 Alright, this is it. This is why I'm here. Three reasons I want to play or do math, and I pretty much always want to do that. I want to talk about independent math assignments, and when we were growing up it was homework, but that was because we all had somebody's home to go to. So right now, if I think about independent assignments, I want to tell you why it's important for kids to have those independent assignments. Independent work, independent learning. And I'm also here because there's dinner. I thought maybe that would be just perfect. If you have questions, I have an Orange Southwest email, and you're welcome to use that. I really genuinely believe that math is fun, and I believe that learning it should be fun. And so you're going to have a smattering of fun while we're doing this, okay? Now I bought this game. This is Think Fun, and I got it at Rite Aid, and I think it was under $6. So it's just a bunch of dice. It happens to have a Decahedron, and regular ordinary dice. So it's good for little kids as well because it's big. But I've thought that it was a great camping game. So when I rolled the dice on my desk, the four came up as the target, and you have five dice with numbers. So you may use each number once, but you can use Add, Subtract, Multiply, or Divide. Remember to use each number only once to reach four. Try to use all five with no paper. All right, go. And you get seven minus six. No, you didn't. Keep going. So you have one. You have this one. That's one. She did not. Yeah. You don't have to use all the operations, but I can. Keep going. You got one? Try it. Go. All right. Go. Yeah, go. Three times four is 12. Good. 12 minus six is six. Six minus three is three, plus one is four. Nice work. You got another one, Heather? Go. So if you add the six die, the three die, and the three die, you've got 12. Yeah. Divide that by four. You get three. Add it to one, four. Similar here, yeah. Oh, similar? Similar, but not always, not all in the same order. This is a fun game. Isn't this great? And it's A, low risk, right? All of your dice is under 10. Okay. Right? So you have low risk. And you don't need to use them all? Well, you know what? This is a high school audience. So I said yes, you need to use them all. Okay. But when you start, you don't. Okay. It's just that you get credit for using each that you use. So you want credit for all five. Yeah. You can. That's one way of scoring. Yeah. And consequently, you know, if you've got littles in the same place you've got bigs, that's a way of dealing. You can also use these numbers if you have bigs around the campfire as exponents or as negative numbers or as absolute values, but you may not want to. And if you really have bigs, then you can use logs. But I don't get there. But I do have a lot of engineers in my family. So they would love that. Okay. One thing I did, I always go to the identity elements, which is zero and one. And they clean up the stuff you don't want. Okay. So if I've already got a four, I went to three and three and I can use it as a one by division, or I can use it as a zero by subtraction. And as soon as I have a zero, I can multiply anything times zero and keep this. Okay. And so that's a property of math that kids assume they don't ever know that it's one they should have learned by name. But it really is very handy. Independent learning, now that we've had a little fun. It's all about really learning how to live responsibly in our world, citizenship, kind of skills. If they can be independent and follow through, then they're being responsible. And we share that task of helping the students accomplish this. So it's appropriate, if I had had a full audience of parents, it would be appropriate that we all share that task, that responsibility. And I think we do share that even with our roles here. If we're a community, we should all share it anyway. Okay. So these are ways, reasons that it's important that we do this independent learning. It creates attention to personal accountability. Kids don't know that if they've done this, they have been personally responsible. And that's a pretty grown up skill. And they should be aware of that as a skill. And how grown up it is. It provides an opportunity to problem solve about how to get the papers together, how to present their answers, how to be sure they have a pencil or a pen working, how to organize their paper. That's problem solving along with the math. And it's always more than just calculation. It's math. It offers a sense of pride in accomplishment. They're not going to say, oh, look at me. I'm proud of me. We have to do that. But after a while, they'll see it. BD is a big deal. It enhances the development and use of language. I can't not talk about language in math. There are all sorts. Hi, come on in. And grab a plate. I'm in the middle of it, so I'm going to keep going. All right. We'll listen while we acknowledge. Excellent. The use of language is enhanced when you have independent learning because they have to be precise. They have to read language that they heard in the classroom and attach it and actually say, oh, my gosh, I heard this. And now I'm reading this. And it's kind of a new experience. It's a different part of your brain that you're going to access. Also, there is directional language. And there's content language. And I've already talked to you about visual language versus auditory language. When the kids are trying to balance all of that, they've got to be independent. They've got to be able to practice on something that is tangible. And so that comes in. So it is a big deal. It gives another reason to celebrate steps forward in maturity. We want any reason for an adolescent to step forward in maturity. And this could give us a chance to celebrate. Hi, Lane. This is a big deal. It creates an event where good questions can be generated for class. So the kid gets there and they're looking at the homework and they're not really sure how to do it. And so they didn't ask any questions in class. Now they know what they're going to ask about. Now they know what they don't know. And a lot of times when they leave class, they don't know what they don't know. Another big deal. Students will begin to see what they do know. Now they're looking at something that is something they've heard a little bit about or they sort of listened and sometimes didn't. And now they know what they do know. And they can make those connections, which is really where the learning goes. The learning doesn't happen in the classroom. The learning happens when they make the connections. And they can't make those connections until they're working on actual, tangible information. Another big deal. Personal learning lasts longer than passive learning. You can try pouring it in there and it's not going to go. There are a couple leaks. I don't know where they are. It also extends the lessons that are worked on in school for a deeper, better understanding of what's going on. It allows the student time to practice a skill so as to create that foundation for something new to be built on. And these are the best reasons. It creates an opportunity for you to know what your student is learning so that you can share that. And it allows for a stronger partnership for your student's real world skills. A partnership with an adolescent. It's golden, you know? A little fun. I love Desmos. Dan Meyer always opens, he's the one who does this. He always opens his talks, his presentations with I used to teach high school and what high school is all about is bring the kids in to do something that they hate doing with you. So he started doing this stuff. I know if I have this one, let's go all the way back so you can see it. Okay. So the goal is get all the stars. Get to no lines. So when you launch, can the marble wipe the stars out? Okay. This is a free app. You can put it on your phone. You can put it on any of your laptops. Right? It's just so incredibly fun. I use this as an instant sub-plan when suddenly I need one. The kids open up and they do this. They're ready. So I'm going to launch this. The line's wrong so we have to do something. It tells me right away I change one number. Do you know which number to change? The one is where it crosses. Do we want it to cross this high? No. Okay. So I'm going to change the one to what? Where do I want it to cross? You want a two? You want a negative two? What do you think? Is it going to work? So far so good. This is just telling me how to reset. So it's scaffolding also. And it's gently scaffolding. But my sixth graders, seventh graders are all working on slope right now. And eighth graders are now building slope and talking about the parts of the equation. And ninth graders, we'll see it again a little more formally. And eighth graders, we'll see it in series of lines or series of graphs of information. So what do I need to do here? It says just change one number in the row below to fix the marble slide. The floor, yeah. Because the floor is telling me how steep it's going to be. I don't think the same way. So I'm trying to hear. I can't, what's the slope of the stars? That'll give you your number. What do you want? Do you want to guess? Do you see how steep the line is? That steepness is a four. And four makes it. So you wanted the line to go through the stars. What number would you guess would go through those stars if you changed the four? If that's a four. Do you want it bigger or smaller than the four? Do you want it bigger or smaller? Smaller than four. So let's get rid of the four and see what happens. So this is a one on one. You want one over two, which is what would we call it? One-half. It's easier for me to do that. Yeah. So I've got smaller. More shallow is smaller. And we did it. Here's the other thing that I wanted to point out right now. With a one on one, at Killington, this is the expert slope cascade. And you can't have it steeper than that. And it doesn't look very steep. I mean, when you're on skis, this looks like it would be really easy to do. But the Killington cascade is this. If you go to Disney World and you go out the water, I forget what the splash mountain I think it's called. And you're in the little boat and the track is done. And now you go over the front and into the pond. That over-the-front slope is a one-on-one. And the problem is, and Lane helped me with this here, your boat is coming out at a certain speed. Or you're going down the mountain at Killington at a certain speed. You would go end over end because the whole gravity adding to this is not helpful. When you have a 7% slope going over Menden Mountain into Rutland, I think it's 7% there. And that's 7 feet dropping for every 100 feet. Doesn't seem like very much at all. But if you're in an 18-wheeler carrying a double load with six brakes to watch and 18 wheels and 13 speeds or 15 speeds, I forget what I had, but it's sizable. I'm going to keep going and come back here. Okay. Back to independent learning. All right. What do we have to do to encourage it? Everybody knows that you provide a quiet space and a neat space with all the materials that you need. A lot of our students don't necessarily have that where they are, but it doesn't mean that it can't be provided somehow. We're trying to do it ourselves. We have lots of after-school programs. We also have other places for independent thinking. It doesn't necessarily have to be what we traditionally had, but the independent thinking is what is really important. When your student is stuck, some of these questions, first of all, it's the I don't get it, and your response is, read it out loud to me because they probably have skimmed it or they may not have read it at all. And also, their life is auditory when they hear it. They might have a whole better view of it. What will your answer look like? I have students that don't know if they're supposed to write the answer in words or in numbers. And if it's supposed to come in code like algebra is, they don't always know the code. Okay. So maybe if they examine what it's supposed to look like, then you can support that. What do you know about the question? Well, I know it's about area. Good. So what do you know about area then? So it promotes some thinking. What will your questions be to your teacher? You're not going to say, I don't get it. You're not going to say, couldn't do it. I have students that write I, what is it, I, D, K, I, D, K. That's the specific. If we can get them to narrow it down, then they have really good questions and they're realizing what it is that they didn't know on top of the fact that they're realizing what they didn't know. Okay. When do you need to hand this in? So you know whether your student has time to ask the questions. Okay. Do you have notes or information in your classwork? Nope. Right? It might encourage more active listening in the classroom. Okay. All right. Back to more fun. Some of the toys that you should have at home. Legos. Do you have, how many Legos do you have? Do you have a wall full? Buckets. Yeah. My mother gave me connects when I was teaching middle school. So I still got Legos when I was grown up. And they are so fun because you can see the motors and you can see the gears working. I love them. Mine didn't have motors on them, except for what I could create. But now they have the Lego robotics, which is really cool. Anything with drones so that there is coordinate plane, three dimensional coordinates that they can work with. Any remote control, bots, cars, any of those things. Those are all great. You're looking at spatial problem solving. It's really cool. Not to mention the fact that you're also looking at all of the coordinates that would be there. Etch-a-sketch. It's one of my favorites. You know, what are you? Two years old and you're carrying your etch-a-sketch around and dragging it everywhere you want to go. But it is a coordinate plane. This is the x-coordinate. And it does go horizontally. And it does go in a positive direction to the right and a negative direction to the left. And this is the y-coordinate. It does go vertically. And it does go positively up and negatively down. And when you're doing integers and you do a positive direction and a negative direction, you're going to have a negative. And your slope will be negative. And when you do positives to positives or negatives and negatives, your slope, your slanted line will be a positive line. Even when you're two years old. I had a sixth grader that brought me this size with George Harrison. Sketched out. Amazing. Rubik's Cube, problem solving, persistence, making sense of repeated structure, all of the eight practices. I have a question about Rubik's Cube. So my son got the Rubik's Cube. But then he went online and he found the algorithm. So then he would practice the different algorithms. And then there was one that was... He was starting to time himself. But then that was a slow algorithm. So then he went back online and he found another one that's faster. And is that still teaching them? Do you see he's learning an algorithm. He's being persistent. He's changed what the problem is. He wants to do it faster now. Though he already knew what the problem was. And I'm sure he practiced for a little while before he gave up and went to internet. Most kids mess with it. So they've already got some practice around what the original task is. But now he's changed the task. And he understands the algorithm. I couldn't... I don't have the... I suppose I could. I believe in my learning ability, but I wouldn't do it. Models. If your student is building models or playing with models, what fun is that? This is a 33 to 1. So the real car is 33 times bigger. I don't know why they said 33, but sometimes it's 34 on these things. But I had students that thought that they had to measure the whole car. Because the whole car was what they were trying to rebuild. And when I asked them quietly, if a headlight that was 33 times bigger than this headlight was in your hands, would it fit in a car that would be 33 times bigger than this car? Then they saw that it was okay to measure any part. And figured out. Because I had two groups. One group was measuring the real car and the other group was measuring this. And they were trying to figure out what it was to get to a unit rate. Okay? I love the cars. But very few of these metal cars now are made in models that we can afford. Spirograph, gears. What fun. And again, structure and colors and all of those things. Love it. What doesn't work? Arguing. More than 20 years I taught middle school and I was the reason for the arguments. And that shouldn't be. And when you're working with adolescents, you have very little time with them anyway. So let's not make it arguing. But don't let the kid off the hook. They've really got to follow through. So figure a solution with them. Find out how you can get through this. Find out what would be the way to complete this independent thinking. And also, like your son, decide whether, in fact, he's accomplished something. It may be that the homework or the independent learning or the opportunity isn't finished. But has there been an accomplishment and reward at least that? Betty, can I just say something on that? When I worked with students, what I noticed too and I used to tell them what I liked about math is there's all these steps. So it's like you're solving a mystery in my opinion. It's fun. Except for geometry. Not so fun. But I'd say show the work you have to your teacher tomorrow. And maybe there's two more steps, but you got this far. Correctly. And now you're stuck. That's okay to go back with that. And it's evidence of genuine effort and genuine thinking. So that is an accomplishment. Disorganized work is exactly what the student remembers. Some jumble. Something that isn't really easy to repeat or figure out again later. How much time, how am I doing for time? Okay, thank you. Doing the work for the student doesn't help anybody. Helping the student start might be appropriate. This last one, don't throw the teacher under the bus because the student will take that inch and create a mile. The student will come in and say mom says, dad says that you're not able to teach. And nobody wins in that. Teacher doesn't, the kid doesn't. Absolutely. And that's the one we have to think about most. Don't you love it? Games. Promote the culture of learning. Cribbage, poker, hearts, yatsi, rummy, canasta pitch. Noted tonight while we were talking. Backgammon is full of problem-solving and choices. Chess also, Monopoly. Battleship. By the way, Desmos has a really cool level of battleship that actually scaffolds. Shoots and ladders. Even high school kids don't have any understanding of what a hundred looks like. Shoots and ladders. It's back and forth, choices, lots of things there. Prime Climb is here. This is a number line. It's coded. And as students actually play this, it gets more and more complicated. But right now, we have one student that plays this twice a week. This student last year gained two grade levels in the testing because this doesn't look like a number line. It's a spiral. And like I said, it's coded. So you can use it for even more of the fluency that you might need in math. And magnitude. The student had no magnitude, which I want to talk about. There's lots of stuff that we use. Muggins is one game that's a target game like this. Multiply or add war. You deal out who gets the highest sum or product. And then you get all the cards. Desmos. Again, this is free. Tang math is kind of fun. It mixes stuff up. It's random fluency. Quizzes we use often at school. It's free. And you can be competitive or you don't have to be. Reading. Outliers. It seems crazy that Malcolm Gladwell might be something a teenager would read. Especially with all of these incredible books out here. But when I have teenagers read this, last year I had a seventh, eighth grade girl with a few other students, but she read it in two nights. She couldn't put it down. It was good. And it's statistics. And you have to decide at the end whether you agree that serendipity plays a part in wealth and success. Or does the 10,000 hours that you're also supposed to put in for practice perhaps play a part? What's math got to do with it? Joe Bowler, I've got that up there. The boy who harnessed the wind. The thinking that was there and modeled is really great. The number devil, kind of a new perspective on a lot of traditional math. Really kind of fun. Bad at math. This will turn your head around as to whether you're really bad at math or not. And Orlan always writes in such a way that it's funny but real good. Movies. I didn't write whether they were PG or not. So you've got to look that up. A beautiful mind, hidden figures, money ball. Adolescents loved it. October sky. Imitation game. Dark and light. The man who knew infinity. This is my favorite. Do you know this one? Any of you? Yeah. Right. I just want you to hear him. Come on. Are you a geometrical journey? Yeah, Mr. Spirit. There's a lot more to mathematics than two games, too. That's right, Donald. And you can find mathematics in games, too. I think that said everything I wanted to say, right? Magnitude. When students have magnitude, and you need to start right from preschool, when students have a sense of magnitude as to how big a number, how small it is, how does it compare with something else, it makes all the difference in their understanding. If this is one on the number line and this is a million, ask them where they think 100 is. It's amazing. They're going to split this thing up into 10 pieces and they're going to say that it's right up here. No. I got an audience that knows that it's right down here because this is a million pieces to get here. Change the number line. Find out where is 12-hundredths. I have high school students that will put it below zero. Where is one-third? Where is eight-thirds? They lose it. They don't really know. Again, this is visual direction. They've heard it, but they haven't tried it out. This one here, 12 and 22. 12 isn't a 20t. So it's not 12t. So they think this is in a whole different realm than the t's earlier. As it grows, we hope they get better at it, but some don't because, again, we're looking at how is the language doing. Experiences in their lives, unit pricing, they're looking for bargains. Can they find them? Gas mileage? They're looking for adventures. Can they afford them? Elapsed time? When do you put the turkey in? And then when do you start the potatoes? Percent tip? Did they get ripped off? In the bargain. Slopes? Lots of them around them. Wheelchair slope? Dog access on the bed, right? Rise and run. Reality of the one-one slope. Gardening. Fertilizer calculations. I don't know. A lot of people who can do that. But the fence post counting is one less if it's all the way around. Right? Building birdhouses or anything that has a roof pitch. Materials that need to be figured out. Board feet. Area to be painted is always an issue. Cost. This is what adolescents want. The cost of the new car plus the insurance plus the interest on the loan plus the gas and how much the insurance went up after the speeding ticket. And mail insurance versus female insurance. Write and read poetry. Poetry is a structure. It's repeated structure. Often in some forms. Okay? Sometimes you're going to repeat and repeat because there is a purpose. That all happens in math. Draw and view all sorts of art. Your span here should be your forearm. Not mine because I'm a little wacky but your wingspan should be close to how tall you are. We are so incredibly proportional that doing art of people is pretty mathematical. Playing large field games. When Title IX was passed women's math test scores went up. They were now actually experiencing the math and they hadn't been able to do that before. Old enough to know that you could only dribble three times and you had to pass the ball off because we were just such delicate flowers. All of us. Personal competitions. They do a lot of math and they do their own. We don't honor that sometimes. This is it. Music. This is the end. Thank you. I love this one. 125,600 million measure, measure right in sunsets, in mid-nights in cups of coffee in inches, in miles and laughter and stride about the sky. Problem solving. Repeated structure. Tons. Precision. Tons. Those are the eight practices. And it's all in that. Best audience. The joke was back. Did the joke? The next slide back. All right. Thank you. Thank you. Thank you. Does anyone have questions for Betty? Take a minute before Lane starts to look at some of the things that I have there. Some of them are the games that I talked about. And...