The purpose of this Warm-up is to introduce the term normal distribution, which will be useful when students interpret a normal curve in a later activity. By articulating things they notice about the histograms, students have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.

Ask students to share what they think the elements are of a normal distribution. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the images.

After all responses have been recorded without commentary or editing, ask students to discuss: “What are some of the properties of a normal distribution?” (It is a distribution that is bell-shaped and symmetric.)

Display two of the example histograms with the normal curves that model the same data.

Tell students that the total area between the -axis and a normal curve should be 1. That is, if the entire area under the bell-shaped curve is shaded (rather than just the bars from the histogram that are sometimes under the curve and sometimes outside of it), the shaded region would have an area of 1. If a distribution has a similar shape to a multiple of a normal curve, then we can say that it is approximately normal.

Tell students that a normal distribution is a specific distribution in statistics that is symmetric and bell-shaped, has an area of 1 between the -axis and the curve, and has the -axis as a horizontal asymptote. Distributions that are approximately bell-shaped and symmetric can often be modeled by a normal distribution, in a similar way to how scatter-plot data could be modeled with a line or other curve. A normal distribution is determined entirely by the mean and standard deviation.

Refer to the displayed images, and point out that the curve that represents the normal distribution with the same mean and standard deviation as the data from the histogram is shown on top of the relative frequency histogram for the actual data.

The mathematical purpose of this activity is for students to collect, represent, and interpret data using a histogram. For most groups of high school students, the distribution of handspans should be approximately normal. If the distribution for your group is not approximately normal, display the distribution from the student response provided in these materials as the data from another class, and ask students to comment on that distribution.

Making statistical technology available gives students an opportunity to choose appropriate tools strategically (MP5).

The mathematical purpose of this activity is for students to use relative frequency histograms to estimate population percentages. Students convert a frequency table into a relative frequency table, and a histogram to a relative frequency histogram, to highlight the proportion of values in certain intervals. In later lessons, students will find areas under normal curves to estimate proportions of values in various regions.

Making spreadsheet technology available gives students an opportunity to choose appropriate tools strategically (MP5).

The mathematical purpose of this activity is to introduce students to curves representing normal distributions. Students compare normal curves with different means and standard deviations to determine how those statistics affect the curve. In particular, ensure students understand that normal curves are entirely defined by the mean and standard deviation: the mean defines the center of the distribution, and the standard deviation affects the spread of the distribution.