##
* *Reflection: Lesson Planning
Straight Walkin' With Statistics - Day #2 - Section 2: Why are we doing what we are doing?

After heading to the board to "sketch an overview idea of the confidence interval" - it hit me...

#1: I don't want to run class this way! I always prefer not to be the sole provider of knowledge for my students. I want them to discover the confidence interval through inquiry and discovery - and through my scaffolding in the remainder of the unit...not because I just tell them what it is.

#2: A trip to the whiteboard (where I was the only one talking) would have killed the positive momentum of our lesson.

For these reasons, I adapted my plan. Instead of mathematically revealing the confidence interval, I simply wrote the words "CONFIDENCE INTERVAL" on the board and probed my students to define what it might mean. The result was an outstanding discussion. Through asking follow up questions like *Can you give me an example of what we are talking about? *the students were able to achieve a working definition of the concept without killing the momentum of the class. After calling this "audible" to my game plan, I went ahead with my original plan of attack and illustrated how this might look on a graph.

*Scrap the Picture - Hold a Discussion*

*Lesson Planning: Scrap the Picture - Hold a Discussion*

# Straight Walkin' With Statistics - Day #2

Lesson 12 of 21

## Objective: The students will dig deeper into yesterday's data, apply previous learning, and explore the concepts of a confidence interval.

#### Break Out Groups

*10 min*

I have introduced this lesson in the video narrative resource. The entry instructions for the start of class procedures have also been attached. MP3: Group Work.

*expand content*

The goal of this investigation is to provide students with the understanding of how normality is determined in a real world application (MP4). Traditionally, most “textbook” problems imply normal distribution right from the start, and don’t ever confront the students with this important primary thought process. That is why the ensuing discussion is so important!

I theme the introduction to our discussion in the following way: (MP2)

*Baseball Player: Would you show up to your next double header with a tennis racquet?*

*Band Member: Would you show up to the next home football game with a basketball?*

*Football Player: Would you show up to Friday night’s game with pom-poms?*

*CLASS: Would you apply properties of the normal distribution to something that is not normal?*

Soooo… THIS is why we are spending all of this time trying to figure out if our data is normally distributed! We have to know what tools to bring to the game! We have already talked about the pitfalls of using a small sample population, but it is going to be impossible for us to test everyone in the world. Although we have a limited sample size, we can still analyze the data to see if it appears normal.

But how accurate are we with our assumption of normality?

This is where I roll out the appropriately named “Confidence Interval” – and EMPHASIZE its connection to the standard deviation. A quick picture on the board is a really helpful tool for the students so that they are not overwhelmed by the calculation. If you are comfortable with your student’s level of understanding on the concept, feel free to introduce them to how they can use technology to make the calculation much simpler! Be sure to compare the answer obtained to the “by hand” answer to see how things align.

*expand content*

#### Work Time

*15 min*

Allow the students the time to work on the above worksheet, as well as answer any questions from the previous Day #1 Worksheet. During this time, I fly around the room visiting students. I work hard to create a high-energy atmosphere with a lot of positive reinforcement. I emphasize NOT getting write answers, but being able to understand and explain mathematical thoughts. The students should finish completing the Straight Walkin’ With Statistics – DAY #2 Worksheet for homework.

*expand content*

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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