{"version":"1.0.0","segments":[{"speaker":"Pam","startTime":1.14,"endTime":4.53,"body":"Hey, fellow mathematicians!"},{"speaker":"Pam","startTime":1.14,"endTime":4.53,"body":"Welcome to the podcast where"},{"speaker":"Pam","startTime":4.53,"endTime":7.59,"body":"Math is Figure-Out-Able. I'm"},{"speaker":"Pam","startTime":4.53,"endTime":7.59,"body":"Pam."},{"speaker":"Kim","startTime":7.83,"endTime":8.49,"body":"And I'm Kim."},{"speaker":"Pam","startTime":8.79,"endTime":12.36,"body":"And you found a place where"},{"speaker":"Pam","startTime":8.79,"endTime":12.36,"body":"math is not about memorizing and"},{"speaker":"Pam","startTime":12.36,"endTime":16.11,"body":"mimicking, waiting to be told or"},{"speaker":"Pam","startTime":12.36,"endTime":16.11,"body":"shown what to do. But it's about"},{"speaker":"Pam","startTime":16.11,"endTime":19.56,"body":"making sense of problems,"},{"speaker":"Pam","startTime":16.11,"endTime":19.56,"body":"noticing patterns, and reasoning"},{"speaker":"Pam","startTime":19.56,"endTime":22.89,"body":"using mathematical"},{"speaker":"Pam","startTime":19.56,"endTime":22.89,"body":"relationships. We can mentor"},{"speaker":"Pam","startTime":22.89,"endTime":26.55,"body":"students to think and reason"},{"speaker":"Pam","startTime":22.89,"endTime":26.55,"body":"like mathematicians. Not only"},{"speaker":"Pam","startTime":26.55,"endTime":30.51,"body":"are algorithms not particularly"},{"speaker":"Pam","startTime":26.55,"endTime":30.51,"body":"helpful in teaching mathematics,"},{"speaker":"Pam","startTime":30.81,"endTime":34.29,"body":"but rotely repeating steps"},{"speaker":"Pam","startTime":30.81,"endTime":34.29,"body":"actually keep students from"},{"speaker":"Pam","startTime":34.29,"endTime":36.33,"body":"being the mathematicians they"},{"speaker":"Pam","startTime":34.29,"endTime":36.33,"body":"can be."},{"speaker":"Kim","startTime":36.96,"endTime":40.2,"body":"So, this week, we are going"},{"speaker":"Kim","startTime":36.96,"endTime":40.2,"body":"to do... Well, actually, Pam,"},{"speaker":"Kim","startTime":40.35,"endTime":43.56,"body":"it's Valentine's Day, right? So,"},{"speaker":"Kim","startTime":40.35,"endTime":43.56,"body":"we're going to tackle another"},{"speaker":"Kim","startTime":43.59,"endTime":45.6,"body":"Problem String that we love to"},{"speaker":"Kim","startTime":43.59,"endTime":45.6,"body":"do."},{"speaker":"Pam","startTime":45.6,"endTime":46.95,"body":"We love Valentine's day."},{"speaker":"Kim","startTime":46.95,"endTime":51.06,"body":"For a strategy that we"},{"speaker":"Kim","startTime":46.95,"endTime":51.06,"body":"love. That we now both love."},{"speaker":"Pam","startTime":51.66,"endTime":53.43,"body":"[Pam laughs] Now. Yeah."},{"speaker":"Pam","startTime":51.66,"endTime":53.43,"body":"Now."},{"speaker":"Kim","startTime":54.93,"endTime":56.49,"body":"[Kim laughs] So, we're"},{"speaker":"Kim","startTime":54.93,"endTime":56.49,"body":"going to do a Problem String"},{"speaker":"Kim","startTime":56.49,"endTime":60.39,"body":"today to tackle a very cool"},{"speaker":"Kim","startTime":56.49,"endTime":60.39,"body":"strategy for addition,"},{"speaker":"Kim","startTime":60.39,"endTime":62.16,"body":"subtraction that."},{"speaker":"Pam","startTime":63.06,"endTime":64.86,"body":"And the reason we're"},{"speaker":"Pam","startTime":63.06,"endTime":64.86,"body":"laughing is because we'll tell"},{"speaker":"Pam","startTime":64.86,"endTime":68.34,"body":"you in a hot minute about the"},{"speaker":"Pam","startTime":64.86,"endTime":68.34,"body":"fact that maybe it wasn't a"},{"speaker":"Pam","startTime":68.34,"endTime":74.31,"body":"favorite to begin with, and why"},{"speaker":"Pam","startTime":68.34,"endTime":74.31,"body":"we like it now. Cool. So, I"},{"speaker":"Pam","startTime":74.31,"endTime":80.4,"body":"remember where I was standing. I"},{"speaker":"Pam","startTime":74.31,"endTime":80.4,"body":"can picture the room. I know who"},{"speaker":"Pam","startTime":80.4,"endTime":83.64,"body":"was in the room. I was doing"},{"speaker":"Pam","startTime":80.4,"endTime":83.64,"body":"professional learning here in"},{"speaker":"Pam","startTime":83.64,"endTime":86.61,"body":"the state of Texas. They had"},{"speaker":"Pam","startTime":83.64,"endTime":86.61,"body":"come and asked me to do eight"},{"speaker":"Pam","startTime":86.64,"endTime":92.13,"body":"days of numeracy training for"},{"speaker":"Pam","startTime":86.64,"endTime":92.13,"body":"K-12 leaders across the state."},{"speaker":"Pam","startTime":92.79,"endTime":96.51,"body":"And it was fantastic. We did"},{"speaker":"Pam","startTime":92.79,"endTime":96.51,"body":"four days right in a row. We"},{"speaker":"Pam","startTime":96.51,"endTime":100.71,"body":"were downtown Austin. We were in"},{"speaker":"Pam","startTime":96.51,"endTime":100.71,"body":"a hotel, ballroom kind of space,"},{"speaker":"Pam","startTime":100.98,"endTime":104.82,"body":"and with way too many leaders in"},{"speaker":"Pam","startTime":100.98,"endTime":104.82,"body":"the room, but they were amazing."},{"speaker":"Pam","startTime":104.85,"endTime":107.76,"body":"And we did four days in a row."},{"speaker":"Pam","startTime":104.85,"endTime":107.76,"body":"And then, we'd let some time"},{"speaker":"Pam","startTime":107.76,"endTime":109.98,"body":"pass, and then we did another"},{"speaker":"Pam","startTime":107.76,"endTime":109.98,"body":"four days. And it was a training"},{"speaker":"Pam","startTime":109.98,"endTime":113.52,"body":"of trainers kind of a thing. And"},{"speaker":"Pam","startTime":109.98,"endTime":113.52,"body":"phenomenal experience. I had"},{"speaker":"Pam","startTime":113.52,"endTime":117.21,"body":"such a good time. We had so many"},{"speaker":"Pam","startTime":113.52,"endTime":117.21,"body":"really, really wonderful leaders"},{"speaker":"Pam","startTime":117.21,"endTime":121.41,"body":"in the state of Texas at that"},{"speaker":"Pam","startTime":117.21,"endTime":121.41,"body":"point. And I remember, near the"},{"speaker":"Pam","startTime":121.41,"endTime":125.01,"body":"beginning of the workshop, we"},{"speaker":"Pam","startTime":121.41,"endTime":125.01,"body":"were doing some subtraction. It"},{"speaker":"Pam","startTime":125.25,"endTime":128.25,"body":"might have been addition. I"},{"speaker":"Pam","startTime":125.25,"endTime":128.25,"body":"don't know. It doesn't matter."},{"speaker":"Pam","startTime":128.25,"endTime":130.77,"body":"It was addition or subtraction,"},{"speaker":"Pam","startTime":128.25,"endTime":130.77,"body":"and I had a particular strategy"},{"speaker":"Pam","startTime":130.77,"endTime":134.16,"body":"in mind, and I gave a problem"},{"speaker":"Pam","startTime":130.77,"endTime":134.16,"body":"like... So, I don't remember"},{"speaker":"Pam","startTime":134.16,"endTime":138.99,"body":"exactly the problem, but I gave"},{"speaker":"Pam","startTime":134.16,"endTime":138.99,"body":"a problem like 63 minus 28, and"},{"speaker":"Pam","startTime":138.99,"endTime":144.72,"body":"I was looking... Oh my word. I'm"},{"speaker":"Pam","startTime":138.99,"endTime":144.72,"body":"sitting at my moveable desk, and"},{"speaker":"Pam","startTime":144.96,"endTime":149.16,"body":"it's going up on me. I reached"},{"speaker":"Pam","startTime":144.96,"endTime":149.16,"body":"for my pen, and all of a sudden"},{"speaker":"Pam","startTime":149.16,"endTime":152.34,"body":"I hit the button. I'm sorry, I"},{"speaker":"Pam","startTime":149.16,"endTime":152.34,"body":"can't. I had. Okay, here we go."},{"speaker":"Pam","startTime":152.55,"endTime":156.9,"body":"Put me on live recording as we"},{"speaker":"Pam","startTime":152.55,"endTime":156.9,"body":"go. So, I'll never forget, I was"},{"speaker":"Pam","startTime":156.9,"endTime":161.01,"body":"looking for 63 minus 28. In the"},{"speaker":"Pam","startTime":156.9,"endTime":161.01,"body":"midst of that Problem String, I"},{"speaker":"Pam","startTime":161.01,"endTime":162.96,"body":"don't remember exactly what"},{"speaker":"Pam","startTime":161.01,"endTime":162.96,"body":"strategy because with that"},{"speaker":"Pam","startTime":162.96,"endTime":164.91,"body":"problem, I could have been"},{"speaker":"Pam","startTime":162.96,"endTime":164.91,"body":"trying to nudge a couple"},{"speaker":"Pam","startTime":164.91,"endTime":166.8,"body":"different strategies, but let's"},{"speaker":"Pam","startTime":164.91,"endTime":166.8,"body":"just say it was going for the"},{"speaker":"Pam","startTime":166.8,"endTime":171.48,"body":"Over strategy. So, I might have"},{"speaker":"Pam","startTime":166.8,"endTime":171.48,"body":"had 63 minus 30 as a helper"},{"speaker":"Pam","startTime":171.48,"endTime":175.14,"body":"problem, and then I gave 63"},{"speaker":"Pam","startTime":171.48,"endTime":175.14,"body":"minus 28. And I'm expecting"},{"speaker":"Pam","startTime":175.17,"endTime":178.68,"body":"everybody to think about 63"},{"speaker":"Pam","startTime":175.17,"endTime":178.68,"body":"minus 30, and then how would you"},{"speaker":"Pam","startTime":178.68,"endTime":183.93,"body":"adjust to get 63 minus 28. And"},{"speaker":"Pam","startTime":178.68,"endTime":183.93,"body":"there was a physics teacher, who"},{"speaker":"Pam","startTime":183.93,"endTime":187.89,"body":"was a... She was a leader, but"},{"speaker":"Pam","startTime":183.93,"endTime":187.89,"body":"she was like more physics than"},{"speaker":"Pam","startTime":187.89,"endTime":190.08,"body":"math. You know, how science"},{"speaker":"Pam","startTime":187.89,"endTime":190.08,"body":"people kind of identify"},{"speaker":"Pam","startTime":190.08,"endTime":192.09,"body":"sometimes as like, \"I'm a"},{"speaker":"Pam","startTime":190.08,"endTime":192.09,"body":"physics...\" And she was"},{"speaker":"Pam","startTime":192.09,"endTime":195.42,"body":"wonderful. I'll never forget."},{"speaker":"Pam","startTime":192.09,"endTime":195.42,"body":"She had this look on her face,"},{"speaker":"Pam","startTime":195.42,"endTime":197.79,"body":"and I was like, \"Oh, cool. Like,"},{"speaker":"Pam","startTime":195.42,"endTime":197.79,"body":"she's really...\" You know, \"I've"},{"speaker":"Pam","startTime":197.79,"endTime":200.94,"body":"taught her something.\" And I"},{"speaker":"Pam","startTime":197.79,"endTime":200.94,"body":"called on her, and I said, \"Hey,"},{"speaker":"Pam","startTime":200.94,"endTime":202.92,"body":"what are you thinking about?\""},{"speaker":"Pam","startTime":200.94,"endTime":202.92,"body":"And she goes, \"Oh, do you want"},{"speaker":"Pam","startTime":202.92,"endTime":205.23,"body":"to know.\" I was like, \"Yeah,"},{"speaker":"Pam","startTime":202.92,"endTime":205.23,"body":"yeah, yeah.\" Like, \"Tell me what"},{"speaker":"Pam","startTime":205.23,"endTime":209.07,"body":"strategy you're thinking about.\""},{"speaker":"Pam","startTime":205.23,"endTime":209.07,"body":"Now, I've learned if I want the"},{"speaker":"Pam","startTime":209.07,"endTime":212.22,"body":"Over strategy, in that moment, I"},{"speaker":"Pam","startTime":209.07,"endTime":212.22,"body":"should have said, \"Did anybody"},{"speaker":"Pam","startTime":212.22,"endTime":214.23,"body":"use the problem before?\" if"},{"speaker":"Pam","startTime":212.22,"endTime":214.23,"body":"that's the one I want to"},{"speaker":"Pam","startTime":214.23,"endTime":216.33,"body":"celebrate. But in this moment, I"},{"speaker":"Pam","startTime":214.23,"endTime":216.33,"body":"didn't know that move, and so"},{"speaker":"Pam","startTime":216.33,"endTime":219.3,"body":"I'm kinda calling on anybody"},{"speaker":"Pam","startTime":216.33,"endTime":219.3,"body":"cold. But I was so excited. She"},{"speaker":"Pam","startTime":219.3,"endTime":220.98,"body":"had this look. I was like, \"Oh,"},{"speaker":"Pam","startTime":219.3,"endTime":220.98,"body":"I want to hear what you're"},{"speaker":"Pam","startTime":220.98,"endTime":226.74,"body":"thinking about.\" And she said,"},{"speaker":"Pam","startTime":220.98,"endTime":226.74,"body":"\"I cannot just see factors.\" And"},{"speaker":"Pam","startTime":226.74,"endTime":229.23,"body":"I said, \"I'm sorry what? Are you"},{"speaker":"Pam","startTime":226.74,"endTime":229.23,"body":"in the room with us right here?\""},{"speaker":"Pam","startTime":229.5,"endTime":231.57,"body":"Like, \"You're off somewhere."},{"speaker":"Pam","startTime":229.5,"endTime":231.57,"body":"You're thinking about something"},{"speaker":"Pam","startTime":231.57,"endTime":237.81,"body":"else.\" She goes, \"No, like I"},{"speaker":"Pam","startTime":231.57,"endTime":237.81,"body":"can't... I see 7s.\" And I was"},{"speaker":"Pam","startTime":237.81,"endTime":241.68,"body":"like, \"What? 63 minus 28.\" And"},{"speaker":"Pam","startTime":237.81,"endTime":241.68,"body":"she goes, \"Yeah, I see nine 7s,"},{"speaker":"Pam","startTime":242.13,"endTime":246.18,"body":"and I see four 7s. And I just"},{"speaker":"Pam","startTime":242.13,"endTime":246.18,"body":"can't stop. I can't stop seeing"},{"speaker":"Pam","startTime":246.18,"endTime":252.27,"body":"that. I see nine 7s is 63 and"},{"speaker":"Pam","startTime":246.18,"endTime":252.27,"body":"four 7s is 28, and it's just"},{"speaker":"Pam","startTime":252.27,"endTime":255.45,"body":"like screaming at me that"},{"speaker":"Pam","startTime":252.27,"endTime":255.45,"body":"therefore nine 7s minus four 7s"},{"speaker":"Pam","startTime":255.45,"endTime":259.59,"body":"would be five 7s. And I know"},{"speaker":"Pam","startTime":255.45,"endTime":259.59,"body":"that's 35. And my brain is just"},{"speaker":"Pam","startTime":259.62,"endTime":266.43,"body":"there.\" And I looked at her. I"},{"speaker":"Pam","startTime":259.62,"endTime":266.43,"body":"was like, \"What?\" I had never. I"},{"speaker":"Pam","startTime":266.43,"endTime":269.52,"body":"was like, \"That's what your"},{"speaker":"Pam","startTime":266.43,"endTime":269.52,"body":"brain did. Like, how do you? How"},{"speaker":"Pam","startTime":269.52,"endTime":271.71,"body":"did your brain go there?\" She"},{"speaker":"Pam","startTime":269.52,"endTime":271.71,"body":"goes, \"I don't know. It just"},{"speaker":"Pam","startTime":271.71,"endTime":276.18,"body":"did. Like, the factors are just"},{"speaker":"Pam","startTime":271.71,"endTime":276.18,"body":"screaming at me.\" Ya'll, I don't"},{"speaker":"Pam","startTime":276.18,"endTime":279.15,"body":"know how long I stood there with"},{"speaker":"Pam","startTime":276.18,"endTime":279.15,"body":"my mouth open. I was like, \"Oh,"},{"speaker":"Pam","startTime":279.42,"endTime":282.21,"body":"does anybody else think that"},{"speaker":"Pam","startTime":279.42,"endTime":282.21,"body":"way?\" Now, honestly, I think"},{"speaker":"Pam","startTime":282.21,"endTime":285.06,"body":"when I said that, there were a"},{"speaker":"Pam","startTime":282.21,"endTime":285.06,"body":"couple of hands in the maybe 50"},{"speaker":"Pam","startTime":285.06,"endTime":287.22,"body":"or 60 people that we had. It was"},{"speaker":"Pam","startTime":285.06,"endTime":287.22,"body":"way too many people for one"},{"speaker":"Pam","startTime":287.22,"endTime":291.0,"body":"training. So, not very many"},{"speaker":"Pam","startTime":287.22,"endTime":291.0,"body":"people, but most people were"},{"speaker":"Pam","startTime":291.0,"endTime":294.66,"body":"intrigued. Most people were"},{"speaker":"Pam","startTime":291.0,"endTime":294.66,"body":"like, \"That's interesting. How"},{"speaker":"Pam","startTime":294.66,"endTime":297.18,"body":"often does that happen? Is that"},{"speaker":"Pam","startTime":294.66,"endTime":297.18,"body":"a thing? Do people actually do"},{"speaker":"Pam","startTime":297.18,"endTime":302.22,"body":"that?\" Well, ya'll, I'll tell"},{"speaker":"Pam","startTime":297.18,"endTime":302.22,"body":"you what. The more I throw"},{"speaker":"Pam","startTime":302.22,"endTime":307.02,"body":"problems like that out, the more"},{"speaker":"Pam","startTime":302.22,"endTime":307.02,"body":"I find that people, if they are"},{"speaker":"Pam","startTime":307.02,"endTime":310.47,"body":"thinking multiplicatively, if"},{"speaker":"Pam","startTime":307.02,"endTime":310.47,"body":"they have built relationships in"},{"speaker":"Pam","startTime":310.47,"endTime":314.22,"body":"their brains to think"},{"speaker":"Pam","startTime":310.47,"endTime":314.22,"body":"multiplicatively, factors can"},{"speaker":"Pam","startTime":314.25,"endTime":318.33,"body":"pop out at the most opportune"},{"speaker":"Pam","startTime":314.25,"endTime":318.33,"body":"times. So, let's do a Problem"},{"speaker":"Pam","startTime":318.33,"endTime":322.08,"body":"String, Kim, to see if we can"},{"speaker":"Pam","startTime":318.33,"endTime":322.08,"body":"kind of build that strategy in"},{"speaker":"Pam","startTime":322.08,"endTime":324.99,"body":"our listeners a little bit. Here"},{"speaker":"Pam","startTime":322.08,"endTime":324.99,"body":"we go. Alright, first problem."},{"speaker":"Pam","startTime":325.35,"endTime":329.94,"body":"Kim, what if I were to ask you a"},{"speaker":"Pam","startTime":325.35,"endTime":329.94,"body":"problem like 88 plus 72. 88 plus"},{"speaker":"Pam","startTime":329.94,"endTime":331.86,"body":"72. Tell us what you're thinking"},{"speaker":"Pam","startTime":329.94,"endTime":331.86,"body":"about."},{"speaker":"Kim","startTime":332.43,"endTime":339.21,"body":"So, 88 and 72 have 8s in"},{"speaker":"Kim","startTime":332.43,"endTime":339.21,"body":"common. So, 88."},{"speaker":"Pam","startTime":339.24,"endTime":339.75,"body":"How so?"},{"speaker":"Kim","startTime":340.59,"endTime":344.22,"body":"Eighty-eight is eleven 8s."},{"speaker":"Kim","startTime":340.59,"endTime":344.22,"body":"So, I just wrote down 11"},{"speaker":"Kim","startTime":344.88,"endTime":346.05,"body":"parentheses 8. Eleven 8s."},{"speaker":"Pam","startTime":346.47,"endTime":346.89,"body":"Okay."},{"speaker":"Kim","startTime":347.1,"endTime":349.71,"body":"Plus 72 is nine 8s."},{"speaker":"Pam","startTime":349.71,"endTime":349.74,"body":"Mmhmm."},{"speaker":"Kim","startTime":350.7,"endTime":354.75,"body":"And so, eleven 8s plus nine"},{"speaker":"Kim","startTime":350.7,"endTime":354.75,"body":"8s is twenty 8s. Which is really"},{"speaker":"Kim","startTime":354.75,"endTime":357.39,"body":"nice because that is 160."},{"speaker":"Pam","startTime":357.81,"endTime":359.34,"body":"How do you know twenty 8s"},{"speaker":"Pam","startTime":357.81,"endTime":359.34,"body":"is 160?"},{"speaker":"Kim","startTime":359.73,"endTime":362.73,"body":"Two times 8 is 16, times 10"},{"speaker":"Kim","startTime":359.73,"endTime":362.73,"body":"is 160."},{"speaker":"Pam","startTime":362.91,"endTime":363.48,"body":"Nice."},{"speaker":"Pam","startTime":363.99,"endTime":367.23,"body":"So, you can look at an addition"},{"speaker":"Pam","startTime":363.99,"endTime":367.23,"body":"problem like 88 plus 72 and"},{"speaker":"Pam","startTime":368.91,"endTime":371.61,"body":"factors popped out for you, and"},{"speaker":"Pam","startTime":368.91,"endTime":371.61,"body":"all of a sudden you have this"},{"speaker":"Pam","startTime":371.61,"endTime":375.48,"body":"nice. Now, if you would have"},{"speaker":"Pam","startTime":371.61,"endTime":375.48,"body":"gotten nineteen 8s."},{"speaker":"Kim","startTime":376.32,"endTime":376.83,"body":"Yeah."},{"speaker":"Pam","startTime":376.98,"endTime":379.47,"body":"I wonder if you might have"},{"speaker":"Pam","startTime":376.98,"endTime":379.47,"body":"gone back to addition and done"},{"speaker":"Pam","startTime":379.47,"endTime":382.26,"body":"like an Over strategy or"},{"speaker":"Pam","startTime":379.47,"endTime":382.26,"body":"something. Or even for these"},{"speaker":"Pam","startTime":382.26,"endTime":385.05,"body":"numbers, Splitting by Place"},{"speaker":"Pam","startTime":382.26,"endTime":385.05,"body":"Value. Sort of that nice 10"},{"speaker":"Pam","startTime":385.05,"endTime":390.27,"body":"sticking in there. So, it's not"},{"speaker":"Pam","startTime":385.05,"endTime":390.27,"body":"like this has to be the strategy"},{"speaker":"Pam","startTime":390.27,"endTime":393.84,"body":"that you do if factors pop out"},{"speaker":"Pam","startTime":390.27,"endTime":393.84,"body":"at you, but it could be one that"},{"speaker":"Pam","startTime":393.84,"endTime":397.14,"body":"you consider. Next problem."},{"speaker":"Pam","startTime":393.84,"endTime":397.14,"body":"Maybe I'll pause a little bit"},{"speaker":"Pam","startTime":397.14,"endTime":400.86,"body":"longer before I let you answer"},{"speaker":"Pam","startTime":397.14,"endTime":400.86,"body":"it, so. Or, listeners, solve the"},{"speaker":"Pam","startTime":400.86,"endTime":403.74,"body":"problem before you maybe hear"},{"speaker":"Pam","startTime":400.86,"endTime":403.74,"body":"what we're doing. You know, give"},{"speaker":"Pam","startTime":403.74,"endTime":407.4,"body":"yourself a chance to see if"},{"speaker":"Pam","startTime":403.74,"endTime":407.4,"body":"factors can pop for you. So,"},{"speaker":"Pam","startTime":407.55,"endTime":410.4,"body":"Kim, how about 81 minus 36?"},{"speaker":"Kim","startTime":411.81,"endTime":416.52,"body":"81 minus 36. So, I'm"},{"speaker":"Kim","startTime":411.81,"endTime":416.52,"body":"looking for what they have in"},{"speaker":"Kim","startTime":416.52,"endTime":422.46,"body":"common, and I'm thinking that"},{"speaker":"Kim","startTime":416.52,"endTime":422.46,"body":"there's some 9s there. So, 81 is"},{"speaker":"Kim","startTime":422.46,"endTime":431.13,"body":"nine 9s and 36 is four 9s. So,"},{"speaker":"Kim","startTime":422.46,"endTime":431.13,"body":"nine 9s minus four 9s is five"},{"speaker":"Kim","startTime":431.13,"endTime":432.93,"body":"9s, which is 45."},{"speaker":"Pam","startTime":433.53,"endTime":438.27,"body":"Nice. And often kids know"},{"speaker":"Pam","startTime":433.53,"endTime":438.27,"body":"they're 5s, so that's a pretty"},{"speaker":"Pam","startTime":438.27,"endTime":441.84,"body":"five 9s once you get there. I"},{"speaker":"Pam","startTime":438.27,"endTime":441.84,"body":"mean, I know you know. But often"},{"speaker":"Pam","startTime":441.84,"endTime":444.18,"body":"kids if they're going to know"},{"speaker":"Pam","startTime":441.84,"endTime":444.18,"body":"facts, they'll know the five, so"},{"speaker":"Pam","startTime":444.18,"endTime":448.32,"body":"that's not too bad to land up"},{"speaker":"Pam","startTime":444.18,"endTime":448.32,"body":"with 5 times 9. Cool. Alright,"},{"speaker":"Pam","startTime":448.32,"endTime":450.3,"body":"next problem. How about"},{"speaker":"Pam","startTime":448.32,"endTime":450.3,"body":"(unclear)."},{"speaker":"Kim","startTime":450.33,"endTime":451.41,"body":"I'm going to tell you real"},{"speaker":"Kim","startTime":450.33,"endTime":451.41,"body":"quick."},{"speaker":"Pam","startTime":451.47,"endTime":451.74,"body":"Yeah, yeah, yeah."},{"speaker":"Kim","startTime":451.74,"endTime":458.13,"body":"I actually like that"},{"speaker":"Kim","startTime":451.74,"endTime":458.13,"body":"strategy more than I like really"},{"speaker":"Kim","startTime":458.13,"endTime":460.8,"body":"any of the strategies that I"},{"speaker":"Kim","startTime":458.13,"endTime":460.8,"body":"would use for subtraction of"},{"speaker":"Kim","startTime":460.8,"endTime":461.4,"body":"that problem."},{"speaker":"Pam","startTime":461.58,"endTime":462.75,"body":"Oh, that's interesting."},{"speaker":"Kim","startTime":462.87,"endTime":463.2,"body":"Yeah."},{"speaker":"Pam","startTime":463.53,"endTime":467.19,"body":"So, I might be tempted to"},{"speaker":"Pam","startTime":463.53,"endTime":467.19,"body":"shift everything up 4 and have"},{"speaker":"Pam","startTime":467.28,"endTime":472.5,"body":"85 minus 40, which is also 45."},{"speaker":"Pam","startTime":467.28,"endTime":472.5,"body":"Which is good, because it should"},{"speaker":"Pam","startTime":472.5,"endTime":476.16,"body":"be. But you're like, \"No, I"},{"speaker":"Pam","startTime":472.5,"endTime":476.16,"body":"actually like that...\""},{"speaker":"Kim","startTime":476.88,"endTime":478.77,"body":"Yeah, for that one. I"},{"speaker":"Kim","startTime":476.88,"endTime":478.77,"body":"really do like that strategy."},{"speaker":"Pam","startTime":478.8,"endTime":479.7,"body":"Okay, nice."},{"speaker":"Pam","startTime":479.76,"endTime":483.51,"body":"Nice. Alright, how about 77 plus"},{"speaker":"Pam","startTime":479.76,"endTime":483.51,"body":"44."},{"speaker":"Kim","startTime":486.33,"endTime":492.15,"body":"There's some elevens there."},{"speaker":"Kim","startTime":486.33,"endTime":492.15,"body":"So, 77 is seven 11s, and 44 is"},{"speaker":"Kim","startTime":492.18,"endTime":499.41,"body":"four 11s, so then I have eleven"},{"speaker":"Kim","startTime":492.18,"endTime":499.41,"body":"11s, which I know is 121."},{"speaker":"Pam","startTime":500.85,"endTime":502.92,"body":"And if a kid didn't know"},{"speaker":"Pam","startTime":500.85,"endTime":502.92,"body":"eleven 11s?"},{"speaker":"Kim","startTime":502.92,"endTime":502.95,"body":"Mmhmm."},{"speaker":"Pam","startTime":504.0,"endTime":504.66,"body":"Then?"},{"speaker":"Kim","startTime":505.14,"endTime":510.51,"body":"They might do ten 11s, plus"},{"speaker":"Kim","startTime":505.14,"endTime":510.51,"body":"one more 11. So, 110 plus 11."},{"speaker":"Pam","startTime":510.96,"endTime":514.32,"body":"Yeah, I like it. I like it."},{"speaker":"Pam","startTime":510.96,"endTime":514.32,"body":"Or they could even back up and"},{"speaker":"Pam","startTime":514.32,"endTime":515.34,"body":"just do an addition strategy."},{"speaker":"Kim","startTime":515.34,"endTime":515.91,"body":"Sure."},{"speaker":"Pam","startTime":516.45,"endTime":520.74,"body":"So, our goal isn't to"},{"speaker":"Pam","startTime":516.45,"endTime":520.74,"body":"pigeonhole anybody into any one"},{"speaker":"Pam","startTime":520.74,"endTime":521.34,"body":"strategy."},{"speaker":"Kim","startTime":521.49,"endTime":522.0,"body":"Right."},{"speaker":"Pam","startTime":522.15,"endTime":525.87,"body":"Our goal is to own lots of"},{"speaker":"Pam","startTime":522.15,"endTime":525.87,"body":"relationships, so strategies"},{"speaker":"Pam","startTime":525.87,"endTime":527.85,"body":"become natural inclinations."},{"speaker":"Kim","startTime":528.03,"endTime":528.33,"body":"Yeah."},{"speaker":"Pam","startTime":528.39,"endTime":531.21,"body":"I'll never forget the day,"},{"speaker":"Pam","startTime":528.39,"endTime":531.21,"body":"Kim, when you said to me, \"I"},{"speaker":"Pam","startTime":531.24,"endTime":533.97,"body":"look at numbers, and I let"},{"speaker":"Pam","startTime":531.24,"endTime":533.97,"body":"things pop, and I go, 'That?"},{"speaker":"Pam","startTime":534.0,"endTime":536.4,"body":"Mmm, how about this? Mmm, how"},{"speaker":"Pam","startTime":534.0,"endTime":536.4,"body":"about that? Oh, actually, the"},{"speaker":"Pam","startTime":536.43,"endTime":540.24,"body":"middle one.'\" Like, you consider"},{"speaker":"Pam","startTime":536.43,"endTime":540.24,"body":"different things you can do, and"},{"speaker":"Pam","startTime":540.24,"endTime":543.93,"body":"then you choose the one that on"},{"speaker":"Pam","startTime":540.24,"endTime":543.93,"body":"that day sort of slides the"},{"speaker":"Pam","startTime":543.93,"endTime":544.59,"body":"easiest."},{"speaker":"Kim","startTime":545.07,"endTime":545.1,"body":"Mmhmm."},{"speaker":"Pam","startTime":545.16,"endTime":547.59,"body":"And I'm working on my"},{"speaker":"Pam","startTime":545.16,"endTime":547.59,"body":"definition of fluency, but"},{"speaker":"Pam","startTime":547.62,"endTime":551.67,"body":"that's my definition of fluency."},{"speaker":"Pam","startTime":547.62,"endTime":551.67,"body":"My definition of fluency is"},{"speaker":"Pam","startTime":551.85,"endTime":554.79,"body":"looking at the numbers, letting"},{"speaker":"Pam","startTime":551.85,"endTime":554.79,"body":"what naturally pops, that"},{"speaker":"Pam","startTime":555.03,"endTime":559.02,"body":"intuition tells you, and then"},{"speaker":"Pam","startTime":555.03,"endTime":559.02,"body":"going with the one that... You"},{"speaker":"Pam","startTime":559.02,"endTime":562.59,"body":"know like, considering all the"},{"speaker":"Pam","startTime":559.02,"endTime":562.59,"body":"things that pop. Not all, but"},{"speaker":"Pam","startTime":562.59,"endTime":565.44,"body":"enough of the things that pop,"},{"speaker":"Pam","startTime":562.59,"endTime":565.44,"body":"and then going with the one that"},{"speaker":"Pam","startTime":565.44,"endTime":569.01,"body":"slides the best that day. I know"},{"speaker":"Pam","startTime":565.44,"endTime":569.01,"body":"that's not a very technical"},{"speaker":"Pam","startTime":569.01,"endTime":572.43,"body":"definition, but I'm working on"},{"speaker":"Pam","startTime":569.01,"endTime":572.43,"body":"it. What it's not is that"},{"speaker":"Pam","startTime":572.43,"endTime":575.4,"body":"students go, \"Oh, for this"},{"speaker":"Pam","startTime":572.43,"endTime":575.4,"body":"problem, I do this procedure."},{"speaker":"Pam","startTime":575.4,"endTime":579.15,"body":"Step, step, step, step.\" That's"},{"speaker":"Pam","startTime":575.4,"endTime":579.15,"body":"not fluent. Okay, ready? Next,"},{"speaker":"Pam","startTime":579.69,"endTime":581.82,"body":"64 minus 48."},{"speaker":"Kim","startTime":584.67,"endTime":591.63,"body":"So, they have 8s in common."},{"speaker":"Kim","startTime":584.67,"endTime":591.63,"body":"So, 64 is eight 8s, and 48 is"},{"speaker":"Kim","startTime":591.63,"endTime":597.21,"body":"six 8s. So, eight 8s minus six"},{"speaker":"Kim","startTime":591.63,"endTime":597.21,"body":"8s is just two 8s, which is 16."},{"speaker":"Pam","startTime":599.13,"endTime":602.37,"body":"I wonder, listeners, as"},{"speaker":"Pam","startTime":599.13,"endTime":602.37,"body":"you're hearing these problems,"},{"speaker":"Pam","startTime":602.4,"endTime":608.31,"body":"if because we've kind of got you"},{"speaker":"Pam","startTime":602.4,"endTime":608.31,"body":"in factor mode that maybe you're"},{"speaker":"Pam","startTime":608.34,"endTime":612.06,"body":"like... Maybe it's starting to"},{"speaker":"Pam","startTime":608.34,"endTime":612.06,"body":"ping a little bit more. Maybe."},{"speaker":"Pam","startTime":612.09,"endTime":616.8,"body":"Maybe it's starting to like"},{"speaker":"Pam","startTime":612.09,"endTime":616.8,"body":"because you're... And that is a"},{"speaker":"Pam","startTime":616.8,"endTime":619.47,"body":"real neurological thing that"},{"speaker":"Pam","startTime":616.8,"endTime":619.47,"body":"once we kind of get you"},{"speaker":"Pam","startTime":619.47,"endTime":623.01,"body":"situated, and factors are kind"},{"speaker":"Pam","startTime":619.47,"endTime":623.01,"body":"of the thing that we're talking"},{"speaker":"Pam","startTime":623.01,"endTime":625.74,"body":"about, then they might pop a"},{"speaker":"Pam","startTime":623.01,"endTime":625.74,"body":"little bit more readily."},{"speaker":"Pam","startTime":625.77,"endTime":630.81,"body":"Alright, let's try another one."},{"speaker":"Pam","startTime":625.77,"endTime":630.81,"body":"How about 144 plus 96?"},{"speaker":"Kim","startTime":633.33,"endTime":636.81,"body":"Cooper would love this one"},{"speaker":"Kim","startTime":633.33,"endTime":636.81,"body":"because he loves 12. So, 144 is"},{"speaker":"Kim","startTime":636.81,"endTime":643.8,"body":"twelve 12s and 96 is eight 12s."},{"speaker":"Kim","startTime":636.81,"endTime":643.8,"body":"So, twelve 12s, plus eight 12s,"},{"speaker":"Kim","startTime":643.83,"endTime":648.21,"body":"is just twenty 12s, which is"},{"speaker":"Kim","startTime":643.83,"endTime":648.21,"body":"240."},{"speaker":"Pam","startTime":648.81,"endTime":651.39,"body":"Because two 12s is 24 times"},{"speaker":"Pam","startTime":648.81,"endTime":651.39,"body":"10."},{"speaker":"Kim","startTime":651.39,"endTime":651.42,"body":"Mmhmm."},{"speaker":"Pam","startTime":651.69,"endTime":656.55,"body":"Yeah. Now, I'm going to be"},{"speaker":"Pam","startTime":651.69,"endTime":656.55,"body":"really honest. 96, I had to"},{"speaker":"Pam","startTime":656.55,"endTime":660.84,"body":"think about. I did not have a"},{"speaker":"Pam","startTime":656.55,"endTime":660.84,"body":"lot of experience with 12s. It"},{"speaker":"Pam","startTime":660.84,"endTime":664.74,"body":"is still the one that I have to"},{"speaker":"Pam","startTime":660.84,"endTime":664.74,"body":"go, \"What do I know? Let's see,"},{"speaker":"Pam","startTime":664.74,"endTime":667.8,"body":"I know 7...\" For some reason, I"},{"speaker":"Pam","startTime":664.74,"endTime":667.8,"body":"know 7 times 12. I think I"},{"speaker":"Pam","startTime":667.8,"endTime":671.79,"body":"actually work off of 6 times 12."},{"speaker":"Pam","startTime":667.8,"endTime":671.79,"body":"I know 6 times 12 well, and so 7"},{"speaker":"Pam","startTime":671.79,"endTime":675.96,"body":"times 12 is pretty, and so I'm"},{"speaker":"Pam","startTime":671.79,"endTime":675.96,"body":"like, \"So, 96... Ah, so that's"},{"speaker":"Pam","startTime":675.96,"endTime":677.61,"body":"got to be 8 times 12.\""},{"speaker":"Kim","startTime":677.64,"endTime":679.92,"body":"That would probably be..."},{"speaker":"Kim","startTime":677.64,"endTime":679.92,"body":"Go ahead. Sorry."},{"speaker":"Pam","startTime":680.55,"endTime":685.71,"body":"Ninety-six does not pop for"},{"speaker":"Pam","startTime":680.55,"endTime":685.71,"body":"me as a 12. However, because the"},{"speaker":"Pam","startTime":685.71,"endTime":691.59,"body":"144 is sitting there. 144 is so"},{"speaker":"Pam","startTime":685.71,"endTime":691.59,"body":"12 squared to me. That one is"},{"speaker":"Pam","startTime":691.59,"endTime":696.24,"body":"just ingrained. Then, I'm kind"},{"speaker":"Pam","startTime":691.59,"endTime":696.24,"body":"of asking myself, \"Is there a 12"},{"speaker":"Pam","startTime":696.24,"endTime":698.49,"body":"in 96? Oh! There is a 12 in 96.\""},{"speaker":"Kim","startTime":698.52,"endTime":698.79,"body":"Yep."},{"speaker":"Pam","startTime":698.82,"endTime":699.54,"body":"Yeah, what were you going"},{"speaker":"Pam","startTime":698.82,"endTime":699.54,"body":"to say?"},{"speaker":"Kim","startTime":699.54,"endTime":702.72,"body":"I would say that's probably"},{"speaker":"Kim","startTime":699.54,"endTime":702.72,"body":"would be true for me until about"},{"speaker":"Kim","startTime":702.72,"endTime":707.46,"body":"a year ago that I don't own 12s"},{"speaker":"Kim","startTime":702.72,"endTime":707.46,"body":"as well as some of the other"},{"speaker":"Kim","startTime":707.46,"endTime":713.28,"body":"ones, but because of Cooper. He"},{"speaker":"Kim","startTime":707.46,"endTime":713.28,"body":"so loves 12s that we talk about"},{"speaker":"Kim","startTime":713.28,"endTime":716.16,"body":"them probably far more often"},{"speaker":"Kim","startTime":713.28,"endTime":716.16,"body":"than we should in this house."},{"speaker":"Pam","startTime":717.51,"endTime":719.16,"body":"So, since you've been"},{"speaker":"Pam","startTime":717.51,"endTime":719.16,"body":"messing with 12."},{"speaker":"Kim","startTime":719.19,"endTime":719.37,"body":"Yeah (unclear)"},{"speaker":"Pam","startTime":719.37,"endTime":721.62,"body":"Twelves is at the top of"},{"speaker":"Pam","startTime":719.37,"endTime":721.62,"body":"your head more and more, and so"},{"speaker":"Pam","startTime":721.62,"endTime":724.29,"body":"now it's a relationship that you"},{"speaker":"Pam","startTime":721.62,"endTime":724.29,"body":"can draw on. Yeah, nice. Do you"},{"speaker":"Pam","startTime":724.29,"endTime":728.07,"body":"know what else is funny about..."},{"speaker":"Pam","startTime":724.29,"endTime":728.07,"body":"No, I'll tell that some other"},{"speaker":"Pam","startTime":728.07,"endTime":733.92,"body":"time. Okay. So, to end this"},{"speaker":"Pam","startTime":728.07,"endTime":733.92,"body":"Problem String, I'm going to ask"},{"speaker":"Pam","startTime":733.92,"endTime":736.05,"body":"the question, and we're not"},{"speaker":"Pam","startTime":733.92,"endTime":736.05,"body":"actually going to answer it on"},{"speaker":"Pam","startTime":736.05,"endTime":738.0,"body":"the Problem String, but I'm"},{"speaker":"Pam","startTime":736.05,"endTime":738.0,"body":"going to ask a question that we"},{"speaker":"Pam","startTime":738.0,"endTime":741.72,"body":"just put out on MathStratChat."},{"speaker":"Pam","startTime":738.0,"endTime":741.72,"body":"So, we've been doing... Might"},{"speaker":"Pam","startTime":741.72,"endTime":744.57,"body":"have been three or four weeks"},{"speaker":"Pam","startTime":741.72,"endTime":744.57,"body":"ago. We've been doing a series"},{"speaker":"Pam","startTime":744.57,"endTime":749.13,"body":"of Problem Strings to try to"},{"speaker":"Pam","startTime":744.57,"endTime":749.13,"body":"build this strategy, this idea"},{"speaker":"Pam","startTime":749.31,"endTime":753.48,"body":"that to add or subtract, I can"},{"speaker":"Pam","startTime":749.31,"endTime":753.48,"body":"see if there are common factors"},{"speaker":"Pam","startTime":753.48,"endTime":758.88,"body":"involved. And if factors pop,"},{"speaker":"Pam","startTime":753.48,"endTime":758.88,"body":"then I can use those factors to"},{"speaker":"Pam","startTime":758.88,"endTime":761.73,"body":"think about adding or"},{"speaker":"Pam","startTime":758.88,"endTime":761.73,"body":"subtracting. And so, one of the"},{"speaker":"Pam","startTime":761.73,"endTime":769.77,"body":"last problems that we posted was"},{"speaker":"Pam","startTime":761.73,"endTime":769.77,"body":"25.6 subtract 12.8. And now that"},{"speaker":"Pam","startTime":769.77,"endTime":771.87,"body":"I've done that, now that we've"},{"speaker":"Pam","startTime":769.77,"endTime":771.87,"body":"done this Problem String today,"},{"speaker":"Pam","startTime":771.87,"endTime":774.45,"body":"and we've been talking about"},{"speaker":"Pam","startTime":771.87,"endTime":774.45,"body":"this idea of factor to add or"},{"speaker":"Pam","startTime":774.45,"endTime":777.72,"body":"subtract, we're going to leave"},{"speaker":"Pam","startTime":774.45,"endTime":777.72,"body":"that problem, listeners. And"},{"speaker":"Pam","startTime":777.72,"endTime":780.84,"body":"maybe if you go check out"},{"speaker":"Pam","startTime":777.72,"endTime":780.84,"body":"MathStratChat, you can search"},{"speaker":"Pam","startTime":780.84,"endTime":786.72,"body":"for hashtag MathStratChat and"},{"speaker":"Pam","startTime":780.84,"endTime":786.72,"body":"see what you can do with 25.6"},{"speaker":"Pam","startTime":786.72,"endTime":790.38,"body":"minus 12.8, and go see what"},{"speaker":"Pam","startTime":786.72,"endTime":790.38,"body":"other people have done for that"},{"speaker":"Pam","startTime":790.38,"endTime":790.74,"body":"problem."},{"speaker":"Kim","startTime":791.01,"endTime":797.64,"body":"Yeah. So, I remember being"},{"speaker":"Kim","startTime":791.01,"endTime":797.64,"body":"in the hotel when you... And I"},{"speaker":"Kim","startTime":797.64,"endTime":799.89,"body":"don't remember the details"},{"speaker":"Kim","startTime":797.64,"endTime":799.89,"body":"exactly, but I feel like what"},{"speaker":"Kim","startTime":799.89,"endTime":805.32,"body":"happened was this person shared"},{"speaker":"Kim","startTime":799.89,"endTime":805.32,"body":"this strategy, and you were"},{"speaker":"Kim","startTime":805.32,"endTime":807.84,"body":"like, \"That's amazing! I want to"},{"speaker":"Kim","startTime":805.32,"endTime":807.84,"body":"come back and think about it.\""},{"speaker":"Kim","startTime":807.84,"endTime":811.35,"body":"And if I'm remembering it"},{"speaker":"Kim","startTime":807.84,"endTime":811.35,"body":"correctly, you came back and you"},{"speaker":"Kim","startTime":811.35,"endTime":813.48,"body":"were like, \"I need to write a"},{"speaker":"Kim","startTime":811.35,"endTime":813.48,"body":"Problem String for that.\" Or..."},{"speaker":"Pam","startTime":814.2,"endTime":814.83,"body":"[Pam laughs] Yeah."},{"speaker":"Kim","startTime":815.04,"endTime":816.6,"body":"(unclear) typically your"},{"speaker":"Kim","startTime":815.04,"endTime":816.6,"body":"response, right, when somebody"},{"speaker":"Kim","startTime":816.6,"endTime":817.53,"body":"shares something cool."},{"speaker":"Pam","startTime":817.74,"endTime":820.5,"body":"Oh, yeah. Because I was so"},{"speaker":"Pam","startTime":817.74,"endTime":820.5,"body":"fascinated that I wanted my"},{"speaker":"Pam","startTime":820.5,"endTime":823.86,"body":"brain to do that, and so a way I"},{"speaker":"Pam","startTime":820.5,"endTime":823.86,"body":"do that is I try to write a"},{"speaker":"Pam","startTime":823.86,"endTime":826.44,"body":"Problem String to teach other"},{"speaker":"Pam","startTime":823.86,"endTime":826.44,"body":"people to do it, and that helps"},{"speaker":"Pam","startTime":826.44,"endTime":827.19,"body":"gets into my brain."},{"speaker":"Both Pam and Kim","startTime":827.19,"endTime":827.52,"body":"Yeah."},{"speaker":"Kim","startTime":827.55,"endTime":827.88,"body":"Yeah."},{"speaker":"Pam","startTime":827.88,"endTime":828.12,"body":"Yeah."},{"speaker":"Kim","startTime":828.15,"endTime":832.56,"body":"So, what I do remember is"},{"speaker":"Kim","startTime":828.15,"endTime":832.56,"body":"that."},{"speaker":"Pam","startTime":833.01,"endTime":834.66,"body":"Is that one of those"},{"speaker":"Pam","startTime":833.01,"endTime":834.66,"body":"moments when you were like, \"Oh,"},{"speaker":"Pam","startTime":834.66,"endTime":835.14,"body":"Pam.\""},{"speaker":"Kim","startTime":838.14,"endTime":841.83,"body":"I don't remember. But I"},{"speaker":"Kim","startTime":838.14,"endTime":841.83,"body":"will say that I remember that I"},{"speaker":"Kim","startTime":841.83,"endTime":843.93,"body":"was there when you were"},{"speaker":"Kim","startTime":841.83,"endTime":843.93,"body":"tinkering with it, and then"},{"speaker":"Kim","startTime":843.96,"endTime":847.89,"body":"there when you did a Problem"},{"speaker":"Kim","startTime":843.96,"endTime":847.89,"body":"String, either that day or some"},{"speaker":"Kim","startTime":847.89,"endTime":850.86,"body":"other time. And I remember. We'd"},{"speaker":"Kim","startTime":847.89,"endTime":850.86,"body":"had this conversation. But I"},{"speaker":"Kim","startTime":850.86,"endTime":856.77,"body":"remember being like, \"Yeah, I"},{"speaker":"Kim","startTime":850.86,"endTime":856.77,"body":"mean, I get it, but I'm not all"},{"speaker":"Kim","startTime":856.77,"endTime":862.44,"body":"that impressed.\" I remember"},{"speaker":"Kim","startTime":856.77,"endTime":862.44,"body":"thinking like, \"It's cool, but"},{"speaker":"Kim","startTime":862.47,"endTime":867.93,"body":"nobody's going to do that.\""},{"speaker":"Kim","startTime":862.47,"endTime":867.93,"body":"Like, \"Why would you ever go to"},{"speaker":"Kim","startTime":867.93,"endTime":872.16,"body":"factors and thinking about"},{"speaker":"Kim","startTime":867.93,"endTime":872.16,"body":"multiplicative relationships to"},{"speaker":"Kim","startTime":872.16,"endTime":876.42,"body":"solve a really straightforward"},{"speaker":"Kim","startTime":872.16,"endTime":876.42,"body":"addition or subtraction"},{"speaker":"Kim","startTime":876.42,"endTime":880.71,"body":"problem?\" And I'll tell you"},{"speaker":"Kim","startTime":876.42,"endTime":880.71,"body":"what, I wasn't really convinced"},{"speaker":"Kim","startTime":880.71,"endTime":885.21,"body":"that people would actually do"},{"speaker":"Kim","startTime":880.71,"endTime":885.21,"body":"it. And really, you said, \"I've"},{"speaker":"Kim","startTime":885.21,"endTime":888.06,"body":"run into this\" and whatever, and"},{"speaker":"Kim","startTime":885.21,"endTime":888.06,"body":"I guess I kind of believed you,"},{"speaker":"Kim","startTime":888.06,"endTime":888.78,"body":"but not really."},{"speaker":"Pam","startTime":891.0,"endTime":891.21,"body":"[Pam laughs]."},{"speaker":"Kim","startTime":891.24,"endTime":896.55,"body":"And it was never one that I"},{"speaker":"Kim","startTime":891.24,"endTime":896.55,"body":"really used. But when you"},{"speaker":"Kim","startTime":896.55,"endTime":900.75,"body":"started putting out the"},{"speaker":"Kim","startTime":896.55,"endTime":900.75,"body":"MathStratChat problems, that had"},{"speaker":"Kim","startTime":900.81,"endTime":901.92,"body":"a factor to add or factor to"},{"speaker":"Kim","startTime":900.81,"endTime":901.92,"body":"subtract."},{"speaker":"Pam","startTime":901.92,"endTime":902.58,"body":"Just recently."},{"speaker":"Kim","startTime":902.61,"endTime":903.6,"body":"Recently, right?"},{"speaker":"Pam","startTime":903.6,"endTime":903.87,"body":"Yep."},{"speaker":"Kim","startTime":904.29,"endTime":907.41,"body":"You know, when"},{"speaker":"Kim","startTime":904.29,"endTime":907.41,"body":"MathStratChat comes out, I hold"},{"speaker":"Kim","startTime":907.41,"endTime":909.6,"body":"my phone in front of my"},{"speaker":"Kim","startTime":907.41,"endTime":909.6,"body":"children's faces and asked what"},{"speaker":"Kim","startTime":909.6,"endTime":914.19,"body":"they would do. And Luke, my"},{"speaker":"Kim","startTime":909.6,"endTime":914.19,"body":"older son, looked at the"},{"speaker":"Kim","startTime":914.19,"endTime":918.6,"body":"problem, and he said an answer."},{"speaker":"Kim","startTime":914.19,"endTime":918.6,"body":"And I said, \"How do you know?\""},{"speaker":"Kim","startTime":919.05,"endTime":922.47,"body":"And he used factor to add or"},{"speaker":"Kim","startTime":919.05,"endTime":922.47,"body":"factor. Whatever it was."},{"speaker":"Kim","startTime":922.47,"endTime":923.07,"body":"Addition, subtraction."},{"speaker":"Pam","startTime":923.07,"endTime":923.31,"body":"Whatever it"},{"speaker":"Pam","startTime":923.31,"endTime":924.81,"body":"was. He totally did it. Oh! Go,"},{"speaker":"Pam","startTime":923.31,"endTime":924.81,"body":"Luke!"},{"speaker":"Kim","startTime":924.81,"endTime":930.0,"body":"And he did it, and I was"},{"speaker":"Kim","startTime":924.81,"endTime":930.0,"body":"like, \"What?!\" Because we've"},{"speaker":"Kim","startTime":930.0,"endTime":933.69,"body":"never talked about it before,"},{"speaker":"Kim","startTime":930.0,"endTime":933.69,"body":"and he just uses those"},{"speaker":"Kim","startTime":933.69,"endTime":935.85,"body":"relationships. And I remember"},{"speaker":"Kim","startTime":933.69,"endTime":935.85,"body":"texting you I'm like, \"Alright,"},{"speaker":"Kim","startTime":935.85,"endTime":937.8,"body":"fine.\" I'm like, \"Okay, people"},{"speaker":"Kim","startTime":935.85,"endTime":937.8,"body":"do.\""},{"speaker":"Pam","startTime":938.61,"endTime":943.86,"body":"Oh, ye of little faith. Way"},{"speaker":"Pam","startTime":938.61,"endTime":943.86,"body":"to go, Luke! Oh, I love that"},{"speaker":"Pam","startTime":943.86,"endTime":946.47,"body":"kid. Good. You know, it's"},{"speaker":"Pam","startTime":943.86,"endTime":946.47,"body":"interesting, because at the same"},{"speaker":"Pam","startTime":946.47,"endTime":950.46,"body":"time period, my particular son"},{"speaker":"Pam","startTime":946.47,"endTime":950.46,"body":"was... I don't even remember"},{"speaker":"Pam","startTime":950.46,"endTime":954.78,"body":"why. But he said to me, \"Wait,"},{"speaker":"Pam","startTime":950.46,"endTime":954.78,"body":"what's that strategy?\" And I"},{"speaker":"Pam","startTime":954.78,"endTime":956.97,"body":"said, \"Well, you know like...\""},{"speaker":"Pam","startTime":954.78,"endTime":956.97,"body":"And I gave him the problem 81"},{"speaker":"Pam","startTime":956.97,"endTime":960.3,"body":"minus 27. I said, \"So, you know,"},{"speaker":"Pam","startTime":956.97,"endTime":960.3,"body":"81 minus 27...\" And he goes,"},{"speaker":"Pam","startTime":960.36,"endTime":964.86,"body":"\"Oh, well, I can clearly see"},{"speaker":"Pam","startTime":960.36,"endTime":964.86,"body":"nine 9s, minus three 9s. So,"},{"speaker":"Pam","startTime":964.86,"endTime":966.99,"body":"it'd be six 9s.\" And then he"},{"speaker":"Pam","startTime":964.86,"endTime":966.99,"body":"goes, \"But I don't really know"},{"speaker":"Pam","startTime":966.99,"endTime":969.96,"body":"six 9s, so I wouldn't do that. I"},{"speaker":"Pam","startTime":966.99,"endTime":969.96,"body":"would just do minus 30, plus 3.\""},{"speaker":"Pam","startTime":970.59,"endTime":971.1,"body":"That's like."},{"speaker":"Kim","startTime":971.13,"endTime":971.37,"body":"Yeah."},{"speaker":"Pam","startTime":971.91,"endTime":974.4,"body":"But that's an example. And"},{"speaker":"Pam","startTime":971.91,"endTime":974.4,"body":"that's my oldest son, by the"},{"speaker":"Pam","startTime":974.4,"endTime":977.7,"body":"way. The one that got me into"},{"speaker":"Pam","startTime":974.4,"endTime":977.7,"body":"all this. That's an example of"},{"speaker":"Pam","startTime":977.7,"endTime":983.07,"body":"someone who owns relationships,"},{"speaker":"Pam","startTime":977.7,"endTime":983.07,"body":"who says, \"Oh, okay. I could do"},{"speaker":"Pam","startTime":983.07,"endTime":985.29,"body":"that thing.\" So, he had never"},{"speaker":"Pam","startTime":983.07,"endTime":985.29,"body":"thought about factor to add or"},{"speaker":"Pam","startTime":985.29,"endTime":989.37,"body":"factor to subtract. But once I"},{"speaker":"Pam","startTime":985.29,"endTime":989.37,"body":"raised it, he goes, \"Oh, yeah, I"},{"speaker":"Pam","startTime":989.37,"endTime":991.95,"body":"could totally see the 9s in"},{"speaker":"Pam","startTime":989.37,"endTime":991.95,"body":"there. But that would give me 6"},{"speaker":"Pam","startTime":991.95,"endTime":995.52,"body":"times 9, which I don't know, so"},{"speaker":"Pam","startTime":991.95,"endTime":995.52,"body":"I probably would have just"},{"speaker":"Pam","startTime":995.52,"endTime":999.24,"body":"done...\" It's exactly what you"},{"speaker":"Pam","startTime":995.52,"endTime":999.24,"body":"said, Kim. People with"},{"speaker":"Pam","startTime":999.24,"endTime":1001.97,"body":"relationships go, \"I could do"},{"speaker":"Pam","startTime":999.24,"endTime":1001.97,"body":"this. I could do that. I"},{"speaker":"Pam","startTime":1001.97,"endTime":1005.33,"body":"could... Oh, I'm going to go"},{"speaker":"Pam","startTime":1001.97,"endTime":1005.33,"body":"with the one that, today, slides"},{"speaker":"Pam","startTime":1005.33,"endTime":1007.52,"body":"the most easily, that my"},{"speaker":"Pam","startTime":1005.33,"endTime":1007.52,"body":"intuition is just like...\""},{"speaker":"Kim","startTime":1008.48,"endTime":1012.68,"body":"Yeah. And I think the extra"},{"speaker":"Kim","startTime":1008.48,"endTime":1012.68,"body":"piece of that, Pam, is that"},{"speaker":"Kim","startTime":1012.89,"endTime":1017.6,"body":"you... It's perfectly okay to"},{"speaker":"Kim","startTime":1012.89,"endTime":1017.6,"body":"get started down the strategy,"},{"speaker":"Kim","startTime":1017.63,"endTime":1020.6,"body":"realize that where it's going to"},{"speaker":"Kim","startTime":1017.63,"endTime":1020.6,"body":"leave you is something that you"},{"speaker":"Kim","startTime":1020.6,"endTime":1023.81,"body":"don't want to mess with or"},{"speaker":"Kim","startTime":1020.6,"endTime":1023.81,"body":"doesn't make, you know, your"},{"speaker":"Kim","startTime":1023.81,"endTime":1028.49,"body":"life easier, and so then you"},{"speaker":"Kim","startTime":1023.81,"endTime":1028.49,"body":"back out of it. And I don't know"},{"speaker":"Kim","startTime":1028.49,"endTime":1030.77,"body":"that... I think we've said it"},{"speaker":"Kim","startTime":1028.49,"endTime":1030.77,"body":"before in the podcast, but it is"},{"speaker":"Kim","startTime":1030.77,"endTime":1033.65,"body":"not a magic like, \"Oh, what do I"},{"speaker":"Kim","startTime":1030.77,"endTime":1033.65,"body":"want to do?\" Like, pick the"},{"speaker":"Kim","startTime":1033.65,"endTime":1037.1,"body":"right thing. Sometimes you try"},{"speaker":"Kim","startTime":1033.65,"endTime":1037.1,"body":"some strategies, and you go,"},{"speaker":"Kim","startTime":1038.33,"endTime":1040.58,"body":"\"Nah, I'm going to back out, and"},{"speaker":"Kim","startTime":1038.33,"endTime":1040.58,"body":"I'm going to do something...\""},{"speaker":"Pam","startTime":1040.579,"endTime":1040.939,"body":"\"Yeah, not today.\""},{"speaker":"Kim","startTime":1041.0,"endTime":1041.75,"body":"Yeah, yeah."},{"speaker":"Pam","startTime":1041.75,"endTime":1045.23,"body":"Yeah, absolutely. And"},{"speaker":"Pam","startTime":1041.75,"endTime":1045.23,"body":"that's mathematical behavior."},{"speaker":"Kim","startTime":1045.349,"endTime":1046.069,"body":"Yeah, absolutely."},{"speaker":"Pam","startTime":1046.099,"endTime":1048.859,"body":"And hopefully it can free"},{"speaker":"Pam","startTime":1046.099,"endTime":1048.859,"body":"everybody up. And maybe one"},{"speaker":"Pam","startTime":1048.859,"endTime":1051.769,"body":"other thing that we'll mention"},{"speaker":"Pam","startTime":1048.859,"endTime":1051.769,"body":"about this is, this is a really"},{"speaker":"Pam","startTime":1051.769,"endTime":1055.789,"body":"cool strategy. But you'll notice"},{"speaker":"Pam","startTime":1051.769,"endTime":1055.789,"body":"that it's not in our major"},{"speaker":"Pam","startTime":1055.789,"endTime":1056.959,"body":"strategies ebook."},{"speaker":"Kim","startTime":1057.14,"endTime":1057.47,"body":"Yeah."},{"speaker":"Pam","startTime":1058.49,"endTime":1063.41,"body":"\"Why, Pam, if it's so"},{"speaker":"Pam","startTime":1058.49,"endTime":1063.41,"body":"cool?\" It's a fun, interesting,"},{"speaker":"Pam","startTime":1063.44,"endTime":1067.49,"body":"great strategy to use. And I"},{"speaker":"Pam","startTime":1063.44,"endTime":1067.49,"body":"would use it. I would do Problem"},{"speaker":"Pam","startTime":1067.49,"endTime":1070.97,"body":"Strings like this with students"},{"speaker":"Pam","startTime":1067.49,"endTime":1070.97,"body":"who you're trying to get them to"},{"speaker":"Pam","startTime":1070.97,"endTime":1074.63,"body":"think and reason either"},{"speaker":"Pam","startTime":1070.97,"endTime":1074.63,"body":"additively and you've got some"},{"speaker":"Pam","startTime":1074.63,"endTime":1077.51,"body":"kids that are already reasoning"},{"speaker":"Pam","startTime":1074.63,"endTime":1077.51,"body":"multiplicatively. And so, throw"},{"speaker":"Pam","startTime":1077.51,"endTime":1081.41,"body":"in some numbers that have common"},{"speaker":"Pam","startTime":1077.51,"endTime":1081.41,"body":"factors, and that can keep those"},{"speaker":"Pam","startTime":1081.41,"endTime":1089.15,"body":"kids that are already reasoning"},{"speaker":"Pam","startTime":1081.41,"endTime":1089.15,"body":"well additively. It can keep"},{"speaker":"Pam","startTime":1089.15,"endTime":1091.76,"body":"them going. It can like, \"Oh,"},{"speaker":"Pam","startTime":1089.15,"endTime":1091.76,"body":"they have something to think"},{"speaker":"Pam","startTime":1091.76,"endTime":1097.4,"body":"about.\" Or, use it with kids"},{"speaker":"Pam","startTime":1091.76,"endTime":1097.4,"body":"that you want to work on"},{"speaker":"Pam","startTime":1097.4,"endTime":1099.41,"body":"multiplicative reasoning. You"},{"speaker":"Pam","startTime":1097.4,"endTime":1099.41,"body":"want to work on sort of some"},{"speaker":"Pam","startTime":1099.41,"endTime":1102.59,"body":"single digit facts with"},{"speaker":"Pam","startTime":1099.41,"endTime":1102.59,"body":"multiplication, but you want to"},{"speaker":"Pam","startTime":1102.59,"endTime":1104.45,"body":"do it in a little bit of a"},{"speaker":"Pam","startTime":1102.59,"endTime":1104.45,"body":"different context. Oh, well you"},{"speaker":"Pam","startTime":1104.45,"endTime":1107.66,"body":"could do it here, where you're"},{"speaker":"Pam","startTime":1104.45,"endTime":1107.66,"body":"hoping those factors begin to"},{"speaker":"Pam","startTime":1107.66,"endTime":1110.78,"body":"pop a little bit more. Consider,"},{"speaker":"Pam","startTime":1107.66,"endTime":1110.78,"body":"if you (unclear) a Problem"},{"speaker":"Pam","startTime":1110.78,"endTime":1115.34,"body":"String like we just did in this"},{"speaker":"Pam","startTime":1110.78,"endTime":1115.34,"body":"podcast, right before you do"},{"speaker":"Pam","startTime":1115.34,"endTime":1118.31,"body":"some things like adding or"},{"speaker":"Pam","startTime":1115.34,"endTime":1118.31,"body":"subtracting fractions, where you"},{"speaker":"Pam","startTime":1118.31,"endTime":1123.83,"body":"want denominators to pop as with"},{"speaker":"Pam","startTime":1118.31,"endTime":1123.83,"body":"common factors, this could be"},{"speaker":"Pam","startTime":1123.83,"endTime":1127.43,"body":"something that could kind of get"},{"speaker":"Pam","startTime":1123.83,"endTime":1127.43,"body":"that warmed up. Now, those"},{"speaker":"Pam","startTime":1127.43,"endTime":1129.71,"body":"numbers are popping with common"},{"speaker":"Pam","startTime":1127.43,"endTime":1129.71,"body":"factors, and now you're like,"},{"speaker":"Pam","startTime":1129.74,"endTime":1132.41,"body":"\"Oh, so if I'm looking at common"},{"speaker":"Pam","startTime":1129.74,"endTime":1132.41,"body":"denominators... Bam! I've got"},{"speaker":"Pam","startTime":1132.41,"endTime":1135.41,"body":"these common factors popping out"},{"speaker":"Pam","startTime":1132.41,"endTime":1135.41,"body":"that could be sort of helpful"},{"speaker":"Pam","startTime":1135.41,"endTime":1138.86,"body":"there.\" So, it's not a major"},{"speaker":"Pam","startTime":1135.41,"endTime":1138.86,"body":"strategy, but it is a fun"},{"speaker":"Pam","startTime":1138.86,"endTime":1143.51,"body":"relationship that we can play"},{"speaker":"Pam","startTime":1138.86,"endTime":1143.51,"body":"with if our goal is to get kids"},{"speaker":"Pam","startTime":1143.6,"endTime":1145.19,"body":"to think and reason like"},{"speaker":"Pam","startTime":1143.6,"endTime":1145.19,"body":"mathematicians."},{"speaker":"Kim","startTime":1145.22,"endTime":1149.36,"body":"Yeah. It reminds me a"},{"speaker":"Kim","startTime":1145.22,"endTime":1149.36,"body":"little bit of how much we love"},{"speaker":"Kim","startTime":1149.36,"endTime":1152.99,"body":"the swapping strategy, which is"},{"speaker":"Kim","startTime":1149.36,"endTime":1152.99,"body":"not something that is on our"},{"speaker":"Kim","startTime":1153.17,"endTime":1157.64,"body":"ebooklet either, but it's a"},{"speaker":"Kim","startTime":1153.17,"endTime":1157.64,"body":"really cool strategy. And when"},{"speaker":"Kim","startTime":1157.64,"endTime":1162.14,"body":"the numbers are there, they're"},{"speaker":"Kim","startTime":1157.64,"endTime":1162.14,"body":"primed for that strategy, why"},{"speaker":"Kim","startTime":1162.14,"endTime":1165.5,"body":"not use it? It's cool and fun to"},{"speaker":"Kim","startTime":1162.14,"endTime":1165.5,"body":"try new things."},{"speaker":"Pam","startTime":1166.16,"endTime":1168.8,"body":"Yeah, and maybe I'll just"},{"speaker":"Pam","startTime":1166.16,"endTime":1168.8,"body":"clarify one other thing. So, why"},{"speaker":"Pam","startTime":1168.8,"endTime":1172.16,"body":"is it not a major strategy? The"},{"speaker":"Pam","startTime":1168.8,"endTime":1172.16,"body":"major strategies that I've"},{"speaker":"Pam","startTime":1172.16,"endTime":1175.88,"body":"chosen, I've chosen because"},{"speaker":"Pam","startTime":1172.16,"endTime":1175.88,"body":"those are the ones kids need to"},{"speaker":"Pam","startTime":1175.88,"endTime":1179.3,"body":"own. Those are the ones we need"},{"speaker":"Pam","startTime":1175.88,"endTime":1179.3,"body":"to work on, so that they can"},{"speaker":"Pam","startTime":1179.42,"endTime":1181.1,"body":"solve any problem that's"},{"speaker":"Pam","startTime":1179.42,"endTime":1181.1,"body":"reasonable to solve without a"},{"speaker":"Pam","startTime":1181.1,"endTime":1181.64,"body":"calculator."},{"speaker":"Kim","startTime":1181.76,"endTime":1182.24,"body":"Yeah."},{"speaker":"Pam","startTime":1182.3,"endTime":1186.47,"body":"So, that's why those are"},{"speaker":"Pam","startTime":1182.3,"endTime":1186.47,"body":"the major ones. We need to work"},{"speaker":"Pam","startTime":1186.47,"endTime":1190.46,"body":"on those. But there are other"},{"speaker":"Pam","startTime":1186.47,"endTime":1190.46,"body":"fun ones that we can also build"},{"speaker":"Pam","startTime":1190.46,"endTime":1193.49,"body":"in kids toward the aim of"},{"speaker":"Pam","startTime":1190.46,"endTime":1193.49,"body":"creating them as mathematicians."},{"speaker":"Pam","startTime":1193.52,"endTime":1196.64,"body":"That's the difference between if"},{"speaker":"Pam","startTime":1193.52,"endTime":1196.64,"body":"we've labeled something as a"},{"speaker":"Pam","startTime":1196.64,"endTime":1199.31,"body":"major one versus not. And maybe"},{"speaker":"Pam","startTime":1196.64,"endTime":1199.31,"body":"we can get into that more in a"},{"speaker":"Pam","startTime":1199.31,"endTime":1200.24,"body":"different podcast."},{"speaker":"Kim","startTime":1200.3,"endTime":1202.85,"body":"Yeah. And maybe if people"},{"speaker":"Kim","startTime":1200.3,"endTime":1202.85,"body":"don't know about that. They're"},{"speaker":"Kim","startTime":1202.85,"endTime":1205.16,"body":"new listeners, and they don't"},{"speaker":"Kim","startTime":1202.85,"endTime":1205.16,"body":"know what we're talking about"},{"speaker":"Kim","startTime":1205.16,"endTime":1207.23,"body":"when we're talking about the"},{"speaker":"Kim","startTime":1205.16,"endTime":1207.23,"body":"major strategies ebooklet."},{"speaker":"Pam","startTime":1207.23,"endTime":1208.37,"body":"Oh, yeah, we should"},{"speaker":"Pam","startTime":1207.23,"endTime":1208.37,"body":"probably give them that."},{"speaker":"Kim","startTime":1208.37,"endTime":1210.23,"body":"We'll throw that link in"},{"speaker":"Kim","startTime":1208.37,"endTime":1210.23,"body":"the show notes as well."},{"speaker":"Pam","startTime":1210.26,"endTime":1213.08,"body":"Absolutely. And it's"},{"speaker":"Pam","startTime":1210.26,"endTime":1213.08,"body":"mathisfigureoutable.com/big."},{"speaker":"Pam","startTime":1214.67,"endTime":1218.06,"body":"Because it's a big, free ebook"},{"speaker":"Pam","startTime":1214.67,"endTime":1218.06,"body":"that you can get."},{"speaker":"Pam","startTime":1218.06,"endTime":1221.63,"body":"mathisfigureoutable.com/big. You"},{"speaker":"Pam","startTime":1218.06,"endTime":1221.63,"body":"can download that free ebook. If"},{"speaker":"Pam","startTime":1221.63,"endTime":1224.03,"body":"you haven't already, check it"},{"speaker":"Pam","startTime":1221.63,"endTime":1224.03,"body":"out. Where you can find those"},{"speaker":"Pam","startTime":1224.03,"endTime":1227.9,"body":"major strategies. Hey, ya'll,"},{"speaker":"Pam","startTime":1224.03,"endTime":1227.9,"body":"thanks for tuning in and"},{"speaker":"Pam","startTime":1227.9,"endTime":1230.69,"body":"teaching more and more Real"},{"speaker":"Pam","startTime":1227.9,"endTime":1230.69,"body":"Math! To find out more about the"},{"speaker":"Pam","startTime":1230.69,"endTime":1232.79,"body":"Math is Figure-Out-Able"},{"speaker":"Pam","startTime":1230.69,"endTime":1232.79,"body":"movement, visit"},{"speaker":"Pam","startTime":1233.09,"endTime":1236.45,"body":"mathisfigureoutable.com. Let's"},{"speaker":"Pam","startTime":1233.09,"endTime":1236.45,"body":"keep spreading the word that"},{"speaker":"Pam","startTime":1236.45,"endTime":1238.04,"body":"Math is Figure-Out-Able!"}]}