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# The HOW and WHY Behind Standard Deviation

Lesson 9 of 21

## Objective: Students will be able to build on their entry level knowledge of standard deviation and extend it to their maze data set in a previous lesson.

## Big Idea: This lesson works to give the teacher the flexibility to “paint” his or her own description of standard deviation, while providing the basic flow and context of the lesson.

#### Entry Question

*6 min*

As the students enter, I have the opening PowerPoint slide pulled up which prompts them to reflect on the connection between data collection, the particular type of study, and the bell curve. The student responses are linked to a www.pollev.com question. This question does not have a “right” answer, and allows the students to respond to a variety of perspectives. Using www.polleverwhere.com ensures that all students feel safe responding to the opening question, regardless of their ability level. Out of your classes sample size, you will be sure to get a great deal of discussion points that not only connect to prior learning, but also help to motivate the day’s lesson.

#### Resources

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To conclude the day’s lesson, I help the students find the standard deviation of the data set that we used for our Maze lesson. Typically, I plan to do either the boys or girls data as an example, and then allow the students to find the other one. This is a really challenging lesson for the students to this point, and they may continue to need support understanding exactly what the standard deviation is. I HIGHLY ENCOURAGE my students to come and see me during homeroom or before school if they would like to see it re-explained in a new way. I tell the students that as long as they are persistent, it will make sense eventually! It is important to me that they understand the how and why behind standard deviation, otherwise, it is nothing more than calculator work!

I save an additional practice problems with standard deviation for later lessons because I want the students to focus on the concepts – I am trying to avoid the “just a teach me how to do it so that I can plug and chug” approach to learning.

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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