This year I’m teaching both Advanced Precalculus and Standard Precalculus. (Totally confusing on a daily basis? Yup.) And I’m working with two other teachers to write the Standard Precalculus curriculum from scratch. Of course this is something that is daunting, but I love to do when I have the time and like-minded colleagues.
I was in charge of spearheading our sequences and series unit. In this post, I want to briefly share how we started the unit. Instead of diving right in, or doing something intense, I wanted to gently get some good conversations percolating. So I handed out this set of cards:
and gave them this set of instructions:
I debated having kids use Desmos for the card sort, but since I have kids work in groups (mostly groups of 3), and I wanted the entire group to be working together, and I wanted them to actually physically move and shuffle cards, I decided to use physical cards. I also had all kids stand up while doing the card sort. I had a feeling that would be magical, in terms of getting kids talking, moving, and engaging with each other (even thought they were all at the same table), and it was! So I highly recommend that.
These cards end up having three different types: arithmetic, geometric, and recursive.
Most kids got the arithmetic sequences quickly, but it was interesting to watch them struggle with the geometric and recursive. There were great conversations, and because I demanded the next number for each of the sequences, kids had to really think through what the pattern was (and in geometric sequences, how to find the common ratio). I had thought that kids would finish this really quickly, but I was totally wrong. It took about 20 minutes. So plan accordingly. (A few groups needed to do a little bit more at the end of class, so I had them take a photo of their card sort and use that photo to finish things up!)
One note: Card H which has the sequence 0,0,0,0,0,0 fits all three categories. So it’s great fun to watch kids try to place it.
I wanted to share this activity because I haven’t really done many card sorts before — and I was so pleased that this particular one generated productive conversations. So I need to keep this teaching tool in my arsenal for generating conversations about something new. (Example: I just thought of giving a bunch of graphs of rational functions to kids on cards, before we start that unit, and say “find different ways to sort these!” There are so many features, so that could lead to so many different ways to sort the cards. I suspect that Desmos would be good for that particular card sort, since there would be many different ways to sort those pictures, and I’d want to project the different ways kids did it to the entire class. I bet through that sort, we could actually recognize vertical asymptotes, horizontal asymptotes, oblique asymptotes, and holes!)
Here is the .docx (2016-10-31-card-sort-for-sequences) and .pdf (2016-10-31-card-sort-for-sequences) for the cards.
I will try to write up some more about my sequences and series unit soon!
Continuous Everywhere but Differentiable Nowhere 
I love card sorts, and so do my students! I have been using them with laminated cards and with Desmos – both work a treat in engaging students’ learning. I love the freedom it allows me to move around the room and listen to student questioning, discussion, reasoning, conjecture, arguing, justification, and exhilaration. Now that is what I call ‘active’ learning.
Yay! Do you have tried-and-true favorite card sorts that you use, that you can link to (either blogposts, files, or desmos)?
Here is a link to an early Desmos Card Sort Activity – ‘which is which’ – applying understanding of linear features to match rules for parabolas to their corresponding graphs.
https://teacher.desmos.com/activitybuilder/custom/5819812ed8252db1518f930c
Also – another Card Sort adapted from a TES resource:
https://docs.google.com/document/d/1O2ZH1xdvddjZjiyc7eK6lXIBd_r465ibPvXnRwsA7DM/edit?usp=sharing
In both cases, I reinforce that the students must identify the two variables that are represented by the relationship, and label the axes.
Both require students to use their intuition to make connections between rules, graph and scenarios.
Thank you for taking the time to type those resources up for me!!!
I have never tried a card sort before and this is just perfect for my next unit–sequences and series!
Oh! Then I’m glad I posted it! I will say that this hit the sweet spot for my standard precalculus kids, but I think it would be too easy and not be effective for my advanced precalculus kids. Just saying that in case it helps you decide whether you need to make a harder version or not.
I teach in a small school and we don’t have differentiated levels of pre-calculus, so I have to hit the sweet spot for both groups. I was glad to see that you had a set of extension cards with quadratic patterns. That will help with the students that finished earlier.
I am also interested in the Precalculus curriculum that you are writing. Do you have a list of topics yet? There is so much that can be included in Precalculus and I am interested in what other teachers emphasize.
Ha! We had a set of topics that we were planning on covering, but we messed up a bit on pacing/timing so we’re going to have to cut or alter some of our plans. If you ask me at the end of the year, I’ll happily share what we’ve done! Right now we’re reworking what and how we’re going to do for the rest of the year.
That is always my problem. I’ve been teaching pre-calculus for 19 years and it seems like the more I learn, the deeper I want to go, and the less I cover. So I have left out a couple of important topics the last couple of years because I run out of time. It sounds like you may be having he same problem.
YES. Exactly. EXACTLY.
Do you have a link to the document for the set of instructions for sorting the cards?
I’ll write a quick blogpost and post the entire packet for you today!
We start back with trig functions and I am thinking that a card sort could be awesome for that.
Cool! I seem to remember seeing a card sort for that before… But I can’t remember where!
If you don’t know about the MTBoS search engine, check it out!
http://www.fishing4tech.com/mtbos.html
You might have luck looking for the card sort there!