Thursday, November 22, 2007

The Prime Rate: A Post-Thanksgiving Class Opener for Grades 6-12 that Stirs the Brain

Many math educators use warmup problems to review, challenge or set the tone as students walk in the room. Routines like this are effective in having students 'hit the ground running'. These mini-problems can be on the board, while an overhead transparency of selected answers are displayed. The instructor then has time to circulate, check homework, engage students, and get a feel for the difficulties they had with the assignment. By the way, do most of your students take these warmups seriously?

Here is a warmup that requires more active participation on the student's part. I may suggest a different one in a later post, but I'd really like readers to share some of their favorites!

Math Bee
All students stand at their seats. They are told they will be have to give the next number in sequence, according to some rule that will be explained. They will have 3 seconds to respond (can be adjusted but no more than 5). If incorrect or time runs out, they will be instructed to sit down and the next person will have to give the correct answer and so on. You may want to start them off by giving them the first number (judgment call here). I suggest you allow a maximum of 5 minutes for this activity.

Here's the problem I gave to a group of high schoolers but it is highly suitable for middle schoolers as well:

Using positive integers, think of primes ending in 1 or 3 (you may want to use the technically precise phrase 'whose units digit is 1 or 3'). For example, 21 'ends in' 1, but it is not prime. You must go in order and you are not allowed to ask the number the previous person gave! You will have 3 seconds to respond. If incorrect or time runs out, I will ask you to sit down and the next person will need to give the correct number. We will continue until there is only one star shining or time runs out and we have co-champions!

Learning Objectives:
(a) Reviews primes (How many of your students do you think would be eliminated early by starting with 1? You can always start them off with 3 if you feel this will help. Some students will begin with 11, assuming that you meant 2-digit numbers. By the way, 51 and 91, in particular, typically knock out many, if they get that far! Finally, are you thinking this question is not particularly relevant for high schoolers? Count how many questions relate to primes on the SATs!)
(b) Improves listening skills and concentration (How many of your students do you think will forget the last number given either because their minds are wandering or from trying to think ahead to their turn?)
(c) Learning how to think under pressure. (Although we know some students will 'freeze up' or be embarrassed if they are eliminated, they will not be alone! Typically, about half of the students in an above-average class will be sitting down on the first pass through the class! With a high-achieving class of very strong students, you may need to make several passes to reach a winner. If there are a couple left after 3-4 minutes, proclaim co-champions.

Let me know how this goes if you try it after the Thanksgiving break. What variations would you use to make this more effective for your students? What other kinds of problems are suitable for this 'Bee?' Were my predicted statistics way off? Did you predict that students would get past 100?
Again, please share some of your favorite warmups!


Totally_Clueless said...

Not a warmup, but a variation on a party game. After playing the standard party game wherein you alternately count from 1 to 100, but say 'Bus' instead of a number that either is a multiple of seven, or has a seven in it, my daughter and I got bored. So, we came up with a variation in which you say 'Bus' for sevens, 'Train' for sixes (or eights), and 'Boat' for both.


Dave Marain said...

This is similar to the wonderful buzz, bizz and bizz-buzz game we used to play in class! I'm hoping others will share their all-time favorite class participation games too! Happy Turkey Day!!