The goal of this task is to provide an argument, appropriate for high school students, for why the sum of the angles in a triangle is 180 degrees.

The purpose of this task is to provide students with an opportunity to calculate joint, marginal and relative frequencies using data in a two-way table.

A triathlon is a multiple-stage athletic endurance competition of three continuous and sequential events, usually long distance swimming, cycling, and running. Triathletes’ overall course completion time includes their time for each event plus their time for transitions between the three events.

Race organizers provide each participant a transition area where he/she can pre-position a bike, running shoes, performance gear and other equipment needed to transition from swimming to cycling and from cycling to running. An athlete’s time in the transition area (denoted as T1 for swimming to cycling and T2 for cycling to running) counts toward the total race time. The race begins with the swimming event and participants start the race in a sequence of waves of groups of swimmers at intervals of some number of minutes apart.

This task presents a foundational result in geometry, presented with deliberately sparse guidance in order to allow a wide variety of approaches.

The purpose of this task is to use similar triangles, setting up a proportion in order to calculate a side length.

The purpose of this task is to focus on studying values of tanx for special angles and conjecturing from these values how the function tanx varies when 0x<90.

This task is designed to allow students to construct a tangent line from a point outside a given circle to the circle.

This task is not about computing the final price of the shirt but about using the structure in the computation to make a general argument.

Unit conversion problems provide a rich source of examples both for composition of functions (when several successive conversions are required) and inverses (units can always be converted in either of two directions).

Temperature conversions provide a rich source of linear functions which are encountered not only in science but also in our every day lives when we travel abroad. The first part of this task provides an opportunity to construct a linear function given two input-output pairs. The second part investigates the inverse of a linear function while the third part requires reasoning about quantities and/or solving a linear equation.

This task is inspired by the derivation of the volume formula for the sphere.

This task could be used for assessment or for practice. It allows the students to compare characteristics of two quadratic functions that are each represented differently, one as the graph of a quadratic function and one written out algebraically. Specifically, we are asking the students to determine which function has the greatest maximum and the greatest non-negative root.

Although this task is quite straightforward, it has a couple of aspects designed to encourage students to attend to the structure of the equation and the meaning of the variables in it.

This task gives students a chance to relate their weather experiences with a simple geometric model which explains why the seasons occur.

This task guides students by asking the series of specific questions and lets them explore the concepts of probability as a fraction of outcomes, and using two-way tables of data.

This task lets students explore the concepts of probability as a fraction of outcomes, and using two-way tables of data.

This is the last task in the series of three, which ask related questions, but use different levels of scaffolding. This task uses a more detailed version of the data table. 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 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 goal of this task is to examine a mathematical statement about the mass of snow, hopefully providing some stimulating thought to go along with the very arduous and demanding physical exercise.

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.