Mathematics Help

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I finally decided to poke around the web and find some websites that help explain mathematical concepts in which my students may have trouble. However, instead of just putting up generic links, I've put up links to sites that explain specific, individual concepts. I try to give links to sites that explain concepts in the same way that I do in class, but I also sometimes link to sites with alternate explanations. Enjoy!

This site is under very serious construction and has been for a while.

• Mathematics Modeling
• Sets
• Interactive Venn Diagrams - The computer asks what region something goes in, and the user clicks the appropriate region.
• An explanation of Union, Intersection, and Complement of sets with Venn Diagrams - With nice, simple drawings.
• Venn Diagram Shape Sorter - Neat interactive activity that lets the user set the rules for the diagrams and sort the pieces or lets the computer set the rule for the pieces and the user must guess the rule.

• Algebra Review Topics
• R.3 Integer Exponents
• R.3 Basic Exponent Definitions - From Purplemath
• R.4 Definitions of Polynomials - From Purplemath
• R.4 Combining Like Terms - From Purplemath
• R.4 Adding and Subtracting polynomials - From Purplemath
• R.4 Adding polynomials - With a simple algebra tile graphic and using multiple colours to help show different terms
• R.4 Subtracting Polynomials - From the same site as above
• R.4 Multiplying polynomials part 1 - From Purplemath. The Distributive Property and FOIL Method
• R.4 Algebra Multiplication Calculator - This calculator multiplies out polynomials.
• R.4 Multiplying polynomials part 2 - From Purplemath. More complicated multiplication.
• R.4 Multiplying Binomials - This site shows four different ways to multiply two binomials, including the "grid".
• R.4 Interactive Multiplication of polynomials
• R.4 Basic explanation of multiplying polynomials
• R.5 Algebra Factoring Calculator - This calculator factors polynomials.
• R.5 Interactive factoring of polynomials
• R.6 Simplifying Complex Fractions - Alternative Method - leaving as a fraction for an extra step.
• R.6 Algebra Cancelling Calculator - This calculator factors and cancels algebraic fractions.

• Lines
• 1.2 Plotting Points - This is actually an interactive applet where a little house is plotted on a grid and you type in the coordinates.
• 1.4 Basic graphical explanation of what a slope is.
• 1.4 Slope - Positive, negative, zero, and undefined. Also with examples of calculating slope.
• 2.1 Graphing Linear Equations – Graphing lines in both slope-intercept form and point-slope form
• 2.1 Graphing Linear Equations – Making a T-Chart/ Finding (x, y) points
• 2.1 Graphing Linear Equations Using Slope – Using Slope and y-intercept to graph lines.
• 2.1 A web program that graphs lines
• 2.1-2.2 Practice with equations of lines
• 2.3 Interactive solving for x - linear
• 2.4 Interactive solving linear inequalities
• Chapter Three
• 3.1-3.2 Quadratic models examples
• 3.1-3.2 A sample page from a book
• 3.1-3.2 Key equations with examples
• 3.1-3.2 Quadratic quiz
• 3.1 Quadratic Function Applet - Check out how the graph changes when a, b, or c change in the standard form of a quadratic equation.
• 3.1-3.2 PurpleMath's commentary on Quadratic models
• 3.2 Part 2 of PurpleMath's site - Quadratic Formula
• 3.2 Quadratic Formula Interactive
• 3.1-3.2 Part 3 of PurpleMath's site - Maximum/Minimum problems
• 3.1-3.2 Comments on Quadratic Functions
• Chapter Four
• 4.1-4.2 Applet that graphs cubic functions
• 4.1-4.2 Applet that graphs quartic functions
• 4.7 Fractional Exponents - From Purplemath
• 4.7 Fractional Exponents
• Chapter Five
• 5.1 Composition of functions - From Purplemath
• 5.1 An example of a composition
• 5.2 Graphing Inverses - From Purplemath
• 5.2 Inverse Functions - A basic explanation
• Chapter Six
• 6.1 Systems of Equations - Using Substitution
• 6.1 Systems of Equations - Substitution at PurpleMath
• 6.2 Systems of Equations - Using Elimination
• 6.2 Systems of Equations - Elimination at PurpleMath

• General Mathematics
• Chapter One
• 1.7 Rounding whole numbers Interactive with explanations
• 1.8 Order of Operations
• 1.8 More Order of Operations
• 1.8 Order of Operations Practice
• 1.10 George Polya's Guide to Problem Solving
• 1.10 Strategies for problem solving With examples
• Chapter Two
• Fractions in General Adding Subtracting, Multiplying, Dividing, Reducing, Converting, etc. Has interactive practice problems as well!
• 2.1 Identifying Fractions Interactive site lets you figure out the numerator and denominator
• 2.2 Changing a fraction to a mixed number - Interactive, with visuals
• 2.2 Changing a mixed number into a fraction - Interactive, with visuals
• 2.2 Changing improper fractions to mixed numbers and from mixed numbers to improper fractions Interactive with explanations
• 2.3 An activity involving sorting prime and composite numbers
• 2.3 Factors and Prime Numbers - With interactive questions.
• 2.3 Factors and Divisibility Rules
• 2.3 Interactive Prime Number Checker - Checks to see if a number is prime and what its prime factorization is if it is composite.
• 2.4 Finding equivalent fractions using and interactive picture
• 2.4 Getting a common denominator - From the same page as the links above.
• 2.4 Reducing fractions - From the same page as the links above.
• 2.5 Multiplying Fractions using Rectangles
• 2.5 Mystery Picture - Multiplying fractions - Interactive puzzle using multiplication of fractions and whole numbers.
• 2.5 Multiplying fractions Interactive with explanations
• 2.7 Dividing fractions Interactive with explanations
• 2.5, 2.7 Fractions - Multiplying and Dividing - With mixed numbers and improper fractions.
• 2.8 Multiplying a whole number by a mixed number Interactive with fraction circles.
• Chapter Three
• 3.1, 3.3 Adding fractions and Mixed Numbers Interactive with explanations
• Chapter Four
• 4.1 Converting from Decimals to Fractions Interactive with explanations
• 4.5 Dividing Decimals With pictures
• 4.5 Division of Decimals Using base ten blocks. Nifty! The long division method is underneath the base ten block example.
• 4.5 Dividing Decimals by multiplying both numbers by a power of ten
• 4.6 Converting fractions to decimals Interactive with examples!
• Chapter Five
• The Golden Ratio - Activities
• 5.1 Ratios - what they are Interactive with examples
• Chapter Six
• 6.6 Calculating sale price Interactive with examples
• 6.7 Simple Interest Interactive with examples
• 6.8 Compound Interest Interactive with examples
• Chapter Seven
• Converting Length Interactive with examples
• Converting Mass Interactive with examples
• 7.5 Conversions - Metric and English Interactive with examples
• 7.5 Conversions with temperature Interactive with examples
• Chapter Eight
• 8.3 Squares Interactive with examples
• 8.3 Rectangles Interactive with examples
• 8.5 Right Triangles Interactive with examples
• 8.6 Circles Interactive with examples
• 8.7 Volume of rectangular solids (boxes) Interactive with examples
• 8.7 Volume of Cylinders Interactive with examples

• Geometry and Trigonometry
• Interactive Sites
• Interactive Unit Circle As you move the point around the circle, the degrees and radian measures are shown.
• Interactive Unit circle and Graphs This applet lets you see what "x" and "y" are as well as the degrees and radians.
• Unit Circle and Trig Functions Click on the applet button on this page and it shows the graphs of the three basic trig functions as the point moves around the unit circle.
• Graphs of the three main trig functions You can move the point on the graph and unit circle to show the values of the sine, cosine, and tangent.
• The Metric System and Conversions
• The Pythagorean Theorem
• The Pythagorean Theorem Interactive - A site wherein the user can input values for two sides of the triangle and the computer will calculate the third side and area of the triangle.
• Pythagorean Triples Generator - This is a web site where you can plug in two values, and it will generate a Pythagorean Triple. Neat!
• Pythagorean Theorem Calculator - This calculator will find the third side of a right triangle if you know the lengths of the other two sides.
• Chapter Six - Trig Book
• 6.2 Right Triangle Trigonometry Word Problems - Includes commentary on the angles of elevation and depression.
• 6.2 More angles of elevation and depression - Also contains a few practice problems with explanations and hints.
• 6.3 Coterminal Angles Definition and picture example.
• Chapter Eight - Trig Book
• 8.1 The Law of Sines - Gives a geometric explanation of where it comes from and works some examples. This link also gives pictorial explanations of why we may get 2, 1, or 0 solutions for certain triangles.
• 8.1 The Law of Sines Interactive Applet - This site lets the user create their own triangles and examine the values for the ratios of the Law of Sines.
• 8.1 Law of Sines Explanation - This explanation is given in the format of a PDF file on slides. It gives examples along with the explanations.
• 8.1 Law of Sines Calculator
• 8.2 Law of Cosines Calculator
• 8.2 The Law of Cosines - The basic statement and a few examples along with some you can work yourself.
• 8.2 Applications of the Law of Cosines Some examples of word problems involving the Law of Cosines. Includes a practice test at the bottom of the page. The next page also has a sample test.
• 8.2 Law of Cosines Explanation - This explanation is given in the format of a PDF file on slides. It gives examples along with the explanations. (Like the Law of Sines slides above.)
• 8.3 Basics of Vectors Describes what a vector is and has lots of drawings and a couple of animations.
• 8.3 Vector Addition Describes the relationship between vectors having forces pulling in different directions. Includes vertical and horizontal forces as well as forces pulling at a particular angle.
• 8.3 Vector Resulants Describes what the result of adding two or more vectors together is.
• 8.3 Vector Components Describes how to find the horizontal and vertical components of a resultant vector. (Breaking down a resultant that is at an angle into the leftward/rightward pull and the upward/downward pull.)
• 8.3 Using Vectors in Statics This is one application using Vector measure. Folks in the Computer Design Graphics Program might want to check it out.
• Chapter Six - Geometry Book
• Extra Math Topics That Are Cool
• Golden Rectangles and how the Golden Ratio is attained algebraically
• Golden Ellipses, Spirals, Polyhedra, and other Golden Shapes
• The Golden Ratio with the Parthenon, Pyramids, and the Mona Lisa
• Music and Mathematics!
• Pattern Shading in Pascal's triangle - Shade in all multiples of a given number. Good practice for divisibility rules.
• Online calculators

Special thanks to Mr. Stennis Johnson for the links to webmath.com

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