Task

Purpose

Horseshoes in Flight

Students analyze the structure of algebraic expressions and a
graph to determine what information each expression readily contributes
about the flight of a horseshoe. This task is particularly relevant to
students who are studying (or have studied) various quadratic
expressions (or functions). The task also illustrates a step in the
mathematical modeling process that involves interpreting mathematical
results in a realworld context.

Taking a Spin

Although students are often asked to find the angles of
rotational symmetry for given regular polygons, in this task they are
asked to find the regular polygons for a given angle of rotational
symmetry, a reversal that yields some surprising results. This task
would be most appropriate with students who have at least some
experience in exploring rotational symmetry.

Tidal Waves

Students analyze a problem faced by the captain of a shipping
vessel. Students may use a range of functions to model the situation and
reflect on their usefulness. Because trigonometric functions can be
useful, this task would be particularly appropriate for students who
have had an introduction to graphing sine and cosine functions.

Eruptions: Old Faithful

Students analyze data and make predictions. They will create a
variety of graphical displays to discover trends in the data, then use
those graphs to support their predictions. This task is appropriate for
students familiar with line graphs and other graphical displays of
univariate data sets.

Fuel for Thought

Students use mathematical reasoning to determine appropriate
numerical measures and patterns in fuel consumption in order to inform
consumer choice for vehicle purchasing. The task promotes a
sophisticated use of number sense including careful attention to units.
It is accessible to beginning high school students.

Bank Shot

Students compare their own
reasoning strategies and those of their classmates, focusing on the
strategies’ usefulness in determining how to make certain bank shots in
billiards. This task is intended to involve multiple geometric
perspectives and would be appropriate for students with an understanding
of similar triangles, rigid motions (especially reflections), and
equations for lines and is designed to strengthen students’
understanding of these concepts.

As the Crow Flies

The distance formula is
often presented as a “rule” for students to memorize. This task is
designed to help students develop an understanding of the meaning of the
formula. It would be appropriate as an introduction (or review) of the
distance formula for students who are familiar with the Pythagorean
theorem and coordinate systems.

Over the Hill

Students determine locations on a hillside for a
cell phone tower erected to provide a signal to people on the other side
of the hill. They identify necessary information, represent the problem
with a scale model, and answer questions in context. This task is
appropriate for students who have had experience in determining
equations of linear functions through two points and in solving systems
of linear equations.

Cash or Gas

State lotteries in Florida and other states give
winners a choice between cash and another prize, such as free gas for
life. In this task, students will evaluate two prize options by
discussing and making reasonable assumptions to simplify a complex
decision. This task is appropriate for students who can extrapolate
quantities over time and are able to make conversions among different
units of measure.
