Open Middle provides math problems that have a closed beginning, a closed end, and an open middle. This means that there are multiple ways to approach and ultimately solve the problems. Open middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding.

The purpose of this task to help students think about an expression for a function as built up out of simple operations on the variable, and understand the domain in terms of values for which each operation is invalid (e.g., dividing by zero or taking the square root of a negative number).

This problem allows the student to think geometrically about lines and then relate this geometry to linear functions. Or the student can work algebraically with equations in order to find the explicit equation of the line through two points (when that line is not vertical).

This task is designed as a follow-up to the task F-LE Do Two Points Always Determine a Linear Function? Linear equations and linear functions are closely related, and there advantages and disadvantages to viewing a given problem through each of these points of view. This task is not intended for assessment purposes: rather it is intended to show the depth of the standard F-LE.2 and its relationship to other important concepts of the middle school and high school curriculum, including ratio, algebra, and geometry.

This task asks students to 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).

Intel® developed its Shooting Starâ„¢ drone and is using clusters of these drones for aerial light shows. In 2016, a cluster of 500 drones, controlled by a single laptop and one pilot, performed a beautifully choreographed light show

It is almost election time and it is time to revisit the electoral vote process. The constitution and its amendments have provided a subjective method for awarding electoral votes to states. Additionally, a state popular vote, no matter how close, awards all electoral votes to the winner of that plurality. Create a mathematical model that is different than the current electoral system.

The Emergency Service Coordinator (ESC) for a county is interested in locating the county’s three ambulances to best maximize the number of residents that can be reached within 8 minutes of an emergency call. The county is divided into 6 zones and the average time required to travel from one zone to the next under semi-perfect conditions is summarized in the following Table 1.

This task has students apply their knowledge of parallel lines to solve a geometric problem on areas of triangles.

Students prove that linear functions grow by equal differences over equal intervals. They will prove this for equal intervals of length one unit, and note that in this case the equal differences have the same value as the slope.

Linear functions grow by equal differences over equal intervals. In this task students prove the property in general (for equal intervals of any length).

Examples in this task is designed to help students become familiar with this language "successive quotient". Depending on the students's prior exposure to exponential functions and their growth rates, instructors may wish to encourage students to repeat part (b) for a variety of exponential functions and step sizes before proceeding to the most general algebraic setting in part (c).

Open Middle provides math problems that have a closed beginning, a closed end, and an open middle. This means that there are multiple ways to approach and ultimately solve the problems. Open middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding.

The purpose of this task is to give students an opportunity use quantitative and graphical reasoning to detect an error in a solution. The equations have been chosen so that finding the exact solution requires significant calculation so that it is easy to make an error.

Open Middle provides math problems that have a closed beginning, a closed end, and an open middle. This means that there are multiple ways to approach and ultimately solve the problems. Open middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding.

Open Middle provides math problems that have a closed beginning, a closed end, and an open middle. This means that there are multiple ways to approach and ultimately solve the problems. Open middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding.

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.

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.