## Reflection: Developing a Conceptual Understanding Comparing Distributions Part II - Section 4: Closing

I changed the Exit ticket this year as well. I wanted to push students to write about this topic. It is not easy. Students have to be pushed to explain their ideas thoroughly though examples and counter-examples. Scoring this exit ticket and giving students another chance to correct any answers encourages the editing process. It normalizes error. I find that students are more likely to discuss math if they are willing to be wrong and want to be convinced through examples. So I ask them to do the same.

I also wanted to focus on comparing data primarily through dot plots. Students should be exposed to various ways of displaying data (histograms, box-and-whisker, stem and leaf, etc), but at the beginning I want students to focus on understanding what the different measures represent and how we can use them to compare data. By using the dot plot in the Exit Ticket, a form they are now familiar with, I am isolating the understanding of the measures of center (mean) and variability (range). I will know students completely understand these concepts if they are able to explain that the mean is a better measure used to compare the data because it is significantly different, as compared to the range which is approximately the same. The range in heights, which is approximately the same, tells us that the boys vary as much as the girls in their heights. The mean for the boys however, is significantly larger than the girls, indicating that they are generally taller.

I use this sample answer to help write feedback on students’ papers for their revision opportunity. Students feel better about making mistakes and developing their understanding when they are given multiple opportunities to write about it. This is how I hope to build fluency in talking about complex statistical concepts.

Developing a Conceptual Understanding: Write More

# Comparing Distributions Part II

Unit 7: Statistics and Probability
Lesson 4 of 11

## Big Idea: students work in groups to compare sets of data in the form of line plots, describing measures of center and variability

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55 minutes