Visualizing_TMC13

Visualizing Mathematics

In visualizing mathematics we discussed the following applications:


 * Fraction operations
 * fraction cakes- showing the how multiplying and adding fractions work visually.
 * see attached.
 * Fraction breakdown. [[file:Fraction Breakdown.docx|transparency sheet]]
 * see attached.


 * Geometric representations of properties - [|Worksheet]
 * associative
 * multiplicative - showing that a box contains the same volume regardless of which side is being considered the base.
 * additive - showing that 3 lines (or strings) put end to end line up to be the same length regardless which you put together first.
 * commutative
 * multiplicative - showing a rectangles area is the same even when it is rotated. length time width is the same as width times length.
 * additive - showing that 2 lines (or strings) put end to end line up to be the same length regardless which you put first.
 * distributive
 * Showing that two rectangles with the same width have the same total area as one rectangle whose length is equal to the sum of the lengths of the original two rectangles.
 * Functions
 * End behavior
 * Monsters - Showing on a graph that a lot can happen in the center of the graph (monster) but we are only interested where the ends of the monster are.
 * Characteristics
 * equation, sketch the graph, x-intercepts, degree, symmetry
 * Completing the square geometrically
 * Flip book
 * Transformation Disco [[file:Transformation Disco revised.ppt|disco powerpoint]]
 * Geogebra
 * Transformation of the function f(x) = sin(x) [[file:Sin Curve.ggb]] [[file:Sin Curve.ggb|Sin Curve Transformations]]
 * Systems of 3 linear equations in 3 variables [[file:System of 3 linear equations in 3 unknowns.ggb]] [[file:System of 3 linear equations in 3 unknowns.ggb|Systems of 3 variables ]]
 * Slope of the tangent line [[file:Slope of Tangent Line.ggb]], [[file:Slope of Tangent Line.ggb|Slope of tangent line]]