Reviewing my group's work

It was great to see the solutions (and attempts) provided for the Jacobian Locks problem by my team member's - Jill and Caleb. Jill's was very neat and gave great visuals of stick people in the village along with great charts illustrating the various scenarios they went through in solving the problem. She made the mathematics behind her solution very easy to follow and came up with, what appears to be, the correct solution. Well done Jill!
Caleb's solution was great to read as well from the pictures on his whiteboard. He used set theory which also provided an easy way to follow his thinking. His many notes along the way made it enjoyable to read. The "oh poo!" comment when he realized it was not working, reminded me of something I have exclaimed at that point myself.
Both of these solutions were great to read and it made me wish that my own weekend had not been turned upsidedown and that I had personally had more time to work on this problem.

Jacobian Locks Problem Solving

The problem from page 176 in Thinking Mathematically goes like this:
A certain village in Jacobean times had all the valuables locked in a chest in the church. The chest had a number of locks on it, each with its own individual and distinct key. The aim of the village was to ensure that any three people in the village would amongst them have enough keys to open the chest, but no two people would be able to . How many locks are required, and how many keys?

I initially figured that there had to be some kind of trick to this. I knew that if every villager had a key to each lock, then there would be no way to prevent two villagers from opening any number of locks. So I began to think of tricks. First, I thought that there is only one lock and each villager has one third of a key that together form a full key. But this would mean not every lock has its own individual key. Then, I thought maybe the chest is up in the air and it requires a human ladder to reach it, but two people could not. This would require only one lock and each villager to have one key. This might be the solution, but I doubt it. Then I thought maybe the chest is very big (it does hold all the valuables for the village) and has three locks spread far around it. Each villager has one key that opens a lock which closes again right away. Three villagers could do this but not two. The same would work for three locks with three keys that break upon their use. Then every villager would need only one key, but the keys would not be distinct. Then I got to thinking that there must be something in the order or way the locks are open.

Two Memorable Moments from Practicum (Quick Write)

1) Teaching Completing the Square - It was my second lesson. The first went well, but was a learning experience. But, with Completing the Square, I got the AHA! moment from the class. I invoved humour and previous review and it felt good to look out at every face, most smiling, some nodding, and many getting the beginnings of a difficult topic.

2) Halloween Costume - Dress up day was the last day of the two week stretch. I had developed a rapport with many of the students and was starting to feel I was well liked. One student that had me wondering on day one, "am I going to have problems with this one" sat in the third seat from the enterance. I walked in in my calculator costume and he said, "you made my day by dressing up as a calculator". It brought an instant smile to my face. As I walked away, I heard him say to a friend, " I want to dress up as a calculator".

Quick Writes

Divide: A word with many meanings - some destructive and othersconstructive. A noun or a verb. A divide could be an area across a valley where one might want to build a bridge. A divide could be a stretch between cultures - a social divide. Of course, to divide is the cutting of another object or number into smaller pieces. Divide is the root word of division, which is the noun that is used to claim where a divide ha been made. Divide begins with the letter D and contains two i's. No other basic mathematics skill begins with the letter D

Zero: Zero is a unique word - a word to describe nothing - truly nothing. Zero is a concept that seems obvious today, but in the early days of mathematical study, zero did not exist. it was completely left off the number line of integers. It is an amazing concept when you think of it - something that's sole purpose is to describe nothing. Zero makes adding, subtracting and multiplying very easy. But something very interesting happens with division. Zero can divide as many times as one wishes. I can give you zero things many, many times over. However, when I try to divide by zero, it becomes mathematically impossible. Why, you ask? Well to dived by zero means that I am not dividing at all, which makes it impossible.

Division by Zero

Some feel a division at the root is all bad
To seprate into groups
Breaking apart makes things lesser
And limits their worth
When seen through clear lenses
It is in all that we do
Thus division by zero should be liked most of all
For it, and it only, does not yield to divergence