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 help students make the connection between the graphs of sint and cost and the x and y coordinates of points moving around the unit circle. Students have to match coordinates of points on the graph with coordinates and angles in the diagram of the unit circle.

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.

The goal of this task is to explore the relationship between sine and cosine of complementary angles for special benchmark angles.

The purpose of this task is to apply translations and reflections to the graphs of the equations f(x)=cosx and g(x)=sinx in order to derive some trigonometric identities.

The purpose of this task is to use the Pythagorean Theorem to establish the fundamental trigonometric identity sin2θ+cos2θ=1 for an acute angle θ. The reasoning behind this identity is then applied to calculate cosθ for a given obtuse angle. In order to successfully complete part (c) students must be familiar with the definitions of trigonometric functions for arbitrary angles using the unit circle (F-TF.2).

The purpose of this task is to examine trigonometric functions for obtuse angles. The values sinx and cosx are defined for acute angles by referring to a right triangle one of whose acute angles measures x. For an obtuse angle, no such triangle exists and so an alternate definition is required. Prior to working on this task, students should have experience working with trigonometric functions and how they relate to the unit circle.

This task is a fleshing-out of the example suggested in A-APR.4 of the Common Core document, using the polynomial identity (x2+y2)2=(x2y2)2+(2xy)2 to generate Pythagorean triples.

Recent events have reminded us about the devastating effects of distant or underwater earthquakes. Build a model that compares the devastation of various-sized earthquakes and their resulting Tsunamis on the following cities: San Francisco, CA; Hilo, HI; New Orleans, LA; Charleston, SC; New York, NY; Boston, MA; and any city of your choice. Prepare an article for the local newspaper that explains what you discovered in your model about one of these cities.

This classroom task is meant to elicit a variety of different methods of solving a quadratic equation.

The purpose of this task is to provide practice using data in a two-way table to calculate probabilities, including conditional probabilities.

This task combines two skills from domain G-C: making use of the relationship between a tangent segment to a circle and the radius touching that tangent segment (G-C.2), and computing lengths of circular arcs given the radii and central angles (G-C.5).

The purpose of this task is to provide students with experience distinguishing between the various types of statistical studies and to understand the purpose of random selection in surveys and observational studies vs. random assignment to treatments in experiments.

The purpose of this task is to construct and use inverse functions to model a a real-life context. Students choose a linear function to model the given data, and then use the inverse function to interpolate a data point.

Trains arrive often at a central Station, the nexus for many commuter trains from suburbs of larger cities on a "commuter" line. Most trains are long (perhaps 10 or more cars long). The distance a passenger has to walk to exit the train area is quite long. Each train car has only two exits, one near each end so that the cars can carry as many people as possible. Each train car has a center aisle and there are two seats on one side and three seats on the other for each row of seats.

The goal of this task is to represent an exponential relationship by an equation and identify, using knowledge of the context and the structure of the equation, possible graphs for the equation.

This task presents a context that leads students toward discovery of the formula for calculating the volume of a sphere.

The goal of this Illustrative Mathematics task is to study the relationship between the roots of a quadratic function and its graph.