Exploring Real-World Data Lesson Seed
Summarize, represent, and interpret data on quantitative variables.
S.ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the
variables are related. (Cross-cutting)
a. Fit a function to the data; use functions fitted to data to solve problems in the context of
the data. Use given functions or choose a function suggested by the context. Emphasize
linear and exponential models.
Create equations that describe numbers or relationships.
A.CED.A.2 Create equations in two or more variables to represent relationships between
quantities; graph equations on coordinate axes with labels and scales. (Cross-cutting)
MP2:
MP3:
MP4:
MP7:
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Common Core Algebra II, Unit 1
Teacher’s Notes:
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For the warm up, students will need to assign a value to minimums or maximums to give
the range. They will use this activity to group for the lesson.
Have students who circled linear raise their hand. If more than 3-4 students circled
linear, divide them by positive/negative slope or y-intercept (or randomly if you wish.)
Repeat with quadratic, cubic, polynomial, exponential, etc. You may have to combine
function types in only 1-2 students circled that type.
The Exploring Real World Data packet was modified from HCPSS Algebra II: A
Function Approach, Unit 1.
Students may need to review how to enter and see a scatter plot on the calculator.
Encourage them to try different models for the data, and use correct vocabulary in their
descriptions.
For the student presentation you can use a document camera to show the graphs, do a
gallery walk of the different graphs, or have them plot the graphs on poster size graph
paper.
Warm-Up:
Make a sketch of 4 different types of functions from the function family, and label the type that
you drew. Give the domain and range for each of the functions that you drew. Assign
appropriate numbers when needed.
Circle one of the four graphs. Use the circled graph type to group for the lesson. Once in the
groups, share the selected sketch and discuss the domain and range for each.
Lesson Task/Activity:
Have students form groups of 3 to 4. Each group will be given 2 Data sets from the Exploring
Real World Data activity in the HCPSS Algebra II: A Function Approach packet. Students will
plot their points on the graph paper and in their calculators. Each group needs to select a
function that best represents the data, and explain why they choose that function type. They will
then find the regression equation for the data. The Questions for Exploring Real World Data
should be divided up to the appropriate groups. Each group will present their findings.
( Look for evidence of MP2, MP3, MP4 and MP7)
Closure:
What limitations do the regression equations have when answering questions about the data?
Does the regression equation have to match the real world data?
Is there a better model for any of the data sets? Explain.
(Look for evidence of MP2 and MP3)
Solutions:
The solutions below are one sample curve of best fit. Depending on the data, students may be
able to justify more than one function to model the data.
Data Set 1: Exponential
best answer: y  .0048(1.1185)x
residuals plot most random of all plots
Data Set 2: Exponential
x
Best answer: y  .0738 1.0111
residuals plot does not show a pattern
Data Set 3: Quadratic
Best answer: y  8400.894x 2  33319003.92x  3.037  1010
Data Set 4: Quadratic
Best answer: y  .0286x 2  115.42x  116552.7229
Data Set 5: Cubic
Best answer: y  .0002x 3  .1625x 2  53.204x  5774.781
Data Set 6: Logarithmic
Best answer: y  104.9814  7.2242 ln x
Data Set 7: Quadratic
Best answer: y  .0826x 2  494.2909x  986473.1417
Data Set 8: Linear
Best answer: y  2.1467x  110.565
Data Set 9: Quartic
Best answer: y  216.1021x 4  1733735x 3  5215993136x 2  6.9744  1012 x  3.4971
Data Set 10: Quartic
best answer y  36.9468x 4  356.7728x 3  1324.361x 2  2351.2379x  1998.5833