We were talking about PD experiences the other day and it inevitably turned to "What was the best PD you've ever been to?" Having never attended a TMC (and unable to go this summer...sad face) I reflected upon one of the more useful district supported PD days. We met a group of math teachers from another high school in the district. Prior to the meeting we were asked to write out a description of our best. It could be a lesson, a technique, an explanation. I honestly don't remember what I brought to the table, but it wasn't nearly as good as the stuff I got out of the day.
Below are quick descriptions of two review games that have been great of great use in the classroom for a tweak on an "quality, basic" problem set.
Equation Golf: Have a problem set of 15 problems that you want the whole class to do? Give students a goal, or a par. You want to get all of the correct answers to the problem set by calling on 18 people or less. (Numbers used are purely for illustrative purposes, you can have 20 problems and call on 26 people, just make the goal reasonably attainable). Have students work on the problem set for the desired amount of time. Individually, partners, groups, your call. At the end of the time, tell students that they must pay attention to play golf. Pick a student at random (Popsicle sticks, random # generator) and that student picks whichever problem they would like to answer. You verify or reject the answer. New person. Each person counts as a "stroke". Goal is to make par.
This helps work on listening skills as well. I always tell the students that they must pay attention to which answers have been given AND marked as correct. The students must announce the problem number first, then give their answer. This way, if a correct answer has been given for #3, and a student says "I'd like to answer #3, the answer is..." I can cut them off, let them know that that question has been answered correctly already and that counts as a stroke.
In the past, I had given an entire class grade for this activity. Usually a relatively small grade that didn't really affect the overall grade in the class, but enough to keep them interested. As I tried to move towards more standards based grading, I might make the change to allowing a student that answers correctly to use that as evidence of learning for a particular objective. This would have the added bonus of helping students to identify their own areas of need, work on that with students in the class during the class work portion, and trying to answer more difficult questions based on their individual needs.
Bluff: Take a similar problem set as Equation Golf but divide the class into two teams. Give one team a problem to complete (the other team should simultaneously complete the problem). On Team 1, after a certain time, ask anyone that feels that they have the correct answer to stand up. Someone from Team 2 picks a Team 1 member to answer. If it is correct, Team 1 gets a point for each person standing. If it is incorrect, Team 2 can steal the points. Then the next question goes to Team 2.
This game can be a bit touchy so you have to have a responsible group of kids that will be willing to put themselves out there. Class culture is extremely important to this game. I have seen times where students will continually pick on one person, so it is up to the teacher to ensure that the game stays positive. In cases like this, the teacher doing it was awesome (disclaimer, it was not me...though I am pretty awesome!) and when this situation arose, he turned it and made the kid a champ when he kept getting the questions correct.
A bit of strategy goes into the game as well. A team cannot call on the same person 2 turns in a row, so the last person called should always stand. I don't share this with kids, but it is fun to watch them figure it out. And a student can stand even if they do not think they have the right answer in an effort to increase the point value for their team (hence the name Bluff).