This is a very open ended task. It poses the question, but the students have to formulate a plan to answer it, and use the two-way table of data to find all the necessary probabilities. The special emphasis is on developing their understanding of conditional probability and independence. This task could be used as a group activity where students cooperate to formulate a plan of how to answer the question and calculate the appropriate probabilities. The task could lead to extended class discussions about the different ways of using probability to justify general claims.

The purpose of this task is to engage students in geometric modeling, and in particular to deduce algebraic relationships between variables stemming from geometric constraints. The modelling process is a challenging one, and will likely elicit a variety of attempts from the students.

This task, while involving relatively simple arithmetic, codes to all three standards in this cluster, and also offers students a good opportunity to practice modeling (MP4), since they must attempt to make reasonable assumptions about the average length of vehicles in the traffic jam and the space between vehicles. Teachers can encourage students to compare their solutions with other students.

This task examines, in a graphical setting, the impact of adding a scalar, multiplying by a scalar, and making a linear substitution of variables on the graph of a function f. The setting here is abstract as there is no formula for the function f. The focus is therefore on understanding the geometric impact of these three operations.

The purpose of this task is to emphasize the adjective "geometric" in the "geometric" series, namely, that the algebraic notion of a common ratio between terms corresponds to the geometric notion of a repeated similarity transformation.

In this task students must investigate this conjecture to discover that it does not work in all cases: Pick any two integers. Look at the sum of their squares, the difference of their squares, and twice the product of the two integers you chose. Those three numbers are the sides of a right triangle.

This task provides an opportunity for 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).

This task provides an opportunity for 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).

This classroom task is meant to elicit a variety of different methods of solving a quadratic equation (A-REI.4).

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

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). It also requires students to create additional structure within the given problem, producing and solving a right triangle to compute the required central angles (G-SRT.8).

The following are some common methods of data collection in statistical studies that involve people.

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.

This task focuses on the fact that exponential functions are characterized by equal successive quotients over equal intervals. This task can be used alongside F-LE Equal Factors over Equal Intervals.

This task focuses on the fact that linear functions are characterized by constant differences over equal intervals. It could be used alongside to F-LE Equal Differences over Equal Intervals I & II.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This task presents a context that leads students toward discovery of the formula for calculating the volume of a sphere. Students who are given this task must be familiar with the formula for the volume of a cylinder, the formula for the volume of a cone, and CavalieriŐs principle.

This task deals with a student error that may occur while students are completing F-IF Average Cost.

The purpose of the task is to explicitly identify a common error made by many students, when they make use of the "identity" f(x+h)=f(x)+f(h). A function f cannot in general be distributed over a sum of inputs.

This task is meant to be a straight-forward assessment task of graph reading and interpreting skills. This task helps reinforce the idea that when a variable represents time, t=0 is chosen as an arbitrary point in time and positive times are interpreted as times that happen after that.