## Heartifacts

- Lesson

This lesson emphasizes the connections between science and mathematics by using a performance, or authentic, assessment format. Students explore applications involving their own heart. This activity involves students in interpreting factual information in a variety of problem-solving situations. Students also create and solve an original problem.

Distribute a copy of the Heartifacts Activity Sheet to each student.

Have the students read and discuss the facts about the heart, as stated at the top of the activity sheet. They will use these facts to answer questions 1‑4 on the activity sheet. Discuss students' responses and how they arrived at their answers. Responses should fall in the range of answers given at the conclusion of the Instructional Plan. For question 2, discuss ways to use mental computation to determine one-half of 1 percent of a person's weight. Emphasize that the students should determine how they arrive at their estimate for problem 3.

Finally, have students use the facts to create an original problem of their own. They should solve the problem and then have a friend try to solve it.

*Answers to the Activity Sheet:*

- Seventy beats per minute equals 100,800 times a day, or 36,288,000 times a year; 100 beats per minute equals 144,000 times a day, or 52,560,000 times a year. Both responses are based on a 365-day year.
- Answers will vary according to students' weight.
- About 7,500 quarts each day.
Estimate: The number of quarts pumped per hour is 5 × 60 = 30,024 to close to 25 and 25 × 3 = 75, so 25 × 300 = 7,500. Or, about 6,500 to 7,300 liters each day. Students might round the number of liters pumped per hour from 4.7 to 5 and the number of hours in a day to 25, so 5 × 60 = 300, and 300 × 25 = 7,500. Since two numbers, 4.7 and 24, were rounded up, the 7,500 estimate should be lowered, say, to 6,500 to 7,300.

- After exercise, the heart would beat 112 ‑ 122 times in one minute based on 70 beats per minute at rest or 160 ‑ 175 times in one minute based on 100 beats per minute at rest.
- Answers will vary.

### References

- Lisa M. Passarello and Francis (Skip) Fennell, "IDEAS: Every Beat of Your Heart." The Arithmetic Teacher, 39, 1 (February 1992) 32-39.
- American Heart Association. Exercise and Your Heart. Dallas, Texas.: The Association, 1990.

Extensions

- Research other fast facts about the heart and design a fast-facts booklet with problem for the students to solve. Display the booklets in the classroom.
- Have the students consult an aerobics or fitness instructor to determine a desirable target heart rate when exercising. Note that the maximum heart rate for one minute is estimated by subtracting a person's age from 220. The target heart rate for exercise is denied by the American Heart Association as 60 - 75 percent of the maximum heart rate. The target heart rate is high enough for conditioning but well within safe limits. Exercising at about 75 percent of the maximum heart rate gives the heart and lungs little conditioning.

### Learning Objectives

- Interpret factual information.
- Solve related problems.
- Create and solve an original problem.

### NCTM Standards and Expectations

- Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.

- Use observations about differences between two or more samples to make conjectures about the populations from which the samples were taken.