today in math

HW
Kings switches due 11/10
quiz wednesday
HW 9?

Today we had a wonderful hour and a half of math. Caitlin laughed, Lilli danced, keith sang a song about the heartland. Good times were had by all. Except for Camilla who huddled in a corner and cried like the little dark emo she is. But on a more serious note, let's talk mathematics. And imagine I'm tellin you this with an irish brooch.

Normal Table Page 398

This handy little table lists numbers of standard deviations, starting at zero and increasing by 0.1, and their corresponding area within the standard deviation of the mean. This comes in handy when finding percentages of natural functions that are between one and two deviations.

HW 8 Page 400

Using the natural table, we rationalized ways to find answers to questions similar to those we have done earlier in this unit. The main idea was finding percentages of graphs that lay between 1 and 2 deviations.

Back to the Circus page 402.

A circus stunt girl rides her bike towards a wall and would like to know how close she can start stopping while crashing only 5% of the time.

It was fun. Long live math

(Wednesday) October 29

Today:
Go over homework 6 & 7
More about normal curves

Next Class:
Finish discussing Classwork

Homework:
Quiz next Wednesday
Revisions due Thursday

Homework 6 (393) Means and More in Middletown
1) a) Only 2.5% of the houses cost over $950
b) 68% cost between $500-800
c) 13.5% cost between $350-500
2) 2.5%
3) 84%

Homework 7 (396) Gifts Aren't Always Free
1) The main idea that we are trying to explain to Craig is if the standard deviation was larger the deviation would be broader where as if it was smaller the deviation would be more concise.
2) $29-$24.50 is 68%

Classwork (397) Normal Areas
1) .38
2) .86

Class was the typical short Wednesday. We didn't actually accomplish much, but there was a pretty rad conversation about carrots going on at the next table. For the next class we'll finish where we left off in the Classwork on page 397.

Next Scribe:
Cody Ullrich (for Thursday October 30th)

Tuesday October 28
In Class:
-go over Homework 6
-Graphing Distribution (page 394) activity with TI-nspire

-Normal Areas (page 397)
-The Normal Curve (page 389)

Homework:
-revisions on test due Friday 31
-homework 7
-homework 8
(-there will be a quiz next week on this unit and end behavior. specifics will come later)


Review in Class of Normal Curves:
-68% of data falls inside the first diviation
-95% of data falls inside the second diviation
-2.5% are the sizes of the outer-most sections
(look at previous post by Ann to see pictures of a standard curve)

-if mean changes: the curve will shift to the left or right
-if standard diviation increases: the curve will spread and flatten out
-if standard diviation decreases: the curve will get skinnier and taller


New Information:


Graphing Distributions: (see page 394)

-the total area under the standard curve equals 1 unit
-finding a specific area under the curve gives a probability
-the area under the curve is called integration (or definitive integral)
-the following equation uses the mean and standard diviation to solve for a probablility of a result at any given interval (for example, on a standard curve if you want to find the probability of something happening between points a and b that do not land directly on a standard diviation 'line' you can use this formula to find the probability)

-for the simplest normal curve (a mean of 0 and standard diviation of 1) a simplified version of this formula can be used to find probabilities

(in class we experimented with these equations on the TI-nspire calculators, seeing how the curve changes as the standard deviation and mean get larger and smaller)

Normal Areas: (see page 397)

-this classwork deals with finding percentages of areas between two points, and also finding two points where a certain area would fall. (these problems were done through estimation in class)

The Normal Table: (see page 398)

- We read through this reference section in class and briefly looked at the table of "z number of standard deviations and corresponding area within that section. ("z" is just the value above or below the mean where a certain area is found. z values are equal to the area between 2 points)

Next Scribe: Nicole Anderson! (for Friday October 31)

Scribe Post- October 27- Period 1- Elizabeth C

The first thing we did in class was go over Homework 5. The big ideas for that were:

• As the number of people polled goes up, the percent that was in favor also went up


• The largest bars in the probability graph are the ones closest to the true proportion

Then we learned about the Central Limit Theorem:

Normal Distribution-

• Based on mean and Standard Deviation
• Represents probability of getting a result in an interval
• 68% of results fall within 1 deviation
• 95% will fall within 2 deviations

Inflection Point: The point where the curve switches from Concave up to Concave down.

Continuous Probability Distribution: When every point on the graph has a value(Like a bell curve)

Discrete Probability Distribution: When nothing happens between points (like a bar graph)

After this discussion, we did Deviations of Swinging while Mr. Marchetti checked the rest of the homework (Homework 12, 1, 2, 3 and the rational functions worksheet 380)

After that we whipped out the TI-nspires and did Graphing Distributions

Homework:

1. Revisions Due Thursday
2. Homework 6 and 7

Next Scribe: Kimmy

Friday October 24th

Announcements:

-Handed back World of Functions Test

-Quiz next week on beginning of Pollster's Dillemma

-There will be a section on next quiz that will allow you to retake the End Function's section on the last test. Mr. Marchetti will take your higher score out of the two End Function's sections and will replace your current grade on that section with the better score.

Notes:

We began taking notes on the normal distribution curve, like the one above. This picutre demonstrates the percent each section takes up of the data. The light gray represents 68%, the darker gray combined with the lighter gray represents 95% and all of the shaded portions combined together represent 98% of the data. The +1, -1 etc, demonstrates how many standard deviations that data point is away from the average, which is the middle line.

This picture demonstrates how many standard deviations each point is away from the mean.

Homework

1. Homework 6

2. Test Revision- Due Friday October 31st

Next Scribe Post: Gretchen Stulock

Blog for period 1 October 23th, 2008

Scribe: Taryn M



Agenda:

Go over HW 4

Return Rational Function Quizzes

The Theory Of Polls

Homework Check



We worked on The Theory of Polls and went over it in class. Mr.M only got half of the class done with the homeowrk check and he will do the rest on Monday.



* If you didn't do a good job on the quiz go talk to Mr.M about fixing it! There is a chnace you can retake parts of it.



Homework: Homework 5 and read pages 387-391



next scribe: Lizzy C

Scribe post for Wednesday October 22

October 22:Scribe- Miranda K

Agenda-

• go over hw 2 and 3
• theory of the 3-person poll

HW 3 big ideas:

• for each voter, the probability that the voter is in favor of your candidate is equal to the proportion in favor of your candidate in the overall population.
• if the overall population is big enough compared to the sample size we can approximate polling by sampling with replacement.
• if the population is big enough to justify the sampling with replacement, we need to limit our polling samples to 5%.

theory of 3 person poll is on p. 378. uses nPr and nCr

homework:

• homework 4
• homework check on thurs/mon. he is checking hw 1-3 in pollsters and stuff on end behavior, and inequalities

*scribe for thursday- taryn M.

Tuesday, October 7, 2008

Agenda

• Begin Pollster's Dilemma unit
• Unit problem
• Review rational functions
• Begin HW

Homework

• POW-A spin on Transitivity
• Quiz on rational functions on friday
• HW 1 & 2

***************************************************
In the Pollster's unit we will examine the validity of polls

• How polls are conducted
• Sampling-what it is, what it means
• Statistics of poll

In groups, read through unit problem and answer questions
***************************************************
Quiz topics

• Algebra of Rational Functions-add, subtract, multiply, divide
• Graphs of rational functions-Vertical Asymptotes, Horizontal Asymptotes
• End behavior
• Inequalities graphically or algebraically

Next scribe-Matt Sattler

Friday 10/3/08

Today in class, we went over the homwork from page 380, and then learned how to solve rational inequalities by algebra.

Solving Inequlities:

• Factor the inequality
• Find where the numerators x values equal zero, and the denominator's vertical asymptotes
• Create a number line using the values found above, going slightly beyond each of them
• Then test different numbers to see if they fit the inequality, and mark possible numbers
• Deterimine the solution based on these tests.

POW Rubric
E= M plus: one successful proof and adresses bullet 4 from part 2
M= Answers to numbers 1-3 with explanation, investigation with results for 2 0f 3 bullets in part 2, and attempts at proofs

The material on the test will be:
Graphing rational functions (asymptotes)
Algebra of rational functions
Inequalities (solving graphically and algebraically)

Homework:
POW due Wednesday
Test on 10/10/08
Review Packets
Next scribe is Joe

Monday 10/06/08

Notes:
We had a substitue in class today
We worked and finished The Pollster's Dilemma wich was handed out on a loose leaf sheet of paper by the sub
We worked for thirty minutes on the review sheet for the quiz
We also did HW1 from the Pollster's Dilemma unit in class
Homework:
Homework was HW2 from Pollster's Dilemma, POW 8, and to study for the quiz on Thursday
Announcements:

• Pow 8 due Wednesday 10/08/08
• Quiz over algebra of rational functions, graphing of rational functions, and end behavior of a function this Thursday 10/09/08

Quiz topic end behavior notes:

The end behavior describes how a graph appears as the independent variable approaches infinity to the right (x increases) or to the left (x decreases). It depends whether the degree of the polynomial is odd or even and the sign of the coefficient of the highest order term, an. The end behavior for all possible cases is:

• if the sign of the coefficient is positive and the degree is even, then y approaches positive infinity as x decreases and as x increases
• is the sign of the coefficient is positive but the degree is odd, then y apporaches negative infinity as x decreases and approaches positive infinity as x increases
• if the sign of the coefficient is negative and the degree is even, then y approaches negative infinity as x decreases and as x increases
• if the sign of the coefficient is negative and the degree is odd, then y approaches positive infinity as x decreases and approaches negative infinity as x increases
  
  

Next Scribe: Evan Anderson

Wednesday, October 1

Today in class we went over inequalities, one of which was x^2+3x-10/x^2-6x+9 < 0. When graphed, the equation goes below zero on the x-axis at (-5,0) and above again at (2,0) and has a vertical asymptote at (3,0). Therefore, the values for x when the function is less than zero can be expressed as -5 < x < 2.

HW: POW due Wednesday, October 8, and pg. 388 #1-14

Thursday, 0ctober 9

Agenda:

• Reveiwed Homework from wed.


• Quiz Review


• POW Rubric
  

Homework Review:

Today in class we reviewed homework from Handout 5.4, proplems 20, 23, and 24. These were all inequality problems.

20.


solution: x<-3

-2

Quiz Review:

We received and worked on review handout for the quiz next Thursday. The first has problems on the first page and an answer key on the second. The second is CH. 5 review and problems 1-14 are the most useful for review of horizontal and vertical, asymptotes, graphing functions, and finding end behavior (21-24 may also be useful).

• Quiz Thursday Oct. 9


• Graphing rational functions (asymptotes)


• Algebra of rational functions


• Inequalities (solving graphically is acceptable, but algebraically is best)

POW 8 Rubric

We also reviewed the rubric for POW 8 (included below).

• E= M plus: one successful proof and adresses bullet 4 from part 2


• M= Answers to numbers 1-3 with explanation, investigation with results for 2 0f 3 bullets in part 2, and attempts at proofs (may not be complete)

Homework

• POW 8- due thurs 10/2- wed 10/8


• Quiz review- Quiz on thurs 10/9

Tuesday, September 30

The agenda:
Review Friday's work
Review Homework 12
Learn how to solve equations/inequalities with rational functions

Homework:
POW due Fri-Wed
Quiz on Rational Functions 10/10
Revisit HW 12

Notes: Starting Pollsters Dilemma on Friday, just finishing Rational Function unit

End Behavior
x to the power of an odd number will give an equation like this

X^any even number:

Example of an exponential function (y=4^x):

Rational Function Review:

Bottom power is bigger-HA=0

Top power is bigger-no HA

Power is same-ratio of leading coefficients is HA

Solving Equations and Inequalities

Algebraically

Technology

Graphing or Table

Intersection on calculator: split equation into two with y equalling both halves, calculate intersection or look at data table for the same Y value

Algebra: cross multiply if fraction=fraction then simplify. If not, multiply both by LCD, input answers back into the initial equation and eliminate the extraneous "solution".

Next scribe is Ben K.

Answers to Questions

Hey all,

Thanks for the feedback and the great questions in class today. I thought that I would address many of them here so that everyone could see the answers. If I don't address your question here please let me know.

First of all for the review for the quiz, I wanted to find out where people felt their weaknesses were. It gives me information so that I can tailor instruction. So the review will focus on two areas, according to the feedback. These two areas pretty much encompass everything. They are:

• Graphing Rational Functions (including asymptotes and behavior)
• Algebra of Rational Functions

As for questions about grading. Here is a list of some of the frequently asked questions, answers:

Raising your grade

I allow the revision process to help students raise their grade. There will be no extra credit. You can revise the first POW and HW 8 even if you received an F on them. These will be the only assignments for which you can revise an F. If you revised an assignment and you did not receive a W (revised work) come see me and we can discuss a second revision. Quizzes and tests can be revised if you receive an R, but not an F.


Why does revised work only get a C?

Revised work only gets a C because I want to reward people who are able to meet my expectations the first time around. I also do not want people to rely on the revsion process alone (I was having problems with students only revising and getting to high a grade). Imagine you were a student who consistently got Ms on assignments anda student who always had to revise received the same grade, would that be fair?

These were the areas where people most had questions. I want to make one more point. I need more feedback from you. I need feedback in class, by asking questions, by answering them, and through your presentations. I had many index cards with people telling me that they are have serious difficulties. These students have not come for extra help and many do not ask questions in class. If I don't hear from you, I don't know if you need more practice, more time on a topic, more instruction, or if we can go on. Help me, help you to do better by giving me feedback. Emailing and texting would work to (just don't text me unless it is a serious school related matter)! Thanks.

September 26, 2008

There was a substitute teacher today.

Agenda

1. POW 8 : A Spin on Transitivity, page: 277
2. Read on Asymptotes, page: 288
3. Classwork: The End of a Function

Homework

1. Homework 12: Creating the Ending You Want, page:290, #'s 1 and 2

The POW is refering to transitive relationships. For example, if Joe is shorter than Kelsey and Kelsey is shorter than Matt, then Joe must be shorter than Matt. Another example would be, if $20 is greater than $10 and $10 is greater than $5, then $20 must be greater than $5. An example of a non-transitive relationship would be like a game of rock, paper, scissors. Where rock may be scissors, and scissors beats paper but then rock certainly cannot beat paper.

Post by: Elca Annis