The purpose of this task is to study an example of a function which varies discretely over time. Step functions are often good examples for this type of function. In practice, instead of a step function, bar graphs are sometimes used. Alternatively, Jessie's method of ''smoothing'' over the jumps is also very common.

This task asks students to use similarity to solve a problem in a context that will be familiar to many, though most students are accustomed to using intuition rather than geometric reasoning to set up the shot.

The purpose of this task is to help students understand what is meant by a base and its corresponding height in a triangle and to be able to correctly identify all three base-height pairs.

This task could be put to good use in an instructional sequence designed to develop knowledge related to students' understanding of linear functions in contexts. Though students could work independently on the task, collaboration with peers is more likely to result in the exploration of a range of interpretations.

This task involves a fairly straightforward decaying exponential. Filling out the table and developing the general formula is complicated only by the need to work with a fraction that requires decisions about rounding and precision.

This task describes two linear functions using two different representations. To draw conclusions about the quantities, students have to find a common way of describing them. We have presented three solutions (1) Finding equations for both functions. (2) Using tables of values. (3) Using graphs.

This task presents a simple but mathematically interesting game whose solution is a challenging exercise in creating and reasoning with algebraic inequalities. The core of the task involves converting a verbal statement into a mathematical inequality in a context in which the inequality is not obviously presented, and then repeatedly using the inequality to deduce information about the structure of the game.

In this card game students play in pairs to practice recognizing the biggest number.

The purpose of this task is for students to interpret two distance-time graphs in terms of the context of a bicycle race. There are two major mathematical aspects to this: interpreting what a particular point on the graph means in terms of the context, and understanding that the "steepness" of the graph tells us something about how fast the bicyclists are moving.

This task asks students to glean contextual information about bird eggs from a collection of measurements of said eggs organized in a scatter plot. In particular, students are asked to identify a correlation and use it to make interpolative predictions, and reason about the properties of specific eggs via the graphical presentation of the data.

This task provides the most famous construction to bisect a given angle. It applies when the angle is not 180 degrees.

In this task, output is given from a computer-generated simulation, generating size-100 samples of data from an assumed school population of 2000 students under hypotheses about the true distribution of yes/no voters.

The purpose of this task is for students to find different pairs of numbers that sum to 4.

The purpose of this task is to assess a student's ability to compute and interpret an expected value. Notice that interpreting expected value requires thinking in terms of a long-run average.

The purpose of this game is to help students think flexibly about numbers and operations and to record multiple operations using proper notation.

This instructional task requires students to figure out word problems that require thinking in base 10.

This task provides an exploration of a quadratic equation by descriptive, numerical, graphical, and algebraic techniques. Based on its real-world applicability, teachers could use the task as a way to introduce and motivate algebraic techniques like completing the square, en route to a derivation of the quadratic formula.

The purpose of this task is to assess a student's ability to explain the meaning of independence in a simple context.