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

# Sequences and Functions

## Common Core Says...

In descriptive modeling, a model simply describes the phenomena or summarizes them in a compact form. Graphs of observations are a familiar descriptive modelâ€”for example, graphs of global temperature and atmospheric CO2 over time. Analytic modeling seeks to explain data on the basis of deeper theoretical ideas, albeit with parameters that are empirically based; for example, exponential growth of bacterial colonies (until cut-off mechanisms such as pollution or starvation intervene) follows from a constant reproduction rate. Functions are an important tool for analyzing such problems.

Common Core Modeling

## Big Picture Lesson Planning for the Common Core

#### Week #18 (Understanding Interest)

• Distinguish between linear and exponential function (F.LE.1b and c)
• Prove that a function is either linear or exponential (F.LE.1a)
• Write a function that describes a relationship between two quantities (F.BF.1a)

#### Week #19 (Sequences)

• Recognize that sequences are functions, sometimes defined recursively (F.IF.3)
• Write arithmetic and geometric sequences both recursively and with an explicit formula (F.BF.2)
• Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (F.LE.2)

## Lesson Ideas

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

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## Common Core Standards

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.BF.1a Write a function that describes a relationship between two quantities. (Emphasize linear, quadratic, and exponential functions). Determine an explicit expression, a recursive process, or steps for calculation from a context. Video explaination

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

F.LE.1b 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.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).

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