Tim Brzezinski, Sep 10, 2018

Resources that Illustrate how GeoGebra can foster DISCOVERY LEARNING & facilitate MEANINGFUL REMEDIATION in Geometry: 1) Quick ACTIVE Discovery that Vertical Angles are always congruent (equal in measure) 2) Resource quickly helps students DISCOVER (or RE-DISCOVER) that the area of a triangle = 1/2 the area of a parallelogram that has the same base and height as the triangle. Proof that the quadrilateral formed IS a parallelogram is also included. 3) Resource helps students powerfully discover the sum of the measures of the interior angles of any n-gon = 180(n - 2) degrees. Also helps students readily discover that the exterior angles of any convex polygon always sum to 360 degrees.

• 1. Vertical Angles Exploration (1)
• 2. Area of a Triangle (Discovery)
• 3. Exploring Polygon Angles: Triangle through Octagon

Resources that Illustrate how GeoGebra can foster DISCOVERY LEARNING & facilitate MEANINGFUL REMEDIATION in Algebra: 1) Activity for students to DISCOVER (or RE-DISCOVER) that if 2 parallel lines are drawn in the coordinate plane, then they have equal slopes. Note: Adjusting the "Tilt" slider causes the slope triangle to turn red if slope becomes negative. 2) Quick illustrator for students to quickly DISCOVER (or RE-DISCOVER) that (perpendicular lines graphed in the coordinate plane have slopes that are opposite reciprocals.

• 1. Special Pair of Lines in the Coordinate Plane
• 2. Perpendicular Lines in the CP: Quick Investigation

Resources that Illustrate how GeoGebra can foster DISCOVERY LEARNING & facilitate MEANINGFUL REMEDIATION in PreCalculus & Trigonometry: 1) Dynamic and modifiable resource that illustrates the HALF-LIFE of a substance is independent of BOTH the initial amount of substance you have AND the amount of substance you have after any time. 2) Conic Section Explorations: This resource helps students explore how the cross section (intersection) of a plane and cone is a CONIC SECTION. Illustrations in GeoGebra's 3D Graphing Calculator and GeoGebra Augmented Reality are provided.

• 1. Half-Life Action (3)!!!
• 2. Conic Section Explorations

Resources that Illustrate how GeoGebra can foster DISCOVERY LEARNING & facilitate MEANINGFUL REMEDIATION in Calculus: 1) This dynamic & modifiable GeoGebra resource powerfully illustrates the concept of derivative of a function (at x = a certain input) in a GRAPHICAL (non-algebraic) setting. 2) This GeoGebra resource allows students to create a custom-made solid of revolution formed by rotating the area between 2 (modifiable) functions about any specified horizontal or vertical line.

• 1. Derivative Function: Without Words
• 2. Calculus: Surface of Revolution formed by Rotating Area Between 2 Functions