Module 4:
AnnenbergVariations about the Mean:
Okay, let me just start by saying how much my mind was blown from watching the beginning video. I really do not think I ever considered it possible to find the mean without adding everything and dividing. When watching the teachers level all of the snap cubes, I honestly was lost. I had no clue where they were going. After the teachers leveled all of the snap cubes into stacks of 5, they had 10 left over and I was still confused! Once they explained that you would put 10 over 17 because there was 10 cubes left over and 17 people recorded their answers I FINALLY got it! The mean would be 5 and 10/17. I am still somewhat blown away that you can find the mean of data a different way than adding and dividing.
For my first question, I chose A2.

I chose this question just because it really caught my attention. At first, I changed the number of coins in my 9 stacks and continued to calculate the mean. When I saw that the mean was 5 as well I honestly thought to myself that was an odd chance, until I saw part b. Then I got to thinking, the mean is the same because there is the same number of coins and the same number of stacks. Just because the stacks looked completely different did not mean they would have a different mean. We would have to change the number of stacks or coins to create a different mean. I think this would be important to show students so they can see how and what effects the mean.
Also, I am confused about Part D. I understand how to get the deviations from the mean and I was answering the questions correctly; however, I’m not really sure what purpose this is used for. I don’t understand what the deviations from the mean tell us about our data.
Generating Meaning Article:
From what I remember, my time in the elementary classroom was completely different than the students in the article. I remember being shown how to find the mean, median, mode, and range, and then being handed worksheets. We were just going through the procedure. I loved how the teacher in the article really engaged the students in the lesson. Even from the beginning, she gave them clues so they could discover how to find the range. Once the students figured out that the range was the distance between the largest and smallest numbers in the set they were so excited! They had figured everything out on their own and were so proud of their work. I believe that this is a much better approach to teaching math. It really gets the students involved. I think it gives them a much better understanding of the concepts as well, instead of just memorizing procedures.
Working with the MeanActivity:
This is my first representation of the data with my cubes. I was completely confused on how to figure out what the other 2 bags of peanuts needed to be without adding up the five bags we already knew. I thought about it and then tried to complete this with one of the examples I watched in the Annenberg videos.
I took all of the cubes and make the columns as even as I could. By making all of the columns an even 5, I only had 1 left over and 8 columns. I wasn’t really sure where to go from there because I knew I should only have 7 columns because there should only be seven bags of peanuts. Then I decided to split up the cubes from the set again, but this time to make sure I did not go over 7 columns. When I did this, I got 6 columns with 6 cubes each and 1 column with only 5 cubes. My conclusion after working with these cubes was that there should have to be around 5 or 6 cubes in the next 2 bags to give us 7 bags of peanuts with a mean of 8.
After completely going crazy working with the cubes and trying to find the mean without adding up the total values, I made my line plot graph, and totaled the values to see if I was close my conclusion from using the cubes.
First I plotted bags 15 and totaled the amount, giving me 41 peanuts. I knew that I needed 7 bags total and that the mean needed to be 8, so I multiplied 7 by 8 giving me 56. I knew that 56 divided by 7 would give me the mean of 8 I needed, so I subtracted the 41 peanuts I already knew I had from 56 giving me the answer that I needed a total of 15 more peanuts in 2 more bags. Because of this, I knew I needed 7 peanuts in one bag and 8 in another. This model helps represent the exact number of peanuts in each bag and gives and easy way to figure out what the mean will exactly be, versus my guesses with the cubes. For the cubes I did not count the total. Because of this I estimated that you would need between 5 and 6 peanuts in the next 2 bags when really we needed 7 and 8 peanuts in the bags. The mean shows us the amount that we could put in each bag if we were dividing them evenly. For example, if we put 8 peanuts in the 7 bags, it would give us the same total of 56. When we divide that by 7 we get our mean of 8.
How Much Taller Video and Mean Case Studies Summary:
It was very interesting to watch the How Much Taller video. I thought that all of the students did a great job drawing conclusions from their data. They used specific number answers to compare and contrast and even came to the point of where they felt they needed to find more data to answer the questions more specifically.
I feel like there was so much information in the case studies that it is hard to summarize. I was surprised at some of the answers some students gave. I thought it was interesting that in every grade level and even the students in the video realized that they needed some sort of middle number. I thought it was really neat to see that the third and fourth grade students came to realize that they needed to add all of the heights together and create one number. They were so close to figuring out the mean on their own and I believe if they hadn’t ran out of time they would have realized the division part as well. I was also surprised by the 5^{th} grade class. I figured as well as the younger grades had done that the 5^{th} graders would have made better progress than they did. Two of the students realized they needed to add all the numbers and divide, but it did not seem that they truly understood what this had to do with their data. It seemed that they had just been given the formula to find the mean.
Blog Questions:
http://www.citydata.com/city/JacksonvilleNorthCarolina.html
Above is a link I found when viewing the online version of the Jacksonville newspaper. This site shows all kinds of data that was collected for the city of Jacksonville, NC. I thought it was really interesting looking at the mean prices in 2001 for all housing units sold, which was $147,647. This information is important because it shows the average prices for houses sold. This number is important so we can now compare the mean of all housing units sold in Jacksonville, NC today and compare whether the housing market is increasing or decreasing.
For researching an annual teacher’s salary, I research Patrick County, Virginia. This is where I grew up and went to school and I am fairly certain I will be teaching here at some point. The only starting teacher’s salary average I could find was from 2012. It was very specific. For a starting elementary school teacher in 2012 with no prior experience, the average salary was $33,400. However, looking at the new 2014 list, just published in January, the average teacher salary for all the teachers in Patrick County was $42,803. Both the averages can be tricky, because there are over 6 different elementary schools in Patrick County, so you do not know if one school will pay much higher starting out than the other. To find this you would have to find the averages of each elementary school in Patrick County and compare them. However, we can see that with more experience, you annual salary should go up!
I’m so glad you mentioned Part D in the Annenberg course. After I read your blog, I realized that I didn’t understand what the purpose of the deviations from the mean tell us about our data either. I got the questions correct, but didn’t know why I was doing what I was doing. I went back and looked at Part D again. The website says that the MAD is the “average” of the variations or the differences from the mean in the data. So, if the mean tells us the average of our data sets, then the MAD indicates to us the average of the variances from our mean. You can look at it like using the blocks for determining the mean. You want all of your stacks to be equally close to your mean, right? So ask yourself, how much do you have to take away from each stack to get them all of equal distance to the mean of your data? So using the MAD you can say that your data tells you on average each of our stacks are deviated ? from our mean. Some are higher or lower, and some are equal to it but on average they are this far away from it. Not sure if that helped you or confused you even more. I hope that I had this correct.
Wow!! I really am confused now that I’ve said all that about MAD, now as I read more I’m not sure what the difference in MAD, variance, and Standard deviation are in their purposes for data. I’ll have to investigate more…
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Check out this website http://www.mathsisfun.com/data/standarddeviation.html#WhySquare. Maybe it will help us out some :).
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So the deviation is basically to show how spread out the data is?
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That’s what the definition says. I’m still a bit confused on this subject, but I feel like I am getting closer to understanding it than I was though. I guess that’s a positive.
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It is a lot to wrap your head around. The deviation is how spread out your data is. If you have a set of data with a large variance it means that your scores are very different and not close to the mean. Not sure that this helps at all.
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There is so much information to understand it I remember learning most of this but then some places are blank. That is a positive as well, knowing that you are finally understanding what is going on. Great work.
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