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# A2-A-1-2

last edited by 5 years, 1 month ago

A2.A.1.2 Represent real-world or mathematical problems using exponential equations, such as compound interest, depreciation, and population growth, and solve these equations graphically (including graphing calculator or other appropriate technology) or algebraically.

In a Nutshell

A variety of real-world applications involving exponential growth or decay will be represented mathematically.  Students will be able to solve equations algebraically or using graphing utilities to answer the question posed in context of the situation.

## Teacher Actions

• Students will develop strategies for problem solving by finding methods and discussing those methods that verify their solutions to exponential growth and decay problems. They will answer in context and will always question the reasonableness of their solutions.

• Students will develop a conceptual understanding of how and when to apply and use the mathematics they know to solve exponential growth and decay problems.

• Students will develop a productive mathematical disposition and hold the belief that mathematics is sensible,as they identify and solve exponential growth and decay problems in their world around them. They will persevere and become resilient, effective problem-solvers.

• Implement tasks involving real world exponential problems that provide multiple entry points through the use of varied tools and representations, these tasks should require a high level of cognitive demand, and encourage students to use varied approaches and strategies to make sense of and solve the tasks.

• Facilitate meaningful mathematical discourse about the application of real life exponential problems through opportunities for exploring and solving problems that build on and extend their current mathematical understanding, and provide students with opportunities to use their own reasoning strategies and methods for solving these problems.

• Support productive struggle as students use, discuss, and make connections, and ensure progress toward a deep understanding of exponential models by making explicit connections to student approaches and reasoning.

## Misconceptions

• Know how to interpret a real-world situation into either an exponential growth or decay, i.e. compound interest is growth; half-lives are decay.

• The growth rate must be added to 1 in an exponential growth situation, and subtracted from 1 in an exponential decay situation.

• Know how to apply equations for varied applications involving exponential growth or decay.

• Be able to choose an efficient method to solve real world exponential problems and come to a realistic solution.

Conceptual:

• Students confuse exponential growth and exponential decay when reading a real-world situation.

• Students confuse situations that grow exponentially in a negative direction with exponential decay.

Procedural:

• Students forget to represent percentages in the growth/decay rate as decimals.