One of these things is not like the others...or is it?

After working with the kits I think I figured out some commonalities. First, a lot of the activities were based upon misconceptions. For example, when guessing the order of objects based on size, many of them looked as if they were obviously larger than another object yet when they were compared using a common measuring device, it turned out that they were either the same size or opposite of what was previously believed. So, I would say one thing that all the activities have in common is that they all deal with the notion that things (size, volume, etc) aren't always what they seem.

Another thing that I noticed was that the activities dealt with comparisons that were based on commonalities. Once one amount or length was known, that could be used to determine the size or amount of another item. I think it's kind of like fractions...you find the common denominator in order to compare the two items. In the case of one of the activities, beans were used to determine the amount that an object could hold. Instead of just blindly guessing how much another object could hold, the amount of beans in one object could help determine the amount of beans the other object could hold. The beans were the common denominator used to compare sizes of different objects.

Excuse my language, but WTF!!!

I have never walked out of a class more frustrated than I was on Wednesday...and I've been in a lot of classes! As I sat there, I couldn't help but think that the same people who were complaining about the class not moving along fast enough were the ones stalling the hell out of the session. If I felt like there was genuine confusion, I would understand and even enjoy the process of discussion but when I look back, all I can say is that the whole time was spent comparing apples to oranges. Correct me if I'm wrong, but the reason you can't put multiplication in terms of change unknown and such is because there is no change. In multiplication and division, you're dealing with a known amount of something...there is no change when you have two numbers that are given. The point is more obvious when dealing with division. You're taking a group of something and putting it into smaller groups...there is no change, there is a dealing of some sort but definitely no change. You can't take something and divide it and consider it changed...it is what it is, no change, just a different size of it. If I lose 30 pounds, I'm still the same person, there's just a different amount of me...that's how I look at this whole division thing! There is no change, there is just a difference of size...12 is 3 groups of 4...still 12 though!