Monday, February 8, 2016

Practice/Review Games


There were two goals for my classroom re-set this January—to make our class more productive and more joyful. An element of this was to make my lessons feel different and more fun than the regular structure I use in about 5 out of the 8 periods a week.  This structure is guided notes that involve a mini-lesson, practice/application, and then discussion. However, the thought of trying to change each lesson so it felt different and fun was overwhelming. Instead, I decided I wanted to have a couple of new practice structures that would meet my goals, but that I could just insert into my regular lessons.

In choosing practice structures, here were the four criteria that were important to me:
a) Easy to Prep
b) Individual Accountability
c) Versatility of Use
c) Didn’t Require a Whole Period

It’s also important to note that I chose these structures  to build fluency with procedures. I don't think they are a good fit to introduce new ideas or to build conceptual understanding.

Practice Games


Climb the Ladder
Description: I first heard of this from my mentor teacher. It involves a series of problems, each with increasing difficulty. Students get each problem checked when they finish (I had three student leaders with answer keys who did the checking) and then they get to “climb the ladder” to the next problem. The worksheet, with directions, is here.
Analysis:
Easy to Prep: It took me a little while to get the formatting to show the ladder on the page, but I can now just modify that sheet whenever. Very easy prep.
Individual Accountability: Students each had their own paper and needed their own answers checked, but they were helping each other out. In general, motivation to get to the next problem was high.
Versatility of Use: I have used it for solving equations and identifying equivalent equations so far, but it could be used for anything. It is especially good if students can build on what they did in the previous rung (ex: Rung 1 is solving x +4 = 10, Rung 2 is solving 2x+4=10)
Didn’t Require a Whole Period: 20 minutes seemed about the ideal amount of time, with about 8 problems. Everyone finished the first ladder (4 problems), and fast finishers got to all of the problems.
Other Notes: I find it is extra fun if you excitedly say "Climb the ladder" every time a student gets a problem correct.

Solve-Crumple-Toss
Description: Students get a half sheet with a problem on it. It is checked for accuracy (I had three students with answer keys to do this in my bigger classes, I personally checked all of them in my smaller class). If it is incorrect, the student revises their work. If it is correct, the student crumples the paper and gets to toss it into a basket to earn their team a point. The directions I projected for students is here. Also read Kate Nowak’s description here.
Analysis:
Easy to Prep: I had to cut up all of the half sheets, but they were extremely easy to make. In the future, I will make fewer of the later sheets because not all students get to all of the sheets.
Individual Accountability: Students each had to put work on their own paper, but were generally helping each other. I saw a handful of students more engaged than I have seen them in a long time because they really wanted to toss their paper. This desire also led to several students just copying their friends’ work so they could throw sooner.
Versatility of Use: Could be used for any type of problem! The problems should be a little bit meaty so that the time spent doing the problems vs. crumpling/tossing is heavily weighted towards doing the problems.
Didn’t Require a Whole Period: I think a minimum of 15 minutes, maximum of 40 is probably appropriate here. I want to make sure that students who are taking their time/checking their notes/explaining to a partner still get the reward of getting to crumple and toss their paper.
Other Notes: I was worried about too many people finishing at the same time and the checking/tossing part being overwhelming for me. Having 3 students checking, each of whom was in charge of a group of about 9, was really helpful. And they didn’t finish as quickly as I anticipated—the line to toss the paper was never over 4 students in a class of 27. I also had one student who was pretty distressed about crumpling her papers up when she finished. I had decided that this was ok because they already had a sample in their notes that they could look back at and I just wanted them to get more practice.

Speed Dating
Description: Students each get their own problem that they have some time to work on individually and become experts at. Then they pair up and trade problems, each person helping their partner if they need it. Every 5 minutes or so, the partners shift. There are more detailed descriptions from  Kate Nowak, Elizabeth Stratmore, Meg Craig, MaryAnn Moore, and Amy Gruen.
Analysis:
Easy to Prep: Pretty easy to prep. You need a different problem for each student (though when I do this with my larger classes, I will split them into 3 groups and then only have 9 different problems rather than 27). Also, whiteboards and dry erase markers are helpful to have for each student (though they could just do all of the problems on a separate piece of paper). This has been the limiting factor for me, so I have only done this with my class of 11 so far.
Individual Accountability: Speed dating is excellent for this! Students get exposed to a ton of problems where they have their own personal helper. They also have to be able to explain really well one particular problem. It’s also good for differentiation in the difficulty level of the problem each student initially gets.
Versatility of Use: Could be used for any type of problem!
Didn’t Require a Whole Period: This one is a little bit longer. 5 to 10 minutes to become an expert at your own problem. Probably about 2 minutes to get set up into the rotating columns. Then 3-7 minutes of work time for each pairing.
Other Notes: I loved how uninvolved I was as students were doing the speed dating. It was amazing to see the amount of math talk going on and how they were really explaining to each other.

Content Auction
Description: Teams get $1000 and an “auction catalog” (read: worksheet with practice problems). They are told what they want to buy (in my case equations with one solution) and given 10 minutes to work on the worksheet in order to plan what they will bid on.  Then the auction begins! Teams bid on the problems, and the problem goes to the highest bidder. After each item is won, we go over the problem to decide whether it was a wise buy. Here's the powerpoint that I used. Further description here and here from Sarah Hagan.
Analysis:
Easy to Prep: Extremely easy to prep. You need a worksheet with some practice problems on it. I also made bidding paddles (a notecard with the table number stuck to a popsicle stick) and a powerpoint with the problems, but those were extras and not required.
Individual Accountability: There wasn’t great individual accountability when teams were working on deciding what to bid on. I did, however, require students to copy down the answer as we went over each problem.
Versatility of Use: There needs to be some way of distinguishing which problems students need to buy and this distinguishing element is where the doing the practicing the math comes in. For example students might want to only buy true true statements (as opposed to false) or functions (as opposed to non-functions).
Didn’t Require a Whole Period: You definitely need a whole period for this one.
Other Notes: I felt like this one was the least successful out of all of the games that I tried because there was a high ratio of unproductive chaos to productive math practice. Students didn’t do that many problems before the auction started and then once the auction started the bidding was a lot of time without math thinking. Then reigning the kids back in to go over the problems after they had been bought was hard. However, I think some tweaks in the future would help. I would probably start with 5-10 minutes of individual work time. I would then have the teams split up their $1000 dollars however they wanted over all of the problems. I would collect this info some way (electronically?). Then we would have volunteers to explain each problem and then reveal which team had the highest bid and thus won it. I think this would be more focused on doing the math, but still have the fun bidding and competition elements.


Student Responses

After we had done Climb the Ladder, Solve-Crumple-Toss, and the Content Auction at least once, I asked my two larger classes for feedback on which game was their favorite and why. Here were the votes:
  • 1st Place: Climb the Ladder (15 votes)
  • 2nd Place: Auction (9 votes)
  • 3rd Place: Solve-Crumple-Toss: (8 votes)
There were enough votes for each one that I let the class know we would be doing all of them again.

Here were some of the best reasons that kids gave for their top choice:



 

Other Practice/Review Games

These are games that I haven’t tried yet because I didn’t want to introduce too many new structures at once and/or they didn’t seem as good a fit for my specific criteria. They may however be useful for others!

War: Descriptions from Denise Gaskins and Kate Nowak
I Have, Who Has: Sarah Hagan and Sarah Hagan again
Ghosts in The Graveyard: Kim Hughey
A couple other compilations of review games:

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