Lesson 16

The mathematical purpose of this activity is for students to write a statistical question for dropping and catching a ruler under different conditions.

Arrange students in groups of 2.

Demonstrate how to drop the ruler and how to measure the distance dropped. Show this video if necessary.

Explain that the ruler is being held by one person at the 12 inch mark and is caught by another person just below the 7 inch mark. The distance the ruler fell is about 6 inches. For groups struggling to think of conditions that might be interesting, here are some examples to help them get started:

• Standing and sitting
• Listening to music and quiet
• Listening to a favorite song and one that is less interesting
• Releasing quickly after they are ready and waiting at least 3 seconds after they are ready before dropping

The goal of this discussion is to make sure that everyone has a statistical question about reaction time that will require collecting data from two different conditions to test.

Check student questions and assist them in creating a question that meets the requirement. Here are some questions for discussion.

• “What are your two conditions?” (Standing on one foot and standing on both feet.)
• “How are you going to collect this data?” (I will hold and drop the ruler while my partner stands on one foot. Then I will repeat this while he is standing on two feet.)
• “How many trials do you think you should do under each condition?” (At least ten)

The mathematical purpose of this activity is for students to design an experiment to answer a statistical question, to collect data, to analyze data using statistics, and to communicate the answer to the statistical question using a display. It may be helpful to have multiple groups combine to allow students to experience the different conditions for many experiments. Making statistical technology available gives students an opportunity to choose appropriate tools strategically (MP5).

Notice groups that create displays that communicate their mathematical thinking clearly, contain an error that would be instructive to discuss, or organize the information in a way that is useful for all to see.

Keep students in groups of 2. Provide each group with tools for creating a visual display. If students have access to statistical technology, suggest that it might be a helpful tool in this activity.

Explain to students that they will collect and analyze data using statistics to answer their statistical question from the warm-up.

Students will create a display showing the statistical questions, the data, a data display, and an answer to the statistical question with any supporting mathematical work.

Select groups to share their visual displays. Encourage students to ask questions about the mathematical thinking or design approach that went into creating the display. For students who had an error in their display, ask “What error do you see in the display and how would you resolve it?” (Answers vary. Sample responses:

• I noticed that they used the mean instead of the median. I would resolve it by using the median since there was an outlier
• I noticed that the IQR was calculated incorrectly. I would have used technology to verify my statistics.)

Here are questions for discussion, if not already mentioned by students:

• “Once you collected your data, how did you answer your statistical question?” (I used two different dot plots to display my data and determined that the mean was the most appropriate measure of center because my dot plot was approximately symmetric. I then calculated the standard deviation using technology because it is appropriate to use with the mean. I then compared the mean and the standard deviation for the two sets of data and determined that standing on two feet gave my partner a slightly faster reaction time and showed less variability than standing on one foot.)
• “How did you choose which measure of center and which measure of variability to use?” (I used the distribution shape to determine the measure of center. My data was skewed so I used the median. I used the IQR as a measure of variability because it is based on the median. If I had used the mean, I would have used the standard deviation.)
• “Using the context of the two treatments, what did the measure of variability tell you?” (The measure of variability told me how spread apart the results were from the measure of center I chose. It let me know how consistent the reaction time was for each treatment.)
• “Imagine that you collected data for the same treatments from all the students in the class. How would this change how you displayed or analyzed your data?” (There would be a lot of data. I would probably have to use technology to find the statistics and to create the data display. I think that I might need to use a histogram to represent the distribution of the data.)

In this activity, students use a large data set to compare the size of students with different dominant hands. Students must select a variable that best represents the size of the students and compare the two groups. By selecting the relevant variable to analyze, students are engaging in aspects of mathematical modeling (MP4). Additionally, students must choose the appropriate tools (MP5) to analyze a large data set such as this.

Arrange students in groups of 2. Distribute a copy of the blackline master to each group.

Select students to share their analysis of the data.