Module 5

Box an Whisker Plots

1. What are some differences in the data that you can observe? 

Our class has a larger range than the German class. The German class has a larger population but their range is smaller. 

2. What does the median for each class tell us about the data?

The median for the German class is approximately 55. This means that half of the German class threw out less than around 55 pounds of trash and the other half threw out more than 55 pounds. The median for our class is 83. This means that about half of the class threw out less that 83 pounds of trash and half threw out more than 83 pounds. 

Common Core

First Impressions:

• My first thought when exploring the standards was that there are A LOT. It is a bit overwhelming, imagining how to fit in all of these standards throughout the school year.
• The second thing that I noticed was how the standards progressed as they advanced in grade level.

How do the concepts progress through the grades?

As you move through the grades, you revisit the same concept but you delve deeper into the content.

How do the concepts change and increase in rigor and complexity for the students?

Each year, students build upon the concepts that were covered in the previous year. For example, in kindergarten students are expected to master addition up to sums of 20. By the end of second grade they are expected to add to sums of 100.

Does the Common Core Standards align with what NCTM states students should be able to know 

and do within the different grade level bands?

For the most part, the Common Core Standards align with NCTM Standards.

Give examples of which standards align as well as examples of what is missing from the Common 

Core but is emphasized in the NCTM standards and vice versa.

I focused on the earlier grade levels since I am assigned to a kindergarten classroom this semester. I thought that the concepts all aligned pretty well. I noticed that one major difference is that NCTM stresses connecting materials to the students and the every day lives. This is not mentioned in the Common Core Standards.

Module 3

Lost Teeth Video 

I think that the teacher asked the students about the range in order to get them to think critically about the different populations that they gathered their data from. Would it make sense for younger grades to have a wide range of tooth loss? Why or why not? etc. I think that the students showed pretty good insight in regards to the range. One of the students mentioned that he lost teeth before he even entered kindergarten. He was able to draw upon his own experienced to explain the variation in ranges.

I think that the students did a great job analyzing the data. They investigated how their predictions differed from their actual results and discussed the differences. I was impressed by their discussion about how the range is constantly subject to change. This was clear when one girl lost an additional tooth during the project, changing the range for that population.  

Annenberg

I thought this module was very informative because these are skills that I have not used in a very long time.

Problem A5  

Since the goal is to estimate when a minute has elapsed, it makes sense to consider how close the estimates are to the correct response, which is 60 seconds.

a.	How many people's estimates were more than five seconds away from one minute? That is, how many of the responses were less than 55 seconds or greater than 65 seconds?
b.	How many estimates were within five seconds of one minute?
c.	How many estimates were more than 10 seconds away from one minute?
d.	How many estimates were within 10 seconds of one minute?

This question tripped me up, at first. I had to reread section A a few times before it clicked. I decided to include this in the blog because, to me, it was a reminder of how important the phrasing of the question is for students' understanding.

Problem B2    Using only the histogram and grouped frequency table, give two descriptive statements that provide an answer to this question.

I included this question because of a little sense of hesitation that I had. I instantly made the observation of the range, and that most of the data was within 10 seconds of 1 minute. However, I felt unsure whether these were sufficiently descriptive enough. When I read the solution to this problem, it was clear that my observations were valid descriptions. I think this uncertainty would also be shared by students who are new to interpreting data and graphs.

Stem-and-Leaf Plots Article

My take away from this week's articles is similar to the article we read last week. I was very impressed at how quickly the students seemed to pick up the concept of the stem and leaf plots. I think the concept of using the stem and leaf plots as a tool to teach 10's and 1's place value is a really great idea! I can definitely see myself incorporating this approach in my own classroom.

Questions

What kinds of graphs can be used for data that can be put into categories?

Bar graphs are a great way to present categorized data. Pie charts also come to mind. 

What is the difference between a bar graph and a histogram?

A bar graph gives you an exact value for the data while a histogram give you an approximate range.

Module 2

Annenberg:

QUESTION B1: Using the data above, answer this question: How many raisins are in a half-ounce box of Brand X raisins? Answer the question in whatever manner seems the most descriptive.

The first thing that I did for this question was plug the data into the chart. This let me see all of the numbers. The first thing that I noticed was that 28 was the most common number of raisins in each box. I was going to stop there since that is the mode, but out of curiosity, I wanted to know if the median would give the same number. I lined the numbers up and, again, I got 28! So I concluded that a box of raisins would have 28 raisins on average.

Problem B3

Does Problem B2's data strongly suggest that the next box will have 28 raisins? Does it prove that the next box will have 28 raisins? If so, why? If not, would there be a way to prove, statistically, that the next box must have 28 raisins? I was a little confused by this question. Initially I would say that, yes, there will be 28 raisins in the next box. The past 17  boxes all had exactly 28 raisins. It seems very likely that the next box would also contain 28. Other than showing the data supporting that claim, I'm not sure how you could prove that this is true.

Median

I actually made a mistake when I first plotted my data! I confused a line plot with a line graph so I had to go back and do it again!

Kindergarten Data:

Mode: 0

Median: 0

1st Grade Data

Mode:7

Median: 5.5

2nd Grade Data

Mode: 8

Median:8

 3rd Grade Data

Mode: 9

Median: ? (I'm not sure how to find the median when there are unknowns)

Just from glancing at the four line plots we can tell that at least one student in each grade has lost at least 1 tooth. As the grade level rises, so does the number of teeth lost. In the Kindergarten class, there were more people who had not lost any teeth than there were people who had lost teeth. In the 2nd and 3rd grade classes everyone had lost at least 2 teeth.

If only the mode for each class was given, we would know the most common number of teeth that each class had lost. If we only knew the mode, we would have no idea about the outliers. For example, the mode for 3rd grade is 9 teeth, yet there is also a student who lost 19 teeth! If I thought that most of the class had lost 9 teeth I would never consider that someone had lost as many as 19.

Only having the median would not really give you a clear picture of the data unless you also knew  the range. When you know the range you know that the class has lost anywhere from x-y many teeth. The median gives you an idea of what the average number lost was.  for 2nd grade you would know that they had lost between 2-13 teeth. On average they lost around 8. You would not know, however, that most of the class had lost 8 or more teeth. 

I Scream

The opening statement was a bit surprising. I don't really think about 4 year-olds gathering and representing data! The kindergarten lesson in the article seemed like it would be a bit ambitious for students to do independently. I think the teacher did a great job letting the students take the lead. They all seems very excited and motivated which I think makes a big impact. The point of the lesson was to let the students individually practice these graphing and data skills that they have been exposed to in a full class setting.  I like that the teacher allowed students to pick their preferred style of graph. Though the data was not the most accurate, all of the students represented their data successfully.