The purpose of this warm-up is to elicit the idea that calculating the standard deviation is very similar to calculating the MAD, which will be useful when students explore standard deviation in a later activity. While students may notice and wonder many things about these dot plots, the similarities and differences between standard deviation and the MAD as measures of variability are the important discussion points.

Ask students to share the things they noticed and wondered. 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, “Is there anything on this list that you are wondering about now?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information. If the concept of variability does not come up during the conversation, ask students to discuss this idea.

The purpose of this activity is to let students investigate what happens to the standard deviation using different data sets. The goal is for students to make conjectures about what standard deviation measures and how relative size of the standard deviation can be estimated from the shape of the distribution. In particular, students should recognize that adding or subtracting the same value from each value in the data set will change the mean by the same amount, but the standard deviation remains unchanged. Multiplying or dividing each value in the data set by the same value scales both the mean and the standard deviation by the same value.

Monitor for students who:

• Check values without much thought until the mean or standard deviation is correct.
• Use a starting set of values, then modify a few of them up or down to match the statistics given.
• Use symmetry to get the mean correct.
• Adjust the data by multiplying all of the values by a number to change the spread of the distribution to get close to the standard deviation.

Plan to have students present in this order from least to more abstract ways of thinking about the data.

The routine of Anticipate, Monitor, Select, Sequence, Connect (5 Practices) requires a balance of planning and flexibility. The anticipated approaches might not surface in every class, and there may be reason to change the order in which strategies are presented. While monitoring, keep in mind the learning goal and adjust the order to ensure that all students have access to the first idea presented (whether that be a common misconception or a different approach).

Identify students who create data sets with different types of distributions for “10 different numbers that have a mean of 1” and “10 different numbers with a standard deviation as close to 2.5 as you can get in one minute.”

The purpose of this mathematical activity is to let students investigate how the standard deviation and other measures of variability change when you add, change, or remove values in a data set. Monitor for students mentioning the concepts of shape, variability, and center. This activity works best when each student has access to statistical technology because it would take too long to do otherwise. If students don't have individual access, projecting the statistical technology would be helpful during the Launch.