calculate heart rate to determine level of fitness
use ratio language to describe a ratio relationship between two quantities
learn how mathematics is used in real-world applications
Common Core State Standards: 6.RP.A.1, 6.RP.A.2
Vocabulary: Target heart rate, recovery rate, resting heart rate, ratio
Materials: Per group of students: stopwatch or timer (if a classroom clock with minute hand is not available), paper, pencils; Calculating Your Recovery Rate recording sheet
1. Introduction (1 minute, whole group)
Ask students if they’ve ever wondered, When am I ever going to use this subject? and Why do I have to learn this? Then, explain that today they will watch a video in which a collegiate athletic trainer describes how he uses mathematics in his profession on a daily basis.
Ask students, What is an athletic trainer? Explain that athletic trainers are healthcare professionals who specialize in diagnosing, treating, and preventing bone and muscle injuries. They work with a wide range of people including children, soldiers, high school and college athletes, and professional athletes.
2. Real-Life Math: Athletic Trainer Video (10 minutes, whole group)
Focus students’ attention on the video by explaining that as they watch, they should listen for specific examples of the trainer’s use of mathematics in his work. Show students the video.
After watching, discuss the video. Ask students the following questions:
What is this athletic trainer’s job? (Answer: He diagnoses, treats, and helps prevent bone and muscle injuries in his athletes. He supports athletes in strengthening and conditioning programs.)
How does he use mathematics in his daily work? What are specific examples? (Answer: He needs to identify the target heart rate for each of his athlete’s training programs, interpret data from the heart monitor by looking at the graphs, plan for road trips, and make calculations for necessary equipment and supplies. He must also budget food and travel expenses and make sure that the athletes eat healthy meals and get plenty of rest.)
What is your target heart rate? Have students calculate their target heart rate by using the following:
220 – [their age] = maximum heart rate
50–85% of maximum heart rate = target heart rate. Results are expressed in beats per minute.
Stress to students that this is only an estimated range. Health history plays a major factor in determining a person’s actual target heart rate.
3. Calculating Heart Recovery Rates (10 minutes, pairs or small groups)
Students will now complete an activity to determine their hearts’ recovery rate. Divide students into groups of two to three and provide each team with a clock or timer (preferably digital) and a copy of the recording sheet. Demonstrate to students how to find their pulse points, either on their wrists or necks, review the instructions on the recording sheet, and then have them complete the activity. (Note: You may wish to lead the entire class through this activity instead of having students work in groups.)
After students have completed the activity, ask them to record their rates on an area of the board entitled Our Heart Rate Calculations.
Have students represent their resting heart rate to their target heart rate in a ratio (e.g., 65:115). How does this compare to the ratio of heart rate after exercise to heart rate during exercise?
4. Conclusion (5 minutes, whole group)
Look at the chart containing heart rate numbers. What do the numbers reveal about the class? How might this information be useful to the athletic trainer in the video? (Answers may include that the trainer could monitor our heart rates and adjust exercises based on our goals, such as strength training or building endurance.)
You may wish to ask students to find the average of the numbers, by adding and then dividing by the number of students.
Activity Extension 1: The amount of time it takes the heart rate to return to the normal resting rate is called recovery time. Recovery time is a measure of the body’s general fitness. The shorter the recovery time, the higher the fitness level. To gauge their general fitness, have students individually record the following in a journal every day for one week:
Resting heart rate
Heart rate after vigorous exercise for 3–5 minutes
Heart rate after resting for 1 minute
Heart rate every minute after, until the heartbeat returns to the resting heart rate
Time it takes to return to the resting heart rate; this is their recovery rate
You may ask students who wish to share their recovery rates with the rest of the class to do so. Then, discuss the similarities or differences in measurements.
Activity Extension 2: Knowing their target heart rate can help people exercise hard enough to get a good workout, but not so hard that it strains their heart. Target heart rate changes with age. For additional math practice, have students work in small groups to create a table showing target heart rates for ages 15–70 in 5-year increments. Give them the following guidelines to make their calculations:
Target heart rate is a range, expressed as a percentage of maximum heart rate.
To find maximum heart rate, subtract age from 220.
To determine target heart rate, calculate 50–85% of the maximum heart rate.
Charts should be labeled with the following headings: Age, Maximum Heart Rate, and Target Heart Rate Zone (50–85%).
Assign directly to your students using the code or link above, without having them log in. Simply tell your students to go to
www.pbsstudents.org and enter the Assignment Code, or click on the Assignment URL to share the assignment as a link.