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Friday, May 12, 2006

Scribe: Introduction to Exponents and Logarithms

Well today was a two day, and lucky me, I got chosen for it fair and square.

Let's see, well the morning started off with Mr. K telling us things to know and expect, when doing something for the first time. Like riding a bike, or in this case dealing with math. Since you're doing it for the first time, you can't expect to learn it right a way, you're going to have to work at it. Education is about pushing yourself, to that level where you're not just satisfied, but to that level of excellence.

Then Mr. K put us into groups, where we had to solve probability questions.

1. Two soccer teams, A and B, have a kickoff to see which team wins the game. The teams take turns to attempt to score a goal. The first team to score wins. The probability of team A winning with one kick is 0.20. The probability of team B winning with one kick is 0.25.

a) Suppose team A kicks first. What is the probability that team B wins on its first kick?
First Kick
(0.8)(0.25)= 0.2

b) Suppose team A kicks first. What is the probability that Team A wins on it's third kick?
1st, 2nd, 3rd kick
=7.2 %

2. Five dimes and five nickels are arranged in 3 boxesas follows: Box 1 has 2 nickles and a dime, Box 2 has 2 nickles and a dime, Box 3 has 3 dimes and a nickel. A box is randomly selected, then a coin is randomly selected from that box.

What is the probability that the coin will be a nickel?
P(1N)= 1/3 * 2/3
= 2/9

P(2N)= 1/3* 2/3
= 2/9

P(3N)=1/3* 1/4

P(N) = P(1N) + P(2N) + P(3N)
= 2/9 + 2/9 + 1/12
=8/36 + 8/36 + 3/36

3. A hand of 13 cards is dealt from a shuffled deck of 52 cards. What is the probability that there are:

a) exactly 5 spades?

b) at Most 5 spades?

Then comes our introduction to the new unit in the afternoon; Exponents and Logarithms. These are some basic stuff we should already know about exponents:

Then Mr. K gave us four numbers on the board. We had to write each of them 4 different ways using only exponents.

***A number can be written in many different ways.

These were the numbers





***Any base must be in reduced form!!

Of course there is a pattern into figuring the different ways of writing a number. Using the basic stuff to find the first couple of ways, then you can use that to help you find the pattern.

Then Mr. K gave us another type of question on the board that had to deal with a variable in the exponent.

Here's another question Mr. K gave us, that I should warn you about.
It is common that people will do this in the next question:

3(5x+1)= 15
15x+1= 15


Because of BEDMAS, exponents should go first before multiplying,

So it is solved like this,
3(5x+1)= 15
5x+1= 5
x + 1 = 1
x= 0

Double check:
3(5x+1)= 15
3(5(0)+1)= 15
3(51)= 15
3(5)= 15

Mr. K gave us many practice questions, so here they are along with the answers:

Q.27x= 92x-1
A. x=2

Q.42x-1= 64
A. x=2

Q. 323x-2= 64
A. x= 16/15

Q. 48x= 1/16
A. x= -1/4

Q. 63x-6=1
A. x=2

Q. 54-x= 1/5
A. x= 5

Q. 32x-1 + 1 = 2
A. 1/2

I just want to say, very sorry guys for the late scribe, but i FINALLY FINISHED.

Okay well thats about it for the two classes today, for the people who weren't in class there wasn't any dictionary notes for today. Oh and there's a pretest tomorrow. Also Homework was page 89 1-16 and 24.

The lucky scribe for tomorrow is Zaenab.=)

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At 5/12/2006 6:52 PM, Blogger Lani said...

Hi Jacky,

Congratulations on a job well done!! I really like your emphasis on "don't do that" to help keep everyone on track and away from a common mistake.

You and your classmates are truly traveling on a path of excellence!! I wonder, can you all meet the challenge of a daily "hall of fame" scribe through to the end of May??


At 5/14/2006 5:26 PM, Anonymous GBG said...

What an extraordinary job you and your classmates are doing. Your explanation is fascinating and just reading your material is an education for me. I plan to use your blog as an example excellence in some workshops I am doing for teachers in upstate New York.


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