9-12
In this lesson, students will use right triangle trigonometry to develop the law of sines.
9-12
In this lesson, students use right triangle trigonometry and the Pythagorean theorem to develop the law of cosines.
9-12
In static nim, the set of possible move sizes remains the same during the play of the game. In various versions of dynamic nim, the rules are such that the maximum number of counters that can be removed on each turn changes as the game is played. This maximum can depend on the current size of the pile, the number of counters removed on the previous play, or the move number of the game. In this lesson, students will explore the second type, where each move determines the maximum move size of the next move.
6-8
Students consider the amount of time that space travelers must spend on their journey. Students improve their concept of time and distance, while at the same time learn more about the solar system.
6-8
Students consider the amount of time that space travelers need to travel to the four terrestrial planets. Students also think about what kinds of events might occur on Earth while the space travelers are on their journey.
9-12
In this lesson, students consider the costs of owning a car and ways to lessen those costs. In particular, highway and city mileage are considered, and optimal mileage is calculated using fuel consumption versus speed data.
9-12
A surprising result occurs when two line segments are drawn through a point on the diagonal of a parallelogram and parallel to the sides. From this construction, students are able to make various conjectures, and the basis of this lesson is considering strategies for proving (or disproving) one of those conjectures.
9-12
By calculating the areas of regular polygons inscribed and circumscribed about a unit circle, students create an algorithm that generates the never-ending digits of π, a common curiosity among high school students.
6-8
In this lesson, students take on the role of a villager in a
third-world country trying to feed her village. While listening to you
read aloud the book
One Grain of Rice by Demi, students work
collaboratively to come up with a bargaining plan to trick the raja
into feeding the village using algebra, exponential growth, and
estimation.
9-12
Archimedes was the first mathematician to develop a converging series
approximation to π. That highly influential discovery guided the
development of calculus many hundreds of years later. However, his
method only gives lower and upper boundaries that form intervals known
to capture π, not a single numeric estimate of π. In this lesson,
students ask, “Where is π located in those intervals?” They also
discover an improvement to Archimedes' method that generates the
infinite digits of π more efficiently and accurately.
