Appendix on Implementing District Standards
My school follows the California Common Core State Standards for Mathematics (CCSSM). The following standards for Integrated Mathematics I are touched upon throughout this unit:
Quantities (N-Q):
Reason quantitatively and use units to solve problems.
1. Use units as a way to understands problems…; choose and interpret units consistently in formulas…
Students will have to identify units to successfully plug values into exponential formulas from word problems.
Creating Equations (A-CED)
Create equations that describe numbers or relationships.
2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Students will be creating exponential functions with the variables y or f(x) and x. Students will graph these functions by solving for individual points which they will compile into a table and graph.
Interpreting Functions (F-IF)
Interpret functions that arise in applications in terms of the context.
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 the 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.
Students will identify key features of exponential functions; students will use academic vocabulary to explain the relationship between the x and y-values of exponential functions.
6. Calculate and interpret the average rate of change of a function (presented…as a table) over a specified interval…
Students will use the tables they created and will identify the rate of change from these tables; they will identify both the change in x and the change in y to determine the overall rate of exponential growth or decay.
Analyze functions using different representations.
7. Graph functions expressed symbolically and show key features of the graph…
- Graph exponential…functions, showing intercepts and end behavior…
Students will graph exponential functions; they will be able to identify intercepts and end behavior, and will be able to explain what this means for the function in its given context.
Linear, Quadratic, and Exponential Models (F-LE)
Construct and compare linear…and exponential models to solve problems.
1. Distinguish between situations that can be modeled with linear functions and with exponential functions.
Students will have to identify whether a given word problem represents a linear or exponential function; it is imperative that they come away from the unit with this understanding to mitigate the effects of exponential growth bias in public health and other consequential matters.
2. Construct…exponential functions…given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Students will have to construct exponential functions, using the three exponential function formulas, from word problems, tables, and graphs.
3. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly…
Students will graph both linear and exponential functions on the same graph; students will realize that the exponential function, despite growing at a much slower rate, will eventually surpass the linear function.
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