Lesson 16

The purpose of this activity is to get familiar with the process of finding heart rate and collecting some initial data for the experiment in the next activity.

Tell students they will find their pulse as part of an experiment to determine if counting while exercising affects heart rate. Demonstrate the process of finding your pulse for the class. Count the number of beats you feel in 10 seconds. Multiply the value by 6 to find your heart rate in beats per minute (bpm). Distribute stopwatches or instruct students to open a stopwatch app on an internet-enabled device by searching for "stopwatch" in an internet browser.

The goal of this activity is for students to measure their resting heart rate and to begin thinking about how it changed after some deep breaths with their eyes closed.

Here are some questions for discussion:

• “How could we determine a typical resting heart rate for the class?” (We could find the mean.)
• “Raise your hand if your heart rate decreased after the deep breaths with your eyes closed.”
• “What was the treatment in this experiment?” (The treatment was taking deep breaths and having your eyes closed.)
• “What are some other reasons that your heart rate may have changed?” (I was nervous that I would take my pulse wrong.)

The mathematical goal of this activity is for students to collect and summarize data from an experiment. Students will measure their heart rate after doing a light exercise and use the difference from their resting heart rate as data to analyze in a later activity.

Arrange students in the 2 groups created at random in the activity Get Ready to Experiment. Tell students, “One group will count out loud while exercising and the other group will remain silent while exercising. Everyone will take their pulse silently after the exercising is finished.” For the exercise, consider asking the students to do 30 jumping-jacks or running in place for 1 minute. The intensity should be such that it raises student heart rates quickly without making them overly sweaty. Adjust the time or level of exercise to meet the needs of your class.

Collect the differences in heart rate from each student and keep them separated by groups. Display the results for all to see. These results will be used later in the lesson.

The goal of this discussion is for students to think about how to analyze the data from the two groups. Here are some questions for discussion:

• “How could you graphically represent the data?” (You could make a histogram showing the distribution of the data from each group.)
• “What are some ways you could analyze the data?” (You could calculate and compare the mean and standard deviation of each data set, or compare the shapes of the two histograms.)
• “How would you find a randomization distribution for this data?” (You could record all of the values in a spreadsheet then choose half of them at random to be the counting group and the other half to be the silent group. Then you would find the means of those two groups and subtract them. You would repeat this many times.)

The mathematical goal of this activity is for students to collect and summarize data from an experiment. Students measure their heart rates under different conditions to collect data for analysis in a later activity.

Rearrange students into 2 new randomly selected groups. Tell students they will do a similar experiment, but this time one group will do 30 jumping-jacks while the other group will just wave their arms 30 times and not jump or move their legs. Ask students if they think this treatment will affect the results of the experiment.

Collect the differences in heart rate from each student and keep them separated by groups. Display the results for all to see. These results will be used in the next activity.

The mathematical purpose of this activity is for students to perform a randomization experiment and analyze the results. Students use the difference in heart rates for the two experiments they did to determine whether the treatment is the likely cause of the difference between the two groups. In most cases, students should find that the difference in mean heart rates from The Counting Experiment should not be significant, but that the difference in mean heart rates for The Flapping Experiment should be significant.

Arrange students in groups of 2. Assign half of the groups to work with the data from The Counting Experiment and the other half of the groups to work with the data from The Flapping Experiment.

Provide access to devices that can run GeoGebra or other statistical technology.

Allow students to work the first three questions and then pause to tell students “You are going to use a randomization distribution to analyze the data.” Then ask, “How did we do this in the previous lesson?” (We divided 10 students into two groups of 5 and then rearranged them into two new groups of 5 by selecting names at random from a bag.) Tell students to read question 4 and ask if they have questions. After question 4, collect class data from the simulations and display a histogram of the results for all to see.

Students may be confused about which values they are measuring and analyzing in the data. The original data is already a difference in heart rates between resting and exercise. Then, means of those differences are found. Then, differences between the means of the groups are analyzed. It may help students to keep track of the different levels of information that are used for this analysis if examples of the information are displayed in separate places so that the values students are currently working with can be pointed out.

The goal of this discussion is for students to share their analysis of the results of the randomization experiment. For groups that are too small to create a good histogram, display the example here for all to see, otherwise display the histogram from the class data.

Here are some questions for discussion:

• “Where does the difference between the mean heart rates of the 2 treatment groups fall in the randomization distribution?” (For The Counting Experiment, it falls right in the middle which means it is very likely that the difference occurred by chance. For The Flapping Experiment, it is far from the typical values which means it is very likely that the difference is not due to chance.)
• “What size difference between the mean heart rates of the 2 treatments would cause you to conclude that the difference did not occur by chance? Explain your reasoning.” (For The Counting Experiment, I think a difference greater than 8 or less than -8 would have allowed me to say it did not occur by chance. This is because most of the values resulting in the randomization distribution were greater than -8 or less than 8. For The Flapping Experiment, I think a difference greater than 10 or less than -10 would have allowed me to say it did not occur by chance.)
• “Do you think counting while exercising affects heart rate? Explain your reasoning.” (I do not think it affects heart rate because the small difference in means we found is likely to happen due to chance alone.)
• “Do you think doing only part of the exercise affects heart rate? Explain your reasoning.” (I do think it affects heart rate because the relatively large difference in means we found is not likely to happen due to chance alone.)
• “Were these experiments failures? Explain your reasoning.” (No, they are not failures. We found evidence that counting after exercise did not significantly affect heart rate. Just because we did not see a change does not mean that the experiment failed.)