Module Two (B)

Box Plots

Another scenario to consider: Your students have been weighing the trash that their family discards each day and adding the totals for a month. The stem and leaf plot below shows the pounds of trash discarded for each student in your class. A class in Germany with which you have been communicating by email is keeping the same data. They have sent the box-and-whisker plot of the pounds of trash discarded in their homes for a month. The German class has 42 students. Yours only has 18. The students in your class have access to the data in their stem-and-leaf plot and they know that the other class has 42 students. They do not have the individual numbers for the German data.

a. Make a box and whisker plot for the data in your class and draw it under the German class’s plot using the same scale.
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b. Suggest three good questions that you could ask your class in making comparisons between the two plots. Answer each of your questions.
-Do you think there are more outliers in the class in Germany or in our class? Why?
-There are more outliers in our class because he “whiskers” are longer.
-Is the median greater in Germany or in our class? Why do you think that is?
-The median is greater in our class. We had a greater range with larger outliers, causing us to have a higher median.
-What would you look at to determine where more trash is produced?
-I would look at the median, which ever place had the highest median, probably produced more trash. I would also look at the maximum, minimum, lower quartile and upper quartile. This would give me a better picture by looking at more points of the data.

Common Core Standards
Write down two “first impressions” you have about the standards.
–I noticed that the standards build each year. The standards use what is learned the previous year to build on a higher learning and deeper understanding of what is being taught. I also noticed that some criteria isn’t taught every year. This is probably because it is above or too far below the understanding of the child at that time.

How do the concepts progress through the grades?
–Each concept uses what the students have used previously to build onto that concept for the next year.

How do the concepts change and increase in rigor and complexity for the students?
–The concepts continuously and consistently increase in rigor and complexity for the students. There aren’t jumps in learning; it is a step by step learning process. The concepts are simple in kindergarten and increase in difficulty into eighth grade. Teachers need to use the standards from the grade before and after the grade they are teaching to know how to prepare students for higher grades and what they should already be aware of.

Common Core and NCTM Standards
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.)
I feel that when you look at the Common Core Standards as bands like the NCTM, that they do align. I feel the Common Core standards are more vague, but that a teacher can easily accomplish the goal of both groups of standards within his/her lessons.

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.
An example of the standards aligning is in Kindergarten students are to classify and count objects, first grade students are to organize the data and know information about what the numbers mean in each category and in second grade, students are to are to draw a picture or bar graph to represent the data. All of these things are included in the NCTM standards. There is something missing from the Common Core standards in this grade level band; students make inferences and predictions according to the NCTM.

Curriculum Resources
Grade Two: Data Day: Standing Jumps and Arm Spans: In this lesson students measure their arm span in centimeters and length of a standing long jump in inches. They then compare the numbers, look at the difference in centimeters and inches and record the data.
·When using this activity, what mathematical ideas would you want your students to work through?
-I would want my students to understand the difference in centimeters and inches so they knew what was being measured. Also, students are to find the median of the class for the arm spans. Finally, the importance of proper data collection is important for this lesson so that all students’ jumps and arm spans are measured correctly and we are to accurately determine our median.
·How would you work to bring that mathematics out?
-I would bring mathematics out by showing students how to measure the arm spans and jumps. I would also show them the difference in centimeters and inches and when would be proper times to use them.
·How would you modify the lesson to make it more accessible or more challenging for your students?
To make the lesson more accessible, I would have students measure the arm spans and jumps using either centimeters or inches, but not different ways like the lesson called for. To make the lesson more challenging, I would have the students convert their centimeters to inches and inches to centimeters using math and not measurement.
·What questions might you ask the students as you watch them work?
I would ask them what they noticed about their arm spans and jumps and how the different lengths compared to their classmates. For example, “Susie” has a shorter arm span and jump than “Mark;” why do you think that is?
·What might you learn about their understanding by listening to them or by observing them?
I might learn that some have a deeper understanding of the correlation between the arm spans and jumps and the similarities and differences between students.
·How do the concepts taught in this lesson align to the Common Core Standards?
-This lesson aligns with the Common Core Standard that has students measure lengths of objects to the nearest whole number in the second grade.