Sunday, November 23, 2008

I am right a fraction of the time!

Be you a student, a teacher or an interested guardian, please ask yourself if you could come up with any more profound statements about the fractions 2/3 and 3/4. Also, please challenge yourself to create accurate models of each as well. To the mathematically uninterested, this may not seem like a grand accomplishment, but to a well-trained math geek, this is poetry!

Yep, all of this was done by a ten-year-old! Could you have done this at ten? Yes, I am quite proud of my students.

Well, chime in now. What do you think?

Peace and have a great holiday!


Sunday, November 9, 2008

I am about to make Mr. Pinchot really mad!

No, the cat will not anger Mr. Pinchot, unless it makes him think of the Mt. Nittany (spelling?) Lions that his beloved Penn State uses as a mascot! You see Penn State lost to Iowa and ruined their perfect record and their chances of an NCAA football national championship. However, none of that is going to make Mr. Pinchot as angry as he will be when he finds out that I actually published a math piece using the sophisticated math terms "chop-chop" and "double-double"! He absolutely hates these terms even though they are based on sound math principles.

The term "chop-chop", as all of my students know, refers to creating an equivalent fraction by reducing the numerator and denominator at the same rate. Usually, the "chop" implies dividing by 2/2, but we could "chop" by any fraction with a value of 1 whole, n/n, 10/10, 4/4...We would create a fraction that has an equivalent value.

For example: 12/16 divided by 2/2 = 6/8, and 6/8 divided by 2/2 = 3/4 ! Oh, I say chop-chopping is a fine way to create new and equivalent fractions!

You could probably guess that he also hates "double-double", which is just multiplying by 2/2 (the whole number 1). This, again, creates a new and equivalent fraction! For example part deux; 3/4 X 2/2 = 6/8, and 6/8 X 2/2 = 12/16..., but we don't have to settle for using 2/2 all the time. We could go crazy and use 13/13 or 3.5/3.5 to multiply by. We could take 1/2 X 3.5/3.5 and get 3.5/7, and that IS equivalent to 1/2. Boooyahhh!

The key is to remember that what we are really doing is multiplying or dividing by 1!

Please be sure to ask Mr. P. about Penn State, and please tell him that we have been chop-chopping a bunch!

Sunday, November 2, 2008

Some of the digits? No, Sum of the digits!

Hello again. Once more, a student has shown how working "smarter" makes for a better and more efficient math student!
In this example of our last homework, this student relied heavily on the "rules for divisibility" in order to make answering the divisibility questions a snap. In general, I am opposed to anything that smacks of being a math "trick" as an aid to completing math problems. However, the rules of divisibility are all based on sound math principles, and these rules do lead to more efficient and more accurate work. We rely heavily on these rules each day as we try to find common factors for the numerator and denominator of fractions. Right now, 5th grade students (and really 4th grade students) should know the "easy to use" divisibility rules for 1, 2, 3, 4, 5, 6, 9, and 10. The rule for 8 is also useful, but the rule for 7 is really too complex to use at this stage.
If you don't know the rules, please contact any worthy math teacher, student or the Internet for help:-}
I also have to comment that the Prime-Factor tree diagram shown is also a huge step towards understanding higher math. I also love PFTs , because they are lateral thinking exercises, as there are many paths to the correct answer. Again, ask a wise student to explain. The kids love doing these "puzzles" too!
Thanks for reading,