This activity focuses on another complex calculation: the number of times a person’s heart has beaten so far in their lifetime. Unlike calculating an exact age, hearts do not beat at a constant rate. Because of this, the answer will be a reasonable estimate and knowing the precise start and end times is unimportant because a few minutes or hours will not significantly impact the answer. Students model with mathematics when they decide what quantities are important and make simplifying assumptions about how to determine the number of heart beats (MP4). 

Direct students’ attention to the reference created using Collect and Display. Ask students to share their process and solution. Invite students to borrow language from the display as needed and update the reference to include additional phrases as they respond. 
Continue to reference the display while discussing students’ strategies and difficulties with questions such as:

• “How did you estimate how often your heart beats?” (by checking my pulse)
• “Is your heart rate always the same?” (No, it is faster when I exercise and slower when I sleep.)
• “Did you use the information you found for your age?” (No because I only have an estimate for my pulse or yes because I already had the information available.)

Time permitting, students can be encouraged to check their pulse while resting and then again after a short amount of exercise (jumping jacks, running in place, push ups). This gives them an idea of the variability involved in how frequently a person's heart beats.

The calculation of the number of heartbeats is only an estimate. One way this can be communicated is with the way the final answer is reported. An answer of 524,344,566 would not be appropriate because that makes it look like it is an exact answer. An answer of 500,000,000 makes it clear that only an estimate is being made. Alternatively, students might say that the number of heartbeats is between 400,000,000 and 700,000,000, where the estimate of 400,000,000 comes from the low value of 60 beats per minute, and the estimate of 700,000,000 comes from the high value of 100 beats per minute.

Students estimate how many hairs they have on their head. Although there is a definite number of hairs on each student’s head, finding this number exactly is not feasible. While it is a much smaller number than the number of heartbeats in a student’s lifetime, it is still too large to count and, even if it could be counted, all of those hairs would need to be cut off to do so! An additional geometric layer of estimation comes into play in this task as students need to estimate the surface area of part of their heads. As students plan their estimation strategy, they make sense of the problem and persevere in solving it (MP1). If one or more students in the class are bald or are otherwise sensitive about their hair, consider asking them to estimate the number of hairs on another student’s head.

Invite students to share their answers and methods. Consider asking the following questions:

• “Why is it challenging to find the exact number of hairs on your head?” (There are too many to count, and they are too small to count accurately. The number changes as time goes by.)
• “How can you estimate the number of hairs on your head?” (Estimate the area of the part of the head covered by hair. Try to find how many hairs there are on a small part of the head.)
• “How did you estimate the area of your head?” (Approximated area with a circle. Covered the head with little pieces of paper [sticky notes] and added up their areas.)

This is a situation where there is a definite number of hairs on a head, but because they are so small (and because they are on a head), this number can not be calculated exactly. Fortunately, for almost any purpose, an estimate will do.