HCPSS Worthwhile Math Task
Peak Heart Rates
Common Core Standard
A.CED.A.2 Create linear equations to represent relationships between quantities; graph
equations on coordinate axes with labels and scales.
MP1:
MP2:
MP3:
MP4:
MP5:
MP6:
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Common Core Algebra I, Unit 1
The Task
Workout World has the following posters displayed to help their members focus on reaching
their peak heart rates during their workouts. Age is given in years, and peak heart rate is in beats
per minute (BPM).
Age
15
20
25
30
35
40
50
60
70
MEN
Peak Heart
Rate
205
200
195
190
185
180
170
160
150
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
WOMEN
Peak Heart
Age
Rate
HCPSS Worthwhile Math Task
15
192.8
20
188.4
25
184
These posters are helpful, if a member’s exact age
30
179.6
on them. How could you help a Workout World
35
175.2
member determine their peak heart rate if it is not
40
170.8
included on the poster? Create an alternative display
50
162
would allow a member of any age to determine
60
153.2
peak heart rate.
70
144.4
appears
that
his/her
Facilitator Notes
1. Display life-sized versions of the posters in the classroom, like members would see in
their gym. Introduce the task to the students.
2. Allow students a few minutes to read the task and begin to develop a strategy for solving.
(Look for evidence of MP1 and MP2.)
3. If necessary, facilitate a classroom discussion around how you could help someone
determine their peak heart rate if their age is not included on the poster. Begin by asking
a basic question, such as “What is the peak heart rate for a 45 year old man?” To extend
thinking ask, “What is the peak heart rate for an 18 year old woman?” (Look for evidence
of MP2 and MP6.)
4. Provide students with a variety of materials, including but not necessarily limited to,
graph paper, graphing calculators, and the PETS Multiple Representations graphic
organizer. (Look for evidence of MP5.)
5. Next, have students work in pairs or small groups to create an alternative display.
Provide students with chart paper. (Look for evidence of MP1, MP3, MP4, and MP5.)
6. As groups work, circulate to monitor what strategies are being used to solve the problem.
Once groups have had an opportunity to solve the task, have groups share their displays
and strategies through a gallery walk or group presentations. (Look for evidence of MP1,
MP3, MP4, and MP5.)
7. Make sure to highlight key methods for solving, focusing on the connection between
multiple representations of linear functions including tables, equations, and graphs. (Look
for evidence of MP1, MP3, MP4, MP5, and MP6.)
Follow-Up Questions
1. Why are there separate peak heart rate posters for men and women?
2. What factors, other than gender and age, could affect peak heart rate?
3. Explain your equation. What is the y-intercept and what does it mean? What is the slope
and what does it mean?
4. Is there ever an age where both men and women have the recommended same peak heart
rate?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
Solutions
Students should see that the information in the posters is in tables and therefore look to the
remaining multiple representations of linear equations as alternative ways of sharing this
information with members at Workout World. Students may create linear equations to represent
the relationship between age and peak heart rate, or they may graph the relationship (see below).
Students may find other creative ways to display the information for members.
Graph
Another strategy is to use the data in the tables or the equations to graph the relationships. The
graph below would be a nice visual display to hang in Workout World to assist members in
determining their peak heart rate.
Relationship between Age and Peak Heart Rate
Men
Women
240
Peak Heart Rate (in beats per minute)
220
200
180
160
140
120
100
80
60
40
20
10 Public
20 Schools
30
40
60
70
80
90
100 Projects
110 has
120
Howard0 County
Office
of50Secondary
Mathematics
Curricular
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Age (in years)
Unported License.
HCPSS Worthwhile Math Task
Equations
One strategy is to use the tables on the posters to find equations that the members could use to
calculate the peak heart rate for any age.
Let x represent age in years. Let y represent peak heart rate in beats per minute. Use two ordered
pairs to calculate the slope. Then use the slope and one ordered pair to determine the y-intercept.
Men
Women
(15, 205)
(20, 200)
200  205  5
m

 1
20  15
5
y  mx  b
(15, 192.8)
(20, 188.4)
188.4  192.8  4.4
m

 0.88
20  15
5
y  mx  b
205  1(15)  b
192.8  0.88(15)  b
205  15  b
192.8  13.2  b
220  b
y   x  220 or y  220  x
206  b
y  0.88 x  206 or y  206  0.88 x
Follow Up Questions:
1. For over two decades, there was one general formula used to calculate peak heart rate,
220 minus age. In 2010, an accurate formula was released for women. For more
information, go to www.sciencedaily.com/releases/2010/06/100628170928.htm.
2. Other factors that could affect peak heart rate are genetics, overall state of health,
physical disabilities, substance abuse, and others.
3. The equation used to calculate their peak heart rate for men can be summed up by doing
220 minus your age. The equation for women represents 206 minus 88% of your age.
4. To determine the age when men and women would have the same peak heart rate, solve
the system comprised of both of the linear equations. See below where the system is
solved using substitution.
 x  220  0.88 x  206
220  0.12 x  206
14  0.12 x
x  116.6
y   x  220
y  116.6  220
y  103.3
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
It is unlikely that a person, man or woman, would live to be 116.6 years old. However, if
that would occur someday and they would be well enough to workout, the peak heart rate
for either gender would be 113.3 BPM.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.