Module 5

Box Plots

Questions for my students…

1. Based on the median in both box plots, who throws away more pounds of trash?  My students throw away more trash per month.
2. Would your answer to number 1 change if we had the same amount of students as the German class?   It would be hard to answer this without data to look at. If we added more data from other students in the school, I think their answers will be similar to our class and would have minimal effect on the box plot.
3. Do you feel this is a fair comparison?  Even thought the number of students in each of the classes was substantial different I do not feel having the same amount students would not effect the numbers.  

Common Core Standards 

Write down two “first impressions” you have about the standards

The first thing I noticed is how well everything is laid out.  It is easy to read and to follow.

  

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

There is what feels to me a natural progression through the grades.  For example In Kindergarten, we are introducing the topic, sorting objects and counting them.  In first, we start to organize, represent and interpret categorical data.  Second grade we and in numerical data and different ways to graph the data in bar graphs and line plots.  They solve simple questions about the data.  The standards continue in this way increasing in complexity and building upon each other in each grade.

Now look at both the Common Core and NCTM standards to respond to the following questions:

Does the Common Core Standards align with what NCTM states students should be able to know and do within the different grade level bands?  (Note that NCTM is structured in grade level bands versus individual grade levels.) 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.

Even thought the wording is somewhat different I do feel like they do somewhat align.  In grade, K-3 the verbiage is very similar.  However, in 3-5 grades I feel like the NCTM is more detailed where the common core just gives a few examples. Looking at 6^th grade this is the most detailed from either source. The verbiage on this page is very similar.

Would You Rather?

We were asked to pick a lesson and to examine the materials to determine which mathematical ideas it could raise for students and to consider how you might highlight those ideas.  The data activity I chose to focus on is Representations of Eagle and Whale Data.  Students were asked the question, “Would you rather be a whale of an eagle?” In this activity, students make their own representations of the results of the eagles and whales survey.

When using this activity, what mathematical ideas would you want your students to work through?  I would want my students to work through organizing, representing and interpreting the data collected.  Organize it into categories and then make a representation of the data by using cubes, stick-on notes, drawings; or any other material I have in my classroom.

How would you work to bring that mathematics out?  After everyone is done with his or her representations, I would have a class discussion.  On the whiteboard, I would make a graph and plot the class data as the students make suggestions to me.  I will ask probing questions to get them to ponder the decisions they have made.

How would you modify the lesson to make it more accessible or more challenging for your students?  By letting my students work with partners and select their own medium to display their data I am making the activity very accessible.  To make it more challenging I might add another category such as students who could not make up their mind.  On the other hand, I could have them show me another way to display the data.

What questions might you ask the students as you watch them work?  I would ask questions like,

·         Are you making sure your representations are clear so that others can read your findings?

·         Does your chart show an accurate count of the numbers of eagles and whales?

·         What does this data tell us?  

·         What animal seems to be the most popular?

What might you learn about their understanding by listening to them or by observing them? 

 By listening to them, I will be able to hear who is interpreting the concept correctly and who still needs more help.  I can ask probing questions to assess just where their inconsistencies are. Observation is a great way to see your students in action. I will use this time to ask questions and make comments on the projects they are working on.  One little question or comment can get them thinking critically about the task.

How do the concepts taught in this lesson align to the Common Core Standards?

CCSS.Math.Content.1.MD.C.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

Questions to ponder Miss Em….

I found this week’s module a little less intimidating, how did you do with this week’s math?

I have yet to observe a lesson on collecting data in any classroom I have been in, have you?

Do you feel it is better to let students work in groups or in pairs in activities such as theses?