Skip to section navigation Skip to main content

Teacher Resources

Home > Teacher Resources > Lesson Resources > X... Y... Zzzzzzz

X... Y... Zzzzzzz

On this page you will find lesson objectives, standards, instructional notes and UDL opportunities.

Estimated Time:  90 minutes

Lesson Objectives:

  • The students will determine population percentages by calculating areas under the normal curve.
  • The students will use tools strategically to solve real-world applications involving estimating areas under the normal curve.

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:

In this final lesson, students revisit some of the presidential data used in the first lessons of this module. Students will engage in tasks that require estimating areas under normal curves. Students will utilize the statistical features of the graphing calculator to generate graphs displaying area under the normal curve as well as calculating the area under the curve.

As with the first three lessons, the calculations in this lesson 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. Students may use other technology tools to perform the necessary calculations. For example, Excel software contains spreadsheets and formulas that will perform the same calculations and graphics. The first two modules have students using the Shodor Applets opens in new window. 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 opens in new window.   Available through the High School Statistics and Probability link are several STEM-related tasks that the students can complete.

> Go to X... Y... Zzzzzzz lesson

Sample Responses

For sample responses to the Algebra II Journal questions, visit the Algebra II Journal in the Teacher Resources.

X... Y... Zzzzzzz - Page 1

In this lesson, students will engage in tasks that require estimating areas under normal curves. Students will utilize the statistical features of the graphing calculator to generate graphs displaying area under the normal curve as well as calculating the area under the curve.

> Go to lesson, page 1

X... Y... Zzzzzzz - Page 7

At this point in the lesson, it would be appropriate to introduce standard normal curves and z-scores. However, z-scores are not specifically mentioned in Common Core Standard S.ID.4, and may be beyond the scope of this course.

> Go to lesson, page 7

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