9-12
In this lesson, students transform images through rotation, reflection, dilation, and translation using matrix multiplication. After digitizing images by representing the images as matrices, they multiply image matrices by various transformation matrices, producing transformed images.
6-8, 9-12
In this lesson, students use proportions and similar figures to adjust
the size of the New York City Subway Map so that it is drawn to scale.
Students are asked to evaluate whether these changes are necessary
improvements.
6-8, 9-12
In this lesson, students will explore reflections,
translations and rotations. Students participate in a modeling activity where
they will learn the rules for translations and reflections. Then students
will practice using these transformations, as well as explore the rules for
rotations, in the game
Flip-n-Slide on Calculation Nation®.
9-12
In this lesson, students will manipulate three paper circles
to explore four circle theorems. Using paper folding allows the lesson to be
more accessible to kinesthetic learners.
6-8, 9-12
In this lesson, students will develop an understanding of the Fibonacci Sequence (and its connection to Golden Rectangles), Golden Ratio, Golden Rectangle, and the term
ratio (as it applies to rectangles). Students will use tools and construction techniques to demonstrate geometry prowess and be able to observe the Golden Rectangle in nature and in the classroom.
6-8, 9-12
This lesson is based upon a story from Virgil's
Aeneid. Students work in groups to
investigate maximizing area with a fixed length of rope. They investigate which
figure results in the greatest area by real-life experimentation as well
algebraically. Students gain an understanding of quadratic functions, the
isoperimetric principle, and parabolas.
9-12
Many
problems in mathematics classes are exactly defined and require very specific
solutions. This lesson is intended to be an open-ended problem with multiple solutions
and multiple entry points. Students use volume formulas and have some decisions
to make about how to use them. After making an initial estimate, students will
use modeling with more concrete parameters to help them refine their choices.
9-12
Astronomers now know that the planets in our solar system travel around the Sun in roughly circular orbits. However, people used to believe that the Sun and other planets orbited the Earth. If that were the case—if the Earth were the center of our solar system—what would the orbit of the other planets look like relative to Earth? That is the question that students will explore in this lesson. Students will generate parametric equations to describe the position of planets relative to the Sun; then, they will combine the equations to describe the position of Mars relative to Earth.
6-8, 9-12
In this lesson, students learn to use a compass and a straight edge to
construct rectangles of leg ratios 1:1; 1:√2; 1:√3; 1:2; and 1:√5. The
lesson culminates with the class constructing a full size façade of a
house using the proportions of the Ancient Maya.
9-12
In this lesson,
students examine and draw representations of cubes and then learn how to analyze
these representations using complex numbers. Students use what they know about
operations on complex numbers to see if a drawing is an accurate representation
of a cube. They also learn how to generate complex numbers that will produce
such representations.
