The #msSunFun topic of the week is promoting number sense, and I think the game of Rule! is a great way to do that. My students love playing the game of Rule! and I love it too, for all of the practice it provides for recognizing and generalizing patterns. I believe that any time you can get kids to repeatedly manipulate numbers to look for patterns, you are building their number sense.
Rule! is an adaptation of an activity by Grayson Wheatley and George Abshire, from their book Developing Mathematical Fluency (http://www.mathematicslearning.org/index.cfm?ref=30606&ref2=12). Their book is one of those resources that all middle school math teachers should know about but I’m afraid few do. It’s full of ready-to-use lessons and even comes with a CD of those activities. I definitely need to blog about other activities I use from this book!
Rule! can be played with a whole classroom of students and every student can stay engaged all along the way. I typically use Rule! as a warm-up activity, although you could also use it as a time-filler if you ever have 5-10 minutes to spare. And if you’re using it as a warm-up, you can start as soon as the first students walk into the room — no reason to wait until everyone is present to get started. One great aspect of this activity is that Rule! takes practically no planning on the part of the teacher — all you have to do is think of a function rule (younger grade teachers may think of this as an input/output table) to be the Rule! for the day. Keep your rule in mind as you call on students around the room. If the student you call on hasn’t figured out the Rule! yet, he/she just gives you a number — this can be any number, although low numbers are usually more helpful in terms of helping others determine the Rule! As students give you their numbers, write these on the board along with your “output” (the outcome when you apply your function rule to their number). I write mine with an arrow in between, so for example if a student gives me the number 10, I would write 10 –> 33, and if a student gives me the number 5, I would write 5 –>18. (Have you figured out my Rule! yet?) Since all of these numbers are written on the board, late students can jump in as they arrive.
Continue around the room calling on students in order (not by hands raised). I usually go from group to group around the room (calling on every student) and I try to start with a different group each day because the kids hate to be in the first group I call on since they don’t have enough evidence to determine the Rule! It really kills them when they figure out the Rule! soon after you’ve called on them. That always makes me smile because I love to see them so motivated to figure out the Rule!
If you call on a student who has determined the Rule!, instead if them giving you a number, they should say “Rule!,” which means you give them a number and they have to apply the Rule! to your number. This is what makes this activity so engaging . . . you can tell whether the student knows the Rule!, but the secret isn’t given away for students who haven’t figured it out yet. (And I choose the number I give the student based on the mathematical ability of the student in question — you can keep it easier for a struggling student or make it harder — incorporating fractions, decimals, or negative numbers — for more advanced students.) I usually continue calling on students until at least 4 or 5 kids have figured out the Rule! before I allow anyone to describe the rule.
At that point, I often have students who had determined a different Rule! from what is being described. For example, with the numbers I gave earlier, one student might describe the rule as “multiply by three and then add three to the product,” while another student might say “add one and then multiply the sum by three.” At times during the year (and as time allows) I have all students practice writing expressions based on the students’ descriptions of the rules, and sometimes we simplify the expressions to show that they are equivalent. You can adapt what you do after the Rule! is determined to fit the needs of your class.
I hope your students love to play Rule! as much as mine do!