Construct and compare linear and exponential models and solve problems
Distinguish between situations that can be modeled with linear functions and with exponential functions.
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4 - Distinguish (between situations modeled with linear functions and with exponential functions)
6 - Prove (linear functions grow by equal differences over equal intervals [a])
6 - Prove (exponential functions grow by equal factors over equal intervals [a])
3 - Recognize (situations in which one quantity changes at a constant rate per unit interval relative to another [b])
3 - Recognize (situations in which a quantity grows or decays by a constant percent per unit interval relative to another [c])
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4 - I can distinguish between situations that can be modeled with linear functions and with exponential functions.
6 - I can prove linear functions grow by equal differences over equal intervals [a].
6 - I can prove exponential functions grow by equal factors over equal intervals [a].
3 - I can recognize situations in which one quantity changes at a constant rate per unit interval relative to another [b].
3 - I can recognize situations in which a quantity grows or decays by a constant percent per unit interval relative to another [c].
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A. Linear and exponential functions can be used as models for problem solving.
B. Linear functions change at a constant rate.
C. Functions can be classified by the type of growth they exhibit.
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A.1 How can I tell when to use a linear model and when to use an exponential model?
B.1 How can I tell that a function is linear?
B.2 What does the slope of a linear function tell me?
C.1 How can I tell whether a function is linear, quadratic, or exponential?
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Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
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6 - Construct (linear and exponential functions given a graph)
6 - Construct (linear and exponential functions given a description of a relationship)
6 - Construct (linear and exponential functions given two input-output pairs)
6 - Construct (arithmetic and geometric sequences given a graph)
6 - Construct (arithmetic and geometric sequences given a description of a relationship)
6 - Construct (arithmetic and geometric sequences given two input-output pairs)
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6 - I can construct linear and exponential functions given a graph.
6 - I can construct linear and exponential functions given a description of a relationship.
6 - I can construct linear and exponential functions given two input-output pairs.
6 - I can construct arithmetic and geometric sequences given a graph.
6 - I can construct arithmetic and geometric sequences given a description of a relationship.
6 - I can construct arithmetic and geometric sequences given two input-output pairs.
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A. Different types of models can be used to represent different types of functions.
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A.1. How do I know what type of model to use?
A.2. How do I know what type of function to use?
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Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
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1 - Observe (using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly)
1 - Observe (using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing quadratically)
1 - Observe (using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing as a polynomial function)
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1 - I can observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly.
1 - I can observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing quadratically.
1 - I can observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing as a polynomial function.
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A. Increasing exponential functions will exceed all other increasing functions at some point.
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A.1 What is the difference between exponential, linear, quadratic, and polynomial functions?
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For exponential models, express as a logarithm the solution to abct = d where a,c, and d are numbers and the base b is 2,10, or e; evaluate the logarithm using technology.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
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Exponential models
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2 - Express (exponential models as logarithms to solve ab^ct = d where a, c, and d are numbers and the base b is 2, 10, or e)
2 - Evaluate (logarithms using technology)
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2 - I can express exponential models as a logarithm the solution to ab^ct = d where a, c, and d are numbers and the base b is 2, 10, or e.
2 - I can evaluate the logarithm using technology.
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A. Exponential models can be expressed as logarithms.
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A.1 What is the connection between exponential and logarithmic functions?
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Interpret expressions for functions in terms of the situation they model
Interpret the parameters in a linear or exponential function in terms of a context.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
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Functions
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2 - Interpret (parameters in a linear function in terms of a context)
2 - Interpret (parameters in an exponential function in terms of a context)
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2 - I can interpret the parameters in a linear function in terms of a context.
2 - I can interpret the parameters in an exponential function in terms of a context.
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A. There are certain parameters that function values must fall within in many types of problems.
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A.1 When do I need to be concerned about parameters?
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