Teaching Divisibility Rules

So we are finishing up our unit on multiplication and division (remainders as fractions & decimals, division by multi-digit numbers, etc.), and will complete the unit with divisibilty rules.  I don't know about you, but I cannot remember a single teacher ever teaching me these rules.  To be honest, I didn't even know they existed (as a set of rules) until I began teaching math.  If you don't have to teach divisibility rules, or you just want a quick refresher, here they are:

2:  If the last digit is even
3: If the sum of the digits is divisible by 3
4: If the last two digits form a number divisible by 4
5. If the last digit is 5 or 0
6: If the number is divisible by both 2 and 3
7: Take the last digit, double it, and subtract it from the rest of the number; if the answer is divisible by 7
8: If the last three digits form a number divisible by 8
9: If the sum of the digits is divisible by 9


I don't know about you, but some of my students have difficulty even dividing 3-digits by 1, so to ask them to do the mental math for 7 or 8 is a huge challenge. Even if they get an answer, the possibility of making an error along the way is so great, that it is almost easier for them to just do the long division.  Regardless, the curriculum demands it, so I wanted to pass something along.  While searching through Smart Exchange (the website for Smart users, but can be for anyone--no sign-up fees), I found an AMAZING presentation on these rules.  Whoever put this together gets my respect medal of the day.  I hope this helps you, if you are teaching these rules!

http://exchange.smarttech.com/details.html?id=db76013b-040a-4fa5-8703-8af6942c4793

Until the next bell...
K.

As 2012 begins...teaching the value of setting goals

As this new year begins, our televisions, newspapers, and digital media are flooded with encouragement/advertisements to begin anew.  Taking this into consideration, I wonder if the value of setting and achieving long-term and short-term goals is being taught in intermediate classrooms across our country, in a manner that will instil these values for life-long purposes in our students?

Classrooms at all levels are no strangers to goal-setting, usually in the form of  token economies or other classroom-management techniques.  Even in my own classroom, we have a class "compliment" chart, that the students "earn" free time or other incentives for excellent behavior that is noticed by myself or other teachers.  There are many positives and negatives to this idea, and I would be interested to hear how other teachers use positive-reinforcement techniques with older students.  Although this does have value in building community in the classroom, it does not have any real value to each individual student.

It has become increasingly clear that the United States culture of adults also has, for the most part, little understanding of long-term goals.  Very few people are saving for houses or other large purchases anymore, choosing instead to make larger payments on large interest rates, in order to get what they want immediately.  

Even the government seems to have lost the idea of long-term thinking, as it struggles every few months with paying its bills or facing a shut-down.

With so few examples for students to draw from, what can we do to show them the value of goal-setting? The first step with students of this age (who are working out their understanding of the concrete vs. abstract) is to give them some reasons to make goals.  Intermediate students still have a desire to prove their worth and goodness, especially those students who feel undervalued in their home environments. By providing some ideas for achievable academic goals, then relating these goals to long-term and life-long goals, the teacher begins to create a classroom of distant gratification.  It is important for teachers to really be a guide in this journey--a student may be able to come up with a goal, but the difficulty becomes figuring out the path to completion.  Helping students to create a practical calendar with very specific check-in points (and sending a copy of this calendar to both the parents/guardians and the resource teachers) will help the students stay on track for success.

The next step is to get the parents involved.  Conferences are the obvious time to get parents on board, but the initial set-up is always the easy part--parents are always on board for improving their child's education.  The hard part becomes staying with it, especially for the teacher who is trying to keep up with 30 or so students. Creating a goal-file for each student to keep in their desks (or for those students who have organizational problems, in their classroom mailbox), and making a point to check-in with students regularly (no less than weekly) will go a long way in keeping students on track and motivated.

Finally, and perhaps, most importantly, is the celebration of reaching the goal.  This is a big deal!  If many students reached a goal all at once, celebrate that achievement together.  Invite administrators, special area teachers, and parents when possible (I have found that many times, they love just as much to have a reason to celebrate the students as I do!). If successes are individual, celebrate each student in a big way.  You want them to desire success and feel valued in the class, what better way then to let every child be an example of success, whenever they have completed the goal.  Remember, not all students learn or complete work at the same pace, so it is important to give as much attention to the last student as to the first-- it is possible that those students need the accolades even more. 

I would be very interested to hear how you help your students to be goal-achievers, what kinds of impact this has in your classroom, and how you keep everything organized and together.

There is an abundance of research articles that relate goal-setting to academic achievement.  Just a few include:

Self-Motivation for Academic Attainment: The Role of Self-Efficacy Beliefs and Personal Goal Setting (Zimmerman, Bandura & Martinez-Pons, 1992)

Building a practically useful theory of goal setting and task motivation: A 35-year odyssey.

Locke, Edwin A.;Latham, Gary P.  American Psychologist, Vol 57(9), Sep 2002, 705-717. 

Improving the compositions of students with learning disabilities using a strategy involving product and process goal setting.  (Graham, MacArthur, Scawartz & Page-Voth) 1992.

Until the next bell...

K.