# Ep 103: Rich Tasks, Investigations, 3-Act Tasks, Pt 2

June 07, 2022 Pam Harris Episode 103
Math is Figure-Out-Able with Pam Harris
Ep 103: Rich Tasks, Investigations, 3-Act Tasks, Pt 2

What are some examples of rich tasks that are designed to intrigue and engage students? In this episode Pam and Kim give some specific examples and describe why they are so rich.
Talking Points:

• Relatable to students not just real world
• An eye towards equity
• Lead to the mathematics
• Packed with patterns
• Natural extensions
• Make the math realizable
• Building Powerful Linear Functions coming Fall 2022

See Ep 47: Fractions as Fair Sharing where we explored the Sub Sandwich rich task!

Pam Harris:

Hey fellow mathematicians. Welcome to the podcast where math is Figure-Out-Able. I'm Pam.

Kim Montague:

And I'm Kim.

Pam Harris:

And we make the case that mathematizing is not about mimicking steps or rote memorizing facts. Y'all, it's about thinking and reasoning,about creating and using mental relationships. We take a strong stance that not only are algorithms not particularly helpful in teaching, but that mimicking algorithms actually keep students from being the mathematicians they can be. We answer the question, if not algorithms and step by step procedures, then what?

Kim Montague:

So last week, we started a conversation about what makes a rich task rich. And of course, we have plenty of things to say about all the things so we decided that we would pick up where we left off and talk some more about rich tasks this week.

Pam Harris:

Yeah, so if you haven't listened to the last episode, check it out. Because we go through some lists and describe some things and ways of thinking about what makes a rich task rich. Today, we'd like to give maybe some examples and further exemplify kind of what we talked about with those lists. And maybe also talk a little bit about what we think rich tasks or not. So I'm going to start by talking about, I had a conversation once with Glenda Lappan, who I give a lot of credit to her and Betty Phillips and the whole Connected Math project team for creating, I think, some wonderful rich tasks. And one of the things that she and I talked about was that they really tried for contexts that made sense to students, things that students could relate to. They actually gave students surveys, to find out what students were interested in, what they thought about, what things that could help them sort of realize the math. And then they tried to stick those contexts where they made sense as they created rich tasks, not in a fake kind of weird way. But I think they did a fantastic job of doing things with pizza and video game reaction times. I love that and bicycles, shoes, clothes,amusement park rides, Olympic times and scores like just to name a few of some of the wonderful contexts that they used that could help make those rich tasks, where they help make the math realizable. Not that it has to be real world. But just things that kids were interested in that would sort of perks of interest. And I honored the fact that they were actually thinking about not just real world, but things that would be sort of interesting to kids. And then let's be clear, they did not make them too hokey, not too,like try to force the math into the context. Often they sometimes had contexts that were more whimsical or more, sort of fantastical. Sometimes they had them purely mathematical. So it's not about making everything real world. But I can honor the fact that they thought about if there were ways they could use things that were that that interest teenagers, like young middle school kids. I thought that was pretty cool.

Kim Montague:

Well, not only did they think about it, but they actually surveyed kids, right?That's really cool. And it's not, you know, you're talking about that, it makes me think about how not too terribly long ago, one of my sons came home and his teacher tried really hard, right, to make the assignment be like something that kids can connect to, by putting her students' names in the worksheet. And so it was like, you know, my son's teacher, it would have his name and one of the problems. But,you know, you run into that risk of, like, what happened with my son is that he was like, "This is a problem about me, but I totally do not like the thing that I'm supposed to be talking about me liking." I was like,"Oh, sorry, buddy. Sorry."

Pam Harris:

Kim Montague:

And it sounds like you spent a lot of time thinking about that, right? It's not like a super quick, just like whip something up?

Pam Harris:

It was no,definitely not. In fact, I tried several different things. And then pilot tested several different things. And then once we sort of decided frozen yogurt was the thing, then we pilot tested different ways of giving kids experience and also different ways of asking the questions to make sure that what we got was kids actually thinking about, "Hmm, well, I could solve that. But I don't know how to, I don't know how to solve that one, because you're like, you haven't told me how...Oh, I could represent all of them." And that's becoming an increasingly important conversation for me in high school math, is how can I represent all of the scenarios?Or how can I represent all of the possibilities, then becomes that linear function. A linear function represents for any x,what would the outputs be for any x in this scenario? So that became a really important question that we found after researching and pilot testing different ways of writing that rich task. So Kim, if that's a way of thinking about what rich tasks are, what are they not?What are some things that we agree which tasks don't have?

Kim Montague:

So you know, I was thinking about this not too long ago, actually, because we like to think about problems right?And so if they're kind of fun or interesting, but they don't lead somewhere, you talked about the fact that you love that they lead somewhere in last week's episode. But if they're fun and interesting, but they don't kind of mathematically go anywhere,that's not going to be a rich task, right? They don't have the extensions that I love, then it's also probably not a rich task. And the reason I was thinking about this is because we have a teammate who loves to throw out some problems in our communication, we slack, but our communication. And they're fun to do and think about and talk about, but we don't consider them a rich task, because they're not really connected.They're kind of in isolation.They don't really go anywhere.It's just a single problem that you might tinker with a little bit. And they're just kind of lame. That's where it is.

Pam Harris:

So to be clear,we're not saying don't ever do those, don't ever throw them out, don't work with students.It's just that when we talk about curriculum design, and we talk about how you sort of set up a unit of study, and we say,"Oh, like it should be centered around rich tasks." What we don't mean are those things that you just said. Things that are aren't extendable, that they don't have, they don't lead somewhere. They're fun in themselves. But when we want to kind of focus or center our sequence of tasks around a rich task, that's not what we mean.

Kim Montague:

Yeah. And it's probably not something, a rich task might not be something that you do every single day. Because they're not the easiest, like you mentioned earlier, they're not the easiest to write or to find, right? It's not like you're going to do a fresh, rich task every single day. But you might have a sequence where a rich task is the center. And you might do some problem strings leading up to it. You might back out of it with a problem string or some other kind of routine.

Pam Harris:

And then we really like those rich tests that you can build from, right? That have like a second step to them.Like,"Ooh, what if we..." and I think we'll mention a couple examples of those in just a minute.

Kim Montague:

Yeah, so I know,you know this. But Cathy Fosnot knows 10 day units are some of my very favorite rich tasks.When you and I were writing it was a lot easier to spend the time to come up with really rich tasks. And so I don't, I never recommend to teachers, like,"Oh, just go whip some out real fast." What I recommend is that they use and take kind of their discernment to parse out, is this that I'm finding a rich task? Is it going to be the best use of my time with my students,rather than to create their own.Although I have seen some people come up with some really good ones. But Fosnot's 10 day units are definitely at the top of my list. Rich.

Pam Harris: