UC MAT Technology

 

UC MAT Technology Activities

Page history last edited by lbollman@... 8 mos ago

This is where we will store the GeoGebra Mathlets for our activities "book."

 

UC MAT Geometry UC MAT Linear Algebra Home

 

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 GeoGebra Mathlets

 

Document Who? Notes
Bisecting lines between any two give points Donald Hawkins Allows students to construct the perpendicular bisectors between any two given points and extend the the process to construct additional geometric figures.
Finding the Translation Distance Steve Blaylock Students will use Pythagorean theorem to find the distance of the translation
Finding the line of reflection Steve Blaylock Students will find the line of reflection
Rotation Steven Blaylock Allows students to find the center of rotation and angle of rotation
Constructing Parallelograms from Quads Donald Hawkins Allows students to construct Varignon's Parallelogram from any arbitrary quadrilateral.
Writing Equations of Conics from Graphs Steve Phelps This mathlet was created for an Algebra 2 class that was working on writing equations of conics. Students can create their own conic graph by dragging the foci and center. They then type in what they think is the equation of the conic. Students receive instant feedback on if their equation is correct!
Pythagorean Theorem Practice Steve Phelps

This mathlet was created for an Algebra 1 class that was working on Right Triangles. This allows the student to practice the Pythagorean Theorem when given any two sides they choose.
Constructing the Centroid Steve Phelps This mathlet was created for a Geometry class that was working on constructing the triangle centers. This mathlet plays the centroid construction step-by-step, allowing the user to stop and start the construction as it plays. The idea behind this activity is for the student to "guess the next step" in the construction.
Classical Triangle Centers Steve Phelps This mathlet was created for a Geometry class studying the triangle centers. Each mathlet (there are four on the page) has five inquiry questions that go along with it.
Centroid Curiosity Steve Phelps This mathlet illustrates a curiosity of the centroid
 Graphing Quadratics with Einstein  Mindy Burcham  This allows students in Algebra 1 to explore the graphs of quadratic functions.  They will use sliders to match the graph of a quadratic function to a picture and then answer questions based on their findings.
Centers of a Triangle Mindy Burcham This was created for a Geometry class that have already discussed the centers of the triangle.  Students can use this to find the coordinates for the incenter, circumcenter, and centroid of a triangle, and check their answers.  There are also some questions at the end of the activity.
Medial Triangle Todd Majestic This mathlet is designed to explore the common relationships of medial triangles.  There are questions at the end to summarize findings
Unit Circle Jillian Maher This applet allows students to explore the unit circle.  The angle can be changed and students find the sine and cosine - relating these values to the coordinates of the unit circle.
Pythagorean Thrm. and Areas of Squares. Mike Seiler This mathlet is a test. Students will deduce how the pythagorean formula works in relation to the areas of squares.
The Wizard of Oz Mike Seiler Prove or disprove the Scarecrows degree in Thinkology!
The Tower of Pisa Mike Seiler This is an application of the pythagorean theorem, law of cosines, and involves converting among metric and standard equivalent.
Football Helmet Graphing Mike Seiler This mathlet displays 5 football helmets displayed on a coordinate plane. The goal is to deduce the formulas so each helmet is "sitting" on a line.
Dartboard Mike Seiler This activity introduces students to probability, expalins the setup of a dart board, and allows students to rotate a point about a fixed axis and any given distance.
Radius of a Circle Mike Seiler A multifunctional mathlet that will require you to determine the radius of a circle and then ask you calculate the volume of a pool and the area of the pool cover.
Nine Point Circle Mitch Ehrman This mathlet illustrates the construction of a Nine Point Circle. It is up to the reader to rationalize each step.
A Pythagorean Theorem Proof Mitch Ehrman A simple illustration of the proof discussed in class is posted here.
Triangle Centers Mitch Ehrman A Geogebra File that shows students the Centroid, Circumcenter, Incenter, Orthocenter.
Geometric Probabilities Mitch Ehrman Students in my Geometry B class may use this file as an aide during Topic 8.

Graph Movement 1 - Translations

 Mitch Ehrman Pre Algebra A - Topic 17, Pt 1
Graph Movement 2 - Reflections Mitch Ehrman Pre Algebra A - Topic 17, Pt 2
Graph Movement 3 - Rotations Mitch Ehrman Pre Algebra A - Topic 17, Pt 3
Graph Movement 4 - Dilations Mitch Ehrman Pre Algebra A - Topic 17, Pt 4
Approximating Areas Todd Majestic An intuitive approach to the area of circles, using inscribed polygons
Parabola Equations in vertex form Linda Johnson Discover the effect of a, h and k on the graph of a parabola when written in vertex form.
Construction of the medians and centriod Brad McDaniel Constructs the centriod of a triangle.
Daisy Design Beth Jordan Design with circles. 

Liner Equations in Slope Intercept form

and worksheet

 Linda Johnson Simple look at y = mx + b and the slope of horizontal lines with a worksheet for a typical algebra I classroom.
Standard Form Linear Equations Linda Johnson Write equations of a line in Standard Form from two points
Upper and Lower Sums Mary Liz Lamb This activity computes Riemann Sums for a function. It allows the student to input functions, drag endpoints, change number of rectangles to see how this affects the sums and the difference between the two values.
Haberdasher Problem Michael Smith This activity demonstrates the Haberdasher Problem of dissecting an equilateral triangle into a square
Altitudes Construction Brad McDaniel This activity shows how to constuct the altitudes and orthocenter.
Families of Functions: Quadratics and Worksheet  Veronica Robinson  This activity explores the effects of a, h, and k on the graph of a quadratic function that's written in vertex form.
 Families of Functions: Absolute Value and Worksheet  Veronica Robinson  This activity explores the effects of a, h, and k on the graph of an absolute value function that's written in vertex form.
 Families of Functions: Cubics and Worksheet  Veronica Robinson  This activity explores the effects of a, h, and k on the graph of a cubic function that's written in vertex form.
 Families of Functions: Square Roots and Worksheet  Veronica Robinson  This activity explores the effects of a, h, and k on the graph of a square root function that's written in vertex form.
Exploring Absolute Value Graphs Catherine O'Neill This worksheet allows students to explore how different operations change the graph of an absolute value function.
Constructing Polygons Catherine O'Neill This worksheet has students constructing polygons with a limited amount of tools.  They are shown an equilateral triangle made with only circles and line segments. 
Investigating Equations of Circles Holly Phelps This worksheet has students explore how changing the h, k, and r values of an equation of a circle effects the graph of the circle.
Exploring Linear and Quadratic Relations with Worksheet Veronica Robinson This worksheet has students exploring domain and range of relations, and determining whether or not a relation is a function.
An Easy Tessellation Kelly Shattuck When I begin teaching about tessellations, I start with an easy example.  This applet allows students to work with the easy example and discover other figures that will tessellate a plane.

Relationships amoung the Graphs of Derivatives  and

Accompanying WS

 Mindy Burcham This appelet allow students to investigate the relationships amoung the graphs of f(x), f'(x), and f"(x).  It allows students to make connections between increasing/decreasing intervals, intervals of concavity, and the graphs of the derivatives.  This includes a worksheet to go along with the applet.
Elementary Dilations Kelly Shattuck Students in my "Algebra & Geometry" classes have a difficult time understanding what the center of dilation is all about.  This applet will allow them to move that point and see how it changes the dilation of a simple triangle.
Estimating Integrals Using Riemann Sums Beth Jordan Use this applet to find the Upper and Lower Riemann Sums for any function.  You can change the number of rectangles used in the sum and also the bounds of the integral.
Constructing the Angle Bisectors Brad McDaniel Construct the incenter of the triangle.
Triangle with its circumcircle Linda Johnson Look at the triangle with its circumcircle
Alternate Interior Angles Linda Johnson A look at alternate interior angles.
Corresponding Angles

 

 

 

 

 

 
Linda Johnson A look at corresponding angles.
Making Connections Jere Issenmann Connecting the corresponding points, shows us they all connect at the same point:)
Messing Up Coordinates Darron Steele  Compare a point plotted properly with the results of three common mistakes.
Trigometric Changes Darron Steele See what happens when you change altitude and period of the cos(x) function.
Intersection of 3 Equations Darron Steele See how rare it is for a system of three equations in two unknowns to have a solution.
The Historic Form of the Pythagorean Theorem Darron Steele The Pythagorean Theorem was not originally presented in an algebraic format.
Basic Properties of Angles Darron Steele Vertical angles, supplemental angles, triangles.
Putting Jackie Southard

This is an activity for kids to practice finding the equation of a line through two points. 

They will have to help a golfer putt his ball into the hole.
Exterior Angles of a Triangle Jackie Southard

This is an activity for basic geometry for kids to discover the relationship between

the exterior angles of a triangle and its two remote interior angles.
Find the equation of a Line Jackie Southard Kids will be able to practice writing the equation of a line from a graph.  There is a WKST on the GeoGebra wiki that goes along with this activity.
SSA Case Jackie Southard This demonstrates why the SSA case is not a congruence criterion for triangles.  There is a WKST on the GeoGebra wiki that goes along with this activity.
Matix Multiplication Catherine O'Neill This worksheet is for practicing matrix multiplication.
Trapezoid Transforms to a Parallelgram Holly Phelps This is a challenging activity for students to try to transform a trapezoid into a parallelogram and compare the area of the two.
Perspective Square Melissa Keller This desmonstrates a way to construct a square in perspective and what happens when the vanishing point changes.
Midpoint of a Line Kelly Shattuck Use this applet to have students find the midpoint of a line segment and discover the formula for finding its coordinates.
Equation of a Line Kelly Shattuck The general form of the equation of a line is y = mx + b.  What does the m represent?  What does the b represent?
Slope of a Line Kelly Shattuck How does changing the slope effect the equation of a line?
Factoring Parabolas Brian Bisignani Explore how a factored equation graphs on the coordinate plane.  Can be used to introduce solving quadratics to Algebra I students!
Pool Table Lines Brian Bisignani Explore the equations of lines on a pool table, using sliders for m and b.
Roller Coaster Parabola Brian Bisignani Very neat activity!  Using a roller coaster as a background, students must use sliders to transform a parabola to fit the coaster's path.  Shows how each component of a quadratic equation affects the graph.
Golden Rectangle Brian Bisignani Explore different aspects of the Golden Rectangle, including why it is called Golden!
Comparing Lines Catherine O'Neill In this worksheet students can compare graphs of lines and see how sliders change the equations.
Given Points, Find Equations Catherine O'Neill In this worksheet students are given 3 sets of points and are asked to come up with the equations of the graphs that go through each set.  Check boxes were not put into this worksheet on purpose.  Students should be familiar with lines, parabolas and absolute value equations and graphs.  They can reset the construction after each try.
Triangle Congruence Theorem (AAA) Carey Costello This applet helps show the triangle congruence theorem for AAA.
Where's Waldo? Holly Phelps This is an activity where students are asked to find a line parallel and perpendicular to a given line using their slopes.
Graph of the Derivative Beth Jordan Graph the derivative function of a specific function on the same page. You can change the function, f(x) by putting the new function into the input bar. 
Constructing the Perpendicular Bisectors Brad McDaniel This exercise constructs the perpendicular bisector of each side of a triangle.
Simple Perspective Construction Melissa Keller This construction shows one way to draw a tiled floor in perspective
Advanced Perpsective Construction Melissa Keller This construction shows another way to draw a tiled floor in perspective.  This has more segments to create more points for the parallel lines.
Euler's Line Brad McDaniel This activity looks at the relationships between the points of concurrency of a triangle.
Equation of a Circle Kelly Harms This activity allows students to derive an equation for circles.
functions and derivatives Mary Liz Lamb this activity helps the students relate a graph and its derivatives
Relationships between a function and its derivative Mary Liz Lamb this activity uses a slider to relate the graph to its derivatives
Reflected Perspective Construction Melissa Keller This construction shows a third way to draw a tiled floor in perspective.  It uses a reflection to create more horizontal lines
Composition of Functions and Worksheet Jillian Maher The applet allows students to change two functions and explore the graph of their composition.  The attached worksheet gives some guidance if worked as an individual activity.
Chord Angles in Circles Todd Majestic This applet lets students work on finding angles made by intersecting chords in a general circle.
Chord lengths in a circle Todd Majestic Allows students to find a relationship between intersecting chords in a circle.  The students can change the points and create their own problems then check them
Secant and Tangent lines of circles Todd Majestic This applet lets students work on find the length of a piece of a secant line to a circle. 
Congruence of Triangle (SSS) Carey Costello This applet helps show the triangle congruence for SSS.
Tessellating Escher's Reptiles Mindy Burcham This applet makes use of sliders so that rotations on Escher's Reptiles drawing are illustrated.
Triangle Congruence (ASA) Carey Costello This applet helps show the triangle congruence for ASA.
Triangle Congruence (SAS) Carey Costello This applet helps show the triangle congruence for SAS.
Triangle Congruence AAS Carey Costello This applet helps show the triangle congruence for AAS.
Parallel and Perpendicular Lines Teresa Munninghoff Here we examine parallel and perpendicular lines and develop a theorem.
Investigating Isometries Steve Blaylock This Investigation allows Students to look at the three main Isometries
Derivatives and Limits at a Cusp Mindy Bucham This applet allows students to investigate what happens to the derivative of a function when the function contains a cusp and is nondifferentiable.
reflecting a triangle Mary Liz Lamb reflecting a trianlge to find new coordinates
triangulation Mary Liz Lamb using three coordinates to find a location
incenter and circumcenters Mary Liz Lamb locating the incenter and circumcenter for a triangle
Regular Hexagon yeilds Regular Triangle Brad McDaniel Make a conjecture about the given picture.
Exploring Sin Graph Jana Rae Debord Adjusting amplitude, vertical shift, and period of the sin function and seeing how it effects the equation
Introduction to Positive and Negative Angles Kelly Harms Introduce the kids to the unit circle, and what positive and negative angles look like.  Next step will be introducing radians.
Investigating Rate of Change Steve Blaylock Introducing rate of change with graphing
Tiling the plane with Triangles Steve Blaylock What lines and and angles do you see when you tile the plane with Triangles
Tiling the plane with a kite or dart. Christy Bredestege Tiling the plane with a kite or a dart.
Classifying Triangles Christy Bredestege Students will see the "basics" of classifying a triangle.
Name the polygon Christy Bredestege Students will be given a polygon and they will try to look at the properties and specifically name it.
Radian Measure and the Unit Circle Jackie Southard This illustrates how the radian measure of the anlge is the same as the length of the arc created by the angle when the circle is the unit circle.  You can also show how this property does not hold for circles that are not the unit circle.
Help Chilly Willy Holly Phelps In this activity students will write translations in coordinate notation in order to give Chilly Willy directions to different places he wants to go. Also they will calculate the distance from points.
Golden Triangle and Rectangle Michael Smith Applet showing relationship between golden rectangle/golden triangle and Fibonacci sequence and golden ratio
Golden ratio Michael Smith Finding golden ratio (phi) through construction of regular pentagon
Identifying Polynomial Graphs Jillian Maher Students use the applet to identify information from the graphs shown.  Students will identify end behavior, roots (number of roots and value) and degree of functions.  Extension included at the end.
Translating Sine Graph Jillian Maher Students use sliders to change the parent sine graph to the translated sine graph.  Students then write the new graph in terms of their slider
Understanding Slope Intercept Jillian Maher Students use sliders to change a linear equation and then write the linear equation in terms of the slider.
homework 1 Mary Liz Lamb This is the picture for Minda's 1st homework problem assigned on 8/7/08
homework 2 Mary Liz Lamb This is the picture for Minda's 2nd homework problem assigned on 8/7/08
Vertical Angles and Linear Pairs Teresa Munninghoff Students create two intersecting lines and measure the angles formed by the lines to develop a theorem about vertical angles and linear pairs.
Probability of Dart Throwing Holly Phelps Students are asked to find the probability of randomly throwing a dart and landing in a certain region on the board. There are also asked to conduct a small experiment and compare their results to the theoretical probability.
Subtracting Integers Jere Issenmann Students will draw the relationship to adding negative integers with subtracting.
Slope Intercept Form Jere Issenmann Students intvestigate slope intercept form and create their own equations.
Graphing the Derivative Using Tangent Lines Beth Jordan Put in f(x) and move the tangent line to produce a graph of the derivative function. Push the yellow arrow to clean the screen and put in a new function to start again. 
Reflections and Rotations Teresa Munninghoff Students reflect a triangle twice and explore what happens to the original triangle.
Making Parallelograms Teresa Munninghoff Here students examine the theorems for parallelograms and use those theorems to create a parallelogram.
Dilations Teresa Munninghoff Here students will examine the relationship between the scale factor and the coordinates of the pre-image and the image.
Point Slope Form Jere Issenmann Investigation of Point Slope Form
Adding Integers Jere Issenmann Students can visually see on a number line how to add integers:)
Standard Form Jere Issenmann Students can investigate Standard Form through sliders
Sine Curve Kelly Harms Students can explore the graph of the sine curve and it's equation.
Cosine Curve Kelly Harms Students can explore the graph of the cosine curve and it's equation.
Tangent Curve Kelly Harms Students can explore the graph of the tangent curve and it's equation.
Investigating Parallel Lines Cut by a Transversal lbollman Investigate the angle measures when parallel lines are cut by a transversal.
Parallel Lines Cut by a Transversal lbollman This mathlet can be used to demonstrate congruent angle pairs when parallel lines parallel lines are cut by a transversal.
Isosceles Triangle lbollman Reflection of a right triangle creates an isosceles triangle.
Tessellating Parallelograms lbollman Tiling a plane with parallelograms.
Tessellating Hexagons lbollman Tiling a plane with hexagons.
Hexagon Puzzle lbollman A spatial visualization puzzle.
Get to Know a Rectangle lbollman Thinking about how a primary student might use GeoGebra to think about geometric figures.
Sangaku#1 Kelly Stidham Sample Sangaku Problem
Sangaku #2 Kelly Stidham Another Sangaku Problem
Basic Constructions Kelly Stidham A "Getting Started" Worksheet

 

 

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