Online Math Resources: High School 2
Geometry
Online
Interactive Geometry
This is by far the most comprehensive & magnificent interactive geometry resource I've
found in the Internet! The link above is to the main page, or use these quick links to access the following tutorials:
www.mathsnet.net/geometry/index.html
Geometric
Construction Course
Develop your skills of compass-and
straightedge constructions with the interactive Java applets
www.mathsnet.net/campus/construction/index.html
Interactive Transformations
Each applet has interactive questions on the side panel so it acts as a great tutorial into rotations, reflections, translations, enlargements and combinations of these.
www.mathsnet.net/transform/index.html
Interactive Shape
Get a clear and complete understanding of shapes, their patterns and properties with the help of interactive pictures.
www.mathsnet.net/shape/index.html
Interactive Pythagoras' Theorem
History, eleven different proofs illustrated with Java applets,
problems, related things, and more.
www.mathsnet.net/dynamic/pythagoras/index.html
Three Dimensions
View 3-D interactive pictures of Platonic solids,
Prisms, Pyramids, practice your ability to visualize 3-dimensional
objects from all viewpoints, and more.
www.mathsnet.net/geometry/solid/index.html
Simulations of Ruler and Compass Constructions
Practice compass & ruler constructions interactively online. Hints and solutions included.
wims.unice.fr/wims/wims.cgi?session=1V77FB9E9B.5&+lang=en&+cmd=intro&+module=tool%2Fgeometry%2Frulecomp.en&+special_parm=1
Absorb Mathematics for GCSE from Crocodile Clips
An on-screen textbook using animations and Crocodile Mathematics models to explain concepts in a straightforward visual manner. Students are able to experiment with models. Click on the "samples" to view free online interactive tutorials of high school geometry topics; as a whole this is commercial software.
www.crocodile-clips.com/absorb/AM4/index.htm
Dynamic Geometry® Explorations
A bunch of interactive geometry activities, along with instructions and questions to guide your exploration. Need a Java-enabled browser.
www.keymath.com/DG/dynamic/index.html
Geometry Gizmos at Explorelearning.com
"Gizmo" is an interactive virtual 'gadget' that lets
you explore the mathematical concept, and serves as a lesson with the included exploration guide. Find gizmos for Lines and angles, Reasoning and proof, Area, Quadrilaterals and other polygons, Triangles, Similarity and transformations, Right triangle trigonometry, Circles,
Three-dimensional figures. You can to register for a free 30 day trial, or
subscribe. Excellent for exploring and understanding!
www.explorelearning.com/index.cfm?method=cResource.dspChildrenForCourse&CourseID=127
Tim's Triangular Page
Lists all the basic facts about triangles followed by some problems.
sakharov.net/triangle.html
Pythagorean Theorem
This interactive figure illustrates the famous theorem
and its proof.
standards.nctm.org/document/eexamples/chap6/6.5/index.htm#applet
Transformations
Use these interactive figures to explore geometric
transformations (rotations, translations, and reflections AND a composition of
these).
standards.nctm.org/document/eexamples/chap6/6.4/index.htm
Symmetries and Their Properties - Lessons from NCTM Illuminations
Ready-to-use online
lessons that use interactive Java applets on symmetries:
Rotational symmetry, reflections, translations,
and glide reflections.
illuminations.nctm.org/index_o.aspx?id=138
Euclid's Elements
A set of Java applets that bring to life the theorems in
the Elements.
aleph0.clarku.edu/~djoyce/java/elements/elements.html
Knowhere
Discover how the structure of space determines the shape of things. Lessons about symmetry of polyhedra, space filling, how atoms pack together, structure of minerals. Also lessons about structural stability such as inbridges, beams, and buildings - basics of engineering.
www.polymorf.net/knowhere.htm
High School Measurement Worksheets
and Geometry Worksheets
www.funmaths.com/worksheets/ws06.htm
How to Write a Solution
An article exploring aspects of how to write a clear solution - or proof. Meant for college students but helpful for anyone who wants to learn to write mathematical proofs.
www.artofproblemsolving.com/Resources/AoPS_R_A_HowWrite.php
Dr. Math Geometry Books
Easy-to-read, excellent explanations of middle and high school geometry questions. $7-$10.
www.homeschoolmath.net/reviews/dr_math_geometry.php
NonEuclid
Interactive Java software for creating ruler and compass constructions
in both the Poincaré disk and the upper half-plane models of hyperbolic geometry. See also, Why is it Important for Students to Study Hyperbolic Geometry?
cs.unm.edu/~joel/NonEuclid/NonEuclid.html
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Trigonometry
Dave's Short Trig Course
Explanations on trigonometry concepts with interactive applets.
aleph0.clarku.edu/~djoyce/java/trig/
The Math Page: Trigonometry
Tutorials on various trigonometry topics accompanied with exercises where the answer is revealed with a mouseover.
www.themathpage.com/aTrig/trigonometry.htm
Trigonometry Realms
from Zona Land
"When you understand this animated diagram, you shall understand the sin(x)." Detailed explanations relating the basic trigonometric functions to the right triangle. Check their Point Definitions for Trig Functions page, where a dynamic graph shows the relationships between the unit circle graph and the standard graph and the right triangle definition of the trigonometric functions.
id.mind.net/~zona/mmts/trigonometryRealms/trigonometryRealms.html
Maths Online Gallery: Trigonometric Functions
Collection of Java applets with exercises for the student. The Definition of trig functions applet illustrates the right-triangle definitions and comes with exercises to guide the exploration. Also included applet Triangle and Law of Sines and Recognize graphs puzzles.
www.univie.ac.at/future.media/moe/galerie/wfun/wfun.html#winkelf
Trigonometric Functions and Calculus for Liberal Arts and Business Majors
A complete tutorial online - modeling with sine function, the six trigonometric funtions, their derivatives and integrals. Includes exercises and answers to odd-numbered ones.
people.hofstra.edu/faculty/Stefan_Waner/RealWorld/trig/trigintro.html
Trigonometry Illustrations
A collection of Java applets graphing or illustrating all trigonometric functions, some inequalities, plus law of sines and law of cosines.
www.ies.co.jp/math/products/trig/menu.html
Explorelearning Trigonometry Gizmos
Gizmos (interactive online activities with exploration guides) for cosine, sine, and tangent functions, unit circle, simplifying, translating and scaling trig functions. Try their free trial
account. Dynamical guided exploring with these gizmos promotes
understanding. Excellent resource!
www.explorelearning.com/index.cfm?method=cResource.dspResourcesForCourse&CourseID=254
Trigonometric Functions Mathplet
This Java applet is worth checking since while graphing the
function it shows the angle changing on the unit circle. However, you can't scale the graph paper.
magnus-karlsson.nu/mathplets/trig/trigfunc.html
Probability & Statistics
Tutorials
Statistics and Probability Interactive Activities
Including different graphs & plots, experimental
probability with dice or coins or spinner, conditional probability with a boxes-and-marbles experiment, sampling with and without replacement with a draw-marbles experiment, the famous MONTY HALL!, and more.
www.shodor.org/interactivate/activities/#pro
The
Regression Line and Correlation
An i-Math Investigation or a series of ready-to-use online
lessons that use an interactive Java applet to help students develop a
conceptual understanding of the least-squares regression line and
correlation. Excellent.
illuminations.nctm.org/imath/912/LinearRelationships/index.html
Online Statistics: An Interactive Multimedia Course of Study
An introductory-level statistics book. The material is presented both as a standard textbook and as a multimedia presentation. The book features interactive demonstrations and simulations, case studies, and an analysis lab.
onlinestatbook.com/
Dau Stat Refresher
An interactive tutorial which gives a comprehensive view of
Probability and Statistics. Good exposition and well arranged
material. Most of it is in the college level, but the beginning parts could be used on high school level. Has exercises too but grading did not work.
cne.gmu.edu/modules/dau/stat/
SurfStat Australia
An online college level text of introductory statistics.
www.anu.edu.au/nceph/surfstat/surfstat-home/surfstat.html
Math Goodies Probability Lessons
Basic explanations with lots of worked-out examples and some online exercises. Some lessons only available on their CD-ROM.
www.mathgoodies.com/lessons/vol6/intro_probability.html
GapMinder
Visualizing human development trends (such as poverty, health, gaps, income on a global scale) via stunning, interactive statistical graphs.
This is an interactive, dynamic tool and not just static graphs. Download the software or the reports for free.
www.gapminder.org/
TalkStats.com - Statistics Help
Discussion forum where you can ask statistics questions.
talkstats.com/
Statistics: Inferences and Predictions
from ExploreLearning.com
Great interactive 'gizmos' about correlation, least squares fit line, scatter plots, and more. All activities include exploration tutorial and assessment questions. Free trial.
www.explorelearning.com/index.cfm?method=cResource.dspResourcesForCourse&CourseID=267
Graphing activities
Data Analysis and Probability gizmos from Explorelearning.com
Interactive exploration activities online, with lesson
plans. Topics include box-and-whisker plots, histograms, stem-and-leaf plots, lines of best fits using least squares, scatter plots; probability topics; and more. This is an excellent resource for all math students. They have a free trial account; after that by subscription.
www.explorelearning.com/index.cfm?method=cResource.dspChildrenForCourse&CourseID=129
Statistics Interactive Activities
(scroll down to Statistics and Probability concepts)
A set of interactive tools for exploring histograms, pie charts, boxplots, stem-leafs, and mean, median, variance, and standard deviation of data. Can enter your own data or explore the examples.
www.shodor.org/interactivate/activities/tools.html
Java Applet Hotlist from SurfStat
Centres (mean and median), growing histogram, linear
regression and discrete probability distributions applets.
See also the graphing software section; many of the programs have statistical plots features.
www.anu.edu.au/nceph/surfstat/surfstat-home/applets.html
Logic
Introduction to Logic
A set of online tutorials for the study of elementary logic covering propositional and predicate calculus. Also an interactive Java applet with exercises.
logic.philosophy.ox.ac.uk/
An Elementary Introduction to Logic and Set Theory
An online tutorial including sentential logic, predicate logic and quantifiers, methods of proof, and naive set theory.
matcmadison.edu/alehnen/weblogic/logcont.htm
How to Write Proofs
A 12-part tutorial on proof writing. Includes direct proof, proof by contradiction, proof by contrapositive, mathematical induction, if and only if, and proof strategies.
csufresno.edu/%7Elarryc/proofs/proofs.html
Dc Proof
Free PC software for learning the fundamentals of logic and proof (for college or advanced high school students).
www.dcproof.com/
Logic Lorksheets
Easy logic puzzles for middle or high school.
www.edhelper.com/logic_puzzles.htm
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