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The Algebra 1 Teacher's guide to the Common Core State Standards for Mathematics.

# Linear and Exponential Models

## Common Core Says...

�The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction.

Mathematice Common Core Standards

## Big Picture Lesson Planning for the Common Core

Students must be able to compare and make judgements. This includes making informed decisions about money, career, housing, and medicine just to name a few.

#### Week #23 Comparing Linear and Exponential Functions

• Prove that linear functions grow by equal differences over equal intervals; and that exponential functions grow by equal factors over equal intervals. (F.LE.1.a)
• Identify linear and quadratic functions (F.LE.1.b & c)
• Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. (F.LE.3)

#### Week #24 Combining Linear and Exponential Functions

• Combine functions using arithmetic (F.BF.1.b)
• Understand situations using these combinations (F.BF.1.b)
• Interpret the parameters in a linear or exponential function in terms of a context. (F.LE.5)

## Lesson Ideas

All of these resources and more can be found in the livebinder below.

## Common Core Standards

F.BF.1.b Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.?

F.LE.1.a Prove that linear functions grow by equal differences over equal intervals; and that exponential functions grow by equal factors over equal intervals.

F.LE.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

F.LE.1.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

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