Teacher Resources
Just How Normal Are You?
On this page you will find lesson objectives, standards, instructional notes and UDL opportunities.
Estimated Time: 90 minutes
Lesson Objectives:
- The students will use the mean and standard deviation of a data set to fit the data to a normal distribution.
- The students will use the normal distribution to estimate percentages.
- The students will determine if a data set represents a normal distribution.
Key Common Core State Standards:
S.ID.4: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
Supporting Common Core State Standards:
N/A
Standards for Mathematical Practice Emphasized:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Instructional Notes:
Recall that in this module, students work alongside the characters Andrew and Khalid as they look at mathematical characteristics of the presidents of the United States. This application of American history will be a recurring theme throughout the module, but each lesson is self-contained.
During this third lesson, the students complete several tasks as well as utilize a dice-rolling simulator in order to analyze contextual situations using standard deviation. The students use the mean and standard deviation of a data set to fit the data to a normal distribution and to estimate percentages using the normal distribution. The students apply the 68-95-99.5 Rule to normal distributions. The students also compare the properties of a skewed data set with the properties of a normal distribution.
Much of the calculations in this module will be done using the graphing calculator. Where appropriate, the steps to utilize the calculator will appear in the Student Lesson pages of the module as well as in the Student Resources. The students may prefer to use more advanced calculator systems, such as the TI nSpire calculator. The Texas Instruments website offers instructions on how to use the statistical features of the TI nSpire as well as statistics activities. Follow the instructions below to access TI Math Nspired:
> Texas Instruments 
Once on the home page, proceed with the following steps:
1. Click Products in the top menu.
2. Click the Calculators & Education Technology link.
3. Click Activities from the top menu and select Math Nspired.
4. Click Statistics from the left-hand sidebar.
5. Select Normal Distributions
. This site provides interactives that the students may prefer to use over the graphing calculator when completing this lesson. There are also many teacher resources (such as lesson plans and discussions) that may prove useful when planning this lesson.
While this lesson applies the concepts of mean and standard deviation to historical references, there are multiple science and technology applications for these topics that are easily accessible through Internet and text resources. Review the mathematical tasks available at Illustrative Mathematics: Content Standards . Available through the High School Statistics and Probability link are several STEM-related tasks that the students can complete.
> Go to Just How Normal Are You? lesson
Sample Responses
For sample responses to the Algebra II Journal questions, visit the Algebra II Journal in the Teacher Resources.
Just How Normal Are You? - Page 1
This is a task-oriented lesson in which the tasks require students to analyze contextual situations using standard deviation. The students will use the mean and standard deviation of a data set to fit the data to a normal distribution and to estimate percentages using the normal distribution. The activities within the task will emphasize the fact that there are data sets that cannot be fit to a normal distribution.
Just How Normal Are You? - Page 6
More time will be spent in the fourth lesson of this module using the graphing calculator to graph normal distributions. The students should not be concerned at this point with what window to choose for their graph. Also, in the fourth lesson of this module, the students will explore the different percentages using the TRACE features of the calculator. The purpose of this third lesson in the module is to have the students interpret the mean and the standard deviation, and apply the 68-95-99.7 percentages in contextual situations.
UDL Opportunities:
Principle 1: Provide Multiple Means of Representation
Checkpoint 1.1 Offer ways of customizing the display of information
Checkpoint 1.2 Offer alternatives for auditory information
Checkpoint 1.3 Offer alternatives for visual information
Checkpoint 2.1 Clarify vocabulary and symbols
Checkpoint 2.2 Clarify syntax and structure
Checkpoint 2.3 Support decoding text, mathematical notation, and symbols
Checkpoint 2.5 Illustrate through multiple media
Checkpoint 3.2 Highlight patterns, critical features, big ideas, and relationships
Checkpoint 3.3 Guide information processing, visualization, and manipulation
Checkpoint 3.4 Maximize transfer and generalization
Principle 2: Provide Multiple Means of Action and Expression
Checkpoint 4.1 Vary the methods for response and navigation
Checkpoint 5.3 Build fluencies with graduated levels of support for practice and performance
Principle 3: Provide Multiple Means of Engagement
Checkpoint 7.1 Optimize individual choice and autonomy
Checkpoint 7.2 Optimize relevance, value, and authenticity
Checkpoint 7.3 Minimize threats and distractions
Checkpoint 8.4 Increase mastery-oriented feedback
Checkpoint 9.3 Develop self-assessment and reflection
