Module Six

Box Plots

Hi Aubrey, I think I finally figured out the box-and-whiskers graph and how they work! So I have decided that I would want to teach a follow-up lesson to Class A. I chose this class because the median score was about 43 or 44 percent, which isn’t great but I felt that most of the students were on the same page as far as their understanding goes. Class B had extremes on both sides that could result in some students being utterly bored with if they had to sit through another lesson about the same thing. I would hope that having a follow-up lesson about the same information would help class A improve the test scores. Do you agree or disagree with my reasons?

Question 1. What kind of comparisons statements can you make of our class and the German class?
~The minimum value for both is about the same at 32 pounds, and that’s about it.
Question 2. Do we or do the Germans produce more trash daily? Support your answer with evidence from the box plot.
~Our class produces more trash daily; the box plot shows that our median value alone is roughly 30 pounds higher.
Question 3.  Does the class size play a difference in the results of the box plots? Why or Why not?
~No, the German class was already larger than our American classroom, and we are already producing more trash than the 42 members of the German class.
Any other questions that you think would have promoted more higher-level thinking?

Common Core Standards

My first impressions are that it seems pretty intense when reading it, almost like wait-what do I have to teach the students...my second impression was that in itself it seems pretty specific on how and what they want of the teaching standards per grade level. I tried to look at the whole of the criteria to get a better understanding, but I stuck with the file that was created.
I am interested to read what your impressions were!

Progression

Kindergarten is classifying object with a category limit of 10.
First grade is organizing and interpreting data and questioning the data collected.
Second Grade is measuring the length and representing the data on a line plot and also creating bar graphs and now having up to four categories.
Third grade is now drawing scaled graphs to represent the data and several categories; the graphs can represent a number of items per square.
Fourth grade is making a line plot with fractional numbers and solving problems that use the line plot as a guideline.
Fifth grade is making the line plot as well, and solve problems but with a different level of difficulty.
Sixth grade is learning about statistics and probability and using data collection as a way to solve statistical problems. They also continue to use the line plot but introduce other graphs, and summarize the data sets.
I’ve listed out the changes that I see from grade level to grade level, some of the ideas are the same, and they build upon each other as the year’s progress. The NCTM is a more detailed description of what the grade levels should be focusing on. 
Do you agree with how I wrote the progression out?

Common Core and NCTM

The earlier grades of K-2nd I think the standards align together quite well. But once the third-fifth grade is read, I feel like they are not all that similar. The NCTM Standards in third through fifth grade is asking students to design investigations allowing the students to formulate questions, it brings in the terms median and comparing the representations of the data, then it says the students should develop and evaluate inferences and prediction. I don’t see anything of the same detail in the CCSS. Both the CCSS and the NCTM have base instructions for the statistical process. They deal with classifying objects, understanding the data, and interpreting the results; all of which are important to the statistic process.
Do you think differently? 

Curriculum Resources

Grade 1 Would You Rather?

The lesson focuses on the question “Would You Rather be an Eagle or a Whale?” and the students learn to not only ask the question of each other but also how to make the representation. They also give reasons why they’d like to be one animal or the other. They then take what they learned from this activity and are given a new question that they are responsible for collecting data from the class.
Learning how to make representations of the given data is essential since there are various ways in while the students can accurately and inaccurately calculate the information. It says that you would have the students work in pairs to collect the data on the new question they were asked, I would have each person in the partnership collect data using a different type of representation. One could use tally marks while the others draw a picture to represent each classmate's answer. Having the students check the data that the other person gathered to ensure they recorded the same results would also be helpful. Finally deciding which way the pair is going to show the data representation, they will have to determine what collection method they liked better or how they could accurately display the results they came up with.
To make this more challenging I would have the pairs come up with their question to ask the class, they would have to ensure that the question is one that follows the “this-or-that” answers that we are currently learning. The question would need to be approved before they can begin the data collection.

Questions that could be asked of the students as they collect the data could be:
What results do you predict to get?
How do their representations align with the number of students in the class?
How are you going to collect your data effectively now that you have a question?
Did your results match your prediction?
At the discussion point, I would ask the students to describe the data that they collect.

As a result of listening to the students and observing the work that they are doing, you will be able to see which students have grasped the concept of data collection methods. Another thing we could learn is their ability to work with a partner; I would try to pair them up with different classmates each time we had activities by using the names on a stick method.
This lesson aligns with the standards because it is asking the students to collect and represent data into categories, they are formulating and asking questions, and then describe the data they collected. It follows both standards, but I think with the modification of the student formulating the questions is more so following the NCTM Standards.

Would you use this lesson plan in your classroom? If so, what changes or modifications would you make?