Episode #244: Micro & Macro Teacher Moves – A Math Mentoring Moment

Jul 31, 2023 | Podcast | 0 comments



Episode Summary:

In this “Where are they now” Math Mentoring Moment Episode, we bring back Jeremy Sarzana, a high school math teacher at a Vocational High School in Boston, Massachusetts. 

Jeremy shares concerns over how to keep “flow” in his math classes when many of his students are engaging at varying levels. 

Stick around to hear Jeremey realize how to plan beyond the lesson of the day to ensure he’s meeting the needs of all his students. 

This is another Math Mentoring Moment episode where we chat with a teacher like you who is working through some problems of practice and together we brainstorm ways to overcome them.

What You’ll Learn:

  • Why starting with a problem is so impactful for students in a math classroom;
  • How thin slicing can be a great tool to help you arrive at your intended learning objective;
  • How to engage students with the distance between two points formula; 
  • How to decide what I should focus on first when designing the structures in my classroom; and,  
  • How do I ensure I’m challenging my students enough when teaching through problem-based lessons?

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. 

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00:00:00:09 – 00:00:16:17
Jeremy Sarzana
We have that exploratory period, Right. That was great. As you guys are saying, seeing all these strategies coming out since like trying things. But then my problem was I was very I went from one extreme to the next extreme versus like, I didn’t really know what to do. They tried that and I was like, Oh, you use the Pythagorean theorem.

00:00:16:17 – 00:00:25:08
Jeremy Sarzana
And then it’s just like kind of like a squared plus D squared. But I felt that like that kind of missing a conceptual piece I was just going from in this.

00:00:25:08 – 00:00:36:10
Kyle Pearce
Where are they now? Math Mentoring Moment Episode We bring back Jeremy Tarzana, a high school math teacher at a vocational high school in Boston, Massachusetts.

00:00:36:12 – 00:00:54:10
Jon Orr
Jeremy shares concerns over how to keep the flow going in his math classes when many of his students are engaging at varying levels. So stick around to hear Jeremy realize his how to plan beyond the lesson of the day to ensure he’s meeting the needs of all his students.

00:00:54:12 – 00:01:26:10
Kyle Pearce
This is another math mentoring Moment episode where we chat with a math moment maker just like you, who is working through some problems of practice. And together we brainstorm ways to overcome them. Here we go. Oh. Welcome to the Making Math Moments That Matter podcast. I’m Kyle.

00:01:26:10 – 00:01:29:24
Jon Orr
Pierce. And I’m John or we are from math moments dot com.

00:01:30:01 – 00:01:39:19
Kyle Pearce
This is the only podcast that coaches you through a six step plan to grow your mathematics program, whether it’s in the classroom or at the district level.

00:01:40:00 – 00:01:46:19
Jon Orr
And we do that by helping you cultivate and foster your mathematics program like a strong, healthy and balanced tree.

00:01:46:21 – 00:02:02:01
Kyle Pearce
The trunk represents a leadership in your organization or the classroom pillars in your math class. While the roots of the tree represent mathematics, content, knowledge, and what it means to be mathematically proficient.

00:02:02:03 – 00:02:18:22
Jon Orr
Like a tree requires soil, water and sunlight. Your mathematics program requires a productive educator mindset and the belief that all students can achieve at all levels. And your professional learning structure is the limbs of the tree, and it represents your professional learning plan.

00:02:18:24 – 00:02:39:12
Kyle Pearce
The branches of your tree represent the development of educator pedagogical content knowledge, which includes effective teaching and equity based teaching practices and finally, the leaves of the tree. Those leaves represent resources, the tools and the classroom environment.

00:02:39:16 – 00:02:47:05
Jon Orr
If you master the six parts of an effective mathematics program, the impact of your math program will reach and grow far and wide.

00:02:47:07 – 00:03:03:09
Kyle Pearce
Every week you’ll get the insight you need to stop feeling overwhelmed, gain back your confidence, and get back to enjoying the planning and facilitating of your math program for the students, for the educators you serve. Let’s dig in here.

00:03:03:14 – 00:03:33:20
Jon Orr
All right, folks, let’s jump right into the conversation with Jeremy. Hey there, Jeremy. Thanks again for coming back, chatting with us all about your math escapades. We chatted way back on episode 177, all about kind of making consolidations count and thinking about what are the big ideas in our math classes, being flexible and thinking about, I think the monitoring and selecting and sequencing pieces of a math class lesson.

00:03:33:20 – 00:03:39:13
Jon Orr
So fill us in. What’s new with you? Take us through the ropes here. Since the last time we chatted.

00:03:39:15 – 00:04:01:01
Jeremy Sarzana
How will this shows in a new role? If the previous show I was teaching and I was kind of a special education teacher in the general ed classroom was an inclusion setting, but this year it was actually I was the only teacher and it was full inclusion and one of the classes was actually an honors class. It was challenging for me because I feel that like this isn’t enough teacher to take on that challenge.

00:04:01:03 – 00:04:07:21
Jeremy Sarzana
But it was challenging for me. So I’m really just really not holding students accountable, but just really, really push them.

00:04:07:21 – 00:04:08:21
Kyle Pearce

00:04:09:01 – 00:04:10:02
Jeremy Sarzana
Need more experience.

00:04:10:04 – 00:04:27:12
Kyle Pearce
Yeah, I was going to ask you and you’re kind of digging in there a little bit more. I was curious what specifically you were feeling or why maybe you were feeling that way and it’s sort of, I think, emerging a little bit. You hear honors class and you’re probably thinking to yourself, So what else am I going to do?

00:04:27:12 – 00:04:32:11
Kyle Pearce
Or maybe provide for those students? Do you mind taking us a little bit down that rabbit hole?

00:04:32:12 – 00:04:48:05
Jeremy Sarzana
Yeah, I mean, I guess in my defense, it was like, Oh, Jeremy, next you’re going to be teaching honors, 10th grade, something like, I mean, that was basically it was basically all up to me. But fortunately, we were using a very good curriculum. I don’t know if you guys know about it, but it’s just a free app.

00:04:48:11 – 00:04:51:20
Kyle Pearce
No, I actually. John, have you come across it?

00:04:52:00 – 00:04:56:20
Jon Orr
No, no. But I think I can guess the structure of it. Jeremy, fill us in.

00:04:56:22 – 00:05:00:10
Jeremy Sarzana
There’s AP classes and but this is for ninth and 10th graders, right?

00:05:00:11 – 00:05:01:02
Jon Orr
That’s what I figured.

00:05:01:08 – 00:05:22:16
Jeremy Sarzana
But I’ll say is exactly all the stuff that you guys talk about. It’s very student centered. Always starts off with there’s no pre teaching. It’s just like, okay, try this. For example, one thing we did this year was like working with a distance formula and it started off with a scenario. It was a field. One person goes around the edge of the perimeter of the field and then the other one goes straight through.

00:05:22:21 – 00:05:43:05
Jeremy Sarzana
And the first questions like, who can get there first, right? And you talk about that. And then it was on like a corner. And Chris, you can count the person walks around the perimeter. Then you ask the students, what is the distance of the diagonal, supposedly, which is 10th grade. So Fisher has some experience with Pythagoras Theorem, but it’s been a while and a lot of people are trying to count the spaces through.

00:05:43:05 – 00:06:16:05
Kyle Pearce
All the diagonals. That’s nothing like it’s going to take to go to diagonals to get there yet. So you learn so much. And I’m envisioning this process right now. I have a very clear vision of this particular task. I love how you’re mentioning it. Sort of like you’re saying, Hey, give this a shot. Let’s see where you’re at and tell me a little bit about and you already scratched the surface a little bit there where you see some students doing certain things and it tells you a lot about where they are now in their thinking, not necessarily what they’re capable of.

00:06:16:05 – 00:06:42:01
Kyle Pearce
Of course. Right. Because like you said, maybe they haven’t seen these concepts in a while and maybe they’re not making a connection that like, oh, this is a rectangle. When you go across a rectangle, it’s a right angle triangle. And we knew this thing some time ago called Pythagorean Theorem. So I love that. So I’m guessing that you’re getting all kinds of diagnostic data for students to go whole.

00:06:42:02 – 00:06:59:08
Kyle Pearce
Okay. These students are making the connection. Maybe some of these students are on to something, and then maybe these students over here either never had a firm grasp on that idea. Maybe they’re just missing the connection there, or maybe it’s just been too long and maybe we’re going to have to spend a little bit more time there.

00:06:59:10 – 00:07:21:02
Jeremy Sarzana
Yeah, exactly. And then some of the honors students, because I have three classes, but some of the honest ones, as they kind of figured out right away their own Pythagorean theorem, you know, what’s next. But then something had to reintroduce the Pythagorean theorem. But then the following part of that lesson was you give them a diagonal line, which is actually the same as the previous thing, but you just say, How did you find the distance between these two points?

00:07:21:08 – 00:07:34:21
Jeremy Sarzana
So I think it’s like that they have to like basically be able to draw in the triangle. And so that’s the beginning of like learning the distance form. So it goes from there. So that’s the second step and it was a great lesson and I thought it was a good curriculum.

00:07:34:23 – 00:07:56:04
Jon Orr
Sounds like it for sure. We’ve even used a similar lesson, that shoe that in almost the exact same way as a scaffolding kind of unfolding of where the progression goes like a thin slicing kind of approach to kind of and keep giving you these little tasks and slightly they’re modified and eventually you’ve just built the distance formula without really building the distance formula.

00:07:56:04 – 00:08:17:21
Jon Orr
We even say, like you should even scrap the idea of the distance formula because it’s really just Pythagorean theorem the whole time. And why are we even kind of bringing this in as something to memorize? It’s not even needed. So, Jaime, I’m wondering, having this lesson here, where did you feel like the trouble kind of comes out of this, or where do you feel like you’re feeling?

00:08:17:21 – 00:08:28:11
Jon Orr
You’re not doing what you need to do. And I only say that because you kind of mentioned this is an example of being into this new role in this honors class. There is a pebble there that you’re kind of trying to shake loose.

00:08:28:13 – 00:08:46:05
Jeremy Sarzana
Yeah. So it basically we have that exploratory period, right? That was great. As you guys are saying, seeing all these strategies coming out, students like trying things. But then my problem was I was very I went from one extreme to the next extreme versus like I didn’t really know what to do. They tried that and I was like, Oh, you use the Pythagorean theorem.

00:08:46:05 – 00:08:55:17
Jeremy Sarzana
And then it’s just like kind of like a squared plus D squared. But I felt that like a kind of missing a conceptual piece. I was just going from exploratory right to theorem.

00:08:55:23 – 00:09:20:15
Kyle Pearce
Got it, Got it. So it sounds like that original pebble that we had discussed the first time around is sort of still kind of and don’t get me wrong, it is a massive, massive pebble, this idea of really trying to select sequence and then essentially determine what connections do we really want students to sort of hang on to.

00:09:20:15 – 00:09:52:02
Kyle Pearce
And it almost puts you as an educator in a decision making process every single day, right? You’re making so many micro decisions. But then there’s these macro decisions in each lesson that we need to sort of make. And I’m going to argue that the more macro decisions we can make before the lesson begins, the better. And then the more, I guess, predicting of micro decisions that might have to come or may come, it almost makes them already taken care of as well.

00:09:52:02 – 00:10:13:18
Kyle Pearce
So it’s almost like if we can reduce the decision making process for ourselves, especially when you went from a two teacher classroom, I know that there was maybe more students between the two teachers. But the reality is when you have two adult teacher brains in there, right, you have these moments where you can walk by and say, hey, I saw this, what do you think?

00:10:13:18 – 00:10:35:10
Kyle Pearce
And now you’re on your own and you’re sort of going, okay, I’ve got all these ideas, I’ve got all these approaches, and I love how you’ve given us sort of a topic that we can sort of dig into. We can use that as sort of a nice way for us to keep this as concrete as possible. But you’re thinking to yourself, you’re going, okay, what is it that I want the students to be able to do at the end?

00:10:35:10 – 00:10:55:08
Kyle Pearce
And that to me is that macro decision. Right? And I think you already knew. You already said it’s like you almost feel like maybe you got too excited and got to that end goal maybe too quickly, almost maybe it’s like, great idea here. Great idea here. I like that. I see that. Awesome. Here’s how we’re going to do it today.

00:10:55:08 – 00:11:13:18
Kyle Pearce
And maybe it’s just this in-between piece. Where you going? Okay. Given that, I’m going to assume in my mind before you said they were going to count those diagonals right away, I was like, they’re going to count diagonals. I know that that’s going to happen. At least one student. And if I don’t notice it, at least one students thinking it.

00:11:13:20 – 00:11:38:22
Kyle Pearce
So I’m like, okay, that’s one thing I’ve anticipated. Now It’s like, all right, how do I take what people are doing? And I call it intuition, but it’s really it’s experience, right? That they’ve had. And it’s sort of like this makes sense given the scenario. How do I take where they are now, which is a place they feel comfortable, and how do I help make that leap and how do I make the leap as small as possible?

00:11:38:22 – 00:11:59:08
Kyle Pearce
And in a perfect world, it’d be like just a little step, right? It’s like from one little stepping stone to the other without it being sort of this big massive. I’m picturing Wipeout. If you’ve ever seen that show. Math class is sort of like Wipeout where you see them and they’re like, okay, they’re going to try to make this leap and then all of a sudden they bounce off the thing and hit their head and then fall into the pit.

00:11:59:10 – 00:12:20:13
Kyle Pearce
That’s like math class in so many cases. So how do we take that wipeout course and how do we bring it together so that it’s a nice smooth ride? And I’m wondering, before that lesson began, what sort of thinking was going on in your mind? Do you feel you’re like, okay, I know certain things are going to happen?

00:12:20:13 – 00:12:33:00
Kyle Pearce
Or were you sort of like, I’m just going to see what happens and then I’m going to direct them towards this end goal? Because of course, we got this checklist of expectations or standards that we need to do.

00:12:33:02 – 00:12:51:12
Jeremy Sarzana
Is like one thing. That whole lesson from beginning to end was really about them building the distance for real as these essays really just the Pythagorean theorem and the scales. But like most of my students were not even to it was almost assumed in the lesson that the students be like, Oh, yeah, the Pythagorean theorem, right?

00:12:51:12 – 00:12:57:15
Kyle Pearce
Yeah. In a perfect world, right? Those three kids over there are like, Oh, yeah, I remember that. Right?

00:12:57:17 – 00:13:13:20
Jeremy Sarzana
Yes, I guess that’s why I just put so much stress on building this distance for real. And then just I don’t really put as much thought into like, well, what if we have to go over the Pythagorean theorem again, which, by the way, the beginning of the year, the first thing that I did and some of the classes they would have called triangles, two rectangles.

00:13:13:20 – 00:13:20:09
Jeremy Sarzana
Yeah, yeah, yeah, yeah. And that’s just amazing. And a show to some of the teachers and they’re saying, Oh, that’s kind of the proof of the Pythagorean theorem.

00:13:20:09 – 00:13:21:19
Jon Orr
But that’s exactly right.

00:13:21:21 – 00:13:28:04
Jeremy Sarzana
What I’m saying with the way you guys did it, it was more like exploratory things as a proof, but it was also then exploratory.

00:13:28:04 – 00:13:45:04
Kyle Pearce
I think that’s the piece right here in my mind as you were talking. And after I posed the last question, I was sort of thinking to myself, I’m like, So what would I do in that scenario? And thank goodness we’re doing it now, having this discussion, because if it was in the moment, I probably would have did what you did.

00:13:45:04 – 00:14:14:15
Kyle Pearce
If I didn’t think of it ahead of time, I would have just been like all right, nice, all of these things. But I wonder if I could craft a question ahead of time if I know that many students are going to bump into this challenge. If I could craft a mini problem. Right. You’ve given them this big problem, the field and all of those things, and you almost craft another purposeful question because you know that this is coming so that they can bump into the Oh, I guess that’s not going to work.

00:14:14:15 – 00:14:15:01
Kyle Pearce

00:14:15:03 – 00:14:34:00
Jon Orr
The other thing I want to add in here about and I think your pebble here is that you’ve planned this lesson We got there fast. I’m not sure exactly what to do to keep the challenge going. Is that where your head’s at? Because we have some suggestions here for sure. But I just want to be clear on you got to a place where you want to do this exploratory activity.

00:14:34:00 – 00:14:48:13
Jon Orr
When it sounds like you were you were doing a thin slicing activity and then it became all right, we use the thing that we’re supposed to teach and then is it now what do I do? Or was it like, how do I drag that out more? Is that where you’re trying to go get this challenge? Like you’re teaching kids who might get there quick?

00:14:48:15 – 00:14:55:08
Jon Orr
So now it’s how do I keep the challenge going so that kids are continuing to think, Is that where your pebble is?

00:14:55:10 – 00:15:12:16
Jeremy Sarzana
Yeah, I just know that I just got derailed. I was like, Well, they don’t know the Pythagorean theorem almost. I put the distance formula, had to just go to the side and just focus on just doing the Pythagorean theorem again. So basically, like a good activity would have been going into squares or triangles thing or whatever it’s called.

00:15:12:18 – 00:15:33:13
Kyle Pearce
Or even on a smaller scale, because what I was thinking as they did this one field and you go, okay, great. And you’re like, All right, I’m not sure if it’s right or wrong or anything. Let’s leave that there. Don’t trace anything. Leave it up there. All right, now I’ve got another field. And now this field is three by four.

00:15:33:13 – 00:15:56:10
Kyle Pearce
And then maybe you have them actually do it on the desk with tiles. So it’s like you pick that super easy. Pythagorean, triple that. You’re going, All right, So you did this one field. Amazing. That’s super cool. I’m not sure because this student over here thinks it’s this. This student thinks it’s over here. Whoever did Pythagorean, they’re like, It’s this over here.

00:15:56:10 – 00:16:14:22
Kyle Pearce
They’re like, Well, I counted a bunch of these diagonals, and it’s actually different. It’s close. Maybe, but maybe not. I don’t know. Now you’re like, Okay, well, here’s another field. And you’re like, right now and all you have. And I said, three, four, five. But you don’t tell them it’s three, four or five. You go, Here’s the field.

00:16:14:22 – 00:16:33:14
Kyle Pearce
And I got a field for each and every one of you. And I even drew the line from corner to corner to show you the path. But the problem is, is we have no rulers. All we have are these square tiles right here. And of course, it’s all scaled perfectly. And now you go, okay, have outer, let me know what’s going on here.

00:16:33:16 – 00:16:53:12
Kyle Pearce
And then all of a sudden it’s like, hmm, I wonder if that opportunity now to go like what is actually happening? Because the reality is I’m going to guess that many of the students may have never actually seen a proof of the Pythagorean theorem. They may have engaged with it, but they may have engaged with it through procedural fashion.

00:16:53:12 – 00:17:13:06
Kyle Pearce
Right. Just steps and here’s the rule. And as long as it’s a right angle triangle in some of their minds, they might even know the definition. But they don’t realize that there’s a right angle triangle inside of there that you’re working with because it’s a rectangle, right? It’s like, well, I thought Pythagorean was for right angle triangles, not for rectangles.

00:17:13:07 – 00:17:34:17
Kyle Pearce
So I’m wondering when I give a problem and it sounds like you’ve got an amazing curriculum that poses a good problem to give you. But the part that I’m wondering about is whether they’ve thought about when that issue, when that struggle arises. What’s my next move as the educator? It’s almost like they’ve sort of given that problem for you to figure out, which is hard.

00:17:34:17 – 00:18:05:19
Kyle Pearce
It’s hard work, and then it’s almost like you got to go, okay, so if they’re going to run into this issue, what’s my next move to now give them another opportunity to kind of grapple with it or to combat the forces of misconception we’ll call it? What’s that move going to look like and sound like? And I’m wondering in your mind if that little tiny little tweak in that lesson may have helped you get a little bit closer to making those walking tiles a little closer?

00:18:05:21 – 00:18:21:09
Jeremy Sarzana
Yeah, I think that would have been a great idea to draw like three, four times because then it’s like they can you could bring up the proof. You can prove that the area of the side plus his side equals the area of square built off of the hypotenuse. I’d be totally happy with them. Just it conceptually like that.

00:18:21:14 – 00:18:41:04
Jeremy Sarzana
And now you got me thinking now that I think what I should have really done was score a sort of thing with the Pythagoras theorem and just have them learn the Pythagorean theorem conceptually and then then go into that lesson again, because then all use the Pythagorean theorem to figure out diagonal through the field, and then you can go on to the next step, which is just well, here, just two points.

00:18:41:10 – 00:18:42:15
Jeremy Sarzana
How do you find I.

00:18:42:15 – 00:19:01:11
Kyle Pearce
Love it and it makes me think as well. Yeah. And don’t even have to change. This is one thing I think we spend too much time on as or at least I know I did. I spent way too much time trying to be creative with making new contexts for everything. But I’m like, if we picked the field, then maybe I just stick with fields and I’m just going to give you a lot of fields today.

00:19:01:13 – 00:19:29:03
Kyle Pearce
And then all of a sudden it’s like that field that began with just some measurements, right? Horizontal, vertical. And that helped you to get to another field, which is now a three by four field, and then the next field, except now it’s on a grid and you go, What about here? And maybe you start it on have that field starting at the origin and have it come out and over and sort of like, Hmm, what’s going on here?

00:19:29:03 – 00:19:51:22
Kyle Pearce
What are you doing with these numbers on this? You got a point here. What matters here? And then the next field is over here in the grid. Now, it’s not on the origin. What matters here? What are you doing? Oh, somebody said it’s seven, and it’s like, is it really seven long? Because the x value is seven. Is it really seven or is it seven?

00:19:51:22 – 00:20:26:03
Kyle Pearce
Subtract these two over here. Now we’re on to something. That thin slicing idea that John was mentioning earlier. I’m envisioning in my mind going like, okay, what’s that next little patio stone that I can place there That’s going to give a little bit of challenge but make everybody feel like it’s like I can do this. And it’s like they want to convince themselves and then it just gets a little harder and a little harder, and then all of a sudden you might get to a point where you just like, okay, now you go, and I want you guys to group up and tell me, like, if you had to write it like a mathematician, what

00:20:26:03 – 00:20:48:15
Kyle Pearce
would you do? What would you say? What would you write it down in words? What are you actually doing? And then now can we make that look like math a little bit? Let’s try to develop or code construct a formula, and then all of a sudden you start to go, Oh, they’re not all going to come up with the perfect formula for distance, but you then get to be the, Hey, what about over here?

00:20:48:15 – 00:21:01:18
Kyle Pearce
When it’s in the negative, it’s like, Oh, that’s going to be problematic. What should we do now? Hmm? Okay. Can I show you what this mathematician I don’t know. Distance formula? Was it Pythagorean? I don’t even know. But whoever it was, it’s.

00:21:01:18 – 00:21:05:00
Jon Orr
Built at the beginning there. Yeah, that’s all it is.

00:21:05:01 – 00:21:08:00
Kyle Pearce
It’s built off of it. But just even the notation, right?

00:21:08:00 – 00:21:08:16
Jon Orr
That’s all it is.

00:21:08:20 – 00:21:29:13
Kyle Pearce
So all of those beautiful things, I think are great conversations that you can have with those students. And I guess for me, my little mini epiphany is sort of like thinking about your macro decision, which is like, what am I hoping to achieve here? And then what are the micro decisions that I can plan ahead of time knowing that it’s never going to go perfect, right?

00:21:29:13 – 00:21:43:21
Kyle Pearce
Some of the stones are going to be further apart than you imagined them to be, but at least it’s like you’ve got somewhat of a path there so that it’s clear enough that you might be able to sort of help some students along from stone to stone.

00:21:43:23 – 00:22:07:01
Jon Orr
Sometimes when I think about designing that pathway, another way to approach it now I know that this task was kind of presented to you through the curriculum. However, sometimes when I think about creating that in slicing pathway that kind of inches students along, I think about sometimes the reverse, the opposite of if I had the answer, would the question look like.

00:22:07:03 – 00:22:25:10
Jon Orr
So for example, I’ve done this lesson where I said, Here’s a coordinate grid, here’s a point zero comma one. So it’s not zero zero, it’s not the origin. And I said, At your groups, at your walls, here’s a grid. Can you find me at points as many as you can that are exactly ten units away from this point.

00:22:25:12 – 00:22:45:06
Jon Orr
So now you’re thinking about they’re already thinking distance and they’re just trying to find points. Naturally, kids, what they do in this case is use the axis to go like, I’m going to go ten units straight across and then I’m going to go ten units back. That’s another point. Right? And then some other kids going to go, I’m going go ten units up and then another kid’s going to go with ten units down and all of a sudden you got four points.

00:22:45:06 – 00:23:04:15
Jon Orr
And then usually my next question is like, what if I told you there are more than four? And so somebody will start to go like, Wow, what happens if I go diagonal, right? If I go diagonal from this point? Like, how do I get ten units from that way? So there are different strategies. You’re going to see rulers come out, but you’re also going to see a student who’s doing the same thing as do somebody who’s going to pick up on the Pythagorean theorem here.

00:23:04:15 – 00:23:24:06
Jon Orr
Could be helpful. How do I get ten units? By going up and over, right? And now you’re starting to go, okay, Well, the beautiful part here is that if you go ten units up and over, some kids eight and six and six and eight, and then that gives me two points over. But if I go this way, I’m going to go back six and up eight or back eight and up six.

00:23:24:11 – 00:23:41:13
Jon Orr
That also gives me Chu ten unit points away by the Pythagorean theorem. Then I go down and then if you keep thinking about that, you are building exactly a circle around this point, which is exactly the formula, right? The equation of a circle is also built off the Pythagorean theorem.

00:23:41:13 – 00:23:43:14
Kyle Pearce
Who’s a pretty special person.

00:23:43:15 – 00:24:05:07
Jon Orr
It’s all connected in a sense, but that is a lesson where sometimes we think, can we think in the reverse to help create these scenarios, these challenges? And this is something that I sometimes hold in reserve as well, to say, Hey, if I’m going to go the route that you went with the rectangles and going across the field, could I also think about my challenge question or my next step?

00:24:05:07 – 00:24:21:11
Jon Orr
If I needs this group, move really fast, right? This group got there really fast, but this group, I’m sluggish and I need to catch them up. So now I have to go over here or I have to bring everybody together. And now maybe that group who went really fast. I pull out the reverse problem and I give it to them and they’re working on that now.

00:24:21:11 – 00:24:41:21
Jon Orr
But then then this group still working on the original problem, and I can get them to the Pythagorean theorem slower or I can get them to a possible solution or strategy a little slower because this group’s got something to work on now, and eventually we’re all going to bring ourselves together to teach to the learning goal we were intended today, which was your distance formula on the different strategies.

00:24:41:21 – 00:24:58:02
Jon Orr
But now this group’s had a little challenge. They’re starting to think about how that distance formula works in relation to what they’re working on. Same with the students who still haven’t say, maybe got to the point where the other students got to so quickly. So the big idea tip is could we think of the reverse when creating some of the problems?

00:24:58:04 – 00:25:14:04
Jeremy Sarzana
It’s funny you should mention that I almost feel that you should go from the Pythagorean theorem to the distance formula and then two circles, because I was the teacher and I was sitting there trying to figure out the equation of a circle’s input is like, Oh, it’s just the distance from my head exploded. Oh, my God.

00:25:14:06 – 00:25:16:10
Kyle Pearce
Why didn’t anyone ever tell me this?

00:25:16:12 – 00:25:23:09
Jeremy Sarzana
Yeah. Oh, my God. And just all those connections. There’s three things you can connect rectangles, triangles and circles.

00:25:23:11 – 00:25:45:21
Kyle Pearce
So it seems like you’ve got some ideas here. And one thing I’ll add to that idea sometimes it can be helpful by intentionally spreading it out so that when you do do circles, you can almost review. It’s kind of almost an excuse like, Hey, remember those fields? And then you’re like, Here, I got a few more. They get another chance to kind of go like, Come on, sir, we already know how to do this.

00:25:45:21 – 00:26:06:06
Kyle Pearce
You’re like, We’ll just show it to me. And they do. And then your next question and then your next question. And then all of a sudden they’re like, Whoa, look what’s happening here. And then all of a sudden you’re like, benefit is bringing back or call it interleaving some of the material a little later and now they’re going, Oh, man, they’ll never forget that connection.

00:26:06:07 – 00:26:27:24
Kyle Pearce
Whereas I was just like you. I thought the circle, the equation for a circle was completely just look the way it did, because it did and I had no thought about it as a student, and it took me a really long time, even as an educator, to go like, Oh, that’s interesting. And then tying it together takes more time and effort as well.

00:26:27:24 – 00:26:45:09
Jeremy Sarzana
So you bring up another kind of pebbles for me too, is just the beginning of the year. We did right triangles and then we did transformations and then we did some statistics. It was just everything that we did in there was always forgotten. So why work in Spiral? You guys talk about it all the time. We just got to try to find out a way to do it.

00:26:45:09 – 00:26:52:02
Jeremy Sarzana
Even I’m just doing my own. I’m going against all the other teachers in my grade level, but I really want to find ways to spiral what you guys talk about.

00:26:52:06 – 00:27:16:24
Kyle Pearce
Yeah, one thing. If I would say your best start is taking things like what you just mentioned about Pythagorean, about the distance forming, about circles that might normally come up at different times. You can think of that as I’m already spiraling, that which is great, right? So rather than some people might actually do the opposite and bring them all together at once, maybe there’s a benefit to keeping that one apart.

00:27:16:24 – 00:27:42:06
Kyle Pearce
And you’re like, Oh, we’re already in good shape there. But then something like, I’m going to pick on statistics because it’s probably one of the concepts and topics or units, a study that we sort of come into. We kind of get it done and then we kind of move on. And that one might be a really good one that you can maybe break up a little bit and instead of if you normally spend, I’m just making up numbers, but let’s say you spent two weeks on statistics.

00:27:42:06 – 00:28:05:07
Kyle Pearce
Maybe you split into three smaller chunks and you put that still have a progression to it. We don’t want it to not make sense, but that one might be a nice one that you take and you go, Well, we always seem to forget that statistics even happened this year. Now it’s like, Hey, let’s do it over here, or you might even pick it as that unit that ends on a Thursday.

00:28:05:09 – 00:28:41:13
Kyle Pearce
And then you’re like Fridays there. And it’s just kind of awkward because the weekends there and people aren’t on track. Maybe Friday is a thing from statistics and then we’ll continue on to the next unit. Right? So trying to starting small I think goes a long way. So instead of taking everything and revamping everything, finding different ways that you can kind of keep a structure that keeps you feeling like you’re still on track, but still offers some of the benefits that you’re trying to gain from that interleaving and that spaced practice could be a really awesome way to begin that journey.

00:28:41:15 – 00:28:58:11
Jeremy Sarzana
Yeah, it’s been that grace, that sandwich and kind of like splits statistics up throughout the year, which is great because yeah, that’s something I different want to think about for next year and also not to go all over the place, but I want to talk about the portfolio day, which is which I because I thought that people were kind of like all over the place.

00:28:58:11 – 00:29:05:04
Jeremy Sarzana
I think that’s something that can kind of bring throughout the year, bring everybody together and give everybody a chance to work on things that they need to work on.

00:29:05:06 – 00:29:06:04
Kyle Pearce
I love that.

00:29:06:04 – 00:29:29:19
Jon Orr
It’s definitely a game changer to change the atmosphere in your room when you focus on assessment for growth versus assessment, as sometimes we call it, punishment in a way to make sure that you’ve been doing your homework. So we’re going to give you a test now or a quiz or a pop quiz instead of thinking about where are we on our journey, how can we showcase that learning and can we do it now in two months?

00:29:29:19 – 00:29:40:11
Jon Orr
Have I shown growth? Can I prove that I’ve shown growth in having a focus on that Growth is super important. Would you take our assessment for growth course yet, Jeremy, or have you explored it?

00:29:40:13 – 00:29:51:01
Jeremy Sarzana
Yes, I have explored. I’ve done the first third of it. I love it and that’s what I want to do. It just makes so much sense. It’s just that I felt like this year I was on survival mode the whole year. And honestly, the.

00:29:51:01 – 00:29:55:07
Kyle Pearce
Total cause I feel in a little bit uncertain. Absolutely.

00:29:55:07 – 00:30:11:01
Jon Orr
That is the reality we’ve said that here many times, is that we want to do everything all at once, but it’s almost impossible to do everything all at once. What can we do now to feel good and move forward? But every month or every semester we start to implement something new. We don’t want to do it all at once.

00:30:11:02 – 00:30:27:18
Jon Orr
It would be too overwhelming to incorporate so many new things into your classroom because you only have so much time in the day. I think choosing where to focus is going to be the best way to move forward. Instead of kind of going like, Let me just bring everything in, otherwise you’ll get burnt out and kind of abandoned those things.

00:30:27:18 – 00:30:51:11
Jon Orr
So I would think about how to use your assessment practices because I think that can be a huge game changer in actually the way that Kyle and I went through this journey. And this is not to say that if someone’s listening, this is the way you should do it. We talk through problem based lessons first and then moved into kind of mixing things up the way Kyle kind of said, and it kind of forced us to go like, we need to change some of our assessment practices in that way.

00:30:51:11 – 00:31:00:24
Jon Orr
So that was kind of our journey. But it doesn’t mean you can’t start with, say, revamping or changing your assessment practices first and then kind of moving in different directions.

00:31:01:01 – 00:31:23:02
Kyle Pearce
Before we ask you, Jeremy, for maybe a takeaway from today, and it’s great because you’re hitting on so many big ideas that I think people are nodding away, going like, Yep, I want to work on that. I want to work on that, I want to work on that. The message I’m hearing from John, which I think is really important, is, yeah, finding a thing that you want to make as your big commitment for yourself.

00:31:23:04 – 00:31:45:09
Kyle Pearce
And I think this past year, having never taught that particular course at that particular level, it is really important not to get too we’ll call it spirally too quick because even you as the teacher need to sort of endure that or experience that to kind of see where some of the connections are that maybe you never recognized in the past.

00:31:45:12 – 00:32:08:23
Kyle Pearce
So I think you had an opportunity to do that, which is great. You’re already on this problem based journey. It sounds like your curriculum sets you up nicely. Not that a curriculum typically a curriculum can’t actually be perfect and do it all for you, but it sounds like this one tees you up nicely to go. Okay, I’ve got these other details that I’m going to have to kind of work through a little bit.

00:32:09:00 – 00:32:40:20
Kyle Pearce
I would say continuing your focus there and as you’re doing that work, you can have will call them secondary goals for yourself of how can I maybe start with a small portfolio idea? Maybe it’s like whatever you consider to be the biggest concept from a unit of study, maybe there’s some time put aside for students to be able to do some of that work, or maybe it’s every so often, but don’t put too much pressure on you to have it all perfect before you say implement.

00:32:40:22 – 00:33:02:05
Kyle Pearce
I would say start small like John saying and you’ll see what’s working and then you’ll see what maybe isn’t. So you can kind of go a little and then you might want to pull back a little bit, right? Because you’re like, That didn’t really work so hot. Now I’m going to maybe rethink that, but don’t allow yourself to get too overwhelmed by too many things because that usually leads to inaction.

00:33:02:07 – 00:33:21:06
Kyle Pearce
Where we have too many ideas. We say it all the time. Too many priorities means no priorities at all. And we certainly don’t want it to be a more stressful situation than teaching already is, right? There’s so many moving parts there. So I want to flip it back to you there. Jeremy, You’ve taken some time out of your day.

00:33:21:08 – 00:33:32:05
Kyle Pearce
Last day of school is tomorrow for you as we’re recording this. So my question for you is, what’s your big takeaway here as you’re getting ready to set sail into the summertime?

00:33:32:07 – 00:34:06:06
Jeremy Sarzana
One thing I definitely want to start to have a day, I mean, because it suggests maybe like one day a week, maybe like on Wednesday to have students work on unfinished work or things I need to work on. I want to have a day that we do the portfolio day. And I want to I guess, what John was saying about, for example, like that test with the Pythagorean theorem and some kids from groups have already done the Pythagorean theorem that I can give them the extension, but of students are still working in some groups are still working on they haven’t found out the content and we can give them that three, four or five triangle

00:34:06:06 – 00:34:15:13
Jeremy Sarzana
so that they all have something that they’re working on because that’s a challenge. I had some students were all over the place, but I wasn’t ready. With extensions and ways to nudge other students forward.

00:34:15:13 – 00:34:36:16
Kyle Pearce
I love it. Those are huge takeaways. And I guess if you are thinking about picking, say, our day, you mentioned Wednesday, we picked Tuesday. It just happened to be, I think honestly because we started school on a Tuesday and we were thinking like we need some time before and then we just kept it from there. But if something came up in the schedule, we bump it like and modify it.

00:34:36:16 – 00:34:58:08
Kyle Pearce
So, you know, you get to kind of think of what that looks like and sounds like. I guess it really comes down to balance as well. Do you feel that, say, four days of learning is maybe enough meat and potatoes for your groups to have enough to kind of work on and do and all of those things? Maybe you want to do it every X number of days.

00:34:58:08 – 00:35:23:19
Kyle Pearce
If you’re on a four day rotation system, It really depends on those details. But ultimately, at the end of the day, I think regardless of how you choose to structure it, you’re giving students and you’re giving yourself an opportunity to kind of look at assessment and evaluation. In the end, this different, I guess, perspective on what it’s all about and why we’re doing it right.

00:35:23:19 – 00:35:43:21
Kyle Pearce
So it’s not like I always think of sometimes it’s like Fridays, there’s always a quiz for some people on this idea of a punishment, whereas we want students to look at that day as a day that I’m going to learn where I’m strong, learn where I’m maybe not so strong, and I’m going to be given some opportunity to improve.

00:35:43:23 – 00:36:02:02
Kyle Pearce
It’s not a judgment day. It’s about figuring out where we’re at and growing from there. And I found in general that most students, they become much better versions of themselves in math class, and they start to look at things a little bit differently.

00:36:02:04 – 00:36:17:24
Jeremy Sarzana
Can I just say one thing I just thought of? It’s almost like having a portfolio is almost a day to like, just like, pause for a sec. I feel like this whole year I just went and I was over. I didn’t really we didn’t ever really let just pause and be with this, put on the brakes for a second and just slow things down for a second.

00:36:17:24 – 00:36:18:22
Kyle Pearce
So totally.

00:36:18:22 – 00:36:29:04
Jeremy Sarzana
That’s one thing I feel about education. It just feels like everything is such a rush. I guess I didn’t have the confidence to be like, We’re going to do a day where we just stop. And just as I was afraid, Oh, what if my evaluator comes in, Hey.

00:36:29:04 – 00:36:52:24
Jon Orr
You, you got reasons. You got reasons, right? So that’s great to hear. And also, I know that feels that way. And I think we all feel that way at times in thinking about how my structured the decisions we make in our classroom are for purposes and if this is the purpose that you’re saying that this is where we’re going to go and this is the purpose of why we’re doing it, then you go down that pathway, and as long as you have the justification, you’re going to be fine.

00:36:53:03 – 00:37:08:20
Jon Orr
So it sounds like, Jeremy, you’ve got lots to think about over the summer. Yeah, lots to kind of plan for come next year. So I do want to thank you for joining us here on the Making Math Moments podcast this is your second go at it. So there’s not too many who come back and share exactly what’s happened.

00:37:08:20 – 00:37:22:11
Jon Orr
So we’re so thankful that you can do that. We want you back again in the future. We want to keep exploring your journey as you strengthen your mathematics classroom. So would you be open to kind of coming back on, let’s say, next year and kind of filling us in on that year’s journey?

00:37:22:13 – 00:37:24:13
Jeremy Sarzana
Yeah, absolutely Thank you so much.

00:37:24:13 – 00:37:25:17
Kyle Pearce
The awesome.

00:37:25:17 – 00:37:27:16
Jon Orr
Stuff. Thanks so much, Jeremy.

00:37:27:18 – 00:37:37:23
Kyle Pearce
Take care. We appreciate you, your students, appreciate you. And of course, the math moment make our community appreciate you. So have a great one. Enjoy that summer and take some time to pause.

00:37:38:00 – 00:37:40:14
Jeremy Sarzana
Okay. Thank you. All right.

00:37:40:16 – 00:38:08:07
Kyle Pearce
Well, John, it was so great having an opportunity to catch up with Jeremy after we hit the stop button on that episode or that interview. I couldn’t help but let Jeremy know. You can hear. The passion for education in his voice, his concern for his students that he is doing the best he possibly can for them, and the reality is, is that he is doing the best he possibly can at this time, in this moment.

00:38:08:09 – 00:38:20:05
Kyle Pearce
But the beauty is, is that he’s also committing to continuing to learn, continuing to grow, and of course, continuing to therefore help many, many students.

00:38:20:07 – 00:38:37:05
Jon Orr
Yeah. And you can hear from this conversation that he was focused primarily on strengthening the branches of his tree. These are the teacher moves. He’s thinking about how to think about his lessons before, how to think about the moves that he needs to make during the lesson, and thinking about the moves he needs to make after the lesson.

00:38:37:05 – 00:38:59:05
Jon Orr
But now he needs to make in the lesson. Where does this progression stretch? If you’re working on a particular topic? He was kind of diving into the distance formula, but what do we need to do after the distance formula? What needs to happen before the distance formula? How are students going to progress along that trajectory? And when I notice where they are in the tree actually, do I have the teacher moves to kind of move them along?

00:38:59:07 – 00:39:23:15
Jon Orr
And do I have the fluency and the flexibility as a teacher to let this group move along before this group so that I can bring them and consolidate all together for that learning goal of the day. So a lot of moving parts when we release that rigid ness of teaching, the I do we do you do model in moving to the problem based model and moving to using, say, the five practices to kind of guide that lesson structure.

00:39:23:15 – 00:39:37:01
Jon Orr
So hat tip to him for a kind of doing that in a course that he was brand new to him and also that continued growth like you said Kyle that continued growth he’s making to strengthening those branches of his tree.

00:39:37:03 – 00:40:01:14
Kyle Pearce
I love it. I love it. Yeah, I see. And I want to really highlight here, when you’re talking about that professional growth and thinking about the limbs of the tree, we talk about the professional growth or his professional learning plan. Many people who are coming on the podcast and chatting with us, they have very strong limbs of their tree because they’re constantly seeking ways to develop to try to improve.

00:40:01:20 – 00:40:26:04
Kyle Pearce
And you can hear that coming out today through his message. And the other piece that I’m really liking to that maybe is more of like a secondary part of his tree is the soil, sun, water of the tree, which is the mindsets, the beliefs, the culture of his classroom. I’m feeling like even just his shift from trying to maybe slow down, he had mentioned he felt like he was just go, go, go.

00:40:26:04 – 00:40:49:23
Kyle Pearce
And he wants to slow down in that portfolio. Day might offer that opportunity for them to build that culture to maybe shift beliefs and mindsets in their classrooms and of course, continue to grow the other parts of the math classroom tree. So awesome stuff there. He had mentioned the assessment for growth course, which is something inside of our academy.

00:40:49:23 – 00:41:17:20
Kyle Pearce
So if you’re listening to this and you’re going, How do I get going? The first module of that course is actually wide open. So if you head over to McMath moments dot com forward slash AFGE its representing assessment for growth McMath moments dot com forward slash AFGE. You can dive into that first module and if you’re liking it and you want to dig in even deeper like Jeremy has, then you can of course go ahead and become an Academy member.

00:41:17:20 – 00:41:40:14
Kyle Pearce
And we do have a 30 day free subscription that you can dig in to cancel any time. So hey, maybe you’re on summer vacation listening to this and you want to dig into some PD, go ahead and get yourself taken care of. So head over to make math moments dot com forward slash AFGE and you can check out that course or any of the other courses inside the academy.

00:41:40:20 – 00:42:01:09
Jon Orr
And if you just want to click you can head on over to the show notes page to make math moments dot com for episode two for four that’s MC math moments dot com forward slash episode 244. On that page you’ll find the link to that course plus all the other links we referenced here, like the squares, the triangle lesson that we talked about and any other links that we have.

00:42:01:09 – 00:42:08:06
Jon Orr
Plus you can get the complete transcript from this episode over on that spot as well.

00:42:08:08 – 00:42:19:11
Kyle Pearce
Awesome stuff, my friends. Hey, listen, if you’ve enjoyed this show, go ahead, hit the subscribe button rate and review and we appreciate you. Until next time.

00:42:19:13 – 00:42:21:18
Jon Orr
I’m Kyle Pierce and I’m John or.

00:42:21:23 – 00:42:25:11
Kyle Pearce
High fives for us.

00:42:25:13 – 00:42:32:12
Jon Orr
And I five for you. Oh.

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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


Each lesson consists of:

Each Make Math Moments Problem Based Lesson consists of a Teacher Guide to lead you step-by-step through the planning process to ensure your lesson runs without a hitch!

Each Teacher Guide consists of:

  • Intentionality of the lesson;
  • A step-by-step walk through of each phase of the lesson;
  • Visuals, animations, and videos unpacking big ideas, strategies, and models we intend to emerge during the lesson;
  • Sample student approaches to assist in anticipating what your students might do;
  • Resources and downloads including Keynote, Powerpoint, Media Files, and Teacher Guide printable PDF; and,
  • Much more!

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,
  • Students are to focus on how they can convince their math community that their solution is valid.

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.