Alg+1+-+Unit+6b

//**F-LE.1.**//Distinguish between situations that can be modeled with linear functions and with exponential functions. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
 * ===**Common Core Standard(s)**===

//**A-CED.1**//. Create equations in one variable and use them to solve problems. **(create and compare linear and exponential models)**

//**F-BF.3.**// Identify the effect on the graph of replacing //f//(//x//) by //f//(//x//) + //k//, //k// //f//(//x//), //f//(//kx//), and //f//(//x// + //k//) for specific values of //k// (both positive and negative); find the value of //k// given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

//**F-IF.3.**// Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.

//**F-LE.2.**// 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).

//**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-BF.1.**// Write a function that describes a relationship between two quantities.★

Determine an explicit expression, a recursive process, or steps for calculation from a context.

//**F-LE.5.**// Interpret the parameters in a linear or exponential function in terms of a context. //**(Be able to interpret everything.)**// || ===**Mathematical Practice(s)**===


 * 1. Makes sense of problems and perseveres in solving them.**
 * 2. Reason abstractly and quantitatively.**
 * 3. Construct viable arguments and critique the reasoning of others.**
 * 4. Model with mathematics**
 * 5. Use appropriately tools strategically**
 * 6. Attend to precision**
 * 7. Look for and make use of structure**
 * 8. Look for and express regularity in repeated reasoning.** ||
 * ===**Information Technology Standard**=== || ===**Revised Bloom's Level of thinking**===

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 * Remembering **
 * Understanding **
 * Applying **
 * Analyzing **
 * Evaluating **
 * Creating ** ||

**I can...**
I can interpret the rate of change of both linear and exponential functions and explain the differences in the two.
 * F-LE.1** I can distinguish between linear and exponential functions.


 * A-CED.1** I can create and compare linear and exponential functions within context.


 * F-BF.3** I can explain the changes to a graph when constants and coefficients are changed.


 * F-IF.3** I can explain how sequences are functions.


 * F-LE.2** I can construct linear and exponential functions using arithmetic and geometric sequences.


 * F-BF.2** I can write recursive and explicit formulas from geometric and arithmetic sequences and can switch back and forth between the two types of formulas.


 * F-BF.1** I can write a functions that describes a relationship between two values.


 * F-LE.5** I can interpret the pieces of linear and exponential functions in terms of context.

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**Essential Vocabulary**
explicit formulas, recursive formulas, arithmetic sequences, geometric sequences, constant rate per unit, constant percent rate per unit

**Sample Assessments**
Mini cumulative quizzes focused on student needs Thumbs up/thumbs down/thumbs sides ways formative assessment Exit tickets Mini projects Weekly cumulative tests

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