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How have temperatures changed around the world? Recent years have been the hottest on record. While some see this as evidence of a dangerous trend that merits drastic action, others find little alarming about such fluctuations.
In this lesson, students use periodic functions to compare long-term average monthly temperatures to recorded monthly temperatures, evaluate evidence of climate change, and discuss possible consequences.
REAL WORLD TAKEAWAYS
Climate scientists combine temperatures from around the world to create an average monthly “global temperature” and track it over time.
In recent years, the global temperature has exceeded the long-term average global temperatures for most months.
MATH OBJECTIVES
Model a periodic phenomena (monthly temperatures) with a trigonometric function.
This complex task is best as a culminating unit activity after students have developed formal knowledge and conceptual understanding.
Algebra 2
Trig. Functions
Algebra 2
Trig. Functions
Content Standards
F.TF.5
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
F.IF.4
For a 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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
F.IF.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. (a) Graph linear and quadratic functions and show intercepts, maxima, and minima. (b) Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. (c) Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. (d) (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. (e) Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
S.ID.6
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. (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, quadratic, and exponential models. (b) Informally assess the fit of a function by plotting and analyzing residuals. (c) Fit a linear function for a scatter plot that suggests a linear association.
Mathematical Practices
MP.3
Construct viable arguments and critique the reasoning of others.
MP.4
Model with mathematics.
MP.5
Use appropriate tools strategically.
MP.6
Attend to precision.
