##
* *Reflection: Developing a Conceptual Understanding
Flaws and Fallacies (cont.) AND Types of Data - Section 2: Types of Data – Looking at Big Bird

Attached you will see the responses that my students generated to describe Big Bird. They obviously love picking on me because one student mixed in "Goofy like Mr. Hammel!" as a response :)

Although the number of responses was less than I anticipated, we still had enough to make the sorting activity a meaningful one. Qualitative and Quantitative results both appeared. To elicit more responses the next time, I might include a second or third character - or perhaps a movie star.

*Developing a Conceptual Understanding: Student Responses*

# Flaws and Fallacies (cont.) AND Types of Data

Lesson 3 of 21

## Objective: Students will be able to take a look at each other’s flawed creations and conclude class by being able to classify the major types of data.

As we transition into the second portion of the lesson, I pull up the PowerPoint slide with Big Bird on it and tell the students that they have 2 minutes to write down as many descriptors as possible about him (gather the data).

After the students have gathered the data, I tell them to turn to their thinking groups and group all of their data into two piles. (Circulate the “Thinking Group” Data Sorting Template”) DO NOT tell them how to classify the two piles! It is up to the students to talk about and agree on how this needs to be done. Almost every group will group the data quantitatively and qualitatively, although they will not likely use these exact classifications. After allowing 5-6 minutes for these discussions to occur, I have each group send a representative to the board to show their 2 categories and 3 of the data points that lie under each category – not all of them. The students will come up with a wide variety of titles that align to quantitative and qualitative, but it is up to the teacher to package them all together and reveal the common terminology! Because the directions were intentionally vague, be sure to give attention to the 1 or 2 groups who classified the data in a different way. As long as they can explain their reasoning to the class when given the opportunity, emphasize to the students that these groups are equally correct, although it was not what we were specifically looking for. This goes a long way to creating a safe learning environment (and emphasizing the math practice standards) early on in the semester. There is not “one set way” to do things!

After defining Qualitative and Quantitative data using the student responses, it is time to break the Quantitative data into two subgroups. Ultimately we are “fishing” for discrete and continuous from the students, although it is NOT likely that they will come up with this actual terminology on their own. I ask the class to do this with me at the board. I jump from group to group asking for a quantitative data point which we discuss how to group as a class. This does two things:

#1 Ensures that all groups participate, even those groups who initially grouped differently than qualitative/quantitative.

#2 Informally assesses the students level of understanding as you go along.

NOTE: The discrete/continuous discussion will likely take time with the students! It is not as clear to them as the quantitative/qualitative grouping. Be creative during the discussion, and do not be afraid to pull in additional examples!

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#### Exit Quiz

*10 min*

The student’s work alone to complete the Exit Quiz shown in the PowerPoint. This gives me a feel at the end of the day if the students have mastered the concepts enough to use them in a new setting. This is vitally important before we attach the real math associated with data collection, and begin to take things to the next level.

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- UNIT 1: Culture Building Unit - Welcome to the New Year!
- UNIT 2: Exponential and Logarithmic Functions
- UNIT 3: Sequences and Series
- UNIT 4: Statistics: Something for Everyone
- UNIT 5: Review Lessons
- UNIT 6: Writing Prompts in Mathematics
- UNIT 7: Trig Tidbits
- UNIT 8: Functions, Problem Solving, and 21st Century Skills
- UNIT 9: Polynomials and Problem Solving
- UNIT 10: Probability
- UNIT 11: Imagine This! Imaginary and Complex Numbers
- UNIT 12: Let's Explore Radicals!

- LESSON 1: Statistics - Opening Activities and Discussion
- LESSON 2: Role Play PLUS Flaws and Fallacies in Statistical Thinking
- LESSON 3: Flaws and Fallacies (cont.) AND Types of Data
- LESSON 4: Stepping into Box Plots
- LESSON 5: An Introduction to Histograms
- LESSON 6: Using Excel to Create a Histogram
- LESSON 7: A-Mazing Inferential and Descriptive Statistics!
- LESSON 8: What does the Bell Curve SOUND like?
- LESSON 9: The HOW and WHY Behind Standard Deviation
- LESSON 10: A Second Dose of Standard Deviation
- LESSON 11: Straight Walkin' With Statistics - Day #1
- LESSON 12: Straight Walkin' With Statistics - Day #2
- LESSON 13: Straight Walkin' With Statistics - Day #3
- LESSON 14: Review and Extensions
- LESSON 15: Student Motivated Workshop
- LESSON 16: Let's Help the 6th Graders!
- LESSON 17: Let’s Help the 6th Graders: Problem Work Time
- LESSON 18: Let’s Help the 6th Graders: Final Day
- LESSON 19: Let's Help the 6th Graders: Debrief
- LESSON 20: Teaching Numbers and Excel
- LESSON 21: Muddying the Waters: Formative Assessment Lesson