9-12
In this lesson, students explore properties of polygons by trying to place the minimum number of security cameras in a room such that the full area can be monitored. From these polygons, students discover the formula for the maximum number of cameras needed. Students then use their discoveries to analyze the floor plan of a museum as a culminating activity.
6-8, 9-12
This lesson allows students to explore linear equations and the effects of changing the slope and
y-intercept on a line. It gives students exposure to
y =
mx +
b,
and can be used as an introduction to the topic. Using graphing
calculators, students are challenged to overlap lines onto the sides of
polygons. To achieve this goal, students change slopes and
y-intercepts of lines, noting observations about behavior as they work. As students change the
y-intercept
of a line, they see it raise or lower the line. As students change the
slope, they see it affect the steepness of the line.
9-12
Students explore and discover conic sections by cutting a cone with a plane. Circles, ellipses, parabolas, and hyperbolas are examined using the Conic Section Explorer tool. Physical manipulatives such as dough can optionally be used as well.
6-8, 9-12
In this lesson, students use polydrons to create nets of rectangular prisms. They discover that there are many configurations for rectangular prisms with the same volume, and determine that certain configurations minimize surface area. The lesson continues in a discovery activity related to building the most cost-efficient and appealing fish tank.
6-8, 9-12
This lesson can be used for students to discover the relationship between dimension and volume. Students create two rectangular prisms and two cylinders to determine which holds more popcorn. Students then justify their observation by analyzing the formulas and identifying the dimension(s) with the largest impact on the volume.
9-12
In this lesson, students are introduced to basic graph theory and Euler circuits. They stitch paths and circuits to create their own graphs. Students also problem solve as they design a route that creates the same pattern on the front and back of a canvas.
9-12
In this lesson students use sidewalk chalk and rope to illustrate the locus definitions of ellipses and parabolas. Kinesthetics, teamwork, and problem solving are stressed as students take on the role of focus, directrix, and point on the conic, and figure out how to construct the shape.
9-12
This lesson allows students to extend their idea of sequences beyond a list of numbers to mathematical objects like intervals by asking them to examine the infinite intersection of these sequences. This lesson works especially well just after students have worked with infinite geometric series. It even contains an unexpected application of geometric sequences and series.
9-12
In the same way that supporting statements are used to reach a
conclusion in a paragraph-style proof, students modify a cliché or
common phrase to use as a punch line to a humorous story. This lesson
works well in aiding in the transition from two-column proofs to
paragraph-style proofs.
9-12
Students sometimes have difficulty using the order of operations when
evaluating expressions. By converting these expressions into binary
expression trees before evaluating them, students gain a better
understanding of the order of operations. In addition, students learn
to represent algebraic expressions using prefix notation, which is
often called "Polish Notation," because of the nationality of its
inventor, Polish logician Jan Łukasiewicz.
