Multiplication Tables For Adults

In about the third grade, I learned my multiplication tables.  Just the other day, I learned them again, only this time the multiplication tables were a little different.  This time they were in base-five.  It was fun watching the other students in my math class taking their time to carefully calculate the multiplication table in base-five.  They looked like many of the students in my third grade math class, learning multiplication for the very first time.  One thing is for sure, the rules and properties of multiplication stay the same whether in base-five or base-ten.  The difference is definately in grouping the numbers.  As you might remember from one of the earlier posts, base-five is groups of five, while base-ten is groups of ten.

An easy way to look at multiplication of whole numbers is by remembering them as repeated addition.  An example of repeated addition is 4x5, that is 5+5+5+5.  So, 4x5=5+5+5+5=20.  Shown in the picture below from http://elko.k12.nv.us/webapps/vmd/mathdictionary/htmldict/english/vmd/full/m/multiplication.htm.

  In class we also learned about multiplication models.  The three models that we went over are the rectangular array, tree diagram, and partial products.  I really like the tree diagram, even though it may be hard to work with when you are using large numbers.  It really is pretty fun.  Here's a website to see how tree diagrams work:  http://www.regentsprep.org/Regents/math/ALGEBRA/APR4/PracTre.htm

I also want to include some information about the rectangular array and partial products.  The picture below is from another blog that I found interesting:  understandingmultiplication.blogspot.com/2007/03/third.html.

A video that may be helpful to understand partial products is:


Until next time...

The Cross Between Math and Ancient History

Recently, I found myself thinking about one of my math lessons in Anthropology class.  We had been talking about how experts in many areas of science and math come together to help anthropologists put pieces of the ancient puzzle together.

The numeration systems that we had gone over in math class came to my mind.  It's interesting to think about the symbols that we use for numbers.  They vary from the Egyptians, to Babylonians, to the Romans, to our own set of numerals, the Hindu-Arabic numeration system.

In class, we did an activity to find out what symbol represented what number in various ancient numeration systems.  This was helpful to understand that there are different ways to group objects, or numbers, other than in groups of ten.  Certain cultures group numbers by different bases.  What I mean by base, is how many numbers or objects that they place in a group.  Our numeration system is a base-ten system.  That means that we group our numbers in groups of ten.  So, the symbol that we use to represent the number eleven is 11, one group of ten, plus one more unit.  To understand base-ten, you can use base-five pieces.  This is grouping of five, instead of grouping of ten.  An example of this would be:  the symbol that represents the number six is 6 in base-ten.  In base-five the symbol is 11;  that is one group of five and one unit.  Learning this helps to understand carrying numbers in addition by making exchanges.  Some examples of base-five and base-ten can be found at this website http://www.basic-mathematics.com/base-five.html