HCPSS Worthwhile Math Task
What’s Your Weather?
Common Core Standard
F.IF.B.4 For a quadratic function that models a relationship between two quantities, interpret key
features of graphs and tables in terms of the quantities, and sketch graphs showing key features
given a verbal description of the relationship.
MP2:
MP3:
MP4:
MP5:
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Common Core Traditional Pathway: Algebra I, Unit 3
The Task
A new student from Cape Town, South Africa has just joined your class in January. He shows
up to class wearing shorts and a t-shirt. He doesn’t understand why his teacher and classmates
are asking him about his choice of clothes. Your math teacher decides to make this a “teachable”
moment. Your class needs to use the data tables showing the monthly average high temperatures
of Cape Town and Baltimore to discover what your math teacher recognizes as a mathematical
relationship.
Baltimore,
Cape Town,
Month
Maryland
South Africa
Jan
41°F
77°F
Feb
45°F
78°F
March
54°F
76°F
April
65°F
72°F
May
74°F
67°F
June
83°F
64°F
July
87°F
62°F
August
85°F
63°F
Sept
78°F
65°F
Oct
67°F
69°F
Nov
56°F
72°F
Dec
45°F
75°F
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
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HCPSS Worthwhile Math Task
1. In L1, enter the numerical number for the months January-December (ex. January-1,
February-2, etc.)
2. In L2, enter the average temperature for each month for Cape Town/Baltimore.
3. Turn on the stat plot and adjust your viewing window. What viewing window did you
use? How did you determine the window?
4. What shape does the data suggest? Explain why you think the data makes this shape.
5. Plot your data on your own graph paper. Label your x- and y-axis according to your data.
6. Does the graph open up or down? What does this suggest about the value of a in the
equation?
7. Using the STAT CALC feature, find the equation of the best-fit curve for the data. Write
the equation below. Did you use LinReg or QuadReg to find the equation? Why?
8. Graph the equation in your viewing window. Sketch this curve on the same graph with
your weather data.
9. Is this the best-fit curve for the data? Explain your thinking.
10. Do you think the maximum or minimum value of the curve will be one of the ordered
pairs from the weather data? Why or why not?
11. Find the vertex using your calculator. Was this point from your weather data?
12. Find the equation for the axis of symmetry.
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
13. Using your equation, predict the weather for the middle of September. Show your
work. Using your graph, predict the weather for the middle of September. Did you
arrive at the same answer? Why or why not?
Facilitator Notes
After introducing the task, divide the students into groups of 3-4. Have half the groups plot the
points for Baltimore and the other half for Cape Town, South Africa on chart paper (steps 1-6).
(Look for evidence of MP4 and MP5.) Come back together to discuss resulting graphs. Focus
discussion on the similarities and differences between the resulting graphs. (Look for evidence
of MP2.) Students will get back into their groups and complete steps 7-13. Have groups who
worked on the same cities data share out their findings. Discuss the vertex, equation of the axis
of symmetry, curve of best fit found by each group. How were they discovered from the
resulting graphs? What method enabled groups to determine the curve of best fit most
appropriate for their data? (Look for evidence of MP2, MP3, and MP5.) Have students consider
why these two cities reflect the quadratic functions opening in opposite directions. Would
similar data occur if the new student were from another city in the U.S.A.? How is this data
different from linear or exponential patterns?
Follow-Up Questions
1. Using your equation, predict the weather for the middle of March. Show your work. Using
your graph, predict the weather for the middle of March. Did you arrive at the same answer?
Why or why not? (Look for evidence of MP3 and MP4.)
2. By the end of the school year, you and your new classmate have become good friends. His
family has invited you to visit them during your summer vacation in July. What kinds of
clothes should you pack based on your research? (Look for evidence of MP2.)
Suggested Homework:
Homework: On ½ sheet of poster board, include all the information listed below for a different
city. Be sure to label your information clearly. Points will be given towards the creativity and
neatness of the presentation as well as accurate data with curve of best fit.
1. Go to CityRating.com, click on weather history at the top of the screen and choose a city.
2. Print out or make a table of average temperatures.
3. On graph paper, plot the ordered pairs for the average temperature of each month
including appropriate labels
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
4. Using your calculator, calculate the best-fit curve to your data and include this equation
in your presentation. Sketch this line on your graph.
5. Label the axis of symmetry and vertex on your curve. (Look for evidence of MP4.)
Solutions
3) X-axis labeled with months and y-axis labeled with Average High Temperature (°F)
Baltimore, MD
Window:
For my x-axis I needed to see numbers 1-12 so I went from 0 to 13 counting by 1s to see each
point clearly. Since the lowest temperature for Baltimore was 41°F and the highest was 87°F I
set my y-axis from 40 to 90 counting by 5s.
X-axis labeled with months and y-axis labeled with Average High Temperature (°F)
Cape Town, S Africa
Window:
For my x-axis I needed to see numbers 1-12 so I went from 0 to 13 counting by 1s to see each
point clearly. Since the lowest temperature for Cape Town was 62°F and the highest was 78°F I
set my y-axis from 60 to 80 counting by 5s.
4) The shape seems to be parabolic. This make sense since the temperatures either start at a high
value then go down to a minimum before going back up (Cape Town) or start at a low value then
go to a maximum before going back down (Baltimore).
6) Baltimore: the graph opens down so a is negative.
Cape Town: the graph opens up so a is positive.
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
7) Since we determined the graph was parabolic, we used a QuadReg to get the following
equation
Baltimore:
Cape Town:
y  1.4 x 2  19.41x  14.81
y  0.44 x 2  6.28 x  87.18
8) Graphs with exact and rounded equations graphs on the data:
Baltimore:
Rounded:
Cape Town:
Rounded:
9) While the curve does not match perfectly it does seem follow the shape of the data. Students
may or may not agree that this is the best curve for the data.
If students see the connection to Unit 3:
Doing a residual plot of Baltimore’s data with the Quadratic curve of best fit shows this graph:
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
Clearly the Quadratic regression is not the best fit since there is
a pattern in the residuals. This may lead into the discussion of what happens to the data the next
year. Hopefully the students recognize that the data will repeat giving us a periodic graph. This
lesson can be modified later when sinusoidal graphs are discussed in future math courses. For
now have students use the quadratic model for the year’s data.
10) Since the curve does not match the data perfectly we will not see the max or min as one of
the ordered pairs of weather data.
11) The vertex for Baltimore is (6.93, 82.09). This was not a point from our weather data.
The vertex for Cape Town is (7.14, 64.77). This was not a point from our weather data.
12) The equation for the axis of symmetry for Baltimore is x = 6.93. The equation for the axis of
symmetry for Cape Town is x = 7.14.
13) Answers may vary for the prediction from their graphs. Using their equations their
predictions should be similar to Baltimore 72.9°F or Cape Town 67.2°F.
Baltimore:
y  1.4 x 2  19.41x  14.81
Cape Town:
y  1.4(9.5) 2  19.41(9.5)  14.81
y  0.44(9.5)2  6.28(9.5)  87.18
y  72.855
y  67.23
y  0.44x2  6.28x  87.18
Follow up Question Solutions:
1) Answers may vary for the prediction from their graphs. Using their equations, their
predictions should be similar to Baltimore 65.6°F or Cape Town 70.6°F.
Baltimore:
y  1.4 x 2  19.41x  14.81
Cape Town:
y  1.4(3.5) 2  19.41(3.5)  14.81
y  0.44(3.5)2  6.28(3.5)  87.18
y  65.595
y  70.59
y  0.44x2  6.28x  87.18
2) Answers may vary but should include evidence that in June or July the temperature will be in
the low 60’s and should bring clothes that they would wear with that weather.
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.