Debbie Poss's Blog

Accelerated Math II - Applications Seriously - September 29, 2011

Today we finally got around to looking at applications and solving problems graphically.  Tonight's assignment is to complete the Applications worksheet that we started in class.  The quiz that was on the calendar for tomorrow has been postponed until probably Monday.  We shall see...

Accelerated Math III - Last day of Statistics - September 29, 2011

Today students had the opportunity to correct their quizzes from last week.  The homework is the work the right triangle test from Acc. Math II to refresh their memory about geometry and basic trig.  HOWEVER, problem #2 does not have a correct answer.  Students must write the correct answer in the space provided.

Accelerated Math II - Applications - September 28, 2011

Today we went over the last 2 problems on the worksheet, since they were applications.  The assignment for tonight is the following worksheet:  Download Analyzing Graphs of Exponential Functions Worksheet .  Answers to this worksheet are: 

1.  The steepest is y = 3^x.  Next is e^x and the closest to the x axis is y = 2^x, because 3^x increases fastest, 2^x increases slowest and 2<e<3.

2.  The highest is y = .85^x, next is y = .8^x and the lowest is y = .7^x, since .7 < .8 < .85.

More later...

Accelerated Math III - More Answers - September 27, 2011

Today we looked at the confidence intervals given proportions.  This wraps up the information about confidence intervals.  Many answers to your questions about definitions and formulas can be found in the 4 page packet entitled, "Some Helpful Definitions for Accelerated Math III - Statistics".  You received this packet Thursday, September 15.  However, here are the rest of the answers to the questions that you had:

1.  When do you use the Central Limit Theorem?  We use the CLT when we want to make a conclusion about a mean or a proportion, but don't have the entire population.  (In other words, we use the CLT when we want to use a sample to inform us about a population.) However, we can only evoke the CLT in a data set when we have a good random sample of at least 30 and the population is larger than 10 times the sample size (otherwise we oversample the population).  We can conclude from the CLT that A) the mean of the population is approximately the mean of the sample and B) the standard error (or standard deviation of those sample means) is the sample standard deviation divided by the square root of n.  This enables us to find a confidence interval for the actual mean of the data.  (Remember we only have a sample and so our mean isn't certian.) 

2.  When do you use Confidence Intervals?  We use confidence intervals to represent the inaccuracy of our predicted mean (the one we found using the CLT).  Suppose we sample 144 random pet cats and find that the average age of these cats is 6 years with a standard deviation of 3 years.  Although our best estimate (called the point estimate) of the average age of pet cats is 6 based on our survey, we aren't 100% sure that this is the true average age of pet cats.  Therefore, we evoke the CLT to get a standard error of 3/12 or 1/4 year.  At this point we must decide how accurate we want our statement to be.  A 95% confidence level is often used so we'll start there.  For a 95% confidence level, the z-score is 1.96. (This number is the invnorm of .975, because 97.5% of the area of a normal curve lies below this particular z-score.  This means that 95% of the area under the normal curve lies within 1.96 standard deviations of the mean.) Therefore the margin of error is 1.96*1/4 or about .49.  We could report that the mean age of pet cats is 6 with a margin of error of .49 years - or we could report that the 95% confidence interval for the mean age of pet cats is {5.51, 6.49}. 

The answers to last nights problems are:  1A) 0.339...  B)  {10.7, 11.9}   C)  {10.6, 12.0}  D)  25000 to 28300 pecans    2A) 2.136..  B) 110 to 116   C) 107 to 119    D) 458 children    3A)  Mean:  90.04  Sample standard deviation:  0.056  Standard error:  0.028   B) 89.99 to 90.09   C) i) Mean: 90.02  Sample standard deviation: .04746...  Standard error: 0.01582...  ii)  90.01 to 90.07   iii) the width of the interval decreased due to the increased number of measurements.

 

Once again, the assignment is to get caught up.  Tomorrow is the last day we spend on statistics, so have all work complete and any leftover questions ready to ask.  

Accelerated Math III - "Catch-Up Day" - September 26, 2011

Today we played "Catch-Up".  I asked students what they did and didn't know and we started by explaining the concept of confidence intervals using data (as opposed to proportions).  Students asked for more problems for practice, and here are some:  Download Problems involving Standard Error   

Accelerated Math II - "Catch-Up" Day - September 26, 2011

Today we played "catch-up".  I asked students what they knew and didn't know and answered questions in order to help them clarify any misunderstandings.  Tonight's assignment is to complete all homework assigned last week.  This means:

Friday, Sept. 16:  Math II book: Pg. 122: 1-3, 5-9 odd without calculator, 10-12 and Pg. 126: 1-6, 7-11 odd without calculator, 13-19 (Most of these answers are in the book)

Monday, Sept. 19: Math III book:  Pg. 115-116, odd and Pg. 112: 1-23 odd  (Answers in the book)

Tuesday, Sept. 20:Exponential Functions WS and Practice and Apply worksheet #1, omit 29 - 34   (Students received odd answers to both of these "Practice and Apply" worksheets on a "hot-dog style" half sheet of paper on Wednesday.)

Wednesday, Sept. 21: Math II book, Pg. 130, odd and Math III book: Pg. 132: 1 - 15 all  (Most answers in book)

Thursday, Sept. 22:  Practice and Apply worksheet #2 odd problems

Friday, Sept. 23:  Discovering "e" worksheet and from Math III book: Pg. 142: 1-28 (Odd answers in book) 

(All of these assignments were on the tentative schedule that was given to students last Friday, Sept. 16, but just in case that has been misplaced, here is another copy.  Download AM2 Exponential Functions Schedule 2011  Note that there is another quiz this Friday on applications of exponential functions.)

Accelerated Math 3 - Notes for the Week - September 16, 2011

Today in class, we completed the Reese's task in 2nd and almost did in 3rd.  I'm confident that 3rd can finish it now.  To summarize the two tasks we've done so far, the Central Limit Theorem states:

When we take many samples of size n from a large population and look at data, as long as the population is at least 10 times the size of our sample, A)  the distribution of the sample means approximates a normal curve, B)  the mean of the sample means is pretty much the mean of the population and C) the standard error of the sample means is the standard deviation of the original population divided by the square root of n.

If we take many samples of size n from a large population and look at proportions, as long as np>10 and n(1-p)>10, A)  the distribution of the sample proportions approximates a normal curve, B) the mean of the sample proportions (p hats) is pretty much the proportion of the population and C) the standard error is sqrt(p(1-p)/n).

The confidence interval task should help you see the "how sure" part of statistics works...  The tentative assignment sheet for this unit is attached:  Download Tentative Schedule and answers to the confidence interval task are attached in 3 parts Download Confidence Task answers A  Download Confidence Task answers B   Download Answers to Confidence Interval 

On Tuesday, you can make up either one (but not both) of the previous quizzes.  The substitute will ask you Monday which one you plan to take.  Here is a review for the first one:  Download Acc Math 3 Summer Review Problems compact 

The solutions to the problems on the back of your definition worksheet are attached here:  Download Answers to definition problems.  If you need anything else, either email me or ask Coach Rinehimer. 

Accelerated Math 2 - Benchmark Test - September 14, 2011

Today students took the first Benchmark test for Math 2.  Due to the fact that many students didn't have time to complete this test, we will start "review sessions" both before and after school starting in October to review material from the first half of math 2 (which was taken in middle school).  These review sessions will not be required, but may be highly recommended after Benchmark test results come out.

Tonight students have a worksheet on properties of exponents that doesn't have a title, but does have "Name" in the upper left hand corner.  Some answers are at the end of this worksheet, but not all.  Tomorrow we will answer questions about this worksheet and then look at some "It sure would be nice" problems, possibly some rational exponents and some graphs of exponential functions. 

Accelerated Math 3 - Reese's Data - September 14, 2011

Here's another attempt to get this data out.  Here's the data in Google https://docs.google.com/spreadsheet/ccc?key=0AqfwTi32dP2kdEltb2FhNk9ONWNYZ2FmcnJiOXE1bUE&hl=en_US

Here's the data on Excel Download Reese's Data

And here's a PDF of the data Download Reese's Data 

If you still can't get it, see me tomorrow morning before school and I'll give you a hard copy...

 Today we managed to understand part IV and hopefully tomorrow, we'll make sense of the rest of the Reese's task.  Do as much of this task as you can tonight for homework.  (You can do a great deal more!)

Accelerated Math 2 - Benchmark Test Tomorrow! - September 13, 2011

Today students got back the first test and we looked at those as well as problems from the previous chapter tests in the text.  They have a benchmark test tomorrow that will count as a quiz grade.  They also received another exponential worksheet (with some answers) that sould be completed by classtime Thursday.