{"version":"1.0.0","segments":[{"speaker":"Pam","startTime":1.29,"endTime":4.53,"body":"Hey, fellow mathematicians!"},{"speaker":"Pam","startTime":1.29,"endTime":4.53,"body":"Welcome to the podcast where"},{"speaker":"Pam","startTime":4.53,"endTime":7.08,"body":"Math is Figure-Out-Able. I'm"},{"speaker":"Pam","startTime":4.53,"endTime":7.08,"body":"Pam."},{"speaker":"Kim","startTime":7.41,"endTime":8.07,"body":"And I'm Kim."},{"speaker":"Pam","startTime":8.37,"endTime":11.55,"body":"And you found a place where"},{"speaker":"Pam","startTime":8.37,"endTime":11.55,"body":"math is not about memorizing and"},{"speaker":"Pam","startTime":11.55,"endTime":14.79,"body":"mimicking, waiting to be told or"},{"speaker":"Pam","startTime":11.55,"endTime":14.79,"body":"shown what to do. But it's about"},{"speaker":"Pam","startTime":14.79,"endTime":18.15,"body":"making sense of problems,"},{"speaker":"Pam","startTime":14.79,"endTime":18.15,"body":"noticing patterns, and reasoning"},{"speaker":"Pam","startTime":18.15,"endTime":21.3,"body":"using mathematical"},{"speaker":"Pam","startTime":18.15,"endTime":21.3,"body":"relationships. We believe we can"},{"speaker":"Pam","startTime":21.3,"endTime":25.56,"body":"mentor students to think and"},{"speaker":"Pam","startTime":21.3,"endTime":25.56,"body":"reason like mathematicians. Not"},{"speaker":"Pam","startTime":25.56,"endTime":28.74,"body":"only are algorithms not"},{"speaker":"Pam","startTime":25.56,"endTime":28.74,"body":"particularly helpful in teaching"},{"speaker":"Pam","startTime":28.74,"endTime":32.7,"body":"mathematics, but rotely"},{"speaker":"Pam","startTime":28.74,"endTime":32.7,"body":"repeating steps actually keeps"},{"speaker":"Pam","startTime":32.73,"endTime":35.55,"body":"students from being the"},{"speaker":"Pam","startTime":32.73,"endTime":35.55,"body":"mathematicians they can be."},{"speaker":"Kim","startTime":36.39,"endTime":36.9,"body":"Hey, Pam?"},{"speaker":"Pam","startTime":37.53,"endTime":37.95,"body":"Hey, Kim?"},{"speaker":"Kim","startTime":38.97,"endTime":41.07,"body":"It's Challenge Week! I'm so"},{"speaker":"Kim","startTime":38.97,"endTime":41.07,"body":"excited!"},{"speaker":"Pam","startTime":42.12,"endTime":43.98,"body":"We love challenge week!"},{"speaker":"Kim","startTime":44.1,"endTime":47.04,"body":"Oh, my God. It's one of the"},{"speaker":"Kim","startTime":44.1,"endTime":47.04,"body":"most fun weeks of the year. We"},{"speaker":"Kim","startTime":47.04,"endTime":50.31,"body":"do it a couple times a year. But"},{"speaker":"Kim","startTime":47.04,"endTime":50.31,"body":"we love, love, love seeing your"},{"speaker":"Kim","startTime":50.31,"endTime":53.13,"body":"faces, and I get to talk to so"},{"speaker":"Kim","startTime":50.31,"endTime":53.13,"body":"many people in the Facebook"},{"speaker":"Kim","startTime":53.13,"endTime":56.79,"body":"group. So, I'm super excited"},{"speaker":"Kim","startTime":53.13,"endTime":56.79,"body":"about the back half of this"},{"speaker":"Kim","startTime":56.79,"endTime":58.86,"body":"week. Not that I don't love the"},{"speaker":"Kim","startTime":56.79,"endTime":58.86,"body":"podcast, but you"},{"speaker":"Kim","startTime":58.86,"endTime":58.92,"body":"know."},{"speaker":"Pam","startTime":58.92,"endTime":62.31,"body":"No, it is so one of the"},{"speaker":"Pam","startTime":58.92,"endTime":62.31,"body":"best things that we do all year."},{"speaker":"Pam","startTime":62.31,"endTime":65.13,"body":"It's totally free. We love it."},{"speaker":"Pam","startTime":62.31,"endTime":65.13,"body":"Obviously, if you're listening"},{"speaker":"Pam","startTime":65.13,"endTime":68.46,"body":"to this podcast at some other"},{"speaker":"Pam","startTime":65.13,"endTime":68.46,"body":"time of the year, just know get"},{"speaker":"Pam","startTime":68.46,"endTime":72.15,"body":"on our mailing list and join in"},{"speaker":"Pam","startTime":68.46,"endTime":72.15,"body":"those free challenges because"},{"speaker":"Pam","startTime":72.15,"endTime":74.04,"body":"they are a blast. Alright."},{"speaker":"Kim","startTime":74.04,"endTime":79.56,"body":"Super fun. Alright, down to"},{"speaker":"Kim","startTime":74.04,"endTime":79.56,"body":"business. If you haven't been"},{"speaker":"Kim","startTime":79.56,"endTime":82.44,"body":"tuning in lately, then you've"},{"speaker":"Kim","startTime":79.56,"endTime":82.44,"body":"been missing some great chatter"},{"speaker":"Kim","startTime":82.44,"endTime":85.35,"body":"about subtraction and how"},{"speaker":"Kim","startTime":82.44,"endTime":85.35,"body":"important it is that we give"},{"speaker":"Kim","startTime":85.35,"endTime":88.08,"body":"kids solid experiences with"},{"speaker":"Kim","startTime":85.35,"endTime":88.08,"body":"subtraction because it affects"},{"speaker":"Kim","startTime":88.11,"endTime":91.83,"body":"so many of the operations, the"},{"speaker":"Kim","startTime":88.11,"endTime":91.83,"body":"other operations, and strategies"},{"speaker":"Kim","startTime":91.83,"endTime":94.41,"body":"that we love. So, today, we're"},{"speaker":"Kim","startTime":91.83,"endTime":94.41,"body":"going to continue from last"},{"speaker":"Kim","startTime":94.41,"endTime":97.41,"body":"week, chatting about subtraction"},{"speaker":"Kim","startTime":94.41,"endTime":97.41,"body":"facts."},{"speaker":"Pam","startTime":97.59,"endTime":99.78,"body":"Yeah, so if you didn't"},{"speaker":"Pam","startTime":97.59,"endTime":99.78,"body":"listen to last week, really do"},{"speaker":"Pam","startTime":99.78,"endTime":102.78,"body":"because we talked all about"},{"speaker":"Pam","startTime":99.78,"endTime":102.78,"body":"memorizing subtraction facts."},{"speaker":"Pam","startTime":103.29,"endTime":108.06,"body":"What are our favorite ways of"},{"speaker":"Pam","startTime":103.29,"endTime":108.06,"body":"helping students really own"},{"speaker":"Pam","startTime":108.48,"endTime":111.54,"body":"subtraction facts, really"},{"speaker":"Pam","startTime":108.48,"endTime":111.54,"body":"getting them into long term"},{"speaker":"Pam","startTime":111.54,"endTime":116.16,"body":"memory with a schema, so that"},{"speaker":"Pam","startTime":111.54,"endTime":116.16,"body":"they stick better and that it's"},{"speaker":"Pam","startTime":116.19,"endTime":119.88,"body":"all more and more"},{"speaker":"Pam","startTime":116.19,"endTime":119.88,"body":"Figure-Out-Able? So, Kim, what's"},{"speaker":"Pam","startTime":119.88,"endTime":121.17,"body":"one of our favorites?"},{"speaker":"Kim","startTime":121.23,"endTime":123.12,"body":"Well, you know, I'm going"},{"speaker":"Kim","startTime":121.23,"endTime":123.12,"body":"to mention the first one that I"},{"speaker":"Kim","startTime":123.12,"endTime":126.45,"body":"love is I Have, You Need. And we"},{"speaker":"Kim","startTime":123.12,"endTime":126.45,"body":"talk about it all the time"},{"speaker":"Kim","startTime":126.45,"endTime":127.62,"body":"because it's so powerful."},{"speaker":"Pam","startTime":127.62,"endTime":127.95,"body":"I Have, You Need. Yep."},{"speaker":"Kim","startTime":128.28,"endTime":133.56,"body":"Like, the silliest little"},{"speaker":"Kim","startTime":128.28,"endTime":133.56,"body":"routine but super helpful at a"},{"speaker":"Kim","startTime":133.56,"endTime":136.74,"body":"young age. We're going to just"},{"speaker":"Kim","startTime":133.56,"endTime":136.74,"body":"mention it here because we've"},{"speaker":"Kim","startTime":136.74,"endTime":140.16,"body":"talked about it before. We'll"},{"speaker":"Kim","startTime":136.74,"endTime":140.16,"body":"link that episode in the show"},{"speaker":"Kim","startTime":140.16,"endTime":140.61,"body":"notes."},{"speaker":"Pam","startTime":140.64,"endTime":142.98,"body":"Well, and to be clear, you"},{"speaker":"Pam","startTime":140.64,"endTime":142.98,"body":"only call it silly because you"},{"speaker":"Pam","startTime":142.98,"endTime":145.26,"body":"made it up. So, you're just"},{"speaker":"Pam","startTime":142.98,"endTime":145.26,"body":"trying to like, \"I'll be, you"},{"speaker":"Pam","startTime":145.26,"endTime":145.83,"body":"know, humble and everything.\""},{"speaker":"Kim","startTime":145.83,"endTime":148.05,"body":"Well, I mean, honestly,"},{"speaker":"Kim","startTime":145.83,"endTime":148.05,"body":"there's nothing like super"},{"speaker":"Kim","startTime":148.08,"endTime":151.38,"body":"magical about it. It's fun"},{"speaker":"Kim","startTime":148.08,"endTime":151.38,"body":"mathematically, but the routine"},{"speaker":"Kim","startTime":151.38,"endTime":153.33,"body":"itself is basic."},{"speaker":"Pam","startTime":153.36,"endTime":154.98,"body":"I mean, I Have, You Need is"},{"speaker":"Pam","startTime":153.36,"endTime":154.98,"body":"amazing!"},{"speaker":"Kim","startTime":154.98,"endTime":155.79,"body":"There's not a million"},{"speaker":"Kim","startTime":155.82,"endTime":161.76,"body":"things to make. I mean, I'm in"},{"speaker":"Kim","startTime":155.82,"endTime":161.76,"body":"for not a lot of prep. And..."},{"speaker":"Pam","startTime":161.76,"endTime":162.51,"body":"Yeah, it's good."},{"speaker":"Kim","startTime":162.51,"endTime":165.3,"body":"...it's okay to do it in"},{"speaker":"Kim","startTime":162.51,"endTime":165.3,"body":"lots of ways, over lots of"},{"speaker":"Kim","startTime":165.3,"endTime":171.42,"body":"experiences. Partners, not"},{"speaker":"Kim","startTime":165.3,"endTime":171.42,"body":"partners, whole class, different"},{"speaker":"Kim","startTime":171.42,"endTime":171.81,"body":"numbers..."},{"speaker":"Pam","startTime":171.84,"endTime":172.11,"body":"Absolutely."},{"speaker":"Kim","startTime":172.11,"endTime":173.76,"body":"...change things up. Yeah,"},{"speaker":"Kim","startTime":172.11,"endTime":173.76,"body":"I'm in for that."},{"speaker":"Pam","startTime":174.24,"endTime":177.45,"body":"Alright, so if you have not"},{"speaker":"Pam","startTime":174.24,"endTime":177.45,"body":"listened to an episode on I"},{"speaker":"Pam","startTime":177.45,"endTime":179.52,"body":"Have, You Need. We'll put the"},{"speaker":"Pam","startTime":177.45,"endTime":179.52,"body":"episode number in the show"},{"speaker":"Pam","startTime":179.52,"endTime":182.19,"body":"notes. But check that out. If"},{"speaker":"Pam","startTime":179.52,"endTime":182.19,"body":"that's new to you, if it's the"},{"speaker":"Pam","startTime":182.19,"endTime":185.16,"body":"first time you listen to the"},{"speaker":"Pam","startTime":182.19,"endTime":185.16,"body":"podcast, I Have, You Need,"},{"speaker":"Pam","startTime":185.19,"endTime":189.21,"body":"wonderful classroom routine, all"},{"speaker":"Pam","startTime":185.19,"endTime":189.21,"body":"grade levels. It's great."},{"speaker":"Kim","startTime":189.54,"endTime":189.87,"body":"Yeah."},{"speaker":"Kim","startTime":190.35,"endTime":193.98,"body":"So, at a young age I Have, You"},{"speaker":"Kim","startTime":190.35,"endTime":193.98,"body":"Need with 10. We're talking"},{"speaker":"Kim","startTime":193.98,"endTime":197.91,"body":"subtraction facts, so I Have,"},{"speaker":"Kim","startTime":193.98,"endTime":197.91,"body":"You Need with 10 would be super"},{"speaker":"Kim","startTime":197.91,"endTime":202.44,"body":"helpful. But then, also, once"},{"speaker":"Kim","startTime":197.91,"endTime":202.44,"body":"your kids are working and have"},{"speaker":"Kim","startTime":202.44,"endTime":205.77,"body":"made sense of the 10 a lot, it"},{"speaker":"Kim","startTime":202.44,"endTime":205.77,"body":"would be really helpful for them"},{"speaker":"Kim","startTime":205.77,"endTime":210.27,"body":"to work on I Have, You Need with"},{"speaker":"Kim","startTime":205.77,"endTime":210.27,"body":"20. And the idea that within the"},{"speaker":"Kim","startTime":210.3,"endTime":215.46,"body":"20, there are two 10's and one"},{"speaker":"Kim","startTime":210.3,"endTime":215.46,"body":"of the 10's is being messed"},{"speaker":"Kim","startTime":215.46,"endTime":217.86,"body":"with, with I Have, You Need, but"},{"speaker":"Kim","startTime":215.46,"endTime":217.86,"body":"the other 10 is just kind of"},{"speaker":"Kim","startTime":217.86,"endTime":219.6,"body":"being left alone. So..."},{"speaker":"Pam","startTime":219.87,"endTime":221.34,"body":"And I almost want to back"},{"speaker":"Pam","startTime":219.87,"endTime":221.34,"body":"you up just a little bit. Let's"},{"speaker":"Pam","startTime":221.34,"endTime":224.7,"body":"just do a quick example with a"},{"speaker":"Pam","startTime":221.34,"endTime":224.7,"body":"total 10. So, if I say the total"},{"speaker":"Pam","startTime":224.7,"endTime":228.12,"body":"is 10. I Have 7, You Need?"},{"speaker":"Kim","startTime":228.51,"endTime":229.02,"body":"Three."},{"speaker":"Pam","startTime":229.08,"endTime":233.04,"body":"Three to make. 10, right?"},{"speaker":"Pam","startTime":229.08,"endTime":233.04,"body":"So, that feels like addition. 7"},{"speaker":"Pam","startTime":233.04,"endTime":236.34,"body":"plus 3 is 10. Then, we want to"},{"speaker":"Pam","startTime":233.04,"endTime":236.34,"body":"help kids make a connection that"},{"speaker":"Pam","startTime":236.34,"endTime":240.21,"body":"therefore, if we own that 7 and"},{"speaker":"Pam","startTime":236.34,"endTime":240.21,"body":"3 are partners of 10, then I now"},{"speaker":"Pam","startTime":240.21,"endTime":245.25,"body":"know the answer to 10 minus 7."},{"speaker":"Pam","startTime":240.21,"endTime":245.25,"body":"Three. And I also know the"},{"speaker":"Pam","startTime":245.25,"endTime":249.18,"body":"answer to 10 minus 3 is 7. And"},{"speaker":"Pam","startTime":245.25,"endTime":249.18,"body":"that takes some time and some"},{"speaker":"Pam","startTime":249.18,"endTime":251.76,"body":"development, but that they own"},{"speaker":"Pam","startTime":249.18,"endTime":251.76,"body":"that. And so, then, you're"},{"speaker":"Pam","startTime":251.76,"endTime":256.02,"body":"saying once we own that, there"},{"speaker":"Pam","startTime":251.76,"endTime":256.02,"body":"is that 10 in the 20."},{"speaker":"Kim","startTime":256.05,"endTime":256.89,"body":"Inside the 20, mmhmm."},{"speaker":"Pam","startTime":256.95,"endTime":260.46,"body":"Yeah, so if I play I Have,"},{"speaker":"Pam","startTime":256.95,"endTime":260.46,"body":"You Need total 20. Kim, if I"},{"speaker":"Pam","startTime":260.46,"endTime":262.53,"body":"have 17, what do you need?"},{"speaker":"Kim","startTime":263.07,"endTime":263.55,"body":"Three."},{"speaker":"Pam","startTime":263.76,"endTime":264.06,"body":"Three."},{"speaker":"Kim","startTime":264.06,"endTime":269.49,"body":"And so, that 10 in your 17."},{"speaker":"Kim","startTime":264.06,"endTime":269.49,"body":"The first 10 is just kind of"},{"speaker":"Kim","startTime":269.49,"endTime":273.48,"body":"sitting by itself. But you"},{"speaker":"Kim","startTime":269.49,"endTime":273.48,"body":"haven't same 7 and 3 partnership"},{"speaker":"Kim","startTime":273.48,"endTime":274.8,"body":"that you had in the 10."},{"speaker":"Pam","startTime":275.01,"endTime":277.59,"body":"Yeah. So, if I say I have"},{"speaker":"Pam","startTime":275.01,"endTime":277.59,"body":"12, what do you need?"},{"speaker":"Kim","startTime":278.49,"endTime":278.85,"body":"Eight."},{"speaker":"Pam","startTime":279.21,"endTime":281.73,"body":"Eight. And you're thinking"},{"speaker":"Pam","startTime":279.21,"endTime":281.73,"body":"about, \"There's that 10 hanging"},{"speaker":"Pam","startTime":281.73,"endTime":284.01,"body":"around, but there's a 2...\" It's"},{"speaker":"Pam","startTime":281.73,"endTime":284.01,"body":"almost like I said, \"I have 2,"},{"speaker":"Pam","startTime":284.01,"endTime":286.23,"body":"what do you need to make 10?\""},{"speaker":"Pam","startTime":284.01,"endTime":286.23,"body":"It's the 2 and the 8 you're kind"},{"speaker":"Pam","startTime":286.23,"endTime":288.87,"body":"of using. And, you know, you"},{"speaker":"Pam","startTime":286.23,"endTime":288.87,"body":"have to help kids kind of"},{"speaker":"Pam","startTime":288.87,"endTime":292.53,"body":"experience that 10. Kind of,"},{"speaker":"Pam","startTime":288.87,"endTime":292.53,"body":"sort of ignore that extra 10 and"},{"speaker":"Pam","startTime":292.53,"endTime":295.62,"body":"the 20. We're kind of focus on"},{"speaker":"Pam","startTime":292.53,"endTime":295.62,"body":"those partners. And then, you"},{"speaker":"Pam","startTime":295.62,"endTime":298.47,"body":"could do the same thing with 30."},{"speaker":"Pam","startTime":295.62,"endTime":298.47,"body":"And not necessarily that you"},{"speaker":"Pam","startTime":298.47,"endTime":301.05,"body":"would play I Have, You Need but"},{"speaker":"Pam","startTime":298.47,"endTime":301.05,"body":"that you make the connection."},{"speaker":"Pam","startTime":301.32,"endTime":304.35,"body":"So, if you're doing 30 minus 8."},{"speaker":"Kim","startTime":305.01,"endTime":305.31,"body":"Yep."},{"speaker":"Pam","startTime":305.73,"endTime":309.09,"body":"Or 30 (unclear), then can"},{"speaker":"Pam","startTime":305.73,"endTime":309.09,"body":"you use the 8 and the 2 in that"},{"speaker":"Pam","startTime":309.3,"endTime":313.53,"body":"10 that's between the 20 and 30."},{"speaker":"Pam","startTime":309.3,"endTime":313.53,"body":"Etc, etc. Yeah. Cool. Cool."},{"speaker":"Kim","startTime":314.73,"endTime":315.39,"body":"What's another one?"},{"speaker":"Pam","startTime":315.75,"endTime":318.66,"body":"Do we want to mention..."},{"speaker":"Pam","startTime":315.75,"endTime":318.66,"body":"Sorry. Do we want to mention..."},{"speaker":"Pam","startTime":318.93,"endTime":322.32,"body":"My brain's all over the place."},{"speaker":"Pam","startTime":318.93,"endTime":322.32,"body":"That, similarly, if we've done"},{"speaker":"Pam","startTime":322.32,"endTime":327.96,"body":"partners of 100 with I Have, You"},{"speaker":"Pam","startTime":322.32,"endTime":327.96,"body":"Need. And if I say, I have 63,"},{"speaker":"Pam","startTime":327.99,"endTime":328.56,"body":"and you say..."},{"speaker":"Kim","startTime":328.56,"endTime":328.68,"body":"Yeah,"},{"speaker":"Kim","startTime":328.68,"endTime":330.81,"body":"but we're talking about"},{"speaker":"Kim","startTime":328.68,"endTime":330.81,"body":"subtraction facts today, Pamela,"},{"speaker":"Kim","startTime":330.84,"endTime":331.71,"body":"so I (unclear)."},{"speaker":"Pam","startTime":331.71,"endTime":333.39,"body":"Oh, don't go higher. That's"},{"speaker":"Pam","startTime":331.71,"endTime":333.39,"body":"why,"},{"speaker":"Pam","startTime":333.87,"endTime":334.77,"body":"Because I was just going higher."},{"speaker":"Kim","startTime":334.89,"endTime":336.69,"body":"What can we do with"},{"speaker":"Kim","startTime":334.89,"endTime":336.69,"body":"subtraction facts. (unclear)."},{"speaker":"Pam","startTime":336.84,"endTime":339.57,"body":"Never mind, stay in"},{"speaker":"Pam","startTime":336.84,"endTime":339.57,"body":"subtraction facts. Stay in"},{"speaker":"Pam","startTime":339.57,"endTime":340.32,"body":"subtraction facts."},{"speaker":"Pam","startTime":340.83,"endTime":343.71,"body":"Not any subtraction. We're"},{"speaker":"Pam","startTime":340.83,"endTime":343.71,"body":"talking about subtraction facts."},{"speaker":"Pam","startTime":343.71,"endTime":347.25,"body":"Okay, cool. Thank you. So,"},{"speaker":"Pam","startTime":343.71,"endTime":347.25,"body":"another thing that we can do."},{"speaker":"Pam","startTime":347.43,"endTime":350.97,"body":"There goes my vertical brain."},{"speaker":"Pam","startTime":347.43,"endTime":350.97,"body":"Another thing that we can do is"},{"speaker":"Pam","startTime":351.51,"endTime":355.29,"body":"think about groups of problems"},{"speaker":"Pam","startTime":351.51,"endTime":355.29,"body":"and what they have in common,"},{"speaker":"Pam","startTime":355.35,"endTime":355.71,"body":"right?"},{"speaker":"Kim","startTime":355.92,"endTime":356.73,"body":"Oh, yeah, yeah."},{"speaker":"Pam","startTime":356.76,"endTime":359.43,"body":"What relationships are"},{"speaker":"Pam","startTime":356.76,"endTime":359.43,"body":"there among groups of"},{"speaker":"Pam","startTime":359.43,"endTime":361.86,"body":"subtraction fact problems? How"},{"speaker":"Pam","startTime":359.43,"endTime":361.86,"body":"they're related? How they're"},{"speaker":"Pam","startTime":361.86,"endTime":365.55,"body":"connected? So, you have a"},{"speaker":"Pam","startTime":361.86,"endTime":365.55,"body":"favorite one. Give us that one."},{"speaker":"Kim","startTime":366.72,"endTime":369.72,"body":"So, on a subtraction chart,"},{"speaker":"Kim","startTime":366.72,"endTime":369.72,"body":"right? If we're looking at a"},{"speaker":"Kim","startTime":369.72,"endTime":373.74,"body":"subtraction, all the subtraction"},{"speaker":"Kim","startTime":369.72,"endTime":373.74,"body":"facts, then you know I might put"},{"speaker":"Kim","startTime":373.74,"endTime":378.48,"body":"up that chart for five minutes a"},{"speaker":"Kim","startTime":373.74,"endTime":378.48,"body":"day for a week, or fifteen"},{"speaker":"Kim","startTime":378.48,"endTime":381.6,"body":"minutes at a time, and have kids"},{"speaker":"Kim","startTime":378.48,"endTime":381.6,"body":"talk about, \"What do you notice?"},{"speaker":"Kim","startTime":381.6,"endTime":383.88,"body":"And what patterns do you see?\""},{"speaker":"Kim","startTime":381.6,"endTime":383.88,"body":"One of the ones that I think is"},{"speaker":"Kim","startTime":384.21,"endTime":384.6,"body":"super fun..."},{"speaker":"Pam","startTime":384.6,"endTime":386.46,"body":"And hey. Sorry, before you"},{"speaker":"Pam","startTime":384.6,"endTime":386.46,"body":"go into the one. Maybe I'll just"},{"speaker":"Pam","startTime":386.46,"endTime":389.31,"body":"describe that just a little bit"},{"speaker":"Pam","startTime":386.46,"endTime":389.31,"body":"more. So, we might look at a"},{"speaker":"Pam","startTime":389.31,"endTime":393.87,"body":"chart where I've got the numbers"},{"speaker":"Pam","startTime":389.31,"endTime":393.87,"body":"0 to 20 across the top, and then"},{"speaker":"Pam","startTime":393.87,"endTime":397.05,"body":"0 to 20 going down the side, and"},{"speaker":"Pam","startTime":393.87,"endTime":397.05,"body":"then we're kind of looking at"},{"speaker":"Pam","startTime":397.05,"endTime":400.83,"body":"where those coincide. And if"},{"speaker":"Pam","startTime":397.05,"endTime":400.83,"body":"we're just dealing with positive"},{"speaker":"Pam","startTime":400.83,"endTime":404.1,"body":"numbers, then I would look at"},{"speaker":"Pam","startTime":400.83,"endTime":404.1,"body":"where, you know, 20 minus 5"},{"speaker":"Pam","startTime":404.1,"endTime":408.81,"body":"would be in the cell, where the"},{"speaker":"Pam","startTime":404.1,"endTime":408.81,"body":"20 column and the 5 coincide."},{"speaker":"Pam","startTime":409.68,"endTime":412.17,"body":"(unclear). In that cell, we're"},{"speaker":"Pam","startTime":409.68,"endTime":412.17,"body":"talking about 20 minus 5. And if"},{"speaker":"Pam","startTime":412.17,"endTime":415.44,"body":"we go down to the cell below it,"},{"speaker":"Pam","startTime":412.17,"endTime":415.44,"body":"that would be 20 minus 6, and"},{"speaker":"Pam","startTime":415.44,"endTime":417.69,"body":"the cell below that would be 20"},{"speaker":"Pam","startTime":415.44,"endTime":417.69,"body":"minus 7, etc."},{"speaker":"Kim","startTime":417.72,"endTime":418.08,"body":"Yep."},{"speaker":"Pam","startTime":418.14,"endTime":420.39,"body":"So, that's the chart. So,"},{"speaker":"Pam","startTime":418.14,"endTime":420.39,"body":"we might pull that chart out,"},{"speaker":"Pam","startTime":420.54,"endTime":422.94,"body":"and then we might look for"},{"speaker":"Pam","startTime":420.54,"endTime":422.94,"body":"commonalities and groups of"},{"speaker":"Pam","startTime":422.94,"endTime":423.81,"body":"related facts."},{"speaker":"Kim","startTime":423.87,"endTime":429.36,"body":"Yeah. So, one really cool"},{"speaker":"Kim","startTime":423.87,"endTime":429.36,"body":"noticing is that every time"},{"speaker":"Kim","startTime":429.36,"endTime":434.04,"body":"you're subtracting 9, you can be"},{"speaker":"Kim","startTime":429.36,"endTime":434.04,"body":"thinking about the teen numbers,"},{"speaker":"Kim","startTime":434.04,"endTime":437.64,"body":"and you can be thinking about,"},{"speaker":"Kim","startTime":434.04,"endTime":437.64,"body":"\"It's always going to be one"},{"speaker":"Kim","startTime":437.64,"endTime":443.25,"body":"more to get to 10 plus all that"},{"speaker":"Kim","startTime":437.64,"endTime":443.25,"body":"extra that was in the teen"},{"speaker":"Kim","startTime":443.25,"endTime":447.33,"body":"number. So, if it was like 17"},{"speaker":"Kim","startTime":443.25,"endTime":447.33,"body":"minus 9, then you could think"},{"speaker":"Kim","startTime":447.33,"endTime":451.8,"body":"about the 1 that you need to get"},{"speaker":"Kim","startTime":447.33,"endTime":451.8,"body":"to 10, plus all the extra 7."},{"speaker":"Pam","startTime":452.13,"endTime":454.86,"body":"So, you're really using the"},{"speaker":"Pam","startTime":452.13,"endTime":454.86,"body":"difference interpretation of"},{"speaker":"Pam","startTime":454.86,"endTime":455.64,"body":"subtraction here."},{"speaker":"Kim","startTime":455.64,"endTime":455.73,"body":"Yep."},{"speaker":"Pam","startTime":455.76,"endTime":458.1,"body":"You're thinking about if"},{"speaker":"Pam","startTime":455.76,"endTime":458.1,"body":"it's 17 minus 9, you're like,"},{"speaker":"Pam","startTime":458.13,"endTime":462.15,"body":"\"From 9 to 17...\" You think"},{"speaker":"Pam","startTime":458.13,"endTime":462.15,"body":"about that 1, and then that"},{"speaker":"Pam","startTime":462.18,"endTime":465.87,"body":"extra, the kind of the teen-ness"},{"speaker":"Pam","startTime":462.18,"endTime":465.87,"body":"of it, right? The 10 to the"},{"speaker":"Pam","startTime":465.87,"endTime":466.35,"body":"teen?"},{"speaker":"Kim","startTime":466.62,"endTime":469.8,"body":"Yeah, and it's true for"},{"speaker":"Kim","startTime":466.62,"endTime":469.8,"body":"every 9. Right, every subtract"},{"speaker":"Kim","startTime":469.8,"endTime":470.37,"body":"9..."},{"speaker":"Pam","startTime":470.49,"endTime":471.6,"body":"Do 13 minus 9."},{"speaker":"Kim","startTime":471.99,"endTime":477.12,"body":"So, 13 minus 9 would be..."},{"speaker":"Kim","startTime":471.99,"endTime":477.12,"body":"From 9, the 1 to get to 10, plus"},{"speaker":"Kim","startTime":477.12,"endTime":478.29,"body":"all that extra 3."},{"speaker":"Pam","startTime":479.34,"endTime":483.66,"body":"So, it's always 9 to 10."},{"speaker":"Pam","startTime":479.34,"endTime":483.66,"body":"So, it's always that 1. And then"},{"speaker":"Pam","startTime":483.66,"endTime":485.04,"body":"it's just the extra to get to"},{"speaker":"Pam","startTime":483.66,"endTime":485.04,"body":"the..."},{"speaker":"Kim","startTime":485.13,"endTime":487.74,"body":"And it's a really nice"},{"speaker":"Kim","startTime":485.13,"endTime":487.74,"body":"transition for kids who are"},{"speaker":"Kim","startTime":487.77,"endTime":491.49,"body":"counting by ones to be thinking"},{"speaker":"Kim","startTime":487.77,"endTime":491.49,"body":"about, \"Oh, I know about teen"},{"speaker":"Kim","startTime":491.49,"endTime":494.85,"body":"numbers. It's just all that"},{"speaker":"Kim","startTime":491.49,"endTime":494.85,"body":"extra, all those 3.\" Instead of"},{"speaker":"Kim","startTime":494.85,"endTime":502.59,"body":"counting 1, 2, 3 from 11, 12,"},{"speaker":"Kim","startTime":494.85,"endTime":502.59,"body":"13. Yeah. So, getting them used"},{"speaker":"Kim","startTime":502.59,"endTime":506.1,"body":"to the idea that you know what"},{"speaker":"Kim","startTime":502.59,"endTime":506.1,"body":"that teen number is made of? So,"},{"speaker":"Kim","startTime":506.1,"endTime":509.67,"body":"you can think about that whole"},{"speaker":"Kim","startTime":506.1,"endTime":509.67,"body":"extra chunk beyond the 10 all in"},{"speaker":"Kim","startTime":509.67,"endTime":510.27,"body":"one group."},{"speaker":"Pam","startTime":510.72,"endTime":513.45,"body":"And so, this is just"},{"speaker":"Pam","startTime":510.72,"endTime":513.45,"body":"screaming at me. This is one"},{"speaker":"Pam","startTime":513.45,"endTime":516.78,"body":"more example of, what we're not"},{"speaker":"Pam","startTime":513.45,"endTime":516.78,"body":"really suggesting is that you go"},{"speaker":"Pam","startTime":516.78,"endTime":518.94,"body":"teach this strategy to kids,"},{"speaker":"Pam","startTime":516.78,"endTime":518.94,"body":"right?"},{"speaker":"Kim","startTime":518.94,"endTime":519.21,"body":"Right (unclear)."},{"speaker":"Pam","startTime":519.24,"endTime":523.38,"body":"It's not... We're"},{"speaker":"Pam","startTime":519.24,"endTime":523.38,"body":"suggesting we notice it because"},{"speaker":"Pam","startTime":523.44,"endTime":526.86,"body":"we're in that noticing. We're"},{"speaker":"Pam","startTime":523.44,"endTime":526.86,"body":"helping kids go, \"Oh, that"},{"speaker":"Pam","startTime":526.86,"endTime":530.88,"body":"really is true that from 10 to"},{"speaker":"Pam","startTime":526.86,"endTime":530.88,"body":"the 13, it's 3. And from 10 to"},{"speaker":"Pam","startTime":530.88,"endTime":534.75,"body":"the 16, it's 6. Or from 10 to"},{"speaker":"Pam","startTime":530.88,"endTime":534.75,"body":"the 17, it's 7. And from...\" It"},{"speaker":"Pam","startTime":534.75,"endTime":537.75,"body":"always is that sort of extra"},{"speaker":"Pam","startTime":534.75,"endTime":537.75,"body":"from the 10 to the teen. And"},{"speaker":"Pam","startTime":537.75,"endTime":539.4,"body":"then, it would just be that"},{"speaker":"Pam","startTime":537.75,"endTime":539.4,"body":"extra 1 because we're"},{"speaker":"Pam","startTime":539.4,"endTime":541.35,"body":"subtracting that every time."},{"speaker":"Pam","startTime":539.4,"endTime":541.35,"body":"(unclear). We're always looking"},{"speaker":"Pam","startTime":541.35,"endTime":543.09,"body":"at the difference being"},{"speaker":"Pam","startTime":541.35,"endTime":543.09,"body":"(unclear). Those"},{"speaker":"Pam","startTime":543.09,"endTime":545.85,"body":"generalizations. Building"},{"speaker":"Pam","startTime":543.09,"endTime":545.85,"body":"numeracy, building the"},{"speaker":"Pam","startTime":545.85,"endTime":548.46,"body":"mathematical relationships that"},{"speaker":"Pam","startTime":545.85,"endTime":548.46,"body":"we want kids to own."},{"speaker":"Kim","startTime":548.82,"endTime":549.18,"body":"Yeah."},{"speaker":"Pam","startTime":549.54,"endTime":552.75,"body":"Because our goal is more"},{"speaker":"Pam","startTime":549.54,"endTime":552.75,"body":"than just those subtraction"},{"speaker":"Pam","startTime":552.75,"endTime":553.44,"body":"facts, right?"},{"speaker":"Kim","startTime":554.22,"endTime":554.25,"body":"Mmhmm."},{"speaker":"Pam","startTime":554.25,"endTime":556.98,"body":"Yeah, totally cool. So,"},{"speaker":"Pam","startTime":554.25,"endTime":556.98,"body":"another group of numbers that we"},{"speaker":"Pam","startTime":556.98,"endTime":560.04,"body":"might look at on a subtraction"},{"speaker":"Pam","startTime":556.98,"endTime":560.04,"body":"chart would be numbers that are"},{"speaker":"Pam","startTime":560.04,"endTime":562.65,"body":"close to each other. So, if I'm"},{"speaker":"Pam","startTime":560.04,"endTime":562.65,"body":"going to subtract something like"},{"speaker":"Pam","startTime":562.86,"endTime":569.55,"body":"9 minus 8, or 7 minus 6, or 3"},{"speaker":"Pam","startTime":562.86,"endTime":569.55,"body":"minus 2, that we can think about"},{"speaker":"Pam","startTime":569.55,"endTime":573.33,"body":"those, again, with a difference"},{"speaker":"Pam","startTime":569.55,"endTime":573.33,"body":"perspective. How far apart are"},{"speaker":"Pam","startTime":573.33,"endTime":575.19,"body":"they, if we're looking at"},{"speaker":"Pam","startTime":573.33,"endTime":575.19,"body":"subtraction as a difference?"},{"speaker":"Pam","startTime":575.46,"endTime":579.36,"body":"Well, if the numbers are always"},{"speaker":"Pam","startTime":575.46,"endTime":579.36,"body":"just 1 apart, then they're"},{"speaker":"Pam","startTime":579.36,"endTime":582.9,"body":"always just 1 apart. Like, you"},{"speaker":"Pam","startTime":579.36,"endTime":582.9,"body":"know, 9 minus 8 is going to be"},{"speaker":"Pam","startTime":582.9,"endTime":586.65,"body":"1. Like, 4 minus 3 is going to"},{"speaker":"Pam","startTime":582.9,"endTime":586.65,"body":"be 1 because they're just... All"},{"speaker":"Pam","startTime":586.65,"endTime":590.16,"body":"those numbers are 1 apart. What"},{"speaker":"Pam","startTime":586.65,"endTime":590.16,"body":"if there were 2 apart? So, if"},{"speaker":"Pam","startTime":590.16,"endTime":592.83,"body":"I'm looking at a subtraction"},{"speaker":"Pam","startTime":590.16,"endTime":592.83,"body":"fact, and the numbers are 2"},{"speaker":"Pam","startTime":592.83,"endTime":596.16,"body":"apart. Bam! Then, the answer to"},{"speaker":"Pam","startTime":592.83,"endTime":596.16,"body":"that subtraction problem is 2."},{"speaker":"Pam","startTime":596.19,"endTime":598.56,"body":"That would be another sort of"},{"speaker":"Pam","startTime":596.19,"endTime":598.56,"body":"group of numbers that are"},{"speaker":"Pam","startTime":598.56,"endTime":600.42,"body":"related that we kind of look at."},{"speaker":"Kim","startTime":601.02,"endTime":605.1,"body":"Yeah. So, I think once"},{"speaker":"Kim","startTime":601.02,"endTime":605.1,"body":"we've spent some time working"},{"speaker":"Kim","startTime":605.1,"endTime":609.33,"body":"with these strategies, I love"},{"speaker":"Kim","startTime":605.1,"endTime":609.33,"body":"the idea of putting up this"},{"speaker":"Kim","startTime":609.33,"endTime":612.45,"body":"chart and saying like, \"Talk to"},{"speaker":"Kim","startTime":609.33,"endTime":612.45,"body":"me. What do you notice?\" You"},{"speaker":"Kim","startTime":612.45,"endTime":615.75,"body":"know, I'm actually glancing at a"},{"speaker":"Kim","startTime":612.45,"endTime":615.75,"body":"subtraction chart right now. And"},{"speaker":"Kim","startTime":615.87,"endTime":621.15,"body":"there's one that I'm loving that"},{"speaker":"Kim","startTime":615.87,"endTime":621.15,"body":"pops out. That going diagonally"},{"speaker":"Kim","startTime":621.15,"endTime":625.98,"body":"down, on the triangular chart"},{"speaker":"Kim","startTime":621.15,"endTime":625.98,"body":"that I'm looking at, there's"},{"speaker":"Kim","startTime":626.01,"endTime":632.31,"body":"very clearly a 5 minus 3 is 2, 6"},{"speaker":"Kim","startTime":626.01,"endTime":632.31,"body":"minus 4 is 2, 7 minus 5 is 2."},{"speaker":"Kim","startTime":632.55,"endTime":636.39,"body":"Like, it's screaming, a little"},{"speaker":"Kim","startTime":632.55,"endTime":636.39,"body":"bit of constant difference to"},{"speaker":"Kim","startTime":636.39,"endTime":641.85,"body":"me. And how cool would that be,"},{"speaker":"Kim","startTime":636.39,"endTime":641.85,"body":"early, early, early, to just"},{"speaker":"Kim","startTime":641.88,"endTime":645.45,"body":"wonder like, \"Oh, my gosh. Why"},{"speaker":"Kim","startTime":641.88,"endTime":645.45,"body":"are those always 2? And the"},{"speaker":"Kim","startTime":645.45,"endTime":652.35,"body":"kids... I think, kids could say,"},{"speaker":"Kim","startTime":645.45,"endTime":652.35,"body":"\"Well, you're subtracting 1 more"},{"speaker":"Kim","startTime":652.35,"endTime":655.38,"body":"from 1 bigger of a number. That"},{"speaker":"Kim","startTime":652.35,"endTime":655.38,"body":"was poorly said, but."},{"speaker":"Pam","startTime":656.49,"endTime":658.2,"body":"That's interesting. Yeah,"},{"speaker":"Pam","startTime":656.49,"endTime":658.2,"body":"yeah."},{"speaker":"Kim","startTime":658.56,"endTime":658.89,"body":"Anyway."},{"speaker":"Pam","startTime":658.89,"endTime":659.85,"body":"Yeah, yeah."},{"speaker":"Kim","startTime":659.94,"endTime":660.63,"body":"(unclear) patterns that"},{"speaker":"Kim","startTime":659.94,"endTime":660.63,"body":"come out."},{"speaker":"Pam","startTime":660.63,"endTime":662.55,"body":"And those of you that are"},{"speaker":"Pam","startTime":660.63,"endTime":662.55,"body":"trying to teach constant"},{"speaker":"Pam","startTime":662.55,"endTime":665.67,"body":"difference later on, could pull"},{"speaker":"Pam","startTime":662.55,"endTime":665.67,"body":"up those. You know like, \"Hey,"},{"speaker":"Pam","startTime":665.7,"endTime":670.35,"body":"look at all this diagonal. All"},{"speaker":"Pam","startTime":665.7,"endTime":670.35,"body":"the answers are 5. So, are you"},{"speaker":"Pam","startTime":670.35,"endTime":673.62,"body":"saying that 12 minus 7 is"},{"speaker":"Pam","startTime":670.35,"endTime":673.62,"body":"equivalent to 13 minus 8, is"},{"speaker":"Pam","startTime":673.62,"endTime":677.52,"body":"equivalent to 14 minus 9, is"},{"speaker":"Pam","startTime":673.62,"endTime":677.52,"body":"equivalent to 15 minus 10? Huh.\""},{"speaker":"Pam","startTime":677.52,"endTime":679.92,"body":"And so, yeah, we're kind of"},{"speaker":"Pam","startTime":677.52,"endTime":679.92,"body":"nudging this idea that we can"},{"speaker":"Pam","startTime":679.92,"endTime":682.44,"body":"think of equivalent subtraction"},{"speaker":"Pam","startTime":679.92,"endTime":682.44,"body":"problems. That's nice."},{"speaker":"Kim","startTime":682.47,"endTime":682.71,"body":"Yep."},{"speaker":"Pam","startTime":682.74,"endTime":683.7,"body":"Yeah, super cool."},{"speaker":"Kim","startTime":684.0,"endTime":689.16,"body":"But, of course, our very"},{"speaker":"Kim","startTime":684.0,"endTime":689.16,"body":"favorite thing to do to work"},{"speaker":"Kim","startTime":689.16,"endTime":693.15,"body":"with basic facts or any"},{"speaker":"Kim","startTime":689.16,"endTime":693.15,"body":"mathematics are Problem Strings,"},{"speaker":"Kim","startTime":693.18,"endTime":698.88,"body":"right? (unclear). They build"},{"speaker":"Kim","startTime":693.18,"endTime":698.88,"body":"relationships. And so, we"},{"speaker":"Kim","startTime":698.88,"endTime":701.79,"body":"thought we would do a little bit"},{"speaker":"Kim","startTime":698.88,"endTime":701.79,"body":"with some Problem Strings today."},{"speaker":"Kim","startTime":701.88,"endTime":703.47,"body":"I'm going to give you numbers"},{"speaker":"Kim","startTime":701.88,"endTime":703.47,"body":"this time, Pam."},{"speaker":"Pam","startTime":703.77,"endTime":704.67,"body":"Okay. Bring it on."},{"speaker":"Kim","startTime":704.67,"endTime":705.54,"body":"I'm always in the hot seat."},{"speaker":"Pam","startTime":705.78,"endTime":706.5,"body":"Alright, I got a pen in my"},{"speaker":"Pam","startTime":705.78,"endTime":706.5,"body":"hand."},{"speaker":"Kim","startTime":706.71,"endTime":708.18,"body":"Okay. Alright get a piece"},{"speaker":"Kim","startTime":706.71,"endTime":708.18,"body":"of paper."},{"speaker":"Pam","startTime":711.09,"endTime":712.44,"body":"This one's kind of a gnarly"},{"speaker":"Pam","startTime":711.09,"endTime":712.44,"body":"pen."},{"speaker":"Pam","startTime":712.44,"endTime":714.36,"body":"It actually leaks a little bit."},{"speaker":"Pam","startTime":712.44,"endTime":714.36,"body":"It's not my favorite."},{"speaker":"Kim","startTime":715.14,"endTime":717.24,"body":"Which is exactly why you"},{"speaker":"Kim","startTime":715.14,"endTime":717.24,"body":"shouldn't use pens."},{"speaker":"Pam","startTime":719.19,"endTime":720.42,"body":"But it's nice and bold."},{"speaker":"Pam","startTime":721.5,"endTime":722.04,"body":"Alright, carry on."},{"speaker":"Kim","startTime":722.04,"endTime":724.56,"body":"Write harder. Okay, here we"},{"speaker":"Kim","startTime":722.04,"endTime":724.56,"body":"go. First problem."},{"speaker":"Pam","startTime":724.56,"endTime":726.87,"body":"[Pam laughs] Write harder."},{"speaker":"Pam","startTime":724.56,"endTime":726.87,"body":"I like it. Okay, first problem."},{"speaker":"Kim","startTime":727.23,"endTime":730.08,"body":"Alright, 13 minus 3."},{"speaker":"Pam","startTime":730.53,"endTime":733.92,"body":"Okay, so if I was going to"},{"speaker":"Pam","startTime":730.53,"endTime":733.92,"body":"do this Problem String with"},{"speaker":"Pam","startTime":733.92,"endTime":737.55,"body":"kids. Because let's be clear, I"},{"speaker":"Pam","startTime":733.92,"endTime":737.55,"body":"don't really have to think about"},{"speaker":"Pam","startTime":737.55,"endTime":741.06,"body":"these problems very much. Okay."},{"speaker":"Pam","startTime":737.55,"endTime":741.06,"body":"Then, I would expect students,"},{"speaker":"Pam","startTime":741.24,"endTime":743.1,"body":"if I'm doing this Problem"},{"speaker":"Pam","startTime":741.24,"endTime":743.1,"body":"String, that I would probably"},{"speaker":"Pam","startTime":743.1,"endTime":747.57,"body":"have a range of development in"},{"speaker":"Pam","startTime":743.1,"endTime":747.57,"body":"the classroom, and I might have"},{"speaker":"Pam","startTime":747.57,"endTime":751.74,"body":"some students going, \"13, 12,"},{"speaker":"Pam","startTime":747.57,"endTime":751.74,"body":"11, 10.\" Like, they might be"},{"speaker":"Pam","startTime":751.74,"endTime":755.22,"body":"counting back by ones. And we're"},{"speaker":"Pam","startTime":751.74,"endTime":755.22,"body":"expecting some 10's. I might"},{"speaker":"Pam","startTime":755.22,"endTime":758.79,"body":"have some kids thinking about"},{"speaker":"Pam","startTime":755.22,"endTime":758.79,"body":"the fact that it's 10 and 3. Or,"},{"speaker":"Pam","startTime":758.85,"endTime":761.7,"body":"you know, the meaning of the"},{"speaker":"Pam","startTime":758.85,"endTime":761.7,"body":"teen. If I sort of get rid of"},{"speaker":"Pam","startTime":761.7,"endTime":766.92,"body":"the 3 and 13 in 3 teen, then I'm"},{"speaker":"Pam","startTime":761.7,"endTime":766.92,"body":"left with the 10 leftover. But"},{"speaker":"Pam","startTime":766.92,"endTime":769.62,"body":"as a teacher, I would kind of"},{"speaker":"Pam","startTime":766.92,"endTime":769.62,"body":"establish that, and then I"},{"speaker":"Pam","startTime":769.62,"endTime":773.61,"body":"would. Kim, am I on a number"},{"speaker":"Pam","startTime":769.62,"endTime":773.61,"body":"rack or am I on a number line?"},{"speaker":"Pam","startTime":776.34,"endTime":780.24,"body":"Let's do both. If I was on a"},{"speaker":"Pam","startTime":776.34,"endTime":780.24,"body":"number rack, I'm going to assume"},{"speaker":"Pam","startTime":780.24,"endTime":784.47,"body":"that if I'm doing this Problem"},{"speaker":"Pam","startTime":780.24,"endTime":784.47,"body":"String, kids have done work on a"},{"speaker":"Pam","startTime":784.47,"endTime":786.69,"body":"number rack, so this is not"},{"speaker":"Pam","startTime":784.47,"endTime":786.69,"body":"their first shot at a number"},{"speaker":"Pam","startTime":786.69,"endTime":789.24,"body":"rack. So, I'm going to say, \"How"},{"speaker":"Pam","startTime":786.69,"endTime":789.24,"body":"are you thinking about that?\""},{"speaker":"Pam","startTime":789.24,"endTime":793.92,"body":"And when a kid says, \"Well, I"},{"speaker":"Pam","startTime":789.24,"endTime":793.92,"body":"removed 3 from 13,\" Then, I'm"},{"speaker":"Pam","startTime":793.92,"endTime":797.76,"body":"going to show 13 by 10 on the"},{"speaker":"Pam","startTime":793.92,"endTime":797.76,"body":"top and 3 on the bottom, and I'm"},{"speaker":"Pam","startTime":797.76,"endTime":799.89,"body":"going to say, \"Oh, you just you"},{"speaker":"Pam","startTime":797.76,"endTime":799.89,"body":"got rid of that 3.\" And I'll"},{"speaker":"Pam","startTime":799.89,"endTime":803.25,"body":"move the 3 on the bottom back"},{"speaker":"Pam","startTime":799.89,"endTime":803.25,"body":"over to the other side. And I'm"},{"speaker":"Pam","startTime":803.25,"endTime":806.16,"body":"just left with 10 beads. If I"},{"speaker":"Pam","startTime":803.25,"endTime":806.16,"body":"was on a number line. So, it"},{"speaker":"Pam","startTime":806.16,"endTime":808.32,"body":"just depends on what my kids"},{"speaker":"Pam","startTime":806.16,"endTime":808.32,"body":"have had more experience with."},{"speaker":"Pam","startTime":808.32,"endTime":810.36,"body":"If they had any experience with"},{"speaker":"Pam","startTime":808.32,"endTime":810.36,"body":"the number rack, I'll probably"},{"speaker":"Pam","startTime":810.36,"endTime":813.24,"body":"do it on a number rack. If they"},{"speaker":"Pam","startTime":810.36,"endTime":813.24,"body":"are ready to think about things"},{"speaker":"Pam","startTime":813.24,"endTime":815.91,"body":"on a number line, then I would"},{"speaker":"Pam","startTime":813.24,"endTime":815.91,"body":"say, \"Oh, so you're saying"},{"speaker":"Pam","startTime":815.94,"endTime":819.15,"body":"13...\" And I would literally"},{"speaker":"Pam","startTime":815.94,"endTime":819.15,"body":"draw a number line, put a 13 on"},{"speaker":"Pam","startTime":819.15,"endTime":823.23,"body":"the right hand side. I would"},{"speaker":"Pam","startTime":819.15,"endTime":823.23,"body":"jump back one jump of 3, and I"},{"speaker":"Pam","startTime":823.23,"endTime":823.98,"body":"would land on 10."},{"speaker":"Kim","startTime":824.49,"endTime":825.24,"body":"Yep. Cool."},{"speaker":"Pam","startTime":825.24,"endTime":828.09,"body":"And that's it. Wouldn't"},{"speaker":"Pam","startTime":825.24,"endTime":828.09,"body":"spend a lot of time here. I"},{"speaker":"Pam","startTime":828.09,"endTime":831.0,"body":"would also, if I'm doing this"},{"speaker":"Pam","startTime":828.09,"endTime":831.0,"body":"problem, probably not have a kid"},{"speaker":"Pam","startTime":831.18,"endTime":834.84,"body":"talk a lot about the fact that"},{"speaker":"Pam","startTime":831.18,"endTime":834.84,"body":"they just removed 1 at a time. I"},{"speaker":"Pam","startTime":834.84,"endTime":836.04,"body":"would just, you know... Yeah."},{"speaker":"Pam","startTime":836.07,"endTime":836.61,"body":"Okay, go ahead."},{"speaker":"Kim","startTime":836.73,"endTime":838.41,"body":"Yep. That's not going to be"},{"speaker":"Kim","startTime":836.73,"endTime":838.41,"body":"something you're modeling at"},{"speaker":"Kim","startTime":838.41,"endTime":838.89,"body":"this point?"},{"speaker":"Pam","startTime":839.07,"endTime":840.6,"body":"No, not if I'm doing this"},{"speaker":"Pam","startTime":839.07,"endTime":840.6,"body":"whole string."},{"speaker":"Kim","startTime":840.99,"endTime":844.89,"body":"Yep. Okay. So, the next"},{"speaker":"Kim","startTime":840.99,"endTime":844.89,"body":"problem is 13 minus 5. What"},{"speaker":"Kim","startTime":844.89,"endTime":848.16,"body":"would you expect to hear and"},{"speaker":"Kim","startTime":844.89,"endTime":848.16,"body":"model for 13 minus 5?"},{"speaker":"Pam","startTime":848.55,"endTime":852.39,"body":"Yeah. So, I might at this"},{"speaker":"Pam","startTime":848.55,"endTime":852.39,"body":"point, say, \"I wonder if the"},{"speaker":"Pam","startTime":852.39,"endTime":855.27,"body":"first problem could help? Maybe?"},{"speaker":"Pam","startTime":852.39,"endTime":855.27,"body":"I don't know if...\" You know, I"},{"speaker":"Pam","startTime":855.3,"endTime":857.25,"body":"almost don't finish my sentence"},{"speaker":"Pam","startTime":855.3,"endTime":857.25,"body":"a little bit. \"I wonder if it"},{"speaker":"Pam","startTime":857.25,"endTime":861.33,"body":"could help you... Maybe? Go"},{"speaker":"Pam","startTime":857.25,"endTime":861.33,"body":"ahead. Use any any strategy you"},{"speaker":"Pam","startTime":861.33,"endTime":865.26,"body":"want.\" And then, I would let"},{"speaker":"Pam","startTime":861.33,"endTime":865.26,"body":"kids think and figure. I would"},{"speaker":"Pam","startTime":865.26,"endTime":868.98,"body":"watch to see who's counting by"},{"speaker":"Pam","startTime":865.26,"endTime":868.98,"body":"ones. I take note of that. And"},{"speaker":"Pam","startTime":868.98,"endTime":873.12,"body":"then, I might say, \"Hey, did"},{"speaker":"Pam","startTime":868.98,"endTime":873.12,"body":"anybody use 13 minus 3 to help"},{"speaker":"Pam","startTime":873.12,"endTime":876.0,"body":"you with 13 minus 5?\" And now,"},{"speaker":"Pam","startTime":873.12,"endTime":876.0,"body":"I'm looking for kids that. And"},{"speaker":"Pam","startTime":876.0,"endTime":878.76,"body":"then, I'll call on the kid who"},{"speaker":"Pam","startTime":876.0,"endTime":878.76,"body":"says. Now, it's still a little"},{"speaker":"Pam","startTime":878.76,"endTime":882.09,"body":"bit of a maybe. Maybe they did."},{"speaker":"Pam","startTime":878.76,"endTime":882.09,"body":"Maybe they didn't. You're never"},{"speaker":"Pam","startTime":882.09,"endTime":885.54,"body":"quite sure with this age of"},{"speaker":"Pam","startTime":882.09,"endTime":885.54,"body":"kids. But I would try to pull"},{"speaker":"Pam","startTime":885.54,"endTime":888.42,"body":"out of a kid, somebody that"},{"speaker":"Pam","startTime":885.54,"endTime":888.42,"body":"said, \"Well, if we know 13 minus"},{"speaker":"Pam","startTime":888.42,"endTime":892.71,"body":"3 is 10...\" And I would redraw"},{"speaker":"Pam","startTime":888.42,"endTime":892.71,"body":"that number line or I would"},{"speaker":"Pam","startTime":893.25,"endTime":896.64,"body":"re-put up the 10 beads and the 3"},{"speaker":"Pam","startTime":893.25,"endTime":896.64,"body":"beads. And I would say, \"So, we"},{"speaker":"Pam","startTime":896.64,"endTime":900.6,"body":"have 13. If I know 13 minus 3 is"},{"speaker":"Pam","startTime":896.64,"endTime":900.6,"body":"10...\" Move the 3 beads over,"},{"speaker":"Pam","startTime":900.96,"endTime":903.51,"body":"jump back the 3 on the number"},{"speaker":"Pam","startTime":900.96,"endTime":903.51,"body":"line, \"...then I can think about"},{"speaker":"Pam","startTime":903.51,"endTime":907.65,"body":"13 minus 5 as 2 more than that.\""},{"speaker":"Pam","startTime":903.51,"endTime":907.65,"body":"So, if I'm on the number rack,"},{"speaker":"Pam","startTime":907.65,"endTime":912.21,"body":"I'd move 2 more beads on the top"},{"speaker":"Pam","startTime":907.65,"endTime":912.21,"body":"over, so I'm left with 8. I can"},{"speaker":"Pam","startTime":912.33,"endTime":916.44,"body":"clearly see those 5 beads and"},{"speaker":"Pam","startTime":912.33,"endTime":916.44,"body":"those 3 beads. Or I would remove"},{"speaker":"Pam","startTime":916.47,"endTime":919.89,"body":"2, jump back a jump of 2 on the"},{"speaker":"Pam","startTime":916.47,"endTime":919.89,"body":"number line. And I would say,"},{"speaker":"Pam","startTime":919.89,"endTime":922.59,"body":"\"Well, what is 2 back from 10?"},{"speaker":"Pam","startTime":919.89,"endTime":922.59,"body":"Oh, that's 8. And so that's how"},{"speaker":"Pam","startTime":922.59,"endTime":924.63,"body":"you guys are getting your 8."},{"speaker":"Pam","startTime":922.59,"endTime":924.63,"body":"Does that make sense to"},{"speaker":"Pam","startTime":924.63,"endTime":927.75,"body":"everybody that we could subtract"},{"speaker":"Pam","startTime":924.63,"endTime":927.75,"body":"the 3 to get to 10, and then"},{"speaker":"Pam","startTime":927.75,"endTime":929.58,"body":"just subtract what's left over"},{"speaker":"Pam","startTime":927.75,"endTime":929.58,"body":"the extra 2?\""},{"speaker":"Kim","startTime":929.94,"endTime":930.18,"body":"Yeah."},{"speaker":"Pam","startTime":930.18,"endTime":930.27,"body":"Cool."},{"speaker":"Kim","startTime":930.27,"endTime":932.04,"body":"Relating those two problems"},{"speaker":"Kim","startTime":930.27,"endTime":932.04,"body":"for sure."},{"speaker":"Pam","startTime":932.04,"endTime":932.34,"body":"Exactly, yeah."},{"speaker":"Kim","startTime":932.34,"endTime":934.74,"body":"What about 17 minus 7?"},{"speaker":"Pam","startTime":935.73,"endTime":937.56,"body":"Again, I'm going to kind of"},{"speaker":"Pam","startTime":935.73,"endTime":937.56,"body":"watch. I'm not spend a lot of"},{"speaker":"Pam","startTime":937.56,"endTime":941.64,"body":"time here. Hopefully, kids are"},{"speaker":"Pam","startTime":937.56,"endTime":941.64,"body":"using the meaning of the teen. I"},{"speaker":"Pam","startTime":941.64,"endTime":943.86,"body":"think I might stick with the"},{"speaker":"Pam","startTime":941.64,"endTime":943.86,"body":"number line from here on out as"},{"speaker":"Pam","startTime":943.86,"endTime":947.16,"body":"I describe it, but it'll be"},{"speaker":"Pam","startTime":943.86,"endTime":947.16,"body":"similar. I'll start on 17. I'll"},{"speaker":"Pam","startTime":947.19,"endTime":951.96,"body":"have some kids suggest that I've"},{"speaker":"Pam","startTime":947.19,"endTime":951.96,"body":"subtracted 7 to get to 10, and"},{"speaker":"Pam","startTime":951.96,"endTime":956.64,"body":"land on the 10. If I may, my"},{"speaker":"Pam","startTime":951.96,"endTime":956.64,"body":"board this point, I've just..."},{"speaker":"Pam","startTime":956.67,"endTime":959.94,"body":"I'm actually drawing as I'm"},{"speaker":"Pam","startTime":956.67,"endTime":959.94,"body":"talking here. That number line"},{"speaker":"Pam","startTime":959.94,"endTime":965.64,"body":"that has the 13 is at a certain"},{"speaker":"Pam","startTime":959.94,"endTime":965.64,"body":"point... How do I say this. Left"},{"speaker":"Pam","startTime":965.64,"endTime":971.25,"body":"and right. And the 17 is about 4"},{"speaker":"Pam","startTime":965.64,"endTime":971.25,"body":"to the right of that on the new"},{"speaker":"Pam","startTime":971.25,"endTime":974.4,"body":"number line. So, when I've drawn"},{"speaker":"Pam","startTime":971.25,"endTime":974.4,"body":"that new number line, I didn't"},{"speaker":"Pam","startTime":974.4,"endTime":977.25,"body":"start the 17 in the same place"},{"speaker":"Pam","startTime":974.4,"endTime":977.25,"body":"that I had started the 13. I've"},{"speaker":"Pam","startTime":977.25,"endTime":981.51,"body":"scootched it over to the right"},{"speaker":"Pam","startTime":977.25,"endTime":981.51,"body":"about 4. And my jump of 7,"},{"speaker":"Pam","startTime":981.72,"endTime":986.67,"body":"landed in the same location as"},{"speaker":"Pam","startTime":981.72,"endTime":986.67,"body":"the 10's were in the top two"},{"speaker":"Pam","startTime":986.67,"endTime":990.27,"body":"number lines. So, I've kept..."},{"speaker":"Pam","startTime":986.67,"endTime":990.27,"body":"Not vertically. Yeah,"},{"speaker":"Pam","startTime":990.27,"endTime":992.76,"body":"vertically. I've kept vertically"},{"speaker":"Pam","startTime":990.27,"endTime":992.76,"body":"aligned... Horizontally aligned?"},{"speaker":"Pam","startTime":992.76,"endTime":995.43,"body":"I don't know how to say that."},{"speaker":"Pam","startTime":992.76,"endTime":995.43,"body":"The tick marks for the 10 are in"},{"speaker":"Pam","startTime":995.43,"endTime":1000.56,"body":"the same horizontal position."},{"speaker":"Pam","startTime":995.43,"endTime":1000.56,"body":"Cut left to right, go in those."},{"speaker":"Pam","startTime":1000.59,"endTime":1002.42,"body":"Now, I have three number lines,"},{"speaker":"Pam","startTime":1000.59,"endTime":1002.42,"body":"right, because I have the number"},{"speaker":"Pam","startTime":1002.42,"endTime":1005.12,"body":"line for the 13 minus 3, the 13"},{"speaker":"Pam","startTime":1002.42,"endTime":1005.12,"body":"minus 5, and the number line for"},{"speaker":"Pam","startTime":1005.12,"endTime":1008.3,"body":"the 17 minus 7. I've landed on"},{"speaker":"Pam","startTime":1005.12,"endTime":1008.3,"body":"the 10 in the same spot. So,"},{"speaker":"Pam","startTime":1008.3,"endTime":1011.99,"body":"I've backed up 7 from that 17"},{"speaker":"Pam","startTime":1008.3,"endTime":1011.99,"body":"that's further to the right. I"},{"speaker":"Pam","startTime":1011.99,"endTime":1014.33,"body":"know that was. It's hard to"},{"speaker":"Pam","startTime":1011.99,"endTime":1014.33,"body":"describe. But that's what it"},{"speaker":"Pam","startTime":1014.33,"endTime":1014.84,"body":"looks like. Okay."},{"speaker":"Kim","startTime":1014.84,"endTime":1016.13,"body":"Yep. Hey, I'm"},{"speaker":"Kim","startTime":1016.13,"endTime":1018.08,"body":"going to derail us for just a"},{"speaker":"Kim","startTime":1016.13,"endTime":1018.08,"body":"second."},{"speaker":"Pam","startTime":1018.11,"endTime":1018.38,"body":"Yeah."},{"speaker":"Kim","startTime":1018.38,"endTime":1023.36,"body":"Because I've heard people"},{"speaker":"Kim","startTime":1018.38,"endTime":1023.36,"body":"say. In fact, people have asked"},{"speaker":"Kim","startTime":1023.39,"endTime":1026.51,"body":"like, \"When kids are"},{"speaker":"Kim","startTime":1023.39,"endTime":1026.51,"body":"representing their thinking, Do"},{"speaker":"Kim","startTime":1026.51,"endTime":1030.89,"body":"you require these specific"},{"speaker":"Kim","startTime":1026.51,"endTime":1030.89,"body":"directions about, like, how far"},{"speaker":"Kim","startTime":1030.89,"endTime":1034.52,"body":"and and does it need to"},{"speaker":"Kim","startTime":1030.89,"endTime":1034.52,"body":"perfectly line up?\" Or teachers"},{"speaker":"Kim","startTime":1034.52,"endTime":1039.41,"body":"will say, \"You know, I struggle,"},{"speaker":"Kim","startTime":1034.52,"endTime":1039.41,"body":"and I try.\" But I think maybe"},{"speaker":"Kim","startTime":1039.41,"endTime":1042.56,"body":"your point is that you're giving"},{"speaker":"Kim","startTime":1039.41,"endTime":1042.56,"body":"it a good go. It's not going to"},{"speaker":"Kim","startTime":1042.56,"endTime":1046.01,"body":"be perfectly proportional every"},{"speaker":"Kim","startTime":1042.56,"endTime":1046.01,"body":"single time, particularly if"},{"speaker":"Kim","startTime":1046.01,"endTime":1049.19,"body":"we're talking about kids, but"},{"speaker":"Kim","startTime":1046.01,"endTime":1049.19,"body":"the 17 should be the right of"},{"speaker":"Kim","startTime":1049.19,"endTime":1053.48,"body":"the 13, which should be... And"},{"speaker":"Kim","startTime":1049.19,"endTime":1053.48,"body":"the 10 should be to the left of"},{"speaker":"Kim","startTime":1053.48,"endTime":1057.38,"body":"the 13, and the 10s should line"},{"speaker":"Kim","startTime":1053.48,"endTime":1057.38,"body":"up together. (unclear)."},{"speaker":"Pam","startTime":1057.38,"endTime":1061.79,"body":"(unclear). Absolutely. And"},{"speaker":"Pam","startTime":1057.38,"endTime":1061.79,"body":"that's only true for the"},{"speaker":"Pam","startTime":1061.79,"endTime":1062.36,"body":"teacher."},{"speaker":"Kim","startTime":1062.57,"endTime":1062.75,"body":"Yeah."},{"speaker":"Pam","startTime":1062.75,"endTime":1064.82,"body":"I think the student doesn't"},{"speaker":"Pam","startTime":1062.75,"endTime":1064.82,"body":"need to be thinking about that"},{"speaker":"Pam","startTime":1064.85,"endTime":1067.97,"body":"at all. The student is just"},{"speaker":"Pam","startTime":1064.85,"endTime":1067.97,"body":"using relationships. Now, if the"},{"speaker":"Pam","startTime":1067.97,"endTime":1071.48,"body":"student wants to draw a number"},{"speaker":"Pam","startTime":1067.97,"endTime":1071.48,"body":"line to jump to be able to keep"},{"speaker":"Pam","startTime":1071.48,"endTime":1074.84,"body":"track of their thinking,"},{"speaker":"Pam","startTime":1071.48,"endTime":1074.84,"body":"absolutely. But in that case,"},{"speaker":"Pam","startTime":1074.87,"endTime":1078.74,"body":"I'm not judging that kid's"},{"speaker":"Pam","startTime":1074.87,"endTime":1078.74,"body":"proportional jumps or where they"},{"speaker":"Pam","startTime":1078.74,"endTime":1081.83,"body":"land at all because they're"},{"speaker":"Pam","startTime":1078.74,"endTime":1081.83,"body":"using it to help them think."},{"speaker":"Pam","startTime":1082.01,"endTime":1085.85,"body":"Now, I might look at what they"},{"speaker":"Pam","startTime":1082.01,"endTime":1085.85,"body":"did and help them find an error"},{"speaker":"Pam","startTime":1086.0,"endTime":1089.78,"body":"if they made a jump and, you"},{"speaker":"Pam","startTime":1086.0,"endTime":1089.78,"body":"know like, they subtracted 3 and"},{"speaker":"Pam","startTime":1089.78,"endTime":1092.48,"body":"they got to... I don't even"},{"speaker":"Pam","startTime":1089.78,"endTime":1092.48,"body":"know. And then, were like, \"Hey,"},{"speaker":"Pam","startTime":1092.48,"endTime":1095.96,"body":"what do you know? What 14 minus"},{"speaker":"Pam","startTime":1092.48,"endTime":1095.96,"body":"3 is?\" Oh, yeah. That's 11, not"},{"speaker":"Pam","startTime":1095.96,"endTime":1099.05,"body":"10.\" Or, you know, whatever."},{"speaker":"Pam","startTime":1095.96,"endTime":1099.05,"body":"Like, that recording their"},{"speaker":"Pam","startTime":1099.05,"endTime":1102.29,"body":"thinking might be helpful. But"},{"speaker":"Pam","startTime":1099.05,"endTime":1102.29,"body":"no. So, yeah, good point. It's"},{"speaker":"Pam","startTime":1102.29,"endTime":1106.43,"body":"not about a perfect"},{"speaker":"Pam","startTime":1102.29,"endTime":1106.43,"body":"representation. It is about when"},{"speaker":"Pam","startTime":1106.43,"endTime":1110.3,"body":"the teacher is modeling student"},{"speaker":"Pam","startTime":1106.43,"endTime":1110.3,"body":"thinking, trying to get just as"},{"speaker":"Pam","startTime":1110.3,"endTime":1113.87,"body":"good as you can, so that the"},{"speaker":"Pam","startTime":1110.3,"endTime":1113.87,"body":"relationships pop a little bit"},{"speaker":"Pam","startTime":1114.23,"endTime":1117.32,"body":"more for students. If the"},{"speaker":"Pam","startTime":1114.23,"endTime":1117.32,"body":"relationships are up, they're"},{"speaker":"Pam","startTime":1117.32,"endTime":1122.18,"body":"lined up, the potential for the"},{"speaker":"Pam","startTime":1117.32,"endTime":1122.18,"body":"relationships to pop, so that"},{"speaker":"Pam","startTime":1122.18,"endTime":1124.88,"body":"kids can develop that number"},{"speaker":"Pam","startTime":1122.18,"endTime":1124.88,"body":"line in their head is a little"},{"speaker":"Pam","startTime":1124.88,"endTime":1125.57,"body":"bit stronger."},{"speaker":"Kim","startTime":1125.96,"endTime":1126.56,"body":"Cool."},{"speaker":"Pam","startTime":1126.62,"endTime":1126.92,"body":"Yeah."},{"speaker":"Kim","startTime":1126.95,"endTime":1130.94,"body":"Okay. Back on track. Sorry."},{"speaker":"Kim","startTime":1126.95,"endTime":1130.94,"body":"We did 13 minus 3. We did 13"},{"speaker":"Kim","startTime":1130.94,"endTime":1135.86,"body":"minus 5. We just did 17 minus 7."},{"speaker":"Kim","startTime":1130.94,"endTime":1135.86,"body":"So, let's talk about 17 minus 8."},{"speaker":"Pam","startTime":1136.19,"endTime":1139.22,"body":"Cool. So, I'm going to,"},{"speaker":"Pam","startTime":1136.19,"endTime":1139.22,"body":"again, ask students, \"Did"},{"speaker":"Pam","startTime":1139.22,"endTime":1143.42,"body":"anybody think about using 17"},{"speaker":"Pam","startTime":1139.22,"endTime":1143.42,"body":"minus 7 to help you get 17 minus"},{"speaker":"Pam","startTime":1143.42,"endTime":1145.67,"body":"8,\" and I'm going to look for a"},{"speaker":"Pam","startTime":1143.42,"endTime":1145.67,"body":"kid that does that. I'm going to"},{"speaker":"Pam","startTime":1145.67,"endTime":1149.18,"body":"redraw the number line for 17"},{"speaker":"Pam","startTime":1145.67,"endTime":1149.18,"body":"minus 7 because the kid's going"},{"speaker":"Pam","startTime":1149.18,"endTime":1152.12,"body":"to say, \"Yeah, because we knew"},{"speaker":"Pam","startTime":1149.18,"endTime":1152.12,"body":"17 minus 7 was 10.\" I redraw"},{"speaker":"Pam","startTime":1152.12,"endTime":1154.7,"body":"that, and now it looks exactly"},{"speaker":"Pam","startTime":1152.12,"endTime":1154.7,"body":"like the one above it. And then,"},{"speaker":"Pam","startTime":1154.7,"endTime":1156.92,"body":"they're going to say, \"But we"},{"speaker":"Pam","startTime":1154.7,"endTime":1156.92,"body":"need to subtract 1 more.\" So,"},{"speaker":"Pam","startTime":1156.92,"endTime":1161.93,"body":"I'll make a jump of 1 after that"},{"speaker":"Pam","startTime":1156.92,"endTime":1161.93,"body":"and land on 9. So, 17 minus 8 is"},{"speaker":"Pam","startTime":1161.93,"endTime":1167.12,"body":"9. And now, I have four number"},{"speaker":"Pam","startTime":1161.93,"endTime":1167.12,"body":"lines on the board, and they've"},{"speaker":"Pam","startTime":1167.12,"endTime":1170.0,"body":"been sort of using the partner"},{"speaker":"Pam","startTime":1167.12,"endTime":1170.0,"body":"problem to help them with the"},{"speaker":"Pam","startTime":1170.09,"endTime":1171.53,"body":"second problem in the set."},{"speaker":"Kim","startTime":1171.95,"endTime":1175.52,"body":"Yeah. And I'm guessing, I'm"},{"speaker":"Kim","startTime":1171.95,"endTime":1175.52,"body":"betting that at some point,"},{"speaker":"Kim","startTime":1175.52,"endTime":1177.83,"body":"you're standing back, and you're"},{"speaker":"Kim","startTime":1175.52,"endTime":1177.83,"body":"like, \"Hmm, that's interesting.\""},{"speaker":"Kim","startTime":1178.19,"endTime":1183.08,"body":"And you're starting to maybe"},{"speaker":"Kim","startTime":1178.19,"endTime":1183.08,"body":"ask, or wonder, or put some"},{"speaker":"Kim","startTime":1183.08,"endTime":1186.29,"body":"words towards like, \"I wonder"},{"speaker":"Kim","startTime":1183.08,"endTime":1186.29,"body":"what's going on here.\""},{"speaker":"Pam","startTime":1186.59,"endTime":1190.04,"body":"Yeah. Yeah, I might."},{"speaker":"Pam","startTime":1186.59,"endTime":1190.04,"body":"Knowing my kids, I might ask"},{"speaker":"Pam","startTime":1190.04,"endTime":1194.78,"body":"somebody like, \"Does anybody see"},{"speaker":"Pam","startTime":1190.04,"endTime":1194.78,"body":"a similarity about how"},{"speaker":"Pam","startTime":1195.02,"endTime":1198.5,"body":"so-and-so? Like Kim, used the 13"},{"speaker":"Pam","startTime":1195.02,"endTime":1198.5,"body":"minus 3 to help get 13 to minus"},{"speaker":"Pam","startTime":1198.5,"endTime":1202.28,"body":"5. And Aaron used 17 minus 7 to"},{"speaker":"Pam","startTime":1198.5,"endTime":1202.28,"body":"help him get 17 minus 8. Was"},{"speaker":"Pam","startTime":1202.28,"endTime":1204.77,"body":"there something similar about"},{"speaker":"Pam","startTime":1202.28,"endTime":1204.77,"body":"how they did that?\" And I might"},{"speaker":"Pam","startTime":1204.77,"endTime":1208.25,"body":"try to pull some words out of"},{"speaker":"Pam","startTime":1204.77,"endTime":1208.25,"body":"kids. I might also say, \"Huh,"},{"speaker":"Pam","startTime":1208.28,"endTime":1214.04,"body":"that's interesting that a lot of"},{"speaker":"Pam","startTime":1208.28,"endTime":1214.04,"body":"you got to the 10 first, and"},{"speaker":"Pam","startTime":1214.04,"endTime":1216.62,"body":"then just kind of subtracted the"},{"speaker":"Pam","startTime":1214.04,"endTime":1216.62,"body":"extra. Huh.\" I might just"},{"speaker":"Pam","startTime":1216.65,"endTime":1218.96,"body":"mention that, and then move on."},{"speaker":"Pam","startTime":1216.65,"endTime":1218.96,"body":"Yeah,"},{"speaker":"Kim","startTime":1218.99,"endTime":1221.63,"body":"Yeah, because in all four"},{"speaker":"Kim","startTime":1218.99,"endTime":1221.63,"body":"number lines, they'd all be"},{"speaker":"Kim","startTime":1221.63,"endTime":1224.48,"body":"lined up together, where there's"},{"speaker":"Kim","startTime":1221.63,"endTime":1224.48,"body":"a 10 on every single one of"},{"speaker":"Kim","startTime":1224.48,"endTime":1226.64,"body":"those number lines. I think that"},{"speaker":"Kim","startTime":1224.48,"endTime":1226.64,"body":"would really pop for your"},{"speaker":"Kim","startTime":1226.64,"endTime":1229.49,"body":"students. Alright, next problem."},{"speaker":"Kim","startTime":1226.64,"endTime":1229.49,"body":"15 minus 5."},{"speaker":"Pam","startTime":1230.48,"endTime":1233.27,"body":"Cool. I probably won't wait"},{"speaker":"Pam","startTime":1230.48,"endTime":1233.27,"body":"as long on this one. I'm"},{"speaker":"Pam","startTime":1233.27,"endTime":1237.32,"body":"watching kids. In fact, maybe I"},{"speaker":"Pam","startTime":1233.27,"endTime":1237.32,"body":"should say. If I saw a lot of"},{"speaker":"Pam","startTime":1237.32,"endTime":1241.34,"body":"kids counting by ones to get"},{"speaker":"Pam","startTime":1237.32,"endTime":1241.34,"body":"from the 13 minus 3 to 10, and"},{"speaker":"Pam","startTime":1241.34,"endTime":1245.06,"body":"the 17 minus 7 to 10, I might"},{"speaker":"Pam","startTime":1241.34,"endTime":1245.06,"body":"have also put... In fact, I"},{"speaker":"Pam","startTime":1245.06,"endTime":1249.02,"body":"might have put more emphasis on"},{"speaker":"Pam","startTime":1245.06,"endTime":1249.02,"body":"this generalization than the one"},{"speaker":"Pam","startTime":1249.02,"endTime":1250.01,"body":"you and I just talked about."},{"speaker":"Kim","startTime":1250.1,"endTime":1250.49,"body":"Right."},{"speaker":"Pam","startTime":1250.7,"endTime":1254.09,"body":"(unclear). I might have"},{"speaker":"Pam","startTime":1250.7,"endTime":1254.09,"body":"said, \"Ooh, so like 13 minus 3,"},{"speaker":"Pam","startTime":1254.12,"endTime":1258.92,"body":"10. 17 minus 7, 10. So, it's"},{"speaker":"Pam","startTime":1254.12,"endTime":1258.92,"body":"almost like we're thinking about"},{"speaker":"Pam","startTime":1259.43,"endTime":1263.81,"body":"the 10 and the teen, the extra"},{"speaker":"Pam","startTime":1259.43,"endTime":1263.81,"body":"7, and we're just getting rid of"},{"speaker":"Pam","startTime":1263.81,"endTime":1267.44,"body":"it. So, it's like there's just"},{"speaker":"Pam","startTime":1263.81,"endTime":1267.44,"body":"this 10 showing up. That's what"},{"speaker":"Pam","startTime":1267.44,"endTime":1270.41,"body":"'teens' mean. Hmm. I wonder if"},{"speaker":"Pam","startTime":1267.44,"endTime":1270.41,"body":"anybody can use that to help you"},{"speaker":"Pam","startTime":1270.41,"endTime":1273.17,"body":"think about 15 minus 5, rather"},{"speaker":"Pam","startTime":1270.41,"endTime":1273.17,"body":"than... You know like, you can't"},{"speaker":"Pam","startTime":1273.17,"endTime":1276.41,"body":"count back, but can you just"},{"speaker":"Pam","startTime":1273.17,"endTime":1276.41,"body":"think about what 15 means to"},{"speaker":"Pam","startTime":1276.41,"endTime":1279.5,"body":"subtract 5?\" Like, I might make"},{"speaker":"Pam","startTime":1276.41,"endTime":1279.5,"body":"that my emphasis. So, again,"},{"speaker":"Pam","startTime":1279.5,"endTime":1283.01,"body":"know your content, know your"},{"speaker":"Pam","startTime":1279.5,"endTime":1283.01,"body":"kids. And then, I will model"},{"speaker":"Pam","startTime":1283.34,"endTime":1286.67,"body":"starting at 15, and I'll jump"},{"speaker":"Pam","startTime":1283.34,"endTime":1286.67,"body":"back that 5. And I'll just note"},{"speaker":"Pam","startTime":1286.67,"endTime":1291.02,"body":"that my 10's are all lined up."},{"speaker":"Pam","startTime":1286.67,"endTime":1291.02,"body":"So, the 15 is in between the 13"},{"speaker":"Pam","startTime":1291.02,"endTime":1295.58,"body":"and the 17. Kind of. I'll be"},{"speaker":"Pam","startTime":1291.02,"endTime":1295.58,"body":"honest it's a little closer to"},{"speaker":"Pam","startTime":1295.58,"endTime":1298.88,"body":"the 13 than I wish it was. It's"},{"speaker":"Pam","startTime":1295.58,"endTime":1298.88,"body":"not right in the middle of a 13"},{"speaker":"Pam","startTime":1298.88,"endTime":1301.52,"body":"and 17. It should be. It should"},{"speaker":"Pam","startTime":1298.88,"endTime":1301.52,"body":"be. But I'm writing in pen,"},{"speaker":"Pam","startTime":1301.55,"endTime":1301.94,"body":"so..."},{"speaker":"Kim","startTime":1302.0,"endTime":1303.5,"body":"I was going to say too bad"},{"speaker":"Kim","startTime":1302.0,"endTime":1303.5,"body":"you don't have a pencil."},{"speaker":"Pam","startTime":1305.72,"endTime":1308.9,"body":"[Pam laughs] With kids, I'd"},{"speaker":"Pam","startTime":1305.72,"endTime":1308.9,"body":"be on a whiteboard, right? In"},{"speaker":"Pam","startTime":1308.9,"endTime":1311.3,"body":"fact, maybe that's worth"},{"speaker":"Pam","startTime":1308.9,"endTime":1311.3,"body":"mentioning. Teachers, if you're"},{"speaker":"Pam","startTime":1311.3,"endTime":1314.48,"body":"on a whiteboard, you can easily"},{"speaker":"Pam","startTime":1311.3,"endTime":1314.48,"body":"erase, and we recommend that. If"},{"speaker":"Pam","startTime":1314.48,"endTime":1318.5,"body":"you are on that document camera,"},{"speaker":"Pam","startTime":1314.48,"endTime":1318.5,"body":"don't be Pam and do it in a pen."},{"speaker":"Pam","startTime":1318.95,"endTime":1323.45,"body":"Do it on a small dry erase"},{"speaker":"Pam","startTime":1318.95,"endTime":1323.45,"body":"board. Put a dry erase board"},{"speaker":"Pam","startTime":1323.48,"endTime":1328.22,"body":"underneath your... Or, be Kim"},{"speaker":"Pam","startTime":1323.48,"endTime":1328.22,"body":"and use a pencil because you do"},{"speaker":"Pam","startTime":1328.22,"endTime":1330.2,"body":"need to be able to erase."},{"speaker":"Pam","startTime":1328.22,"endTime":1330.2,"body":"Though, don't you think, Kim,"},{"speaker":"Pam","startTime":1330.23,"endTime":1333.74,"body":"dry erase board is easier to"},{"speaker":"Pam","startTime":1330.23,"endTime":1333.74,"body":"erase than a pencil?"},{"speaker":"Kim","startTime":1334.04,"endTime":1335.96,"body":"You know, honestly, it"},{"speaker":"Kim","startTime":1334.04,"endTime":1335.96,"body":"depends on the magnitude of the"},{"speaker":"Kim","startTime":1335.96,"endTime":1338.6,"body":"numbers because sometimes if I'm"},{"speaker":"Kim","startTime":1335.96,"endTime":1338.6,"body":"dealing with large numbers but"},{"speaker":"Kim","startTime":1338.6,"endTime":1342.56,"body":"also decimals like that's... You"},{"speaker":"Kim","startTime":1338.6,"endTime":1342.56,"body":"know, it gets a little bit more"},{"speaker":"Kim","startTime":1342.56,"endTime":1345.17,"body":"challenging. I want like a"},{"speaker":"Kim","startTime":1342.56,"endTime":1345.17,"body":"longer line to show a little bit"},{"speaker":"Kim","startTime":1345.17,"endTime":1348.02,"body":"more of the magnitude of the big"},{"speaker":"Kim","startTime":1345.17,"endTime":1348.02,"body":"numbers, so. And there's only so"},{"speaker":"Kim","startTime":1348.02,"endTime":1350.93,"body":"much space under a document"},{"speaker":"Kim","startTime":1348.02,"endTime":1350.93,"body":"camera with a dry erase. Dry"},{"speaker":"Kim","startTime":1350.93,"endTime":1352.49,"body":"erase markers are fat, and so..."},{"speaker":"Pam","startTime":1353.48,"endTime":1356.18,"body":"I mean, you can get thin"},{"speaker":"Pam","startTime":1353.48,"endTime":1356.18,"body":"ones. You can get thin. I mean,"},{"speaker":"Pam","startTime":1356.18,"endTime":1359.03,"body":"you would want to. So, you're"},{"speaker":"Pam","startTime":1356.18,"endTime":1359.03,"body":"saying a pencil might be nice"},{"speaker":"Pam","startTime":1359.03,"endTime":1363.11,"body":"because you could draw finer"},{"speaker":"Pam","startTime":1359.03,"endTime":1363.11,"body":"stuff. Yeah. I also think it"},{"speaker":"Pam","startTime":1363.11,"endTime":1365.87,"body":"might depend on the reflection"},{"speaker":"Pam","startTime":1363.11,"endTime":1365.87,"body":"that you get off of the dry"},{"speaker":"Pam","startTime":1365.87,"endTime":1367.97,"body":"erase board under. Yeah."},{"speaker":"Pam","startTime":1365.87,"endTime":1367.97,"body":"Alright, make that work. Okay,"},{"speaker":"Pam","startTime":1367.97,"endTime":1370.34,"body":"so we got 15 minus 5 is 10."},{"speaker":"Kim","startTime":1370.82,"endTime":1373.52,"body":"Okay. Last problem. 15"},{"speaker":"Kim","startTime":1370.82,"endTime":1373.52,"body":"minus 8."},{"speaker":"Pam","startTime":1374.18,"endTime":1374.87,"body":"Cool. So,"},{"speaker":"Pam","startTime":1374.87,"endTime":1377.87,"body":"I'm going to ask, \"Hey, did"},{"speaker":"Pam","startTime":1374.87,"endTime":1377.87,"body":"anybody do that thing that Kim"},{"speaker":"Pam","startTime":1377.87,"endTime":1381.59,"body":"did and Aaron did with this? Did"},{"speaker":"Pam","startTime":1377.87,"endTime":1381.59,"body":"anyboy use the 15 minus...\" And"},{"speaker":"Pam","startTime":1381.59,"endTime":1386.36,"body":"I'm looking for glimmers of kids"},{"speaker":"Pam","startTime":1381.59,"endTime":1386.36,"body":"going, \"Oh, yeah.\" And then, I"},{"speaker":"Pam","startTime":1386.36,"endTime":1388.37,"body":"might be like, \"Oh, you were"},{"speaker":"Pam","startTime":1386.36,"endTime":1388.37,"body":"thinking about that? Even if you"},{"speaker":"Pam","startTime":1388.37,"endTime":1392.36,"body":"didn't finish, could you..."},{"speaker":"Pam","startTime":1388.37,"endTime":1392.36,"body":"Let's think that together. So,"},{"speaker":"Pam","startTime":1392.48,"endTime":1397.16,"body":"if 15 minus 5 is 10, but we need"},{"speaker":"Pam","startTime":1392.48,"endTime":1397.16,"body":"to subtract 8. How much more,"},{"speaker":"Pam","startTime":1397.46,"endTime":1400.13,"body":"so-and-so?\" Whoever I'm working"},{"speaker":"Pam","startTime":1397.46,"endTime":1400.13,"body":"with. \"Oh, yeah. So, we can just"},{"speaker":"Pam","startTime":1400.16,"endTime":1404.69,"body":"the extra 3? And what is what is"},{"speaker":"Pam","startTime":1400.16,"endTime":1404.69,"body":"10 minus 3, everybody? We know"},{"speaker":"Pam","startTime":1404.69,"endTime":1407.54,"body":"that I Have, You Need. If I have"},{"speaker":"Pam","startTime":1404.69,"endTime":1407.54,"body":"3, what do you need. Oh, 7. Sure"},{"speaker":"Pam","startTime":1407.54,"endTime":1410.03,"body":"enough.\" So 15 minus 8 is 7."},{"speaker":"Kim","startTime":1410.87,"endTime":1410.9,"body":"Mmhmm."},{"speaker":"Pam","startTime":1411.14,"endTime":1411.5,"body":"Yeah."},{"speaker":"Kim","startTime":1412.04,"endTime":1416.03,"body":"And so, at the end of the"},{"speaker":"Kim","startTime":1412.04,"endTime":1416.03,"body":"string, depending on is this"},{"speaker":"Kim","startTime":1416.03,"endTime":1419.9,"body":"your first go, is this the third"},{"speaker":"Kim","startTime":1416.03,"endTime":1419.9,"body":"time you've done this kind of"},{"speaker":"Kim","startTime":1419.9,"endTime":1422.72,"body":"string, will you talk just a"},{"speaker":"Kim","startTime":1419.9,"endTime":1422.72,"body":"minute about a little bit of a"},{"speaker":"Kim","startTime":1422.72,"endTime":1423.44,"body":"wrap up?"},{"speaker":"Pam","startTime":1423.98,"endTime":1426.74,"body":"Yeah, absolutely. So, it"},{"speaker":"Pam","startTime":1423.98,"endTime":1426.74,"body":"kind of depends on what I want"},{"speaker":"Pam","startTime":1426.74,"endTime":1429.92,"body":"to emphasize with my students at"},{"speaker":"Pam","startTime":1426.74,"endTime":1429.92,"body":"this point. So, if a lot of them"},{"speaker":"Pam","startTime":1429.92,"endTime":1433.76,"body":"were counting by ones to do the"},{"speaker":"Pam","startTime":1429.92,"endTime":1433.76,"body":"13 minus 3, the 17 minus 7, the"},{"speaker":"Pam","startTime":1433.76,"endTime":1439.28,"body":"15 minus 5, I might make that be"},{"speaker":"Pam","startTime":1433.76,"endTime":1439.28,"body":"my point here. \"Ya'll, like we"},{"speaker":"Pam","startTime":1439.28,"endTime":1442.61,"body":"have this pattern that if I have"},{"speaker":"Pam","startTime":1439.28,"endTime":1442.61,"body":"a teen, and I subtract off that"},{"speaker":"Pam","startTime":1442.64,"endTime":1445.58,"body":"bit of it that's the extra from"},{"speaker":"Pam","startTime":1442.64,"endTime":1445.58,"body":"the 10, what am I left? Wow, I'm"},{"speaker":"Pam","startTime":1445.58,"endTime":1448.64,"body":"always left with the 10. That"},{"speaker":"Pam","startTime":1445.58,"endTime":1448.64,"body":"seems important.\" Might that be"},{"speaker":"Pam","startTime":1449.03,"endTime":1451.61,"body":"something that I would pull out"},{"speaker":"Pam","startTime":1449.03,"endTime":1451.61,"body":"of kids, help them help me"},{"speaker":"Pam","startTime":1451.61,"endTime":1456.83,"body":"verbalize. But if that's not"},{"speaker":"Pam","startTime":1451.61,"endTime":1456.83,"body":"where most kids are struggling,"},{"speaker":"Pam","startTime":1456.86,"endTime":1459.53,"body":"then I might say, \"Well, this is"},{"speaker":"Pam","startTime":1456.86,"endTime":1459.53,"body":"really interesting that we could"},{"speaker":"Pam","startTime":1459.62,"endTime":1462.68,"body":"get to the 10, and then just"},{"speaker":"Pam","startTime":1459.62,"endTime":1462.68,"body":"subtract the extra stuff. I"},{"speaker":"Pam","startTime":1462.68,"endTime":1464.39,"body":"wonder if that could help us"},{"speaker":"Pam","startTime":1462.68,"endTime":1464.39,"body":"with with problems in the"},{"speaker":"Pam","startTime":1464.39,"endTime":1469.67,"body":"future.\" So, in some way, we"},{"speaker":"Pam","startTime":1464.39,"endTime":1469.67,"body":"kind of verbalize, put in words,"},{"speaker":"Pam","startTime":1469.67,"endTime":1472.79,"body":"help kids sharpen their thinking"},{"speaker":"Pam","startTime":1469.67,"endTime":1472.79,"body":"by putting it in words the"},{"speaker":"Pam","startTime":1472.79,"endTime":1476.3,"body":"relationships that we're using"},{"speaker":"Pam","startTime":1472.79,"endTime":1476.3,"body":"in the string. In this case, can"},{"speaker":"Pam","startTime":1476.3,"endTime":1479.06,"body":"we get to the... If we're"},{"speaker":"Pam","startTime":1476.3,"endTime":1479.06,"body":"subtracting, can we subtract to"},{"speaker":"Pam","startTime":1479.06,"endTime":1481.34,"body":"the 10, and then just subtract"},{"speaker":"Pam","startTime":1479.06,"endTime":1481.34,"body":"what's leftover?"},{"speaker":"Kim","startTime":1481.67,"endTime":1484.55,"body":"Yeah, which is one of our"},{"speaker":"Kim","startTime":1481.67,"endTime":1484.55,"body":"major relationships that we want"},{"speaker":"Kim","startTime":1484.55,"endTime":1486.26,"body":"kids to own for subtraction."},{"speaker":"Pam","startTime":1486.26,"endTime":1486.62,"body":"Absolutely. Yep."},{"speaker":"Kim","startTime":1486.62,"endTime":1487.37,"body":"So, it's a good experience."},{"speaker":"Pam","startTime":1487.37,"endTime":1487.43,"body":"Yeah."},{"speaker":"Kim","startTime":1487.67,"endTime":1489.74,"body":"I think we have time for"},{"speaker":"Kim","startTime":1487.67,"endTime":1489.74,"body":"one more experience."},{"speaker":"Pam","startTime":1489.8,"endTime":1490.58,"body":"Okay, cool, cool."},{"speaker":"Kim","startTime":1490.58,"endTime":1493.88,"body":"So, will you talk through"},{"speaker":"Kim","startTime":1490.58,"endTime":1493.88,"body":"these problems as well?"},{"speaker":"Pam","startTime":1493.97,"endTime":1494.33,"body":"I'm ready."},{"speaker":"Kim","startTime":1494.84,"endTime":1500.87,"body":"Okay, new piece of paper"},{"speaker":"Kim","startTime":1494.84,"endTime":1500.87,"body":"and clunky pen. 12 minus 6."},{"speaker":"Pam","startTime":1501.14,"endTime":1504.17,"body":"And my pen just leaked."},{"speaker":"Pam","startTime":1501.14,"endTime":1504.17,"body":"Your loving it right now. Okay,"},{"speaker":"Pam","startTime":1504.32,"endTime":1507.56,"body":"so 12 minus 6, if we're doing"},{"speaker":"Pam","startTime":1504.32,"endTime":1507.56,"body":"this Problem String, I'm not"},{"speaker":"Pam","startTime":1507.56,"endTime":1510.65,"body":"waiting very long on this."},{"speaker":"Pam","startTime":1507.56,"endTime":1510.65,"body":"Doubles are things that kids"},{"speaker":"Pam","startTime":1510.65,"endTime":1513.2,"body":"kind of... Like, we want to do"},{"speaker":"Pam","startTime":1510.65,"endTime":1513.2,"body":"things to help our kids build"},{"speaker":"Pam","startTime":1513.2,"endTime":1516.53,"body":"doubles, but they are a thing"},{"speaker":"Pam","startTime":1513.2,"endTime":1516.53,"body":"that kids tend to know. So, I'll"},{"speaker":"Pam","startTime":1516.53,"endTime":1518.84,"body":"just usually, you know, \"What is"},{"speaker":"Pam","startTime":1516.53,"endTime":1518.84,"body":"that?\" Everybody's going to say"},{"speaker":"Pam","startTime":1518.84,"endTime":1522.02,"body":"6. At this point, I'm going to"},{"speaker":"Pam","startTime":1518.84,"endTime":1522.02,"body":"draw a number line starting at"},{"speaker":"Pam","startTime":1522.02,"endTime":1525.83,"body":"12. And I'm going to jump back"},{"speaker":"Pam","startTime":1522.02,"endTime":1525.83,"body":"of 6, and landing on 6."},{"speaker":"Kim","startTime":1526.13,"endTime":1526.61,"body":"Cool."},{"speaker":"Pam","startTime":1526.88,"endTime":1527.12,"body":"Okay."},{"speaker":"Kim","startTime":1527.15,"endTime":1528.59,"body":"Thirteen minus 6."},{"speaker":"Pam","startTime":1528.92,"endTime":1529.64,"body":"To be clear, though."},{"speaker":"Pam","startTime":1529.67,"endTime":1532.04,"body":"Not because I said that. Because"},{"speaker":"Pam","startTime":1529.67,"endTime":1532.04,"body":"I'm asking a kid to say that,"},{"speaker":"Pam","startTime":1532.04,"endTime":1533.9,"body":"and then I'm representing their"},{"speaker":"Pam","startTime":1532.04,"endTime":1533.9,"body":"thinking, Yeah, okay."},{"speaker":"Kim","startTime":1533.9,"endTime":1534.02,"body":"Yeah."},{"speaker":"Pam","startTime":1534.02,"endTime":1534.32,"body":"So,"},{"speaker":"Pam","startTime":1534.32,"endTime":1535.52,"body":"sorry, what was the next one you"},{"speaker":"Pam","startTime":1534.32,"endTime":1535.52,"body":"said?"},{"speaker":"Kim","startTime":1535.52,"endTime":1537.2,"body":"It's okay. 13 minus 6."},{"speaker":"Pam","startTime":1537.56,"endTime":1539.57,"body":"So, with 13 minus 6, I'm"},{"speaker":"Pam","startTime":1537.56,"endTime":1539.57,"body":"going to let them figure. Okay,"},{"speaker":"Pam","startTime":1539.57,"endTime":1541.22,"body":"that's the next problem. Let"},{"speaker":"Pam","startTime":1539.57,"endTime":1541.22,"body":"them figure. And I'm going to"},{"speaker":"Pam","startTime":1541.22,"endTime":1543.32,"body":"expect that there will be some"},{"speaker":"Pam","startTime":1541.22,"endTime":1543.32,"body":"kids counting back. I'm going to"},{"speaker":"Pam","startTime":1543.32,"endTime":1545.24,"body":"expect that there will be some"},{"speaker":"Pam","startTime":1543.32,"endTime":1545.24,"body":"kids kind of, you know like,"},{"speaker":"Pam","startTime":1545.27,"endTime":1547.37,"body":"nodding their head a little bit."},{"speaker":"Pam","startTime":1545.27,"endTime":1547.37,"body":"And I can kind of almost see"},{"speaker":"Pam","startTime":1547.37,"endTime":1550.1,"body":"them counting back by ones. But"},{"speaker":"Pam","startTime":1547.37,"endTime":1550.1,"body":"I'm going to ask, \"Did anybody"},{"speaker":"Pam","startTime":1550.1,"endTime":1553.73,"body":"use the problem before?\" Like,"},{"speaker":"Pam","startTime":1550.1,"endTime":1553.73,"body":"\"If you know 12 minus 6 is 6,"},{"speaker":"Pam","startTime":1553.73,"endTime":1557.84,"body":"can that help you with 1 more,"},{"speaker":"Pam","startTime":1553.73,"endTime":1557.84,"body":"13 minus 6?\" And I will probably"},{"speaker":"Pam","startTime":1557.84,"endTime":1562.25,"body":"even say that, \"1 more, 13 minus"},{"speaker":"Pam","startTime":1557.84,"endTime":1562.25,"body":"6.\" And then, as kids describe"},{"speaker":"Pam","startTime":1562.25,"endTime":1565.28,"body":"their thinking, I'm going to"},{"speaker":"Pam","startTime":1562.25,"endTime":1565.28,"body":"draw a number line with a 13"},{"speaker":"Pam","startTime":1565.28,"endTime":1569.36,"body":"just to the right of that 12."},{"speaker":"Pam","startTime":1565.28,"endTime":1569.36,"body":"About 1 to the right. And I'm"},{"speaker":"Pam","startTime":1569.36,"endTime":1571.7,"body":"going to say, \"So, if I jump"},{"speaker":"Pam","startTime":1569.36,"endTime":1571.7,"body":"back that. If this jump is the"},{"speaker":"Pam","startTime":1571.7,"endTime":1574.94,"body":"same distance...\" Try to make"},{"speaker":"Pam","startTime":1571.7,"endTime":1574.94,"body":"that really the same distance."},{"speaker":"Pam","startTime":1574.94,"endTime":1577.91,"body":"\"...where would I land if I"},{"speaker":"Pam","startTime":1574.94,"endTime":1577.91,"body":"subtract the same but from 1"},{"speaker":"Pam","startTime":1577.91,"endTime":1583.46,"body":"bigger? Where would I land?\" And"},{"speaker":"Pam","startTime":1577.91,"endTime":1583.46,"body":"someone will say 7, and we'll"},{"speaker":"Pam","startTime":1583.46,"endTime":1587.39,"body":"land on that 7. So, I should"},{"speaker":"Pam","startTime":1583.46,"endTime":1587.39,"body":"have two number lines that look"},{"speaker":"Pam","startTime":1587.39,"endTime":1591.41,"body":"exactly the same, but one is"},{"speaker":"Pam","startTime":1587.39,"endTime":1591.41,"body":"shifted to the right 1. Where in"},{"speaker":"Pam","startTime":1591.41,"endTime":1594.59,"body":"the first one it's 6 to 12, and"},{"speaker":"Pam","startTime":1591.41,"endTime":1594.59,"body":"on the second one, it's 7 to 13."},{"speaker":"Pam","startTime":1594.62,"endTime":1596.27,"body":"But the jumps are still all 6."},{"speaker":"Pam","startTime":1597.32,"endTime":1597.65,"body":"Cool."},{"speaker":"Kim","startTime":1597.68,"endTime":1601.49,"body":"Which is why those attempt"},{"speaker":"Kim","startTime":1597.68,"endTime":1601.49,"body":"to be as proportional as"},{"speaker":"Kim","startTime":1601.49,"endTime":1608.78,"body":"possible is a huge goal because"},{"speaker":"Kim","startTime":1601.49,"endTime":1608.78,"body":"that gap or that minus 6 should"},{"speaker":"Kim","startTime":1608.78,"endTime":1609.5,"body":"look the same."},{"speaker":"Pam","startTime":1609.83,"endTime":1612.35,"body":"Yeah, absolutely. And"},{"speaker":"Pam","startTime":1609.83,"endTime":1612.35,"body":"teachers, if you're trying to do"},{"speaker":"Pam","startTime":1612.35,"endTime":1614.9,"body":"that, and you're like, \"Oh!\" You"},{"speaker":"Pam","startTime":1612.35,"endTime":1614.9,"body":"know like, in the in the bit of"},{"speaker":"Pam","startTime":1614.9,"endTime":1618.11,"body":"it, you're... It's not what you"},{"speaker":"Pam","startTime":1614.9,"endTime":1618.11,"body":"want. You can, at that moment,"},{"speaker":"Pam","startTime":1618.11,"endTime":1620.9,"body":"go \"Whoa, this doesn't look"},{"speaker":"Pam","startTime":1618.11,"endTime":1620.9,"body":"right. Ya'll, help me. What"},{"speaker":"Pam","startTime":1620.9,"endTime":1622.16,"body":"should this look like?\""},{"speaker":"Kim","startTime":1622.25,"endTime":1622.61,"body":"Yes!"},{"speaker":"Pam","startTime":1622.64,"endTime":1625.46,"body":"And as the kids describe"},{"speaker":"Pam","startTime":1622.64,"endTime":1625.46,"body":"with the number line, you know"},{"speaker":"Pam","startTime":1625.46,"endTime":1628.55,"body":"like, \"Oh, like the 13 should be"},{"speaker":"Pam","startTime":1625.46,"endTime":1628.55,"body":"to the right of the 12.\" \"Well,"},{"speaker":"Pam","startTime":1628.55,"endTime":1630.98,"body":"then, guys, how big should the"},{"speaker":"Pam","startTime":1628.55,"endTime":1630.98,"body":"jump be? You know, when I drew"},{"speaker":"Pam","startTime":1630.98,"endTime":1633.2,"body":"it, I drew it way too big"},{"speaker":"Pam","startTime":1630.98,"endTime":1633.2,"body":"because... How should it relate"},{"speaker":"Pam","startTime":1633.2,"endTime":1636.23,"body":"to this jump of 6 up here?\" I"},{"speaker":"Pam","startTime":1633.2,"endTime":1636.23,"body":"mean, as they discuss that with"},{"speaker":"Pam","startTime":1636.23,"endTime":1639.44,"body":"you, they're getting... It's not"},{"speaker":"Pam","startTime":1636.23,"endTime":1639.44,"body":"that they're really learning to"},{"speaker":"Pam","startTime":1639.44,"endTime":1642.44,"body":"model better, though they are,"},{"speaker":"Pam","startTime":1639.44,"endTime":1642.44,"body":"but they're really getting"},{"speaker":"Pam","startTime":1642.44,"endTime":1645.26,"body":"better at the relationships."},{"speaker":"Pam","startTime":1642.44,"endTime":1645.26,"body":"They're owning like, \"That"},{"speaker":"Pam","startTime":1645.26,"endTime":1647.99,"body":"should be the same length.\""},{"speaker":"Pam","startTime":1645.26,"endTime":1647.99,"body":"Like, they're building spatial"},{"speaker":"Pam","startTime":1648.02,"endTime":1649.31,"body":"spatial relationships. Yeah,"},{"speaker":"Pam","startTime":1648.02,"endTime":1649.31,"body":"okay."},{"speaker":"Kim","startTime":1649.43,"endTime":1651.5,"body":"Yeah, I've seen you and I"},{"speaker":"Kim","startTime":1649.43,"endTime":1651.5,"body":"both do Problem Strings where"},{"speaker":"Kim","startTime":1651.5,"endTime":1654.77,"body":"we've sketched, you know, an"},{"speaker":"Kim","startTime":1651.5,"endTime":1654.77,"body":"area model or a number line, and"},{"speaker":"Kim","startTime":1654.77,"endTime":1658.7,"body":"then we look at it, and we've"},{"speaker":"Kim","startTime":1654.77,"endTime":1658.7,"body":"redrawn two or three times even."},{"speaker":"Kim","startTime":1658.85,"endTime":1662.51,"body":"And the kids are involved in"},{"speaker":"Kim","startTime":1658.85,"endTime":1662.51,"body":"like, \"Why is she fussing with"},{"speaker":"Kim","startTime":1662.51,"endTime":1666.98,"body":"this?\" Like, What's wrong with"},{"speaker":"Kim","startTime":1662.51,"endTime":1666.98,"body":"this representation, so that she"},{"speaker":"Kim","startTime":1666.98,"endTime":1670.1,"body":"wants to redo it and make it"},{"speaker":"Kim","startTime":1666.98,"endTime":1670.1,"body":"better?\" And we are totally"},{"speaker":"Kim","startTime":1670.1,"endTime":1672.71,"body":"talking about like, \"Ooh, does"},{"speaker":"Kim","startTime":1670.1,"endTime":1672.71,"body":"that feel okay?\" Like, \"Does"},{"speaker":"Kim","startTime":1672.74,"endTime":1674.21,"body":"that seem close?\""},{"speaker":"Pam","startTime":1674.39,"endTime":1676.34,"body":"Yeah. \"Ooh, how would you"},{"speaker":"Pam","startTime":1674.39,"endTime":1676.34,"body":"change that?\" And they're like,"},{"speaker":"Pam","startTime":1676.49,"endTime":1678.38,"body":"\"That doesn't look like a"},{"speaker":"Pam","startTime":1676.49,"endTime":1678.38,"body":"rectangle at all.\" Like, it"},{"speaker":"Pam","startTime":1678.38,"endTime":1680.96,"body":"should be more square.\" Or,"},{"speaker":"Pam","startTime":1678.38,"endTime":1680.96,"body":"\"That line isn't parallel.\" And"},{"speaker":"Pam","startTime":1680.96,"endTime":1683.45,"body":"you're like, \"Oh.\" Like, \"The"},{"speaker":"Pam","startTime":1680.96,"endTime":1683.45,"body":"sides of a rectangle should be"},{"speaker":"Pam","startTime":1683.45,"endTime":1686.09,"body":"parallel? Well, that seems"},{"speaker":"Pam","startTime":1683.45,"endTime":1686.09,"body":"important.\" Like, all that stuff"},{"speaker":"Pam","startTime":1686.09,"endTime":1686.84,"body":"can come in. Yeah."},{"speaker":"Pam","startTime":1686.87,"endTime":1687.14,"body":"Okay."},{"speaker":"Kim","startTime":1687.17,"endTime":1688.64,"body":"Okay, cool. Ready for the"},{"speaker":"Kim","startTime":1687.17,"endTime":1688.64,"body":"next problem?"},{"speaker":"Pam","startTime":1688.76,"endTime":1689.12,"body":"Yep."},{"speaker":"Kim","startTime":1689.9,"endTime":1691.13,"body":"16 minus 8."},{"speaker":"Pam","startTime":1691.67,"endTime":1693.92,"body":"Cool, another double. I'm"},{"speaker":"Pam","startTime":1691.67,"endTime":1693.92,"body":"not going to wait too long. I'm"},{"speaker":"Pam","startTime":1693.92,"endTime":1696.2,"body":"going to expect someone to say"},{"speaker":"Pam","startTime":1693.92,"endTime":1696.2,"body":"16 minus 8. I'm going to draw a"},{"speaker":"Pam","startTime":1696.2,"endTime":1699.08,"body":"number line at 16 with a jump of"},{"speaker":"Pam","startTime":1696.2,"endTime":1699.08,"body":"8 and landing on 8."},{"speaker":"Kim","startTime":1699.08,"endTime":1699.17,"body":"Yep."},{"speaker":"Pam","startTime":1699.29,"endTime":1699.65,"body":"Yep."},{"speaker":"Kim","startTime":1699.71,"endTime":1701.3,"body":"Cool. 16 minus 9."},{"speaker":"Pam","startTime":1702.68,"endTime":1705.59,"body":"Do you want to know that I"},{"speaker":"Pam","startTime":1702.68,"endTime":1705.59,"body":"just kind of... I drew the jump,"},{"speaker":"Pam","startTime":1705.59,"endTime":1708.17,"body":"and then realized that my jump"},{"speaker":"Pam","startTime":1705.59,"endTime":1708.17,"body":"was too short, so then I"},{"speaker":"Pam","startTime":1708.17,"endTime":1710.15,"body":"scratched out and made it a"},{"speaker":"Pam","startTime":1708.17,"endTime":1710.15,"body":"little bit longer. Anyway. Okay,"},{"speaker":"Pam","startTime":1710.15,"endTime":1714.05,"body":"so now 16 minus 9. I'm going to"},{"speaker":"Pam","startTime":1710.15,"endTime":1714.05,"body":"ask, \"Hey, is anybody...\" And I"},{"speaker":"Pam","startTime":1714.05,"endTime":1716.75,"body":"will actually suggest, as I say"},{"speaker":"Pam","startTime":1714.05,"endTime":1716.75,"body":"16 minus 9, \"I wonder if this"},{"speaker":"Pam","startTime":1716.75,"endTime":1719.15,"body":"problem could be helpful. I"},{"speaker":"Pam","startTime":1716.75,"endTime":1719.15,"body":"don't know. Maybe. Go ahead, and"},{"speaker":"Pam","startTime":1719.15,"endTime":1721.67,"body":"solve it any way you want.\" But"},{"speaker":"Pam","startTime":1719.15,"endTime":1721.67,"body":"then, I'm going to ask, \"Did"},{"speaker":"Pam","startTime":1721.67,"endTime":1725.87,"body":"anybody use the 16 minus 8? And"},{"speaker":"Pam","startTime":1721.67,"endTime":1725.87,"body":"now, this time I'm going to"},{"speaker":"Pam","startTime":1725.87,"endTime":1727.28,"body":"start at the same 16."},{"speaker":"Kim","startTime":1727.58,"endTime":1728.03,"body":"Yeah."},{"speaker":"Pam","startTime":1728.12,"endTime":1729.83,"body":"And I'm going to say, \"What"},{"speaker":"Pam","startTime":1728.12,"endTime":1729.83,"body":"should the jump look like?"},{"speaker":"Pam","startTime":1729.86,"endTime":1732.98,"body":"Should it be shorter or longer"},{"speaker":"Pam","startTime":1729.86,"endTime":1732.98,"body":"than the jump of 8? Oh, it's a"},{"speaker":"Pam","startTime":1732.98,"endTime":1736.07,"body":"jump of 9, it should be a little"},{"speaker":"Pam","startTime":1732.98,"endTime":1736.07,"body":"bit longer. How much longer? 1"},{"speaker":"Pam","startTime":1736.07,"endTime":1738.11,"body":"longer. Well, if it's 1 longer,"},{"speaker":"Pam","startTime":1736.07,"endTime":1738.11,"body":"then where are we going to land?"},{"speaker":"Pam","startTime":1738.14,"endTime":1742.25,"body":"Ooh, we're going to land on 7."},{"speaker":"Pam","startTime":1738.14,"endTime":1742.25,"body":"So, if I know 16 minus 8 is 8,"},{"speaker":"Pam","startTime":1742.28,"endTime":1747.53,"body":"then 16 minus 1 more than that"},{"speaker":"Pam","startTime":1742.28,"endTime":1747.53,"body":"should be 7.\" Cool. Again,"},{"speaker":"Pam","startTime":1747.53,"endTime":1750.35,"body":"pulling that out of kids, right?"},{"speaker":"Pam","startTime":1747.53,"endTime":1750.35,"body":"I'm trying to ask questions to"},{"speaker":"Pam","startTime":1750.35,"endTime":1751.55,"body":"get that for kids to say that,"},{"speaker":"Pam","startTime":1751.85,"endTime":1751.88,"body":"mmhmm."},{"speaker":"Kim","startTime":1751.88,"endTime":1754.88,"body":"Mmhmm. Next problem. 14"},{"speaker":"Kim","startTime":1751.88,"endTime":1754.88,"body":"minus 7."},{"speaker":"Pam","startTime":1755.27,"endTime":1757.07,"body":"Again, a double. I'm not"},{"speaker":"Pam","startTime":1755.27,"endTime":1757.07,"body":"going to wait too long."},{"speaker":"Pam","startTime":1757.58,"endTime":1761.18,"body":"Someone's going to say 7. I'm"},{"speaker":"Pam","startTime":1757.58,"endTime":1761.18,"body":"going to draw a number line with"},{"speaker":"Pam","startTime":1761.18,"endTime":1764.51,"body":"the 14, jump of 7, landing on 7."},{"speaker":"Pam","startTime":1761.18,"endTime":1764.51,"body":"(unclear)."},{"speaker":"Kim","startTime":1766.31,"endTime":1768.74,"body":"And 14"},{"speaker":"Kim","startTime":1768.74,"endTime":1769.22,"body":"minus 5."},{"speaker":"Pam","startTime":1769.73,"endTime":1772.49,"body":"Fourteen minus 5. And in"},{"speaker":"Pam","startTime":1769.73,"endTime":1772.49,"body":"this case, again, I might say,"},{"speaker":"Pam","startTime":1772.52,"endTime":1774.92,"body":"\"I wonder if anybody... Ooh,"},{"speaker":"Pam","startTime":1772.52,"endTime":1774.92,"body":"this seems a little different."},{"speaker":"Pam","startTime":1774.92,"endTime":1777.02,"body":"It's not just 1 off, but that's"},{"speaker":"Pam","startTime":1774.92,"endTime":1777.02,"body":"okay. Go ahead.\" You know like,"},{"speaker":"Pam","startTime":1777.05,"endTime":1779.93,"body":"\"Do whatever you want.\" Let them"},{"speaker":"Pam","startTime":1777.05,"endTime":1779.93,"body":"solve it. And then ask, \"Did"},{"speaker":"Pam","startTime":1779.93,"endTime":1783.92,"body":"anybody use the 14 minus 7?\" And"},{"speaker":"Pam","startTime":1779.93,"endTime":1783.92,"body":"try to draw out someone who"},{"speaker":"Pam","startTime":1783.92,"endTime":1786.83,"body":"says, \"Well, this time I didn't"},{"speaker":"Pam","startTime":1783.92,"endTime":1786.83,"body":"subtract as much.\" \"So, should"},{"speaker":"Pam","startTime":1786.83,"endTime":1789.53,"body":"the jump be shorter? longer? It"},{"speaker":"Pam","startTime":1786.83,"endTime":1789.53,"body":"should be shorter. How much"},{"speaker":"Pam","startTime":1789.53,"endTime":1793.88,"body":"shorter? It should be 2 shorter."},{"speaker":"Pam","startTime":1789.53,"endTime":1793.88,"body":"Well, what is 2 to the right of"},{"speaker":"Pam","startTime":1793.91,"endTime":1797.54,"body":"7? Oh, yeah. Sure enough, that's"},{"speaker":"Pam","startTime":1793.91,"endTime":1797.54,"body":"9.\" So, if I've drawn that jump"},{"speaker":"Pam","startTime":1797.54,"endTime":1801.44,"body":"shorter, and I'm comparing it to"},{"speaker":"Pam","startTime":1797.54,"endTime":1801.44,"body":"the one above, I should be able"},{"speaker":"Pam","startTime":1801.44,"endTime":1804.92,"body":"to go, \"Well, then, if it's 2"},{"speaker":"Pam","startTime":1801.44,"endTime":1804.92,"body":"this way? What is 2 that way of"},{"speaker":"Pam","startTime":1804.92,"endTime":1809.21,"body":"7? Sure enough, that's 9. Oh,"},{"speaker":"Pam","startTime":1804.92,"endTime":1809.21,"body":"nice.\" So, to finish up the"},{"speaker":"Pam","startTime":1809.21,"endTime":1814.13,"body":"string. \"Wow, we really can use"},{"speaker":"Pam","startTime":1809.21,"endTime":1814.13,"body":"what we know. You guys, a lot of"},{"speaker":"Pam","startTime":1814.13,"endTime":1817.67,"body":"you are owning these doubles."},{"speaker":"Pam","startTime":1814.13,"endTime":1817.67,"body":"Well, way to go. That's super"},{"speaker":"Pam","startTime":1817.67,"endTime":1820.94,"body":"that you know 12 minus 6. You"},{"speaker":"Pam","startTime":1817.67,"endTime":1820.94,"body":"know 16 minus 8. You know 14"},{"speaker":"Pam","startTime":1820.94,"endTime":1824.87,"body":"minus 7. You know those doubles."},{"speaker":"Pam","startTime":1820.94,"endTime":1824.87,"body":"Wow, knowing those, you can use"},{"speaker":"Pam","startTime":1824.87,"endTime":1829.01,"body":"what you know to just adjust"},{"speaker":"Pam","startTime":1824.87,"endTime":1829.01,"body":"either moving where you start or"},{"speaker":"Pam","startTime":1829.01,"endTime":1831.32,"body":"how big you jump. You can just"},{"speaker":"Pam","startTime":1829.01,"endTime":1831.32,"body":"adjust a little bit from when"},{"speaker":"Pam","startTime":1831.32,"endTime":1833.9,"body":"you know. Nicely done. Yeah,"},{"speaker":"Pam","startTime":1831.32,"endTime":1833.9,"body":"using doubles is super helpful.\""},{"speaker":"Pam","startTime":1833.9,"endTime":1834.26,"body":"Cool."},{"speaker":"Kim","startTime":1834.56,"endTime":1837.26,"body":"Yeah, which is another one"},{"speaker":"Kim","startTime":1834.56,"endTime":1837.26,"body":"of our major strategies. And you"},{"speaker":"Kim","startTime":1837.26,"endTime":1839.63,"body":"have said a couple of times,"},{"speaker":"Kim","startTime":1837.26,"endTime":1839.63,"body":"\"I'm not going to stay long on"},{"speaker":"Kim","startTime":1839.63,"endTime":1842.96,"body":"this particular problem because"},{"speaker":"Kim","startTime":1839.63,"endTime":1842.96,"body":"my kids know their doubles.\" And"},{"speaker":"Kim","startTime":1842.96,"endTime":1845.39,"body":"so, I can hear a teacher right"},{"speaker":"Kim","startTime":1842.96,"endTime":1845.39,"body":"now saying, \"My kids don't know"},{"speaker":"Kim","startTime":1845.39,"endTime":1849.89,"body":"their doubles.\" And so, one of"},{"speaker":"Kim","startTime":1845.39,"endTime":1849.89,"body":"our favorite routines is similar"},{"speaker":"Kim","startTime":1849.89,"endTime":1853.46,"body":"to I Have, You Need. It's just a"},{"speaker":"Kim","startTime":1849.89,"endTime":1853.46,"body":"call and response, is we do a"},{"speaker":"Kim","startTime":1853.46,"endTime":1856.04,"body":"lot with Doubling and Halving"},{"speaker":"Kim","startTime":1853.46,"endTime":1856.04,"body":"because we know that kids have"},{"speaker":"Kim","startTime":1856.04,"endTime":1858.92,"body":"some intuitive intuition with"},{"speaker":"Kim","startTime":1856.04,"endTime":1858.92,"body":"Doubling. But we can strengthen"},{"speaker":"Kim","startTime":1858.92,"endTime":1862.67,"body":"that in moments of time, where"},{"speaker":"Kim","startTime":1858.92,"endTime":1862.67,"body":"we double numbers together, or"},{"speaker":"Kim","startTime":1862.67,"endTime":1865.91,"body":"we halve numbers together later"},{"speaker":"Kim","startTime":1862.67,"endTime":1865.91,"body":"on as they get older."},{"speaker":"Pam","startTime":1866.33,"endTime":1866.99,"body":"Absolutely."},{"speaker":"Kim","startTime":1867.11,"endTime":1868.67,"body":"Briefly, tell us what that"},{"speaker":"Kim","startTime":1867.11,"endTime":1868.67,"body":"looks like."},{"speaker":"Pam","startTime":1869.54,"endTime":1871.97,"body":"Well, and let me also"},{"speaker":"Pam","startTime":1869.54,"endTime":1871.97,"body":"mention that we can also work on"},{"speaker":"Pam","startTime":1871.97,"endTime":1876.14,"body":"a number rack is going to just"},{"speaker":"Pam","startTime":1871.97,"endTime":1876.14,"body":"scream. The doubles just scream."},{"speaker":"Pam","startTime":1876.14,"endTime":1878.57,"body":"So, if I would have done that"},{"speaker":"Pam","startTime":1876.14,"endTime":1878.57,"body":"string on a number rack, as soon"},{"speaker":"Pam","startTime":1878.57,"endTime":1882.65,"body":"as I have 12 up there. Depending"},{"speaker":"Pam","startTime":1878.57,"endTime":1882.65,"body":"on how I put the 12, if I put it"},{"speaker":"Pam","startTime":1882.65,"endTime":1890.03,"body":"at 6 and 6, like were looking at"},{"speaker":"Pam","startTime":1882.65,"endTime":1890.03,"body":"the double of 6 being 12. And"},{"speaker":"Pam","startTime":1890.03,"endTime":1893.21,"body":"so, we want to... Work on a"},{"speaker":"Pam","startTime":1890.03,"endTime":1893.21,"body":"number rack can really help"},{"speaker":"Pam","startTime":1893.21,"endTime":1896.66,"body":"build doubles. But Doubling and"},{"speaker":"Pam","startTime":1893.21,"endTime":1896.66,"body":"Halving looks like literally..."},{"speaker":"Pam","startTime":1896.66,"endTime":1899.81,"body":"You know, I've got a little bit"},{"speaker":"Pam","startTime":1896.66,"endTime":1899.81,"body":"of time. I got 90 seconds before"},{"speaker":"Pam","startTime":1899.84,"endTime":1903.56,"body":"we're standing in line, the bell"},{"speaker":"Pam","startTime":1899.84,"endTime":1903.56,"body":"ring, whatever. And I might just"},{"speaker":"Pam","startTime":1903.56,"endTime":1907.37,"body":"say, \"Hey, guys, random number."},{"speaker":"Pam","startTime":1903.56,"endTime":1907.37,"body":"15. What's double 15?\" And then,"},{"speaker":"Pam","startTime":1907.37,"endTime":1909.26,"body":"I have to know my kids, so I"},{"speaker":"Pam","startTime":1907.37,"endTime":1909.26,"body":"have to know, do they have to"},{"speaker":"Pam","startTime":1909.26,"endTime":1912.02,"body":"think about that, but either"},{"speaker":"Pam","startTime":1909.26,"endTime":1912.02,"body":"way, once they tell it to me,"},{"speaker":"Pam","startTime":1912.02,"endTime":1914.39,"body":"then I ask them, \"How are you"},{"speaker":"Pam","startTime":1912.02,"endTime":1914.39,"body":"thinking about that? How did you"},{"speaker":"Pam","startTime":1914.39,"endTime":1919.67,"body":"find that? Okay, you knew double"},{"speaker":"Pam","startTime":1914.39,"endTime":1919.67,"body":"15. Double 14? Double 16?\" So, I"},{"speaker":"Pam","startTime":1919.67,"endTime":1922.61,"body":"might string it a little bit. I"},{"speaker":"Pam","startTime":1919.67,"endTime":1922.61,"body":"might do numbers. And when I say"},{"speaker":"Pam","startTime":1922.61,"endTime":1924.65,"body":"\"string it\", you know like do a"},{"speaker":"Pam","startTime":1922.61,"endTime":1924.65,"body":"series of problems that are kind"},{"speaker":"Pam","startTime":1924.65,"endTime":1927.47,"body":"of related. So, if you know"},{"speaker":"Pam","startTime":1924.65,"endTime":1927.47,"body":"double 15, can it help you with"},{"speaker":"Pam","startTime":1927.47,"endTime":1930.41,"body":"double 16, could help you with"},{"speaker":"Pam","startTime":1927.47,"endTime":1930.41,"body":"double 17? So, yeah, you"},{"speaker":"Pam","startTime":1930.41,"endTime":1932.6,"body":"literally just throw out a"},{"speaker":"Pam","startTime":1930.41,"endTime":1932.6,"body":"number, ask them to double it,"},{"speaker":"Pam","startTime":1932.6,"endTime":1936.8,"body":"tell them, \"How they're thinking"},{"speaker":"Pam","startTime":1932.6,"endTime":1936.8,"body":"about it?\" And after kids have"},{"speaker":"Pam","startTime":1937.19,"endTime":1942.2,"body":"doubled a bit, a bunch over"},{"speaker":"Pam","startTime":1937.19,"endTime":1942.2,"body":"time, then a day I might go"},{"speaker":"Pam","startTime":1942.23,"endTime":1944.75,"body":"\"Hey, we've been finding lots of"},{"speaker":"Pam","startTime":1942.23,"endTime":1944.75,"body":"doubles. Let's halve. Okay, guys"},{"speaker":"Pam","startTime":1944.75,"endTime":1950.0,"body":"ready? What's half of 24? What's"},{"speaker":"Pam","startTime":1944.75,"endTime":1950.0,"body":"half of 75?\" Well, now, I would"},{"speaker":"Pam","startTime":1950.0,"endTime":1953.21,"body":"do some work out before I do 75."},{"speaker":"Pam","startTime":1950.0,"endTime":1953.21,"body":"But they might say, \"There is no"},{"speaker":"Pam","startTime":1953.21,"endTime":1957.17,"body":"half of 75. It's odd.\" And I"},{"speaker":"Pam","startTime":1953.21,"endTime":1957.17,"body":"might go, \"If we have $75.00,"},{"speaker":"Pam","startTime":1957.17,"endTime":1960.74,"body":"can we split that? Oh!\" And"},{"speaker":"Pam","startTime":1957.17,"endTime":1960.74,"body":"then, I want to sort of model"},{"speaker":"Pam","startTime":1960.74,"endTime":1962.24,"body":"the chunks they're doing."},{"speaker":"Pam","startTime":1960.74,"endTime":1962.24,"body":"Anyway, so we can talk more"},{"speaker":"Pam","startTime":1962.24,"endTime":1964.28,"body":"about Doubling and Halving at"},{"speaker":"Pam","startTime":1962.24,"endTime":1964.28,"body":"some point, but that's a short"},{"speaker":"Pam","startTime":1964.28,"endTime":1967.43,"body":"routine that can help kids get"},{"speaker":"Pam","startTime":1964.28,"endTime":1967.43,"body":"facility with doubles?"},{"speaker":"Kim","startTime":1967.61,"endTime":1968.06,"body":"Yeah."},{"speaker":"Kim","startTime":1968.3,"endTime":1971.06,"body":"And once they own these"},{"speaker":"Kim","startTime":1968.3,"endTime":1971.06,"body":"strategies, right, once kids"},{"speaker":"Kim","startTime":1971.06,"endTime":1973.34,"body":"have had experience with them"},{"speaker":"Kim","startTime":1971.06,"endTime":1973.34,"body":"all these strategies that we've"},{"speaker":"Kim","startTime":1973.34,"endTime":1976.58,"body":"been mentioning over the last"},{"speaker":"Kim","startTime":1973.34,"endTime":1976.58,"body":"couple episodes, it's okay, in"},{"speaker":"Kim","startTime":1976.58,"endTime":1980.27,"body":"my mind, to say, \"I see you"},{"speaker":"Kim","startTime":1976.58,"endTime":1980.27,"body":"counting, and I know you can"},{"speaker":"Kim","startTime":1980.27,"endTime":1983.18,"body":"count fast. You've been doing"},{"speaker":"Kim","startTime":1980.27,"endTime":1983.18,"body":"that a while, and so your"},{"speaker":"Kim","startTime":1983.18,"endTime":1986.87,"body":"fingers fly, but we have"},{"speaker":"Kim","startTime":1983.18,"endTime":1986.87,"body":"relationships that we can use,"},{"speaker":"Kim","startTime":1986.9,"endTime":1989.39,"body":"and so I want you to use them.\""},{"speaker":"Kim","startTime":1986.9,"endTime":1989.39,"body":"You know?"},{"speaker":"Pam","startTime":1989.39,"endTime":1990.05,"body":"Yeah."},{"speaker":"Pam","startTime":1990.08,"endTime":1992.24,"body":"Hey, you reminded me. We were"},{"speaker":"Pam","startTime":1990.08,"endTime":1992.24,"body":"going to mention that in last"},{"speaker":"Pam","startTime":1992.24,"endTime":1995.45,"body":"week's episode about the Trinity"},{"speaker":"Pam","startTime":1992.24,"endTime":1995.45,"body":"story. Because literally, that"},{"speaker":"Pam","startTime":1995.45,"endTime":1999.2,"body":"happened, right? You had a group"},{"speaker":"Pam","startTime":1995.45,"endTime":1999.2,"body":"of first grade kids, and we were"},{"speaker":"Pam","startTime":1999.2,"endTime":2001.09,"body":"talking, and you said, \"Yeah,"},{"speaker":"Pam","startTime":1999.2,"endTime":2001.09,"body":"Pam. These kids own the"},{"speaker":"Pam","startTime":2001.09,"endTime":2005.65,"body":"strategies. And they're just"},{"speaker":"Pam","startTime":2001.09,"endTime":2005.65,"body":"quick, so whenever they're... We"},{"speaker":"Pam","startTime":2005.65,"endTime":2008.17,"body":"clearly have developed"},{"speaker":"Pam","startTime":2005.65,"endTime":2008.17,"body":"strategies with them. But they"},{"speaker":"Pam","startTime":2008.17,"endTime":2012.61,"body":"count really quickly, and so,"},{"speaker":"Pam","startTime":2008.17,"endTime":2012.61,"body":"when we say, 'We're working with"},{"speaker":"Pam","startTime":2012.61,"endTime":2015.07,"body":"strategies,' they do them. But"},{"speaker":"Pam","startTime":2012.61,"endTime":2015.07,"body":"when we just give them a"},{"speaker":"Pam","startTime":2015.07,"endTime":2017.08,"body":"problem, or they're in the midst"},{"speaker":"Pam","startTime":2015.07,"endTime":2017.08,"body":"of another problem, they're deal"},{"speaker":"Pam","startTime":2017.08,"endTime":2019.21,"body":"is counting by ones.\" And I was"},{"speaker":"Pam","startTime":2017.08,"endTime":2019.21,"body":"like, \"What are you going to"},{"speaker":"Pam","startTime":2019.21,"endTime":2020.44,"body":"do?\" And you're like, \"Oh, I'm"},{"speaker":"Pam","startTime":2019.21,"endTime":2020.44,"body":"just going to tell them to"},{"speaker":"Pam","startTime":2020.44,"endTime":2025.33,"body":"stop.\" And I was like, \"What?\""},{"speaker":"Pam","startTime":2020.44,"endTime":2025.33,"body":"And so, you did, right? If I"},{"speaker":"Pam","startTime":2025.33,"endTime":2027.7,"body":"remember right, you pulled them"},{"speaker":"Pam","startTime":2025.33,"endTime":2027.7,"body":"together, and you said, \"You"},{"speaker":"Pam","startTime":2027.7,"endTime":2029.83,"body":"guys, you own these strategies."},{"speaker":"Pam","startTime":2027.7,"endTime":2029.83,"body":"When you see these problems, oh"},{"speaker":"Pam","startTime":2029.83,"endTime":2031.63,"body":"you're supposed to actually use"},{"speaker":"Pam","startTime":2029.83,"endTime":2031.63,"body":"the strategy?\" And the kids were"},{"speaker":"Pam","startTime":2031.63,"endTime":2033.1,"body":"like, \"Oh, we are?\" And you're"},{"speaker":"Pam","startTime":2031.63,"endTime":2033.1,"body":"like, \"Yeah.\""},{"speaker":"Kim","startTime":2033.1,"endTime":2033.52,"body":"Yeah."},{"speaker":"Pam","startTime":2034.12,"endTime":2036.01,"body":"Then, you did it with them."},{"speaker":"Pam","startTime":2034.12,"endTime":2036.01,"body":"You're like, \"Okay, so when when"},{"speaker":"Pam","startTime":2036.01,"endTime":2039.97,"body":"I see a problem like 13 minus 7,"},{"speaker":"Pam","startTime":2036.01,"endTime":2039.97,"body":"what's a strategy you could"},{"speaker":"Pam","startTime":2039.97,"endTime":2041.86,"body":"use?\" And the kids start"},{"speaker":"Pam","startTime":2039.97,"endTime":2041.86,"body":"counting, and you're like, \"No,"},{"speaker":"Pam","startTime":2041.86,"endTime":2044.47,"body":"no, no, no. We're not going to"},{"speaker":"Pam","startTime":2041.86,"endTime":2044.47,"body":"count on these anymore. I'm"},{"speaker":"Pam","startTime":2044.47,"endTime":2047.5,"body":"telling you, use these"},{"speaker":"Pam","startTime":2044.47,"endTime":2047.5,"body":"strategies.\" So, those of you"},{"speaker":"Pam","startTime":2047.5,"endTime":2049.69,"body":"that are pushing back and you're"},{"speaker":"Pam","startTime":2047.5,"endTime":2049.69,"body":"saying to yourself, \"Pam, we"},{"speaker":"Pam","startTime":2049.69,"endTime":2053.02,"body":"don't want kids refiguring these"},{"speaker":"Pam","startTime":2049.69,"endTime":2053.02,"body":"problems all the time.\" There is"},{"speaker":"Pam","startTime":2053.02,"endTime":2055.78,"body":"a moment where you can say, \"I"},{"speaker":"Pam","startTime":2053.02,"endTime":2055.78,"body":"don't want you refiguring it"},{"speaker":"Pam","startTime":2055.78,"endTime":2059.89,"body":"with a less sophisticated,"},{"speaker":"Pam","startTime":2055.78,"endTime":2059.89,"body":"therefore take too much"},{"speaker":"Pam","startTime":2059.89,"endTime":2065.5,"body":"cognitive load, strategy. I want"},{"speaker":"Pam","startTime":2059.89,"endTime":2065.5,"body":"you to actually dive into the"},{"speaker":"Pam","startTime":2065.5,"endTime":2068.59,"body":"strategy that might, in the"},{"speaker":"Pam","startTime":2065.5,"endTime":2068.59,"body":"moment, actually take a little"},{"speaker":"Pam","startTime":2068.59,"endTime":2072.04,"body":"bit more thinking because I want"},{"speaker":"Pam","startTime":2068.59,"endTime":2072.04,"body":"to build these relationships,"},{"speaker":"Pam","startTime":2072.16,"endTime":2076.87,"body":"then the facts become a natural"},{"speaker":"Pam","startTime":2072.16,"endTime":2076.87,"body":"outcome and so much more.\""},{"speaker":"Kim","startTime":2077.02,"endTime":2077.53,"body":"Yeah."},{"speaker":"Pam","startTime":2077.98,"endTime":2081.46,"body":"Yeah, nicely done. Alright,"},{"speaker":"Pam","startTime":2077.98,"endTime":2081.46,"body":"ya'll, let's help kids build"},{"speaker":"Pam","startTime":2081.46,"endTime":2084.94,"body":"their fact relationships and"},{"speaker":"Pam","startTime":2081.46,"endTime":2084.94,"body":"work with them enough to build,"},{"speaker":"Pam","startTime":2085.0,"endTime":2088.9,"body":"so that they have the facts at"},{"speaker":"Pam","startTime":2085.0,"endTime":2088.9,"body":"their fingertips. Thanks for"},{"speaker":"Pam","startTime":2088.9,"endTime":2092.56,"body":"tuning in and teaching more and"},{"speaker":"Pam","startTime":2088.9,"endTime":2092.56,"body":"more real math. To find out more"},{"speaker":"Pam","startTime":2092.56,"endTime":2094.36,"body":"about the Math is"},{"speaker":"Pam","startTime":2092.56,"endTime":2094.36,"body":"Figure-Out-Able movement, visit"},{"speaker":"Pam","startTime":2094.51,"endTime":2097.93,"body":"mathisfigureoutable.com. Let's"},{"speaker":"Pam","startTime":2094.51,"endTime":2097.93,"body":"keep spreading the word that"},{"speaker":"Pam","startTime":2097.93,"endTime":2099.22,"body":"Math is Figure-Out-Able!"}]}