Commutative Fraction Rods 2

In this activity, we have two multiplication rods that grew in two different ways.  The speed box tells you how many squares were added each second.  You can see how the rods grew by clicking on the "next second" button.  If you want to rewind the action, click on the "last second" button.  Every time you click the "start" button, you start up again with a different speed.

Use the buttons to examine the growth of the rods.

What patterns do you see?

The squares in the multiplication rods are grouped in different ways by color.  Which rod keeps the same group size as it grows?  Which rod keeps the same number of groups as it grows?  How do the group size and number of groups relate to the speed and number of seconds?

As you grow the rods, when do both rods look exactly the same?

Will rod number 1 always be the same length as rod number 2?  Why?

The commutative law of multiplication states that you can multiply two factors in any order and you will still get the same product.  For example, 2 times 3 gives you the same answer as 3 times 2 (both equal six).  Ten times five and five times ten are both fifty.  How do the multiplication rods in this activity illustrate the commutative law?

How is the total length of each rod related to the speed of growth and number of seconds of growth?