The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways.

The purpose of this task is to provide students with an opportunity to explain fraction equivalence through visual models in a particular example.

Starting with explicit cases, this task derives the formula for an arbitrary circle in the plane.

This task serves as an introduction to the family of sinusoidal functions. It uses a desmos applet to let students explore the effect of changing the parameters in y=Asin(B(x−h))+k on the graph of the function.

This task requires students to use the fact that the value of an exponential function f(x)=a⋅bx increases by a multiplicative factor of b when x increases by one. It intentionally omits specific values for c and d in order to encourage students to use this fact instead of computing the point of intersection, (p,q), and then computing function values to answer the question. This task is preparatory for standard F.LE.1a.

In this task students prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

This problem illustrates how an exponentially increasing quantity eventually surpasses a linearly increasing quantity.

In this task students observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

This problem shows that an exponential function takes larger values than a cubic polynomial function provided the input is sufficiently large.

The purpose of this task is twofold: first using technology to study the behavior of some exponential and logarithmic graphs and secondly to manipulate some explicit logarithmic and exponential expressions.

The task provides a reasonably straight-forward introduction to interpreting the parameters of an exponential function in terms of a modeling context. The task has students both generate an exponential expression from a contextual description, and in reverse, interpret parameters in a context from an algebraic expression.

The purpose of this task it to have students discover how (and how quickly) an exponentially increasing quantity eventually surpasses a linearly increasing quantity.

The purpose of this task it to have students discover how (and how quickly) an exponentially increasing quantity eventually surpasses a linearly increasing quantity.

This problem shows that an exponential function takes larger values than a cubic polynomial function provided the input is sufficiently large.

The purpose of this task is to help students see the "why" behind properties of logs that are familiar but often just memorized (and quickly forgotten or misremembered). The task focuses on the verbal definition of the log, helping students to concentrate on understanding that a logarithm is an exponent, as opposed to completing a more computational approach.

This task and its companion, F-BF Exponentials and Logarithms I, is designed to help students gain facility with properties of exponential and logarithm functions resulting from the fact that they are inverses.

This task and its companion, F-BF Exponentials and Logarithms I, is designed to help students gain facility with properties of exponential and logarithm functions resulting from the fact that they are inverses.

This is an instructional task meant to generate a conversation around the meaning of negative integer exponents. While it may be unfamiliar to some students, it is good for them to learn the convention that negative time is simply any time before t=0.

The goal of this task is to develop an understanding of why rational exponents are defined as they are (N-RN.1), however it also raises important issues about distinguishing between linear and exponential behavior (F-LE.1c) and it requires students to create an equation to model a context (A-CED.2

The goal of this task is to develop an understanding of why rational exponents are defined as they are (N-RN.1), however it also raises important issues about distinguishing between linear and exponential behavior (F-LE.1c) and it requires students to create an equation to model a context (A-CED.2)