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The mathematical purpose of the lesson is to find areas under a normal curve and interpret the area as a proportion of values in the interval using different contexts. When students find areas under a normal curve and interpret the proportion of values in certain intervals for a given context, they are looking for and making use of structure (MP7).
One activity is optional because finding an interval that fits a certain percentage of the data goes beyond the needs of this course.
Some of the activities in this lesson work best when each student has access to a device that can run statistical software such as Geogebra. This allows students to quickly find the areas under the normal curve, which will continue to be useful throughout the unit. By using technology to find the area, students can focus on the interpretation of the results rather than computing intermediate values to find the area.
If students are not using statistical technology, they will need access to an alternative method for calculating areas under a normal curve, such as using a table of z-scores.