This activity gives students an opportunity to determine and request the information needed to assess whether the results from an experiment are either significant or due to chance groupings.

The Information Gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for information they need to solve it. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6). Students must model the sampling distributions using a normal distribution based on the mean and standard deviation (MP4).

If students use language that indicates definitive conclusions can be drawn from the data, consider asking:

• “Do we know that for sure? How can we describe our conclusions while still acknowledging our uncertainty?”

• “What was your initial assumption? Does the evidence support that assumption?”

After students have completed their work, share the correct answers and ask students to discuss the process of solving the problems. Here are some questions for discussion:

• “What questions did you ask that were helpful? Explain your reasoning.” (It was helpful to start by asking about the difference in means from the original groupings. That gave me a benchmark to measure the information about the trials in which the data was randomly regrouped.)
• “Select a piece of information from one of the data cards. How could people collect or compute that information?” (After collecting the data from the experiments, find the mean of each group and subtract them.)

Math Community

Invite 2–3 students to share the norm they chose and how it supported the work of the group or a realization they had about a norm that would have worked better in this situation. Provide these sentence frames to help students organize their thoughts in a clear, precise way:

• “I picked the norm ‘.’ It really helped me/my group because .”
• “I picked the norm ‘.’ During the activity, I realized the norm ‘’ would be a better focus because .”

This activity is helpful for students to better understand normal distributions, how to understand the relative extremity of values on a normal distribution, and connections between areas under a normal curve.

In this activity, students explore the use of tables to find the area under a normal curve bounded by certain values. Students are first introduced to z-scores and then use a table to find the area under the normal curve that is less than the value associated with that z-score.

If students struggle to identify the area given by the z-score table, consider asking:

• “What is the total area under the normal curve?”

• “What do we know about a region under the curve that has an area greater than 0.5?”

The purpose of the discussion is for students to understand how to use a table to find areas under a normal curve.

Invite students to share their solutions for all of the questions, including their reasoning for the area under the normal curve between 142 and 149 grams.

Some additional questions for discussion:

• "Why are all the areas for positive z-scores greater than 0.5?" (Because positive z-scores represent values greater than the mean and the mean is the center of the distribution, at least half of the area is less than the value.)
• "Remember that the area under the entire normal curve is 1. How could you find the area of the region greater than a value that has a z-score of 0.95?" (The area under the normal curve and less than the value with a z-score of 0.95 is 0.8289. Because the entire area is 1 and , the area greater than that value is 0.1711.)