Develop some thinking skills with a different approach to multiplication. Consider the following:
Find the product of 21 and 32....==> P = (21) (32) ......Let P = (2x+1) (3x+2) ......where x=10
Expanding this results in P= 6x^2 + 7x + 2 .........this essentially means that we have 6 groups of (10)^2, 7 groups of (10)^1 and 2 groups of (10)^0; also know as six hundred and seventy two.....==> 672.
For those students who say "What's the point" to this approach and "It's faster to do this on a calculator", then by all means use your calculator. The "point" of this exercise is NOT to get the product of 672 (in this case); its purpose is to look at this so-called laborious procedure from a different perspective and CONNECT it to something students have already studied. This opens up many "new" exploration opportunities for students (and teachers) as well. For example, what does this product relate to on the function itself? How about other values of "x"; where would they be on the function and what is their relationship relative to one another? What would happen if we let "x" = 100? How would we represent multiplication of a 2-digit number by a 3-digit number? This is a very "rich" activity and a powerful opportunity for us to explore.
I have several more examples worked out as hand-written notes; you can view those by clicking on the following link.
James Tanton has made many methods of multiplication available for us to benefit from. Click on the link below to view those.
James Tanton's "Weird Multiplication"
More links to interesting methods of multiplication are found below.
My Belief Statement
My Belief Statement: _It is better to be defeated on principle than to win on lies._ Arthur Calwell
Many students have a serious phobia when it comes to Math class, let alone writing an exam in that subject. I believe this phobia can be dispelled by "digging" into the "WHY " and the "HOW". In fact, many students WANT this. I attempt, wherever possible, to connect a geometric representation to its algebraic counterpart; an analysis of how the two versions interact is important. Contrary to what SOME individuals may think, I'm not at all afraid of technology. I AM, however, cautious to not "jump into the deep end"; we need to grow with this and "dovetail" the old with the new so that they COMPLIMENT each other.
I have several links in the sidebar at the right, as well as some of my own discriptions on various topics. These will grow in number and evolve over time, as will my hand-written notes; these can be viewed by following appropriate links which you will find throughout this blog. These notes will also be posted on my facebook site if that happens to be your preferred mode of viewing; I've included a link to that in the sidebar as well.