","startTime":847.74,"endTime":851.01,"body":"build like what does it mean to"},{"speaker":"Pam","startTime":847.74,"endTime":851.01,"body":"have a fourth? So, you said"},{"speaker":"Pam","startTime":851.04,"endTime":853.44,"body":"three-fourths. What does it mean"},{"speaker":"Pam","startTime":851.04,"endTime":853.44,"body":"to have one-fourth? And what"},{"speaker":"Pam","startTime":853.44,"endTime":856.26,"body":"does it mean to have three of"},{"speaker":"Pam","startTime":853.44,"endTime":856.26,"body":"those one-fourths? What does it"},{"speaker":"Pam","startTime":856.26,"endTime":859.11,"body":"mean to have one-seventh, and"},{"speaker":"Pam","startTime":856.26,"endTime":859.11,"body":"then five of those one-sevenths."},{"speaker":"Pam","startTime":859.59,"endTime":862.32,"body":"So, there's lots of things that"},{"speaker":"Pam","startTime":859.59,"endTime":862.32,"body":"we're going to build with just"},{"speaker":"Pam","startTime":862.32,"endTime":867.18,"body":"fraction sense, and then we're"},{"speaker":"Pam","startTime":862.32,"endTime":867.18,"body":"also going to build a sense of"},{"speaker":"Pam","startTime":867.6,"endTime":870.9,"body":"addition and subtraction of"},{"speaker":"Pam","startTime":867.6,"endTime":870.9,"body":"fractions using a double open"},{"speaker":"Pam","startTime":870.9,"endTime":875.04,"body":"number line. So, that would be"},{"speaker":"Pam","startTime":870.9,"endTime":875.04,"body":"one of the models of choice"},{"speaker":"Pam","startTime":875.07,"endTime":879.09,"body":"first. So, it would not be a"},{"speaker":"Pam","startTime":875.07,"endTime":879.09,"body":"ratio table first. And I'm not"},{"speaker":"Pam","startTime":879.09,"endTime":881.34,"body":"going to go into that today."},{"speaker":"Pam","startTime":879.09,"endTime":881.34,"body":"Maybe we'll spend a whole other"},{"speaker":"Pam","startTime":881.49,"endTime":885.51,"body":"podcast on that. But ratio table"},{"speaker":"Pam","startTime":881.49,"endTime":885.51,"body":"wouldn't be the first model that"},{"speaker":"Pam","startTime":885.51,"endTime":888.81,"body":"I'd use. But after I have"},{"speaker":"Pam","startTime":885.51,"endTime":888.81,"body":"students using double open"},{"speaker":"Pam","startTime":888.81,"endTime":891.63,"body":"number lines. Well, at least..."},{"speaker":"Pam","startTime":888.81,"endTime":891.63,"body":"Maybe I'll say it this way."},{"speaker":"Pam","startTime":891.87,"endTime":895.47,"body":"After I'm helping students"},{"speaker":"Pam","startTime":891.87,"endTime":895.47,"body":"reason about the addition and"},{"speaker":"Pam","startTime":895.47,"endTime":898.59,"body":"subtraction of fractions where"},{"speaker":"Pam","startTime":895.47,"endTime":898.59,"body":"I'm modeling their thinking"},{"speaker":"Pam","startTime":898.59,"endTime":903.3,"body":"using a double open number line,"},{"speaker":"Pam","startTime":898.59,"endTime":903.3,"body":"and we've got that going, and"},{"speaker":"Pam","startTime":903.33,"endTime":907.2,"body":"simultaneously I've got students"},{"speaker":"Pam","startTime":903.33,"endTime":907.2,"body":"thinking and reasoning about"},{"speaker":"Pam","startTime":907.2,"endTime":911.91,"body":"multiplication on a ratio table."},{"speaker":"Pam","startTime":907.2,"endTime":911.91,"body":"Once we have those two main"},{"speaker":"Pam","startTime":911.91,"endTime":916.98,"body":"pieces then it's going to be a"},{"speaker":"Pam","startTime":911.91,"endTime":916.98,"body":"very natural transition for"},{"speaker":"Pam","startTime":916.98,"endTime":921.03,"body":"students to use a ratio table to"},{"speaker":"Pam","startTime":916.98,"endTime":921.03,"body":"do the following for a problem"},{"speaker":"Pam","startTime":921.03,"endTime":924.0,"body":"like three-fourths plus"},{"speaker":"Pam","startTime":921.03,"endTime":924.0,"body":"five-sevenths. So, I would say"},{"speaker":"Pam","startTime":924.0,"endTime":925.77,"body":"that students would look at"},{"speaker":"Pam","startTime":924.0,"endTime":925.77,"body":"three-fourths plus"},{"speaker":"Pam","startTime":925.77,"endTime":928.77,"body":"five-sevenths. And they would"},{"speaker":"Pam","startTime":925.77,"endTime":928.77,"body":"say, \"Hmm. Let's see. I need the"},{"speaker":"Pam","startTime":928.77,"endTime":931.8,"body":"same kinds of pieces. If I'm"},{"speaker":"Pam","startTime":928.77,"endTime":931.8,"body":"going to add fractions together,"},{"speaker":"Pam","startTime":931.8,"endTime":934.11,"body":"we need to have the same kinds"},{"speaker":"Pam","startTime":931.8,"endTime":934.11,"body":"of pieces to add them."},{"speaker":"Pam","startTime":934.14,"endTime":937.05,"body":"Otherwise, I can picture"},{"speaker":"Pam","startTime":934.14,"endTime":937.05,"body":"three-fourths of something, and"},{"speaker":"Pam","startTime":937.05,"endTime":940.59,"body":"I can picture five-sevenths of"},{"speaker":"Pam","startTime":937.05,"endTime":940.59,"body":"something, and I can see that"},{"speaker":"Pam","startTime":940.59,"endTime":943.98,"body":"I've got more than one of a"},{"speaker":"Pam","startTime":940.59,"endTime":943.98,"body":"thing.\" That would be delightful"},{"speaker":"Pam","startTime":943.98,"endTime":946.32,"body":"for them to kind of. If they can"},{"speaker":"Pam","startTime":943.98,"endTime":946.32,"body":"picture those amounts,"},{"speaker":"Pam","startTime":946.35,"endTime":949.29,"body":"three-fourths is only one-fourth"},{"speaker":"Pam","startTime":946.35,"endTime":949.29,"body":"from one. Five-sevenths is only"},{"speaker":"Pam","startTime":949.32,"endTime":952.89,"body":"two-sevenths from one. So, I'm"},{"speaker":"Pam","startTime":949.32,"endTime":952.89,"body":"adding almost one to almost one."},{"speaker":"Pam","startTime":952.89,"endTime":955.08,"body":"Gee, that's going to be more"},{"speaker":"Pam","startTime":952.89,"endTime":955.08,"body":"than one. So, there should be"},{"speaker":"Pam","startTime":955.08,"endTime":959.4,"body":"this sense already of kind of a"},{"speaker":"Pam","startTime":955.08,"endTime":959.4,"body":"feel of what's happening. Then,"},{"speaker":"Pam","startTime":959.4,"endTime":962.04,"body":"they can say, \"But in order to"},{"speaker":"Pam","startTime":959.4,"endTime":962.04,"body":"know exactly how much I've got,"},{"speaker":"Pam","startTime":962.04,"endTime":964.65,"body":"I've got to have the same kind"},{"speaker":"Pam","startTime":962.04,"endTime":964.65,"body":"of pieces.\" Let's see fourths"},{"speaker":"Pam","startTime":964.68,"endTime":968.64,"body":"and sevenths. Now, I'm going"},{"speaker":"Pam","startTime":964.68,"endTime":968.64,"body":"very kind of general here. I"},{"speaker":"Pam","startTime":968.64,"endTime":971.79,"body":"would never start with fourths"},{"speaker":"Pam","startTime":968.64,"endTime":971.79,"body":"and sevenths to get students to"},{"speaker":"Pam","startTime":971.82,"endTime":974.37,"body":"get a feel for equivalent"},{"speaker":"Pam","startTime":971.82,"endTime":974.37,"body":"pieces. But now that we're"},{"speaker":"Pam","startTime":974.37,"endTime":978.48,"body":"there, we would have students"},{"speaker":"Pam","startTime":974.37,"endTime":978.48,"body":"go, \"Let's see, what is fourths"},{"speaker":"Pam","startTime":978.48,"endTime":980.79,"body":"and sevenths? What do they have"},{"speaker":"Pam","startTime":978.48,"endTime":980.79,"body":"in common?\" Well, in this case,"},{"speaker":"Pam","startTime":980.88,"endTime":984.78,"body":"four and seven are relatively"},{"speaker":"Pam","startTime":980.88,"endTime":984.78,"body":"prime. And so, they could think,"},{"speaker":"Pam","startTime":984.81,"endTime":988.02,"body":"\"Well, I know I could deal with"},{"speaker":"Pam","startTime":984.81,"endTime":988.02,"body":"twenty-eighths. Because both of"},{"speaker":"Pam","startTime":988.02,"endTime":992.19,"body":"those I can make. I can cut"},{"speaker":"Pam","startTime":988.02,"endTime":992.19,"body":"fourths up into twenty-eighths,"},{"speaker":"Pam","startTime":992.34,"endTime":996.21,"body":"and I can cut sevenths up and"},{"speaker":"Pam","startTime":992.34,"endTime":996.21,"body":"make twenty-eighths. If I have"},{"speaker":"Pam","startTime":996.21,"endTime":998.7,"body":"pizzas, I can cut them both up"},{"speaker":"Pam","startTime":996.21,"endTime":998.7,"body":"and make twenty-eighths. Okay,"},{"speaker":"Pam","startTime":998.7,"endTime":1000.59,"body":"cool. So, I'm gonna turn them"},{"speaker":"Pam","startTime":998.7,"endTime":1000.59,"body":"into twenty-eighths. Now, at"},{"speaker":"Pam","startTime":1000.59,"endTime":1002.12,"body":"this point, you might be like,"},{"speaker":"Pam","startTime":1000.59,"endTime":1002.12,"body":"\"Well, yeah, then I'm going to"},{"speaker":"Pam","startTime":1002.12,"endTime":1004.49,"body":"do that procedure. You said"},{"speaker":"Pam","startTime":1002.12,"endTime":1004.49,"body":"earlier 4 goes into 28. And"},{"speaker":"Pam","startTime":1004.49,"endTime":1007.85,"body":"28...\" No, no, no. Actually,"},{"speaker":"Pam","startTime":1004.49,"endTime":1007.85,"body":"what I'm going to do is I'm"},{"speaker":"Pam","startTime":1007.85,"endTime":1010.79,"body":"looking at a ratio table, and"},{"speaker":"Pam","startTime":1007.85,"endTime":1010.79,"body":"I'm going to say to myself,"},{"speaker":"Pam","startTime":1011.15,"endTime":1016.76,"body":"\"Three-fourths... I've put on a"},{"speaker":"Pam","startTime":1011.15,"endTime":1016.76,"body":"horizontal ratio table. So, I"},{"speaker":"Pam","startTime":1016.76,"endTime":1020.0,"body":"have three on the top and four"},{"speaker":"Pam","startTime":1016.76,"endTime":1020.0,"body":"on the bottom. And I'm then"},{"speaker":"Pam","startTime":1020.39,"endTime":1023.93,"body":"drawing a line next to it. And"},{"speaker":"Pam","startTime":1020.39,"endTime":1023.93,"body":"then, I've drawn 28. And I'm"},{"speaker":"Pam","startTime":1023.93,"endTime":1027.41,"body":"saying to myself, \"Hmm, what"},{"speaker":"Pam","startTime":1023.93,"endTime":1027.41,"body":"does it take for me to get from"},{"speaker":"Pam","startTime":1027.41,"endTime":1030.56,"body":"fourths to twenty-eighths or"},{"speaker":"Pam","startTime":1027.41,"endTime":1030.56,"body":"from 4 to 28?\" Because I'm"},{"speaker":"Pam","startTime":1030.56,"endTime":1032.84,"body":"cutting those. It's like I'm"},{"speaker":"Pam","startTime":1030.56,"endTime":1032.84,"body":"thinking about fourths, and I'm"},{"speaker":"Pam","startTime":1032.84,"endTime":1036.89,"body":"thinking if I can cut them all"},{"speaker":"Pam","startTime":1032.84,"endTime":1036.89,"body":"up into pieces to make"},{"speaker":"Pam","startTime":1036.92,"endTime":1041.12,"body":"twenty-eighths. But how many"},{"speaker":"Pam","startTime":1036.92,"endTime":1041.12,"body":"pieces would I have? Or how many"},{"speaker":"Pam","startTime":1041.12,"endTime":1044.18,"body":"times I have to cut that fourth"},{"speaker":"Pam","startTime":1041.12,"endTime":1044.18,"body":"up to get twenty-eighths? So,"},{"speaker":"Pam","startTime":1044.84,"endTime":1047.63,"body":"I'd have to do it 7 times. It's"},{"speaker":"Pam","startTime":1044.84,"endTime":1047.63,"body":"kind of like Cameron said. \"If"},{"speaker":"Pam","startTime":1047.66,"endTime":1052.22,"body":"you cut the...\" Why did we use 4"},{"speaker":"Pam","startTime":1047.66,"endTime":1052.22,"body":"and 7, Kim? It's alright. It's"},{"speaker":"Pam","startTime":1052.22,"endTime":1055.43,"body":"just a crazy big number. It's"},{"speaker":"Pam","startTime":1052.22,"endTime":1055.43,"body":"just like Cameron said, \"If"},{"speaker":"Pam","startTime":1055.43,"endTime":1058.28,"body":"you're going to cut the pieces"},{"speaker":"Pam","startTime":1055.43,"endTime":1058.28,"body":"in half, then you get twice as"},{"speaker":"Pam","startTime":1058.28,"endTime":1060.56,"body":"many. Or you would need to have"},{"speaker":"Pam","startTime":1058.28,"endTime":1060.56,"body":"twice as many.\" So, if I'm going"},{"speaker":"Pam","startTime":1060.56,"endTime":1064.73,"body":"to cut each of those fourths"},{"speaker":"Pam","startTime":1060.56,"endTime":1064.73,"body":"into seven pieces, then I would"},{"speaker":"Pam","startTime":1064.73,"endTime":1068.36,"body":"have twenty-eighths. So, on the"},{"speaker":"Pam","startTime":1064.73,"endTime":1068.36,"body":"ratio table, I've just said,"},{"speaker":"Pam","startTime":1068.45,"endTime":1073.37,"body":"\"Ooh, to get from 4 to 28,"},{"speaker":"Pam","startTime":1068.45,"endTime":1073.37,"body":"that's times 7. So, I've scaled"},{"speaker":"Pam","startTime":1073.37,"endTime":1077.15,"body":"from 4 to 28, and I've drawn a"},{"speaker":"Pam","startTime":1073.37,"endTime":1077.15,"body":"little arrow, and then I've"},{"speaker":"Pam","startTime":1077.15,"endTime":1081.95,"body":"written times 7. Then I would"},{"speaker":"Pam","startTime":1077.15,"endTime":1081.95,"body":"also have to scale the number of"},{"speaker":"Pam","startTime":1083.18,"endTime":1086.69,"body":"pieces that I would have. So,"},{"speaker":"Pam","startTime":1083.18,"endTime":1086.69,"body":"the 3 also has to scale times 7."},{"speaker":"Pam","startTime":1086.93,"endTime":1089.93,"body":"Three times 7 is 21. So, now"},{"speaker":"Pam","startTime":1086.93,"endTime":1089.93,"body":"three-fourths is equivalent to"},{"speaker":"Pam","startTime":1089.93,"endTime":1096.02,"body":"21/28 on that ratio table. Now,"},{"speaker":"Pam","startTime":1089.93,"endTime":1096.02,"body":"very importantly, I have to have"},{"speaker":"Pam","startTime":1096.05,"endTime":1099.38,"body":"a new ratio table to deal with"},{"speaker":"Pam","startTime":1096.05,"endTime":1099.38,"body":"the five-sevenths."},{"speaker":"Kim","startTime":1099.47,"endTime":1099.8,"body":"Right."},{"speaker":"Pam","startTime":1100.16,"endTime":1102.05,"body":"\"What? Pam, why can't we"},{"speaker":"Pam","startTime":1100.16,"endTime":1102.05,"body":"put those all on the same ratio"},{"speaker":"Pam","startTime":1102.05,"endTime":1104.39,"body":"table?\" I'm going to get at that"},{"speaker":"Pam","startTime":1102.05,"endTime":1104.39,"body":"in just a minute. They need a"},{"speaker":"Pam","startTime":1104.39,"endTime":1107.72,"body":"new ratio table to think about"},{"speaker":"Pam","startTime":1104.39,"endTime":1107.72,"body":"five-sevenths to get to"},{"speaker":"Pam","startTime":1107.75,"endTime":1110.57,"body":"twenty-eighths. So, I've just"},{"speaker":"Pam","startTime":1107.75,"endTime":1110.57,"body":"written a tiny ratio table next"},{"speaker":"Pam","startTime":1110.57,"endTime":1114.11,"body":"to that one. I've got 5 on the"},{"speaker":"Pam","startTime":1110.57,"endTime":1114.11,"body":"top, 7 on the bottom. I've got"},{"speaker":"Pam","startTime":1114.11,"endTime":1118.01,"body":"28 Next to the 7. Drawn the"},{"speaker":"Pam","startTime":1114.11,"endTime":1118.01,"body":"line. 28 next to the 7. And I'm"},{"speaker":"Pam","startTime":1118.01,"endTime":1121.19,"body":"saying to myself, \"How do I get"},{"speaker":"Pam","startTime":1118.01,"endTime":1121.19,"body":"from 7 to 28? Oh, yeah. That's"},{"speaker":"Pam","startTime":1121.19,"endTime":1125.03,"body":"times 4.\" So, then I'm going to"},{"speaker":"Pam","startTime":1121.19,"endTime":1125.03,"body":"have to scale up the 5 times 4"},{"speaker":"Pam","startTime":1125.03,"endTime":1128.72,"body":"as well. And 5 times 4 is 20."},{"speaker":"Pam","startTime":1125.03,"endTime":1128.72,"body":"And so, the equivalent to"},{"speaker":"Pam","startTime":1128.72,"endTime":1131.99,"body":"five-sevenths is 20/28."},{"speaker":"Kim","startTime":1132.38,"endTime":1133.1,"body":"Mmhmm."},{"speaker":"Pam","startTime":1133.64,"endTime":1136.76,"body":"I did those two things on"},{"speaker":"Pam","startTime":1133.64,"endTime":1136.76,"body":"ratio tables. I got the"},{"speaker":"Pam","startTime":1136.76,"endTime":1140.54,"body":"equivalence of three-fourths of"},{"speaker":"Pam","startTime":1136.76,"endTime":1140.54,"body":"21/28. I got the equivalent of"},{"speaker":"Pam","startTime":1140.54,"endTime":1144.77,"body":"five-sevenths of 20/28. And now"},{"speaker":"Pam","startTime":1140.54,"endTime":1144.77,"body":"I can say to myself, literally"},{"speaker":"Pam","startTime":1144.77,"endTime":1150.35,"body":"could just reason, \"Well, I got"},{"speaker":"Pam","startTime":1144.77,"endTime":1150.35,"body":"21/28, and 20/28, then, I've got"},{"speaker":"Pam","startTime":1150.5,"endTime":1156.56,"body":"21 plus 20 twenty-eights. or"},{"speaker":"Pam","startTime":1150.5,"endTime":1156.56,"body":"41/28. So really, I'm using the"},{"speaker":"Pam","startTime":1156.56,"endTime":1161.0,"body":"ratio table to help me reason"},{"speaker":"Pam","startTime":1156.56,"endTime":1161.0,"body":"about what I need to scale the"},{"speaker":"Pam","startTime":1161.0,"endTime":1163.61,"body":"numerator, the denominator in"},{"speaker":"Pam","startTime":1161.0,"endTime":1163.61,"body":"order to get equivalent"},{"speaker":"Pam","startTime":1163.61,"endTime":1167.72,"body":"fractions that make sense in the"},{"speaker":"Pam","startTime":1163.61,"endTime":1167.72,"body":"either addition or subtraction"},{"speaker":"Pam","startTime":1167.72,"endTime":1168.56,"body":"of fraction problem."},{"speaker":"Kim","startTime":1169.25,"endTime":1172.34,"body":"What I love so much about"},{"speaker":"Kim","startTime":1169.25,"endTime":1172.34,"body":"what you just described is that"},{"speaker":"Kim","startTime":1172.34,"endTime":1175.67,"body":"if you've already. You know, if"},{"speaker":"Kim","startTime":1172.34,"endTime":1175.67,"body":"you've already worked with kids"},{"speaker":"Kim","startTime":1175.67,"endTime":1180.26,"body":"a little bit with ratio tables,"},{"speaker":"Kim","startTime":1175.67,"endTime":1180.26,"body":"with multiplication, then"},{"speaker":"Kim","startTime":1180.38,"endTime":1186.05,"body":"scaling up is not a new idea."},{"speaker":"Kim","startTime":1180.38,"endTime":1186.05,"body":"You're just bringing it to a new"},{"speaker":"Kim","startTime":1186.05,"endTime":1192.41,"body":"topic. And then, when you said"},{"speaker":"Kim","startTime":1186.05,"endTime":1192.41,"body":"21/28 and 20/28. There was space"},{"speaker":"Kim","startTime":1192.41,"endTime":1195.17,"body":"for me in my brain. I was like,"},{"speaker":"Kim","startTime":1192.41,"endTime":1195.17,"body":"\"Oh, I'm going to do a little"},{"speaker":"Kim","startTime":1195.17,"endTime":1199.28,"body":"Give and Take here and"},{"speaker":"Kim","startTime":1195.17,"endTime":1199.28,"body":"create...\" There wasn't this"},{"speaker":"Kim","startTime":1199.28,"endTime":1204.86,"body":"procedure of, \"I'm going to add"},{"speaker":"Kim","startTime":1199.28,"endTime":1204.86,"body":"20/28, 21/28, then I have 41/28"},{"speaker":"Kim","startTime":1204.86,"endTime":1208.07,"body":"that I have to pull out the"},{"speaker":"Kim","startTime":1204.86,"endTime":1208.07,"body":"whole.\" When I had the... I was"},{"speaker":"Kim","startTime":1208.07,"endTime":1210.77,"body":"kind of writing as you were"},{"speaker":"Kim","startTime":1208.07,"endTime":1210.77,"body":"describing, and I had 20/28 plus"},{"speaker":"Kim","startTime":1210.77,"endTime":1217.91,"body":"21/28. And I did a little Give"},{"speaker":"Kim","startTime":1210.77,"endTime":1217.91,"body":"and Take of 7/28. Does that make"},{"speaker":"Kim","startTime":1217.91,"endTime":1218.45,"body":"sense?"},{"speaker":"Pam","startTime":1218.69,"endTime":1220.13,"body":"No, keep going. Why would"},{"speaker":"Pam","startTime":1218.69,"endTime":1220.13,"body":"you do that?"},{"speaker":"Kim","startTime":1220.13,"endTime":1224.12,"body":"Oh, so I had written down"},{"speaker":"Kim","startTime":1220.13,"endTime":1224.12,"body":"20/28 plus 21/28."},{"speaker":"Pam","startTime":1224.69,"endTime":1225.59,"body":"Oh!"},{"speaker":"Pam","startTime":1225.71,"endTime":1227.06,"body":"Okay, keep going, keep going."},{"speaker":"Kim","startTime":1227.09,"endTime":1229.85,"body":"So, then I said, \"Okay,"},{"speaker":"Kim","startTime":1227.09,"endTime":1229.85,"body":"that's equivalent to...\" You're"},{"speaker":"Kim","startTime":1229.85,"endTime":1234.83,"body":"talking about equivalence."},{"speaker":"Kim","startTime":1229.85,"endTime":1234.83,"body":"That's equivalent to 13/28 plus"},{"speaker":"Kim","startTime":1234.83,"endTime":1242.18,"body":"28/28, which is 1. So, I got 1"},{"speaker":"Kim","startTime":1234.83,"endTime":1242.18,"body":"and 13/28. So, no longer is it a"},{"speaker":"Kim","startTime":1242.18,"endTime":1245.12,"body":"little bit of like, \"Do another"},{"speaker":"Kim","startTime":1242.18,"endTime":1245.12,"body":"procedure on top of that.\""},{"speaker":"Pam","startTime":1246.11,"endTime":1248.48,"body":"That is so awesome. So,"},{"speaker":"Pam","startTime":1246.11,"endTime":1248.48,"body":"once you knew that you were"},{"speaker":"Pam","startTime":1248.48,"endTime":1253.58,"body":"thinking about 20 plus 21/28,"},{"speaker":"Pam","startTime":1248.48,"endTime":1253.58,"body":"you said, \"I'm obviously over"},{"speaker":"Pam","startTime":1253.58,"endTime":1255.5,"body":"1...\" Which we'd already"},{"speaker":"Pam","startTime":1253.58,"endTime":1255.5,"body":"discussed, right? Where we knew"},{"speaker":"Pam","startTime":1255.5,"endTime":1257.6,"body":"we were over 1. And you're like,"},{"speaker":"Pam","startTime":1255.5,"endTime":1257.6,"body":"\"So, I'm going to pull that 1"},{"speaker":"Pam","startTime":1257.6,"endTime":1261.35,"body":"out. I'm not going to add them"},{"speaker":"Pam","startTime":1257.6,"endTime":1261.35,"body":"together and get 41/28, and then"},{"speaker":"Pam","startTime":1261.35,"endTime":1263.72,"body":"have to think about what's the 1"},{"speaker":"Pam","startTime":1261.35,"endTime":1263.72,"body":"in there.\""},{"speaker":"Kim","startTime":1263.72,"endTime":1264.02,"body":"Sure, yeah."},{"speaker":"Pam","startTime":1264.02,"endTime":1266.33,"body":"\"I'm going to find that 1"},{"speaker":"Pam","startTime":1264.02,"endTime":1266.33,"body":"right off the bat.\" So, you're"},{"speaker":"Pam","startTime":1266.33,"endTime":1268.85,"body":"just like, \"Well, I'm almost"},{"speaker":"Pam","startTime":1266.33,"endTime":1268.85,"body":"there. I'm just going to grab"},{"speaker":"Pam","startTime":1269.15,"endTime":1273.38,"body":"from the 1, grab from the 20,"},{"speaker":"Pam","startTime":1269.15,"endTime":1273.38,"body":"grab 7 to get to the 21.\" I know"},{"speaker":"Pam","startTime":1273.38,"endTime":1277.22,"body":"I'm re-saying it because it's so"},{"speaker":"Pam","startTime":1273.38,"endTime":1277.22,"body":"cool! So, you made. You"},{"speaker":"Pam","startTime":1277.22,"endTime":1279.53,"body":"basically made 28/28. And then"},{"speaker":"Pam","startTime":1277.22,"endTime":1279.53,"body":"you thought, well, what's"},{"speaker":"Pam","startTime":1279.53,"endTime":1281.18,"body":"leftover? Oh, the 13/28.\""},{"speaker":"Kim","startTime":1281.66,"endTime":1283.88,"body":"Yeah, and it just makes me"},{"speaker":"Kim","startTime":1281.66,"endTime":1283.88,"body":"think about, you know, sometimes"},{"speaker":"Kim","startTime":1283.91,"endTime":1287.45,"body":"we... This is maybe off topic."},{"speaker":"Kim","startTime":1283.91,"endTime":1287.45,"body":"Sorry, pull me back if so. But"},{"speaker":"Kim","startTime":1287.45,"endTime":1290.09,"body":"it makes me think about how..."},{"speaker":"Kim","startTime":1287.45,"endTime":1290.09,"body":"You know, sometimes we hear from"},{"speaker":"Kim","startTime":1290.09,"endTime":1294.53,"body":"teachers, \"How do I get give"},{"speaker":"Kim","startTime":1290.09,"endTime":1294.53,"body":"kids some experience using"},{"speaker":"Kim","startTime":1294.56,"endTime":1298.31,"body":"addition strategies or using"},{"speaker":"Kim","startTime":1294.56,"endTime":1298.31,"body":"multiplication strategies in the"},{"speaker":"Kim","startTime":1298.31,"endTime":1302.84,"body":"midst of my content if I'm the"},{"speaker":"Kim","startTime":1298.31,"endTime":1302.84,"body":"older grade teacher?\" And so,"},{"speaker":"Kim","startTime":1302.93,"endTime":1305.36,"body":"these are just. You know, right"},{"speaker":"Kim","startTime":1302.93,"endTime":1305.36,"body":"here, we've talked about some"},{"speaker":"Kim","startTime":1305.36,"endTime":1309.35,"body":"addition strategies with Give"},{"speaker":"Kim","startTime":1305.36,"endTime":1309.35,"body":"and Take and some scaling for"},{"speaker":"Kim","startTime":1309.35,"endTime":1313.4,"body":"multiplication. That (unclear)."},{"speaker":"Pam","startTime":1313.4,"endTime":1313.43,"body":"(unclear)."},{"speaker":"Kim","startTime":1313.49,"endTime":1315.59,"body":"Yeah, it's (unclear)"},{"speaker":"Kim","startTime":1313.49,"endTime":1315.59,"body":"content that they're supposed to"},{"speaker":"Kim","startTime":1315.59,"endTime":1316.04,"body":"be doing."},{"speaker":"Pam","startTime":1316.52,"endTime":1318.62,"body":"Yeah, like fraction"},{"speaker":"Pam","startTime":1316.52,"endTime":1318.62,"body":"addition, subtraction. It's a"},{"speaker":"Pam","startTime":1318.62,"endTime":1321.53,"body":"super, super good. Yeah, I'm so"},{"speaker":"Pam","startTime":1318.62,"endTime":1321.53,"body":"glad you mentioned that. So,"},{"speaker":"Pam","startTime":1321.53,"endTime":1325.25,"body":"teachers that are teaching"},{"speaker":"Pam","startTime":1321.53,"endTime":1325.25,"body":"fraction operations, as you're"},{"speaker":"Pam","startTime":1325.25,"endTime":1329.24,"body":"doing that, you could consider"},{"speaker":"Pam","startTime":1325.25,"endTime":1329.24,"body":"on the day you're about to do"},{"speaker":"Pam","startTime":1329.24,"endTime":1331.76,"body":"something like... What was it?"},{"speaker":"Pam","startTime":1329.24,"endTime":1331.76,"body":"Three-fourths plus"},{"speaker":"Pam","startTime":1331.79,"endTime":1335.33,"body":"five-sevenths. You could"},{"speaker":"Pam","startTime":1331.79,"endTime":1335.33,"body":"consider doing a Give and Take"},{"speaker":"Pam","startTime":1335.33,"endTime":1339.29,"body":"addition string, and then"},{"speaker":"Pam","startTime":1335.33,"endTime":1339.29,"body":"bringing out that idea as"},{"speaker":"Pam","startTime":1339.29,"endTime":1342.32,"body":"students are messing with"},{"speaker":"Pam","startTime":1339.29,"endTime":1342.32,"body":"problems like this, or scaling"},{"speaker":"Pam","startTime":1342.32,"endTime":1345.41,"body":"with multiplication, and then"},{"speaker":"Pam","startTime":1342.32,"endTime":1345.41,"body":"bringing out that idea as"},{"speaker":"Pam","startTime":1345.41,"endTime":1348.32,"body":"students are messing with"},{"speaker":"Pam","startTime":1345.41,"endTime":1348.32,"body":"fraction addition and"},{"speaker":"Pam","startTime":1348.32,"endTime":1348.86,"body":"subtraction."},{"speaker":"Kim","startTime":1348.92,"endTime":1349.28,"body":"Yeah."},{"speaker":"Pam","startTime":1349.34,"endTime":1352.46,"body":"Yeah. Well said, Hey, so,"},{"speaker":"Pam","startTime":1349.34,"endTime":1352.46,"body":"Kim, it also occurs to me that"},{"speaker":"Pam","startTime":1352.46,"endTime":1356.24,"body":"there are some things that we"},{"speaker":"Pam","startTime":1352.46,"endTime":1356.24,"body":"might just want to highlight."},{"speaker":"Pam","startTime":1356.24,"endTime":1359.09,"body":"And I mentioned, I was going to"},{"speaker":"Pam","startTime":1356.24,"endTime":1359.09,"body":"come back to it. Why did I use"},{"speaker":"Pam","startTime":1359.09,"endTime":1362.6,"body":"two different ratio tables to"},{"speaker":"Pam","startTime":1359.09,"endTime":1362.6,"body":"add three-fourths and"},{"speaker":"Pam","startTime":1362.63,"endTime":1365.84,"body":"five-sevenths? Why didn't I"},{"speaker":"Pam","startTime":1362.63,"endTime":1365.84,"body":"just? I mean, clearly, I could"},{"speaker":"Pam","startTime":1365.84,"endTime":1370.22,"body":"have just used a ratio table,"},{"speaker":"Pam","startTime":1365.84,"endTime":1370.22,"body":"wrote three-fourths. 3 on top, 4"},{"speaker":"Pam","startTime":1370.22,"endTime":1373.85,"body":"on the bottom. And then, in the"},{"speaker":"Pam","startTime":1370.22,"endTime":1373.85,"body":"next entry, I could have put 5"},{"speaker":"Pam","startTime":1373.97,"endTime":1376.22,"body":"on the top and 7 on the bottom."},{"speaker":"Pam","startTime":1373.97,"endTime":1376.22,"body":"And then, I could have added"},{"speaker":"Pam","startTime":1376.22,"endTime":1379.34,"body":"those together, right? So, I"},{"speaker":"Pam","startTime":1376.22,"endTime":1379.34,"body":"could have had 3 plus 5 is 8."},{"speaker":"Pam","startTime":1379.37,"endTime":1382.13,"body":"And then, the 4 plus 7 is 11."},{"speaker":"Pam","startTime":1379.37,"endTime":1382.13,"body":"And the answer could be"},{"speaker":"Pam","startTime":1382.16,"endTime":1384.89,"body":"eight-elevenths. And clearly"},{"speaker":"Pam","startTime":1382.16,"endTime":1384.89,"body":"eight-elevenths is equivalent"},{"speaker":"Pam","startTime":1384.89,"endTime":1389.57,"body":"to. Or not. Like, it's not,"},{"speaker":"Pam","startTime":1384.89,"endTime":1389.57,"body":"right? It's an incorrect answer."},{"speaker":"Kim","startTime":1389.69,"endTime":1389.81,"body":"Yeah."},{"speaker":"Pam","startTime":1389.87,"endTime":1392.78,"body":"And you're like, \"Pam, no."},{"speaker":"Pam","startTime":1389.87,"endTime":1392.78,"body":"You can't just add fractions."},{"speaker":"Pam","startTime":1392.78,"endTime":1395.6,"body":"You have...\" Like I said"},{"speaker":"Pam","startTime":1392.78,"endTime":1395.6,"body":"earlier, you have to have the"},{"speaker":"Pam","startTime":1396.53,"endTime":1400.52,"body":"same kind of pieces, can't just"},{"speaker":"Pam","startTime":1396.53,"endTime":1400.52,"body":"add fourths and sevenths"},{"speaker":"Pam","startTime":1400.52,"endTime":1405.35,"body":"together. However, teachers of"},{"speaker":"Pam","startTime":1400.52,"endTime":1405.35,"body":"multiplication, and division,"},{"speaker":"Pam","startTime":1405.41,"endTime":1410.3,"body":"and proportional reasoning,"},{"speaker":"Pam","startTime":1405.41,"endTime":1410.3,"body":"haven't we been adding ratios in"},{"speaker":"Pam","startTime":1410.3,"endTime":1415.73,"body":"ratio tables? Consider a sticks"},{"speaker":"Pam","startTime":1410.3,"endTime":1415.73,"body":"of gum Problem String. So, if"},{"speaker":"Pam","startTime":1415.73,"endTime":1418.37,"body":"that's new to you, maybe we'll"},{"speaker":"Pam","startTime":1415.73,"endTime":1418.37,"body":"put in the show notes where you"},{"speaker":"Pam","startTime":1418.37,"endTime":1420.68,"body":"can go listen to a sticks of gum"},{"speaker":"Pam","startTime":1418.37,"endTime":1420.68,"body":"Problem String. But basically,"},{"speaker":"Pam","startTime":1420.89,"endTime":1424.91,"body":"where we have a Problem String"},{"speaker":"Pam","startTime":1420.89,"endTime":1424.91,"body":"like if I have a pack that has"},{"speaker":"Pam","startTime":1425.0,"endTime":1431.3,"body":"27 sticks in it. And so, I just"},{"speaker":"Pam","startTime":1425.0,"endTime":1431.3,"body":"wrote down 1 to 27. And I've got"},{"speaker":"Pam","startTime":1431.63,"endTime":1435.5,"body":"2 packs would then have 54"},{"speaker":"Pam","startTime":1431.63,"endTime":1435.5,"body":"sticks. I did that kind of fast."},{"speaker":"Pam","startTime":1436.1,"endTime":1441.71,"body":"So, I have two entries right"},{"speaker":"Pam","startTime":1436.1,"endTime":1441.71,"body":"now. I have 1 to 27, and 2 to"},{"speaker":"Pam","startTime":1441.71,"endTime":1445.97,"body":"54. And then, if I said, \"How"},{"speaker":"Pam","startTime":1441.71,"endTime":1445.97,"body":"many sticks would be in 3 packs?"},{"speaker":"Pam","startTime":1445.97,"endTime":1450.08,"body":"Couldn't we add the 1 plus the 2"},{"speaker":"Pam","startTime":1445.97,"endTime":1450.08,"body":"to get 3 and the 27 plus the 54?"},{"speaker":"Kim","startTime":1450.08,"endTime":1450.11,"body":"Mmhmm."},{"speaker":"Pam","startTime":1452.9,"endTime":1455.18,"body":"Now, I'm sorry. I'm"},{"speaker":"Pam","startTime":1452.9,"endTime":1455.18,"body":"thinking 14 things at the same"},{"speaker":"Pam","startTime":1455.18,"endTime":1461.78,"body":"time. So, 27 plus 54 is that 81?"},{"speaker":"Pam","startTime":1455.18,"endTime":1461.78,"body":"So, wouldn't it be 3 packs would"},{"speaker":"Pam","startTime":1461.78,"endTime":1466.55,"body":"have 81 sticks? Well, that's"},{"speaker":"Pam","startTime":1461.78,"endTime":1466.55,"body":"actually correct. Wait, why can"},{"speaker":"Pam","startTime":1466.55,"endTime":1472.52,"body":"I add those to that ratio 1 to"},{"speaker":"Pam","startTime":1466.55,"endTime":1472.52,"body":"27, 2 to 54? Why can I add those"},{"speaker":"Pam","startTime":1472.52,"endTime":1479.03,"body":"together to get 3 to 81, but I"},{"speaker":"Pam","startTime":1472.52,"endTime":1479.03,"body":"can't add 3 to 4 plus 5 to 7 and"},{"speaker":"Pam","startTime":1479.03,"endTime":1485.09,"body":"get 8 to 11. And I recognize"},{"speaker":"Pam","startTime":1479.03,"endTime":1485.09,"body":"right now I'm raising kind of an"},{"speaker":"Pam","startTime":1485.12,"endTime":1488.66,"body":"interesting idea that if you've"},{"speaker":"Pam","startTime":1485.12,"endTime":1488.66,"body":"never thought about might be a"},{"speaker":"Pam","startTime":1488.66,"endTime":1493.04,"body":"little mind blowing, maybe just"},{"speaker":"Pam","startTime":1488.66,"endTime":1493.04,"body":"a little bit. And I'm hating the"},{"speaker":"Pam","startTime":1493.04,"endTime":1496.76,"body":"fact I'm about to tell, but I'm"},{"speaker":"Pam","startTime":1493.04,"endTime":1496.76,"body":"going to tell. It has everything"},{"speaker":"Pam","startTime":1496.76,"endTime":1501.17,"body":"to do with the fact that in the"},{"speaker":"Pam","startTime":1496.76,"endTime":1501.17,"body":"sticks of gum scenario, those"},{"speaker":"Pam","startTime":1501.17,"endTime":1508.64,"body":"ratios are equivalent. That 1 to"},{"speaker":"Pam","startTime":1501.17,"endTime":1508.64,"body":"27 is equivalent to 2 to 54. So,"},{"speaker":"Pam","startTime":1508.67,"endTime":1514.25,"body":"I'm not talking about the"},{"speaker":"Pam","startTime":1508.67,"endTime":1514.25,"body":"fraction 1/27 plus the fraction"},{"speaker":"Pam","startTime":1514.28,"endTime":1518.45,"body":"2/54 and adding those together."},{"speaker":"Pam","startTime":1514.28,"endTime":1518.45,"body":"I'm talking about equivalent"},{"speaker":"Pam","startTime":1518.45,"endTime":1523.07,"body":"ratios. 1 pack to 27 sticks is"},{"speaker":"Pam","startTime":1518.45,"endTime":1523.07,"body":"equivalent to 2 packs to 54"},{"speaker":"Pam","startTime":1523.07,"endTime":1528.53,"body":"sticks. Since those ratios are"},{"speaker":"Pam","startTime":1523.07,"endTime":1528.53,"body":"equivalent, you can just add the"},{"speaker":"Pam","startTime":1528.53,"endTime":1531.35,"body":"numerators and denominators in"},{"speaker":"Pam","startTime":1528.53,"endTime":1531.35,"body":"those ratios. I hate even using"},{"speaker":"Pam","startTime":1531.35,"endTime":1533.33,"body":"the names \"numerator\" and"},{"speaker":"Pam","startTime":1531.35,"endTime":1533.33,"body":"\"denominator\". You can add the"},{"speaker":"Pam","startTime":1533.33,"endTime":1536.99,"body":"parts of those ratios together"},{"speaker":"Pam","startTime":1533.33,"endTime":1536.99,"body":"and get an equivalent ratio, if"},{"speaker":"Pam","startTime":1536.99,"endTime":1541.13,"body":"the ratios are equivalent."},{"speaker":"Pam","startTime":1536.99,"endTime":1541.13,"body":"Notice in our fraction addition"},{"speaker":"Pam","startTime":1541.13,"endTime":1543.02,"body":"problem that Kim gave me."},{"speaker":"Pam","startTime":1541.13,"endTime":1543.02,"body":"Three-fourths plus"},{"speaker":"Pam","startTime":1543.02,"endTime":1546.32,"body":"five-sevenths. Those fractions"},{"speaker":"Pam","startTime":1543.02,"endTime":1546.32,"body":"are not equivalent."},{"speaker":"Pam","startTime":1546.77,"endTime":1550.31,"body":"Three-fourths is not equivalent"},{"speaker":"Pam","startTime":1546.77,"endTime":1550.31,"body":"to five-sevenths, so we cannot"},{"speaker":"Pam","startTime":1550.31,"endTime":1555.74,"body":"put them on the same ratio table"},{"speaker":"Pam","startTime":1550.31,"endTime":1555.74,"body":"because by definition a ratio"},{"speaker":"Pam","startTime":1555.74,"endTime":1559.22,"body":"table is where all of the"},{"speaker":"Pam","startTime":1555.74,"endTime":1559.22,"body":"entries, all of the ratios are"},{"speaker":"Pam","startTime":1559.25,"endTime":1560.06,"body":"equivalent."},{"speaker":"Kim","startTime":1560.24,"endTime":1560.63,"body":"Yeah."},{"speaker":"Pam","startTime":1561.38,"endTime":1563.93,"body":"So, that's kind of an"},{"speaker":"Pam","startTime":1561.38,"endTime":1563.93,"body":"important distinction to make,"},{"speaker":"Pam","startTime":1564.35,"endTime":1568.94,"body":"that maybe now we can help you"},{"speaker":"Pam","startTime":1564.35,"endTime":1568.94,"body":"start thinking about, so that"},{"speaker":"Pam","startTime":1568.97,"endTime":1571.73,"body":"when you run into it, which you"},{"speaker":"Pam","startTime":1568.97,"endTime":1571.73,"body":"will because you are teaching"},{"speaker":"Pam","startTime":1571.73,"endTime":1574.79,"body":"fractions. If you're teaching"},{"speaker":"Pam","startTime":1571.73,"endTime":1574.79,"body":"addition of fractions, ratios"},{"speaker":"Pam","startTime":1574.79,"endTime":1577.79,"body":"are appearing in your work. If"},{"speaker":"Pam","startTime":1574.79,"endTime":1577.79,"body":"you are teaching solving"},{"speaker":"Pam","startTime":1577.79,"endTime":1580.31,"body":"proportions with ratios,"},{"speaker":"Pam","startTime":1577.79,"endTime":1580.31,"body":"addition and subtraction of"},{"speaker":"Pam","startTime":1580.31,"endTime":1583.82,"body":"fractions is appearing in"},{"speaker":"Pam","startTime":1580.31,"endTime":1583.82,"body":"places. And so, we as teachers"},{"speaker":"Pam","startTime":1583.82,"endTime":1587.84,"body":"need to parse out when are we"},{"speaker":"Pam","startTime":1583.82,"endTime":1587.84,"body":"dealing with equivalent ratios"},{"speaker":"Pam","startTime":1588.17,"endTime":1591.44,"body":"and when are we dealing with"},{"speaker":"Pam","startTime":1588.17,"endTime":1591.44,"body":"fractions, part/whole fractions"},{"speaker":"Pam","startTime":1591.44,"endTime":1595.49,"body":"that are not equivalent. And we"},{"speaker":"Pam","startTime":1591.44,"endTime":1595.49,"body":"need to help students parse out,"},{"speaker":"Pam","startTime":1595.52,"endTime":1599.75,"body":"so then what makes sense to do"},{"speaker":"Pam","startTime":1595.52,"endTime":1599.75,"body":"with those when we're dealing"},{"speaker":"Pam","startTime":1599.75,"endTime":1602.69,"body":"with those different entities,"},{"speaker":"Pam","startTime":1599.75,"endTime":1602.69,"body":"part/whole fractions that aren't"},{"speaker":"Pam","startTime":1602.69,"endTime":1604.7,"body":"equivalent versus ratios that"},{"speaker":"Pam","startTime":1602.69,"endTime":1604.7,"body":"are. Go ahead."},{"speaker":"Kim","startTime":1604.76,"endTime":1607.7,"body":"I think you're bringing up"},{"speaker":"Kim","startTime":1604.76,"endTime":1607.7,"body":"such a really important point."},{"speaker":"Kim","startTime":1607.7,"endTime":1611.75,"body":"And I think maybe for you and I,"},{"speaker":"Kim","startTime":1607.7,"endTime":1611.75,"body":"it's one of the reasons why"},{"speaker":"Kim","startTime":1612.38,"endTime":1615.44,"body":"context is so important when"},{"speaker":"Kim","startTime":1612.38,"endTime":1615.44,"body":"we're working with students on a"},{"speaker":"Kim","startTime":1615.44,"endTime":1618.11,"body":"ratio table. Because they can"},{"speaker":"Kim","startTime":1615.44,"endTime":1618.11,"body":"really feel what's happening the"},{"speaker":"Kim","startTime":1618.11,"endTime":1621.41,"body":"ratio table, and it's not just a"},{"speaker":"Kim","startTime":1618.11,"endTime":1621.41,"body":"series of digits or numbers that"},{"speaker":"Kim","startTime":1621.41,"endTime":1624.5,"body":"we're throwing at them. They"},{"speaker":"Kim","startTime":1621.41,"endTime":1624.5,"body":"really kind of own the packs and"},{"speaker":"Kim","startTime":1624.5,"endTime":1628.76,"body":"the sticks, and it makes sense"},{"speaker":"Kim","startTime":1624.5,"endTime":1628.76,"body":"to them that when you add packs"},{"speaker":"Kim","startTime":1628.76,"endTime":1632.03,"body":"of sticks together. I mean,"},{"speaker":"Kim","startTime":1628.76,"endTime":1632.03,"body":"packs... Yeah, packs, packs of"},{"speaker":"Kim","startTime":1632.03,"endTime":1635.21,"body":"gum, then you're adding the"},{"speaker":"Kim","startTime":1632.03,"endTime":1635.21,"body":"corresponding sticks as well."},{"speaker":"Pam","startTime":1636.47,"endTime":1639.53,"body":"Mmhmm. Yeah. And that that"},{"speaker":"Pam","startTime":1636.47,"endTime":1639.53,"body":"makes so much sense that we can"},{"speaker":"Pam","startTime":1639.53,"endTime":1642.44,"body":"be grounded in that. So, when"},{"speaker":"Pam","startTime":1639.53,"endTime":1642.44,"body":"students are adding fractions,"},{"speaker":"Pam","startTime":1642.44,"endTime":1645.02,"body":"then we can help them go, \"Wait,"},{"speaker":"Pam","startTime":1642.44,"endTime":1645.02,"body":"wait wait. Is this packs and"},{"speaker":"Pam","startTime":1645.02,"endTime":1647.48,"body":"sticks? Or are we talking about"},{"speaker":"Pam","startTime":1645.02,"endTime":1647.48,"body":"three-fourths of a candy bar"},{"speaker":"Pam","startTime":1647.48,"endTime":1651.08,"body":"plus five-sevenths of a candy"},{"speaker":"Pam","startTime":1647.48,"endTime":1651.08,"body":"bar? How much of a candy bar"},{"speaker":"Pam","startTime":1651.08,"endTime":1654.23,"body":"would we have? Ah, we're dealing"},{"speaker":"Pam","startTime":1651.08,"endTime":1654.23,"body":"with a part/whole fraction, not"},{"speaker":"Pam","startTime":1654.23,"endTime":1656.87,"body":"with ratios, especially not with"},{"speaker":"Pam","startTime":1654.23,"endTime":1656.87,"body":"the equivalent ratios."},{"speaker":"Kim","startTime":1656.87,"endTime":1657.05,"body":"Yeah."},{"speaker":"Pam","startTime":1657.08,"endTime":1657.92,"body":"Yeah, nicely said."},{"speaker":"Kim","startTime":1658.01,"endTime":1663.5,"body":"Yeah. You also have some"},{"speaker":"Kim","startTime":1658.01,"endTime":1663.5,"body":"work in your Workouts that you."},{"speaker":"Pam","startTime":1663.71,"endTime":1664.73,"body":"Oh, yeah, totally."},{"speaker":"Kim","startTime":1664.73,"endTime":1666.08,"body":"You do some work with that."},{"speaker":"Kim","startTime":1664.73,"endTime":1666.08,"body":"You want to talk about that for"},{"speaker":"Kim","startTime":1666.08,"endTime":1666.44,"body":"a minute?"},{"speaker":"Pam","startTime":1666.77,"endTime":1671.39,"body":"Yeah. So, we help you with"},{"speaker":"Pam","startTime":1666.77,"endTime":1671.39,"body":"this in my book Lessons \u0026"},{"speaker":"Pam","startTime":1671.39,"endTime":1674.81,"body":"Activities for Building Powerful"},{"speaker":"Pam","startTime":1671.39,"endTime":1674.81,"body":"Numeracy help parse out the"},{"speaker":"Pam","startTime":1674.81,"endTime":1682.43,"body":"different kinds of problems and"},{"speaker":"Pam","startTime":1674.81,"endTime":1682.43,"body":"different ways you can deal with"},{"speaker":"Pam","startTime":1682.64,"endTime":1686.03,"body":"fractions versus dealing with"},{"speaker":"Pam","startTime":1682.64,"endTime":1686.03,"body":"equivalent ratios. So, yeah. If"},{"speaker":"Pam","startTime":1686.03,"endTime":1689.54,"body":"you're interested, totally check"},{"speaker":"Pam","startTime":1686.03,"endTime":1689.54,"body":"out Lessons \u0026 Activities for"},{"speaker":"Pam","startTime":1689.54,"endTime":1693.11,"body":"Building Powerful Numeracy,"},{"speaker":"Pam","startTime":1689.54,"endTime":1693.11,"body":"which has these super cool black"},{"speaker":"Pam","startTime":1693.11,"endTime":1697.1,"body":"line masters called Workouts."},{"speaker":"Pam","startTime":1693.11,"endTime":1697.1,"body":"And remember that we need to"},{"speaker":"Pam","startTime":1697.1,"endTime":1702.23,"body":"have fraction understanding come"},{"speaker":"Pam","startTime":1697.1,"endTime":1702.23,"body":"before what we did today with"},{"speaker":"Pam","startTime":1702.23,"endTime":1706.1,"body":"ratio tables. And then, once"},{"speaker":"Pam","startTime":1702.23,"endTime":1706.1,"body":"kids really have the sense and a"},{"speaker":"Pam","startTime":1706.1,"endTime":1709.19,"body":"feel for fractions, what they"},{"speaker":"Pam","startTime":1706.1,"endTime":1709.19,"body":"mean, then the ratio table is"},{"speaker":"Pam","startTime":1709.22,"endTime":1713.66,"body":"sort of this natural tool to use"},{"speaker":"Pam","startTime":1709.22,"endTime":1713.66,"body":"to create equivalent fractions."},{"speaker":"Kim","startTime":1713.9,"endTime":1717.32,"body":"Yep. We really hope this"},{"speaker":"Kim","startTime":1713.9,"endTime":1717.32,"body":"series all about the ratio table"},{"speaker":"Kim","startTime":1717.32,"endTime":1720.89,"body":"has been helpful so far. You"},{"speaker":"Kim","startTime":1717.32,"endTime":1720.89,"body":"will want to join us next week"},{"speaker":"Kim","startTime":1720.89,"endTime":1724.55,"body":"as Pam takes us to using the"},{"speaker":"Kim","startTime":1720.89,"endTime":1724.55,"body":"ratio table in higher math and"},{"speaker":"Kim","startTime":1724.55,"endTime":1728.27,"body":"we wrap up with some pro-tips"},{"speaker":"Kim","startTime":1724.55,"endTime":1728.27,"body":"you do not want to miss. Thanks"},{"speaker":"Kim","startTime":1728.27,"endTime":1731.15,"body":"for joining us each week! We are"},{"speaker":"Kim","startTime":1728.27,"endTime":1731.15,"body":"trying to grow, and we would"},{"speaker":"Kim","startTime":1731.15,"endTime":1734.51,"body":"love it if you'd support us by"},{"speaker":"Kim","startTime":1731.15,"endTime":1734.51,"body":"giving us a five star rating. Or"},{"speaker":"Kim","startTime":1734.51,"endTime":1736.88,"body":"if you think we don't deserve"},{"speaker":"Kim","startTime":1734.51,"endTime":1736.88,"body":"that, reach out and let us know"},{"speaker":"Kim","startTime":1736.88,"endTime":1737.81,"body":"how we can improve."},{"speaker":"Pam","startTime":1738.23,"endTime":1740.45,"body":"Yeah, we would super"},{"speaker":"Pam","startTime":1738.23,"endTime":1740.45,"body":"appreciate that. And thank you"},{"speaker":"Pam","startTime":1740.45,"endTime":1744.32,"body":"for tuning in, and teaching more"},{"speaker":"Pam","startTime":1740.45,"endTime":1744.32,"body":"and more real math. To find out"},{"speaker":"Pam","startTime":1744.32,"endTime":1747.14,"body":"more about the Math is"},{"speaker":"Pam","startTime":1744.32,"endTime":1747.14,"body":"Figure-Out-Able movement, visit"},{"speaker":"Pam","startTime":1747.14,"endTime":1751.31,"body":"mathisfigureoutable.com. Let's"},{"speaker":"Pam","startTime":1747.14,"endTime":1751.31,"body":"keep spreading the word that"},{"speaker":"Pam","startTime":1751.31,"endTime":1752.78,"body":"Math is Figure-Out-Able!"}]}