Episode #272: How To Consolidate & Close Your Building Thinking Classroom Lesson [Part 2]

Feb 12, 2024 | Podcast | 0 comments



Episode Summary:

As educators of mathematics around the world embrace the ideas shared in Building Thinking Classrooms, more and more students are being positioned to think collaboratively during math class instead of simply mimicking steps, rules, and procedures. 

While this shift in mathematics teaching practice is a massive leap in the right direction, our work does not stop once students solve the thinking task at hand. 

Rather, the real work for the facilitator now begins. 

Join Peter Liljedahl, Jon Orr, and Kyle Pearce from the opening session of the 2023 Make Math Moments Virtual Summit as they discuss one of the most important, yet often overlooked parts of an effective problem based mathematics lesson: the closing.

This is part 2 of the hour-long Keynote session from this past year’s Virtual Summit in November. 

What You’ll Learn:

  • Practical Strategies for Dynamic Teaching: Learn how to adapt your teaching style to meet the evolving needs of your students, ensuring that each lesson is as effective as possible.
  • Deep Dive into Consolidation Techniques: Gain insights into powerful consolidation methods, such as gallery walks and group discussions, that can enhance student understanding of complex concepts.
  • Innovative Note-Taking Approach: Discover a structured note-taking method that not only aids in student learning but also encourages active participation and reflection.

Attention District Math Leaders:

How are you ensuring that you support those educators who need a nudge to spark a focus on growing their pedagogical-content knowledge? 

What about opportunities for those who are eager and willing to elevate their practice, but do not have the support? 

Book a call with our District Improvement Program Team to learn how we can not only help you craft, refine and implement your district math learning goals, but also provide all of the professional learning supports your educators need to grow at the speed of their learning. 

Book a short conversation with our team now


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00:00:00:04 – 00:00:21:24
Peter Liljedahl
So how do we do something different than this? How do we shift from note taking to note making, which is where the students take ownership. They are responsible for their using notes as a way to consolidate their learning, including the learning that happened in the consolidation. How are they going to.

00:00:21:24 – 00:00:51:07
Jon Orr
Raise their math homemakers? In this episode, you are going to learn practical strategies for dynamic teaching. You’re to learn how to adapt your teaching style, to meet the evolving needs of your students, ensuring that each lesson is effective as possible. We’re going to talk innovative note Taking strategies. You’re going to discover a structured note taking strategy from Peter Little dull on a method that not only AIDS in student learning, but also encourage active participation and reflection.

00:00:51:09 – 00:01:18:20
Jon Orr
You’re about to hear part two of our webinar, our keynote session from the 2023 McMath Moments Virtual Summit with Peter Little Dell. We titled that How to Consolidate and Close Your Building Thinking Classrooms Lesson. This is part two. We had part one, so we split the session, the hour long keynote session into two episodes. If you are hearing this and you did not hear part one, head back to episode 270.

00:01:18:20 – 00:01:39:07
Jon Orr
It’s a couple episodes before this and give that one a listen and then come back here and listen to part two. On how to consolidate in close Your Building Thinking Classroom Lessons. It is Kyle Pearce, myself, John Awe and Peter Little Doll. We are talking all about how to closing that lesson. We specifically talked about note taking in this episode.

00:01:39:09 – 00:02:00:01
Jon Orr
So go ahead, click or continue to listen to this. You don’t have to click anything. You’re already listening to this and we’re going to dig right in. Here we go. Oh, oh.

00:02:00:03 – 00:02:04:14
Kyle Pearce
Welcome to the Making Mouth Moments That Matter podcast. I’m Kyle Pierce.

00:02:04:14 – 00:02:07:08
Jon Orr
And I’m John or we are from make math moments dot com.

00:02:07:10 – 00:02:18:03
Kyle Pearce
This is the only podcast that coaches you through a six step plan to grow your mathematics program whether at the classroom level or at the district level.

00:02:18:05 – 00:02:23:19
Jon Orr
And we do that by helping you cultivate and foster your mathematics program like a strong, healthy and balanced tree.

00:02:23:22 – 00:02:33:07
Kyle Pearce
If you master the six parts of an effective mathematics program, the impact of your math program will grow and reach far and wide.

00:02:33:09 – 00:02:58:23
Peter Liljedahl
So what we’re talking about here, what you’re talking about here is a sort of consolidation that uses student work. That’s a gallery walk, right? Which works really well When we use a divergent task. A divergent task is like a three act task or anything where I give the task in ten groups to going eight different directions, right? And now we can go and look at we can look at different solutions because there’s so much richness in the ways they’re thinking.

00:02:59:03 – 00:03:18:19
Peter Liljedahl
And like you said, we can go from most common to least common. We can also go from most accessible to least accessible. We can go from basic to complex, or we can go from concrete to abstract. There’s lots of ways to progress and there’s a lot of redundancy between those. But just because a student is up here at the Uncommon doesn’t mean they went through common.

00:03:19:00 – 00:03:38:05
Peter Liljedahl
Not every student followed the progression that the consolidation is going to take us on. A lot of students jumped in here. It’s a flip, a coin. Let’s do it this way. But they didn’t get to see the other solutions. And they’re standing. They’re going to made a lot more sense. That was way easier for me to understand than we were wrestling with this complex thing up here right.

00:03:38:07 – 00:04:04:05
Peter Liljedahl
And so there’s interest in that. Now, what if it’s not a divergent task? What if it’s a convergent task, meaning like, okay, we’re multiplying three digit numbers, we’re turning decimals into fractions or vice versa. We’re doing areas of complex shapes or factoring quadratic solving systems of linear equations. We’re ordering integers, or we are simply completing patterns at a younger grade.

00:04:04:07 – 00:04:33:21
Peter Liljedahl
These are not so divergent. Yes, we’re going to see a variety, but they’re not super divergent. So if you skip ahead a couple of slides here, we’re going to see an example of how the new consolidation for a diverse or a convergent task looks like we’re going to do more. Teacher Scribe So here’s two examples. So this is what this consolidation that’s not in the book, but we’ve been playing with a lot, which is how do I consolidate a lesson on patterns or factoring quadratics.

00:04:33:23 – 00:04:52:15
Peter Liljedahl
And the way we have sound works really well is that I put up three questions and I’m going to be the scribe here. I’m going to put up three questions and then I gather the students around the board and I say, I put up three questions from today’s lesson, but I may have put them in the wrong order.

00:04:52:17 – 00:05:19:09
Peter Liljedahl
What order should the questions be in and why? And as the audience is watching this, we always say turn and talk to the person next to you. What order should these questions be in and why? And what’s amazing about that is great for two grade 12, they get the order right every single time. But what’s even more interesting is the conversations they have, because they’re looking at those patterns and they’re going, well, the middle ones first, because I can continue that pattern.

00:05:19:13 – 00:05:39:19
Peter Liljedahl
The second one would be the top one because like I can work backwards on that pattern. But that third one at the bottom, I got to do some trial and error. I got to think about it really hard. Like that’s the conversations they’re having unprompted by me just simply saying, what should they be in and why? Same with the second one there.

00:05:39:19 – 00:06:00:10
Peter Liljedahl
They’re going, Yeah, the bottom one is definitely the easiest one. That’s the one that should be first, right? Everything’s positive, right? The top one is probably second. I got some negatives in there. And that middle one that’s tricky with that three in the front, right. So what they’re doing is they’re noticing a naming variance in invariants. You use that term yourself.

00:06:00:10 – 00:06:21:10
Peter Liljedahl
You said noticing your naming, they’re noticing in naming here, we don’t have to go look at other white boards because if we’re looking at other white boards, like there’s no work on the boards because this is a kind of work that happens in discussion and then answers hit the board. So we have to create more thinking in this consolidation space by doing this.

00:06:21:12 – 00:06:45:22
Peter Liljedahl
But what’s even more interesting is what we do next. So if you go to the next image, just advance one. So here is those same quadratic ones. If you press, if you just advance once more, it’ll start playing automatically. Is how do we actually progress through the solving of this as a class now? Right. So now we’ve figured out that the bottom one is first that students are telling me this top one second, the middle one’s third.

00:06:45:24 – 00:07:02:14
Peter Liljedahl
Now what do we do? Right? We go, okay, well, is there something I can do on the first one? Is there something I can do right away without too much thinking? Oh, yeah, I can put the parentheses there telling me. So I do that. But here’s the interesting part. Can I do that on the second one too? No, I can.

00:07:02:16 – 00:07:17:22
Peter Liljedahl
Can I do that on the third, right. Yeah, I can. Okay. What? Go back to the first one. Is there something else I can do? And this is going to keep playing and what you’re going to see is that we’re moving. We’re not solving all of one together. I’m acting as a scribe. We’re jumping. And what are we seeing?

00:07:17:22 – 00:07:20:11
Peter Liljedahl
What are the students seeing when we do that?

00:07:20:13 – 00:07:44:11
Kyle Pearce
I love it because you’re giving them again, not only the opportunity to think, but it’s really about trying to uncover those behaviors as we’re talking about, right? So we’re truly going like so this isn’t random here. Mathematics is really logical. It really hurts your soul as math teachers. It doesn’t matter what grade you’re. And when students go, none of this makes sense.

00:07:44:13 – 00:08:04:14
Kyle Pearce
Yeah. And I mean, I used to hear that in the early days teaching, and I recognized now many years later that, oh my gosh. Well, of course, it didn’t make any sense. They were just following me blindly. Right. And in reality here, you’re allowing them to truly think through it and really trying to figure out what the heck is going on here.

00:08:04:14 – 00:08:25:15
Kyle Pearce
And of course, you as the facilitator are there to guide that conversation. Right. Not to shut down ideas, not to tell a student like, nice try, but no, but you just do what they say and let it break itself. Let the rule take over. Like, okay, so you’re saying to do this, let’s try that.

00:08:25:17 – 00:08:42:21
Peter Liljedahl
Yeah. Or I’m going to write what you say and then someone else in the room is going to go, No, no, no, that’s not what they meant, right? So it’s like we have to allow the room to breathe here. But I’m driving the bus, right? I picked these three tasks and I’m saying, What can I do on this one?

00:08:42:21 – 00:09:07:06
Peter Liljedahl
Can I do the same on that one image doing that? What the kids are starting to see is how these tasks are connected and where the connection stops, where the differences are. They’re seeing the invariants and they’re seeing the variant. And it’s so this isn’t three distinct tasks anymore, and this is a full range of what happened in the lesson that video that you played earlier of the kids working, that was this lesson.

00:09:07:08 – 00:09:37:24
Peter Liljedahl
They covered the entire sequence of factoring quadratics in this lesson. They went from having never seen it before to factoring quadratics where the leading coefficient was greater than one and not a prime number. Now how do we then consolidate that Right? Doing a gallery walk is not going to work, not with this kind of task. We have to come up with a different type of consolidation that’s still think about that video of that consolidation is still consolidating from the but it’s still noticing in name.

00:09:38:01 – 00:09:45:20
Peter Liljedahl
It’s still achieving all of those things. But we’re doing it for a type of task that a gallery walk doesn’t work well for.

00:09:45:22 – 00:10:15:20
Kyle Pearce
I want to mention something I saw in the chat here and then Sorry, John, I’ll let you jump in there, but I saw a few people saying like, So is this the consolidation stage? And I think sometimes we look for like, does it always look this exact way? And what I’m hearing you say, and I want to be super explicit for everybody in the chat is that no, we have to figure out what do we want kids to take away and how can we help to bring this and draw this out.

00:10:15:20 – 00:10:38:16
Kyle Pearce
So you’ve done sort of a great job here with a scenario like this where you’re going and you set it all reiterated that a gallery walk, you might still do a gallery walk and have a look, but ultimately that’s not going to do the trick is that we’ve got to be very, very explicit and we could either do it the old way, which is, all right, now you did all this work.

00:10:38:16 – 00:11:00:16
Kyle Pearce
Now here’s exactly what you learned. Bang, bang, bang, bang. But guess what? Over time, kids are going to go he’s going to tell me anyway, or we could do something like you’ve described here. Now, when I say that something like which means it might look very different for a different topic or a different concept, the real question comes down to again, last year’s session.

00:11:00:16 – 00:11:23:07
Kyle Pearce
We talked a lot about intentionality, right? And the intentionality, all of the thinking is to get us to the place where we can go. They’re going to walk away knowing blank. And when I say blank, that could be multiple blanks, right? It could be many different things. It might be a model, it might be a strategy, it might be a process or a procedure.

00:11:23:07 – 00:11:45:16
Kyle Pearce
But ultimately, at the end of the day, we’ve got to be clear on that. We don’t just want kids thinking for thinking sake, even though that’s amazing and it gives teachers so much happiness when it happens, we really need that work to be leading us towards what I’ll call the real work, which is kids understanding what it was that they were thinking about.

00:11:45:18 – 00:12:08:19
Peter Liljedahl
And it’s like I said, here’s a difference with a gallery walk. I’m trying to pull the consolidation out of the boards, right? With this type of consolidation, I’m trying to pull the consolidation out of the discourse because when the students are at the whiteboards doing this type of a task, a thin slicing task that the boards don’t carry the thinking.

00:12:08:19 – 00:12:29:18
Peter Liljedahl
The thinking happened in discussion. So looking at the boards isn’t going to help. I need to now recreate some of that discussion and then create some sort of an artifact and experience out of it so that I can pull from their discussions the thoughts and organize and structure and formalize them here. I see lots of questions for what would this look like in this unit?

00:12:29:18 – 00:12:51:24
Peter Liljedahl
What will it look like in this topic? The answer is this You pick three tasks from your sequence that they got through, right? You pick three tasks, you put your jumble the order and you ask them to unscramble it. That’s how you start. What order should they be in? And then, okay, let’s go to the first one, the one you’ve labeled for one.

00:12:52:05 – 00:13:11:07
Peter Liljedahl
What can I do first here? What’s my first step? Does the first step work on the second task? Two? Can I do that same first step? Will it work on the third one? Right. And what we’re trying to do is highlight the parts where there is invariance, but then also talk about when there is variance. Now, I said earlier, this works amazing.

00:13:11:07 – 00:13:28:24
Peter Liljedahl
4 to 12 K to three is a bit of a different animal because the in K to three when I say put these back in order, I got kids going. I like the second one best because it’s got a seven in it. Yeah. Right. Yeah. And I want it to be really hard. So we’re going to start there and like, okay, yeah, you’re missing the point a little bit.

00:13:29:01 – 00:13:51:07
Kyle Pearce
That’s like a small example though, of what happens in lessons where we leave the strings untied right at the end, right? Kids walk out, they go, Oh, that was a really cool task. It was. It was a contextual task which we try to use context whenever we can. We use a contextual design goal that was great. You know, they were salting the driveway and we found out that it took this many bags of salt and it was about dividing fractions.

00:13:51:08 – 00:13:54:21
Kyle Pearce
That’s, you know, like, that’s what we really that’s what we’re really trying to do.

00:13:54:21 – 00:13:57:02
Peter Liljedahl
Is about salting the driveway. Yeah.

00:13:57:04 – 00:13:59:17
Kyle Pearce
We need to make sure that those ends are tight.

00:13:59:17 – 00:14:07:20
Peter Liljedahl
Go for Heidi from Hawaii. Just so you know, Heidi, that means that salting is what we do when it gets cold and we get ice, right? Yeah.

00:14:07:22 – 00:14:26:07
Jon Orr
Peter, we’ve got a chat about making meaningful notes and using meaningful notes because I think that topic on our podcast is the one that I think we still get asked about the most. What that looks like, what are the examples? Walk us through now that like let’s say we’ve had the meaningful discussions. Let’s talk about note taking, because I think a lot of people are saying we’re not no taking.

00:14:26:07 – 00:14:27:13
Jon Orr
We’re just working at the boards.

00:14:27:15 – 00:14:44:08
Peter Liljedahl
Oh yeah. And no taking or like if you just advanced to the next one, I think what’s going to happen. Yeah. And then once more and then we’re going to just see here’s that sort of I write you right note that we all grew up loving. Right. We’d sit in our desks and for 27 and a half minutes, we’d be writing notes.

00:14:44:10 – 00:15:08:05
Peter Liljedahl
And then I’m in classrooms and teachers are going like we saw this earlier time. It’s such an issue. I’m so out of time and I’m watching this and I’m going, Whoa, that’s 27 and a half minutes. We’re never going to get back. So how do we do something different than this? How do we shift from note taking to note making, which is where the students take ownership they are responsible for.

00:15:08:07 – 00:15:31:18
Peter Liljedahl
They’re using notes as a way to consolidate their learning, including the learning that happened in the consolidation. How are they going to represent this in such a way that what’s in their head gets out on paper? So we play with a whole bunch of different things early on and you can advance through this. We tried limiting space and that worked okay.

00:15:31:19 – 00:15:53:14
Peter Liljedahl
We tried graphic organizers. That was really good. We tried this model and pause here. This is sort of the Cornell model or the ferry model, which is we’re just going to divide into four quadrants. And these worked. Okay. We went from 20% of kids being cognitively engaged to 60 to 80% being cognitively engaged. And we went from 10% looking back at their notes to 60 to 80% looking back at their notes.

00:15:53:16 – 00:16:05:20
Peter Liljedahl
So this was a huge improvement, but we still had 20 to 40% of kids opting out. Going out. I’ll remember it. Never underestimate a student’s ability to overestimate their ability. All right.

00:16:05:22 – 00:16:08:00
Kyle Pearce
So that was totally me.

00:16:08:02 – 00:16:31:01
Peter Liljedahl
Yeah. So we kept and here comes the new format. The format that works so well if you advanced to the next one. I think the next one is even. This is what the students work looks like when they’ve been doing it. It always follows the same structure. Yeah, it’s more quadrants. And I know Richard’s on here and Richard just posted a whole bunch of on Twitter today of what this looks like.

00:16:31:01 – 00:16:55:08
Peter Liljedahl
It’s for quadrants Quadrant one. Top left hand corner is a fill in the blank set. Okay. And it is shot through with structure and formalism. This is where I’m actually trying to get them to showcase what it looks like. Right. The second one is I’m giving them the task and I want them to turn it into a worked example.

00:16:55:14 – 00:17:26:03
Peter Liljedahl
Now those words are very particular. It’s not I don’t want you to get the answer. I want you to use this task as a way to showcase your understanding you’re learning today for your future forgetful self. What are you going to put in in quadrant two, which is top right hand corner so that three weeks from now you remember what you did today, Quiet three, which is a bottom right hand corner, is you pick your own example, you choose what you want to do.

00:17:26:05 – 00:17:47:06
Peter Liljedahl
Right. But I’m giving you some restrictions on one area parameter and then quadrant four things to remember. And if you back it up to where we actually see a student example, you can see that they’re doing it, they’re showcasing. You can actually see in that example one top right hand corner how they’re there, showing what it is that they’re thinking, right?

00:17:47:08 – 00:17:54:02
Peter Liljedahl
And then they pick their own and then they’re showing what they were doing. You can actually see the little arrows explaining where things are coming from.

00:17:54:02 – 00:18:18:04
Jon Orr
This works great, Peter, because I had always done note taking as a priority after our consolidation before we had the discussion a couple of months ago on the podcast and when I started this year’s classes, I moved to your four quadrants. And what I love about, say, the on your own is that it keeps the thinking going. And I think that’s what happens is like when we start to take notes, it’s like, Oh, I’m going to show you this one and then I’m going to show you this one.

00:18:18:04 – 00:18:38:19
Jon Orr
So we’re putting it down for our future forgetful self, but they’re still the ones going like, I’m going to create this one. And some kids will challenge. Sometimes we will say like, make one that you think is easier or make one that they think is hard. And then that one goes up on the walls and then all of a sudden we’re created another round of kind of checking our understanding to say, like, I thought this one was easy.

00:18:38:21 – 00:18:42:10
Jon Orr
You thought that one was hard. It keeps that thinking going.

00:18:42:12 – 00:19:07:19
Peter Liljedahl
Yeah. And this is a one phase. One phase is where they’re going to do it. The whiteboards will take some pictures. We’ll put three examples into the class Google folder or the students will take a picture and put it in their OneNote or something like that. But we also have a two phase version, which is a first do it in the boards together, and they do this together at the whiteboards in their group that they did the vertical whiteboard work with that day and then they sit down on the individually make one paper.

00:19:07:19 – 00:19:25:12
Peter Liljedahl
It has to happen inside the same lesson and in a two phase one, they’ll copy quadrant one to quadrant two right from their board. But when they get to quadrant three, they start looking around the room going, Oh, I like that group’s example. Their question better. That feels more like where I’m at. And then when they get to the things to remember, they’re going.

00:19:25:12 – 00:19:31:24
Peter Liljedahl
I like what we said there, but I also like what that group said there and I like what that group said there, and it’s becomes very metacognitive.

00:19:32:05 – 00:19:49:08
Kyle Pearce
I love that really. It forces again for students to now notice a name just like the teachers, to notice a name in before the consolidation. Students are looking around and going, they do their example and they go, okay, I did my example. I look at John’s example. I’m like, Well, actually John’s I think would be more helpful.

00:19:49:10 – 00:19:54:03
Peter Liljedahl
Yeah, later. And I like the way they actually showed their example more like, okay.

00:19:54:06 – 00:20:02:24
Kyle Pearce
It’s like, I really like how you highlighted the y intercept or whatever it is or what the point where it goes through the line that’s up and down. That might be the language you’re using at that time.

00:20:02:24 – 00:20:21:12
Peter Liljedahl
Yeah. And I see Tammy on here with some notes. Thanks, Tami. And we’ve done this with kids as young as kindergarten, right? With a very young kids. We just did the top two quadrants to begin with. Right. And we may never get to quadrant three and four. And I know those of you who teach Trig are freaking out at the way I numbered the quadrants.

00:20:21:12 – 00:20:27:12
Peter Liljedahl
But I’m sorry, human psychology doesn’t follow standard position angle. But I mean, it’s just the way.

00:20:27:14 – 00:20:52:12
Kyle Pearce
Well, and let’s be honest friends, remember, you can take this idea and you can modify It doesn’t have to be exactly organized. And I think that’s one of the big pieces here. It’s like, what’s the goal? What’s the intentionality? And if you change something about anything that’s been said tonight or in any other session, if you change something, does it still help you to get to the same end goal, which again is all about every math lesson?

00:20:52:12 – 00:21:02:04
Kyle Pearce
Does it help to get me closer to my intended goal? And if that’s the case, we’re in great shape now. Peter, we’ve only got a couple of minutes left here.

00:21:02:04 – 00:21:11:15
Peter Liljedahl
Let me say one last thing. Just go ahead. Go ahead. So teachers often ask what do I do about we used to do eight pages of notes in a lesson. What do I do with that? To put them online. Parents will love you.

00:21:11:16 – 00:21:14:19
Kyle Pearce
I know you’re going to say burn them in the fire. Oh, I’m just kidding.

00:21:14:19 – 00:21:22:12
Peter Liljedahl
Get I’m on line, then burn them in the park. Yeah. Yeah. I love you. It’s a great backstop. It’s not what’s connecting to the kids. This connects to the kids.

00:21:22:14 – 00:21:42:11
Kyle Pearce
Right? I love that. And just to kind of reiterate as well, I think sometimes people think when we do things differently, right? You talked about the normative math classroom, and it’s like when we do something different, it’s almost like people feel like you’re never allowed to use anything from the traditional math class, which is like, I can’t use those notes or I can’t use this.

00:21:42:13 – 00:22:03:04
Kyle Pearce
Some people are like, Hey, I can’t watch those. I don’t even want to name it and get in trouble for it. But certain videos where the speaker is kind of monotone, but those can be helpful at some point, but maybe just not in the beginning. When you’re trying to learn and introduce these concepts. But when your forgetful self shows up to the party, maybe that’s the time where that could still be a useful tool, right?

00:22:03:04 – 00:22:17:01
Kyle Pearce
So, Peter, we don’t want to get ourselves in trouble because we said we’d talk about all three. I think we have one more we want to talk about. And this one I think you do a great job in summarizing and it doesn’t take to too much.

00:22:17:01 – 00:22:33:14
Peter Liljedahl
Time, doesn’t say, here are some of the key pieces here. So first of all, what does homework looks like? We call it Check your understanding questions. Advanced. This is what it looks like. And we give it now in three categories mild, medium spice. So we’ve seen those in the other. We saw the consolidation at three levels of tasks.

00:22:33:18 – 00:22:57:15
Peter Liljedahl
We took the notes. There was three opportunities for examples. And now here comes the check your understanding questions. And they are three levels mild, medium, spicy. It’s nonjudgmental, is non evaluative. It’s about preference. What happens here is that the picture of those students, they’re having a mastery experience. They are totally in control of their learning. And what do we need to have for mastery experience?

00:22:57:15 – 00:23:15:20
Peter Liljedahl
We need to have success and challenge. So where’s the success coming from? Well, I gave them level tasks and I gave them choice. So the rules here is you choose where you want to start. That’s real one where you do your own, but you choose where you want to start. Rule two is check your answer with the other students at your table.

00:23:15:22 – 00:23:35:11
Peter Liljedahl
And if you need help, get help. If you can give help, give help. We’re ensuring success, choice and support ensures success. But then we’re offering challenge and then they’re seizing that challenge. And when we get that happening, we get that mastery experience. And the biggest problem we have is we can’t get the kids to stop. We can’t get them to leave.

00:23:35:11 – 00:23:51:07
Peter Liljedahl
You’ve got to go. The busses are here. It’s recess. You got to leave. The other class is coming in. I need to get you out and they don’t want to leave because they’re having that moment where they feel like I’m in charge here of my learning. I know what I know and I’m doing great.

00:23:51:12 – 00:24:10:02
Kyle Pearce
You know what, Peter? I must say, I’ve got a funny feeling that we’re going to have the same problem here tonight in this very session with our math moment. Make her friends when we have to say friends time to go. Time to go. It’s time to go. Peter is at it’s now 9:00 where you are. I believe right now are your time.

00:24:10:02 – 00:24:19:20
Kyle Pearce
So 9 p.m. now. Meanwhile, our friends in Australia and all around the world here are laughing. They’re like, yes, Peter Saturday. Yeah, I got it.

00:24:19:20 – 00:24:20:11
Peter Liljedahl
So that should.

00:24:20:11 – 00:24:42:10
Kyle Pearce
Be. Yeah, but my goodness gracious, we covered a lot of ground. Peter It is always a massive, massive delight to have you when we have you on the podcast. Of course, even better when we have you on the summit. And nothing beats having some great conversations in the hallway at nighttime or any of these events that we get a chance to bump into you at.

00:24:42:12 – 00:25:00:24
Kyle Pearce
Peter, if you had one sort of final message for those people who came in to hear all about the close, what would be sort of your takeaway for them as they get pumped up for the other 30 plus sessions that they’re going to be digging into all weekend? Yeah.

00:25:01:01 – 00:25:19:07
Peter Liljedahl
The close is important. We always have to do it. Set a timer for yourself. I saw Ed Campbell say the same thing, Set a timer for yourself so you don’t get carried away. Make sure you’re close. Second thing is the close has to be dynamic. It has to be responsive to what happened in the lesson that day. The third thing is we don’t have to do all three.

00:25:19:11 – 00:25:36:03
Peter Liljedahl
We don’t have to do all three. But you got to do one. We got to do something to close off the lesson, right? I tried to do two. Sometimes I get three and I’m going to be teaching in classrooms next week. I’m definitely doing one in all of them. I’m going to try to win some of them. Right?

00:25:36:03 – 00:25:46:18
Peter Liljedahl
It depends on what the lesson is. I’ve got to be responsive. I got to be ready and I got to listen to what the room is telling me. And I’m giving students opportunities to be responsible for their learning rather than accountable.

00:25:46:18 – 00:25:55:12
Jon Orr
I love it. I love it. Peter, I want to thank you one more time for joining us here, everyone. There’s a million thank you’s coming in through here. So thank you again, Peter.

00:25:55:12 – 00:25:57:20
Kyle Pearce
Thanks so much, my friend. Always a pleasure.

00:25:58:01 – 00:26:01:20
Peter Liljedahl
Thanks, everybody. Thanks for being here. Thanks, Carol. Thanks, John.

00:26:01:22 – 00:26:27:00
Jon Orr
All right. There you have it, folks. That’s part two. That ends the keynote session from the 2023 Make Math Moments, Virtual Summit. In that summit, we had over 30 speakers over the course of that weekend in November of 2023. And this concludes that kind of keynote session where Kyle, Peter, myself, talk all about how to close our lessons and the three components of closing those lessons.

00:26:27:00 – 00:26:48:12
Jon Orr
And specifically we’re talking about our tree on the six areas that we want to strengthen in our classroom trees or our district planting trees. I think what we talked about most here is the branches of our tree, which are the teacher moves. These are the pedagogical moves. And I think my big takeaway is always to think about that closing style.

00:26:48:12 – 00:27:14:12
Jon Orr
But the note taking approach for me when I shifted to doing Peter’s suggestion in having those four sections on your piece of paper laid out and doing example one, example two, example three, and then notes to future forgetful selves, that was a game changer because it not only allowed our students creativity and choice in their example, but it acted when they create, say, that example.

00:27:14:12 – 00:27:33:12
Jon Orr
I had them usually create example three and when they created example three, it almost became we treated it like a challenge that you could give to your neighbor, your elbow partner, or put it up on one of our whiteboards around the room. And now we were completing new problems around the room at that stage. And I think that was a game changer for me.

00:27:33:12 – 00:27:53:24
Jon Orr
It allowed that element that could keep the practice going and applying the concepts that we just summarize it. And I think that was my big takeaway when I applied that in my classroom. So I would challenge you to think about how you’re doing. Note Taking in your classroom. Are you doing it at the beginning like I used to, or are you doing at the end like we are doing now in our classrooms?

00:27:53:24 – 00:28:21:11
Jon Orr
And just like where the thinking happens, folks, if you want to pick up and start listening to the other summit sessions, you can do that. All the replays of that summit are in our McMath Math Moments Academy. You can join that academy. Now. It is open to join. You can head on over to make math moments dot com forward slash academy get in there you can listen and binge all of those 30 sessions from there was the follow up session to this Peters opening session was Pam Harris.

00:28:21:11 – 00:28:42:06
Jon Orr
We had Pamela sata. We also had many other speakers in that summit. So you can head on over to make map Omnicom force as Academy and continue the learning alongside all of our classroom ready units and tasks are part of that academy membership. All downloads, handouts for students and anything you need to run those lessons. Teacher guides, they’re all there for you.

00:28:42:10 – 00:29:05:01
Jon Orr
We also have courses on how to strengthen the six parts of your classroom tree, and we have our full assessment course over there on the Complete Guide to Assessment and Mathematics. So head on over there folks, to make math moments dot com for such academy and hey, show notes and links to resources. From this episode you can find and get links to all those of your on the fly head on over to make math moments dot com for episode 272.

00:29:05:03 – 00:29:05:23
Jon Orr
Thanks folks.

00:29:06:00 – 00:29:11:21
Kyle Pearce
Well there my man’s mom and make her friends until next time I’m Kyle Pierce.

00:29:11:21 – 00:29:13:09
Jon Orr
And I’m John or.

00:29:13:11 – 00:29:16:11
Kyle Pearce
High fives for us.

00:29:16:13 – 00:29:31:14
Jon Orr
Hey Ed Woo high five for you Oh baby.

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The Making Math Moments That Matter Podcast with Kyle Pearce & Jon Orr
Weekly interviews, strategy, and advice for building a math classroom that you wish you were in.


Download the 2-page printable 3 Act Math Tip Sheet to ensure that you have the best start to your journey using 3 Act math Tasks to spark curiosity and fuel sense making in your math classroom!

3 Act Math Tip Sheet


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Each Teacher Guide consists of:

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Each Make Math Moments Problem Based Lesson begins with a story, visual, video, or other method to Spark Curiosity through context.

Students will often Notice and Wonder before making an estimate to draw them in and invest in the problem.

After student voice has been heard and acknowledged, we will set students off on a Productive Struggle via a prompt related to the Spark context.

These prompts are given each lesson with the following conditions:

  • No calculators are to be used; and,
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Students are left to engage in a productive struggle as the facilitator circulates to observe and engage in conversation as a means of assessing formatively.

The facilitator is instructed through the Teacher Guide on what specific strategies and models could be used to make connections and consolidate the learning from the lesson.

Often times, animations and walk through videos are provided in the Teacher Guide to assist with planning and delivering the consolidation.

A review image, video, or animation is provided as a conclusion to the task from the lesson.

While this might feel like a natural ending to the context students have been exploring, it is just the beginning as we look to leverage this context via extensions and additional lessons to dig deeper.

At the end of each lesson, consolidation prompts and/or extensions are crafted for students to purposefully practice and demonstrate their current understanding. 

Facilitators are encouraged to collect these consolidation prompts as a means to engage in the assessment process and inform next moves for instruction.

In multi-day units of study, Math Talks are crafted to help build on the thinking from the previous day and build towards the next step in the developmental progression of the concept(s) we are exploring.

Each Math Talk is constructed as a string of related problems that build with intentionality to emerge specific big ideas, strategies, and mathematical models. 

Make Math Moments Problem Based Lessons and Day 1 Teacher Guides are openly available for you to leverage and use with your students without becoming a Make Math Moments Academy Member.

Use our OPEN ACCESS multi-day problem based units!

Make Math Moments Problem Based Lessons and Day 1 Teacher Guides are openly available for you to leverage and use with your students without becoming a Make Math Moments Academy Member.

MMM Unit - Snack Time Fractions Unit


Partitive Division Resulting in a Fraction

Shot Put Multi Day Problem Based Unit - Algebraic Substitution


Equivalence and Algebraic Substitution

Wooly Worm Race - Representing and Adding Fractions


Fractions and Metric Units


Scavenger Hunt - Data Management and Finding The Mean


Represent Categorical Data & Explore Mean

Downloadable resources including blackline mastershandouts, printable Tips Sheetsslide shows, and media files do require a Make Math Moments Academy Membership.


Pedagogically aligned for teachers of K through Grade 12 with content specific examples from Grades 3 through Grade 10.

In our self-paced, 12-week Online Workshop, you'll learn how to craft new and transform your current lessons to Spark Curiosity, Fuel Sense Making, and Ignite Your Teacher Moves to promote resilient problem solvers.