Focusing Lens(es) Modeling Standards and Grade MA10-GR.HS-S.1-GLE.2 Level Expectations MA10-GR.HS-S.2-GLE.2 Addressed in this Unit MA10-GR.HS-S.2-GLE.3 MA10-GR.HS-S.2-GLE.4 Inquiry Questions What are the parameters that affect gas mileage in a car and how would you model them? (MA10-GR.HS-S.2-GLE.2-EO.b.i) (Engaging- What are the consequences of a population that grows exponentially? Debatable): Unit Strands Algebra: Reasoning with Equations and Inequalities Algebra: Creating Equations Algebra: Seeing Structure in Expressions Functions: Interpreting Functions Functions: Linear and Exponential Models Concepts Models, quantity, growth, decay, constant rate of change, constant rate of growth, functions, linear functions, exponential functions, exponentially, linearly, quadratically, polynomial function, arithmetic sequence, geometric sequence, relationships, tables, graphs, equations, parameters, equations, inequalities, real world contexts Generalizations Guiding Questions Factual Conceptual Understand My students will that… How do you determine from an equation whether an Why are differences between linear and exponential Linear and exponential functions provide the means to exponential function models growth or decay? functions visible in equations, tables and graphs? model constant rates of change and constant rates of How do you determine whether a situation can be Why does a common difference indicate a linear function growth, respectively (MA10-GR.HS-S.2-GLE.2-EO.a) modeled by a linear function, an exponential and common ratio an exponential function? function, or neither? What are typical situations modeled by linear functions? What are typical situations modeled by exponential functions? A quantity increasing exponentially eventually exceeds a How does the rate of growth in linear and exponential Why can so many situations be modeled by exponential quantity increasing linearly or quadratically. functions differ? growth? How can you determine when an exponential function Why is important to consider the limitations of an will exceed a linear function? exponential model?
Focusing Lens(es) Modeling Standards and Grade Level Expectations Addressed in this Unit MA10-GR.HS-S.1-GLE.2 MA10-GR.HS-S.2-GLE.2 MA10-GR.HS-S.2-GLE.3 MA10-GR.HS-S.2-GLE.4 Inquiry Questions (Engaging- Debatable): What are the parameters that affect gas mileage in a car and how would you model them? (MA10-GR.HS-S.2-GLE.2-EO.b.i) What are the consequences of a population that grows exponentially? Unit Strands Algebra: Reasoning with Equations and Inequalities Algebra: Creating Equations Algebra: Seeing Structure in Expressions Functions: Interpreting Functions Functions: Linear and Exponential Models Concepts Models, quantity, growth, decay, constant rate of change, constant rate of growth, functions, linear functions, exponential functions, exponentially, linearly, quadratically, polynomial function, arithmetic sequence, geometric sequence, relationships, tables, graphs, equations, parameters, equations, inequalities, real world contexts Generalizations My students will Understand that… Guiding Questions Factual Conceptual Linear and exponential functions provide the means to model constant rates of change and constant rates of growth, respectively (MA10-GR.HS-S.2-GLE.2-EO.a) How do you determine from an equation whether an exponential function models growth or decay? How do you determine whether a situation can be modeled by a linear function, an exponential function, or neither? What are typical situations modeled by linear functions? What are typical situations modeled by exponential functions? Why are differences between linear and exponential functions visible in equations, tables and graphs? Why does a common difference indicate a linear function and common ratio an exponential function? A quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically. How does the rate of growth in linear and exponential functions differ? How can you determine when an exponential function will exceed a linear function? Why can so many situations be modeled by exponential growth? Why is important to consider the limitations of an exponential model?