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 asks students to use inverse operations to solve the equations for the unknown variable, or for the designated variable if there is more than one.

The purpose of this task is to apply knowledge about triangles to calculate the sine and cosine of 30 and 60 degrees.

This is a standard problem phrased in a non-standard way. Rather than asking students to perform an operation, expanding, it expects them to choose the operation for themselves in response to a question about structure.

This task is designed for the student to apply geometric concepts in modeling situations.

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.

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.

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.

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 involves a reasonably direct application of similar triangles, coupled with a moderately challenging procedure of constructing a diagram from a verbal description.

The goal of this task is to examine how extraneous solutions can arise when solving rational equations.

A ladder 5 meters long is leaning against a vertical wall with its foot on a rug on the floor. Initially, the foot of the ladder is 3 meters from the wall. The rug is pulled out, and the foot of the ladder moves away from the wall at a constant rate of 1 meter per second. Build a mathematical model or models for the motion of the ladder. Use your model (or models) to find the velocity at which the top of the ladder hits the floor and the distance the top of the ladder will be from the wall at the moment that it hits the ground.

This purpose of this task is to examine in a concrete situation a common statistical fallacy where two conditional probabilities are confused.

This is a very straight forward task that addresses the second part of F-TF.C.8 exactly. It could be used as an introductory example, practice or assessment.

This task examines how to calculate the area of an equilateral triangle using high school geometry.

The purpose of this task is to use similar triangles in order to study the coordinates of points which divide a line segment in a given ratio.

This task is the last in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically.

Your team has been approached by the Forest Service to help allocate resources to fight wildfires. In particular, the Forest Service is concerned about wildfires in a wilderness area consisting of small trees and brush in a park shaped like a square with dimensions 80 km on a side. Several years ago, the Forest Service constructed a network of north-south and east-west firebreaks that form a rectangular grid across the interior of the entire wilderness area. The firebreaks were built at 5 km intervals.

Wildfires are most likely to occur during the dry season, which extends from July through September in this particular region. During this season, there is a prevailing westerly wind throughout the day. There are frequent lightning bursts that cause wildfires.