Helene Chidsey and Lou Ann Lovin
Considerations of the graphs of the equation,
Family of Hyperbolas
xy = ax + by + c.
For an eploration of this equation click
Construction of a rhombus, parallelogram, isosceles trapezoid, and an isosceles
triangle given particular elements. GSP
GSP Scripts and Sketches
Given a rectangular sheet of cardboard 15 in. by 25 in., what size square
should be cut from each corner to produce a box with a volume of 400 cu.
in.? What size square would produce the maximum volume? (The square cut
from each corner needs to be the same size since we want to fold each side
up along the cuts to form a lidless box.) Below are three ways to investigate
The Lidless Box Problem
Click here to look at
an Excel (Spreadsheet) investigation.
to look at an Algebra Xpresser (Relational Grapher) investigation.
Click here to look at a Geometer's SketchPad (Interactive
Geometric Environment) investigation.
This investigation is interactive. The user can see the dimensions and volume
of the box change either by using the provided animation or by manually
manipulating the box.
Ratio of Areas
Consider any triangle ABC and a point p inside the triangle. Draw lines
AP, BP, and CP extended to their intersections with the opposite sides in
points D,E, and F respectively. Various explorations based on this triangle
can be viewed by clicking here.
An Exploration of Linear Functions
Combinations of operations (addition, multiplication, division, and composition)
on various linear functions. Click
here to view the investigation.