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Teacher Resources

Plinko

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

Estimated Time:  90 minutes

Lesson Objectives:

  • The students will explore normal distributions and population percentages.
  • The students will determine if a given set of data forms 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:
6.SP.5c: Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

7.SP.3: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

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.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

Instructional Notes:

In this module, the students will 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.

For this second lesson in the module, the students explore normal distributions and population percentages. They are introduced to normal distributions using a game simulator. Following this, the students work with skewed distributions and population percentages using the presidents’ application. Unlike the first lesson in this module, this lesson is entirely new learning.

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 inthe Student Resources. The 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 the 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. The Texas Instruments Illuminations site also provides engaging explorations related to normal distributions, such as Illuminations: Resources for Teaching Math opens in new window.

While this lesson applies the concepts of normal distributions and population percentages 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 Plinko lesson

Sample Responses

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

Plinko - Page 1

It is important for the students to complete the experiment 50-100 times. The dot plot should begin to form a normal curve.

Note that students using screen readers need to partner with another student for the Algebra II Journal: Reflection 1 activity.

> Go to lesson, page 1

Plinko - Page 3

From this point forward in the lesson, discussion focuses on normal curves and normal distributions. You may choose to spend time discussing density curves with your students. A density curve describes the overall pattern of the distribution in a data set. The area under the curve has a value of 1. Density curves do not have to be symmetric, and can be skewed because of outliers in the data. In a normal curve, because of the symmetry, the mean is (approximately) equal to the median. This does not have to be true for density curves, since density curves can be skewed. The value of the mean is pulled towards the skewed tail of the curve; this happens because of the outliers in the data. While normal curves may have outliers, they are usually not extreme.

> Go to lesson, page 3


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 7.2nOptimize 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