The National Library of Virtual Manipulatives (NLVM) for mathematics has been online for about 10 years. It provides webbased virtual manipulatives for children to interact with to help them develop a better understanding of math. The math manipulatives are for children in grades PreK through 12. The math concepts addressed include:
 Numbers and Operations – developing an understanding numbers, number representation, number relationships, and number systems.
 Algebra – understanding the relationships among quantities using symbols and modeling mathematical change.
 Geometry – using spatial sense to interpret and reflect on the physical environment.
 Measurement – developing the understanding how to measure objects using tools and formulas to determine measurements.
 Data Analysis and Probability – using questions to make predictions for analyzing data.
For an interactive math website to engage children, it must present problems which require the use of thinking skills to solve problems. Problem solving and interactivity go handinhand for children to develop a complete understanding of mathematics. The NLVM website provides these two key components – problem solving and interactivity.
Elementary Math Website
The interactive math on this website is broken down into two grade bands for elementary school, PreK2 and 35. Some of the interactive math topics found includes:
Grades PreK2
 Base Blocks Addition – using base ten blocks to model grouping
 Number Patterns – discovering a pattern to complete a sequence of numbers
 Color Patterns – arranging colors to complete patterns
 Spinners – working with spinners to learn about probabilities of numbers
 Pattern Blocks – using geometric shapes to build patterns and solve problems
Grades 35

 Base Blocks Subtraction – using base ten blocks to model separation of groups through subtraction
 Circle 99 – puzzle solving by adding positive and negative integers to sum ninetynine
 Fraction Equivalents – illustrating relationships between equivalent fractions
 Tangrams – using Chinese puzzle pieces to make shapes and solve problems
 Geoboard – using virtual geoboards to illustrate area, perimeter, and rational number concepts
 Transformations – interacting with and seeing the result of a dilation transformation
 Bar Chart – creating a bar chart to show quantities or percentages
Middle School Math Website
The interactive math on this website for middle school is broken down into grades 68. Some of the interactive math topics found includes:


 Number Line Bars – dividing fractions using number lines
 Algebra Balance Scales – solving linear equations using a balance beam for representation
 Algebra Tiles – visualizing multiplying and factoring algebraic expressions with tiles
 Pythagorean Theorem – solving puzzles which illustrate the proof of Pythagorean’s Theorem
 Congruent Triangles – building similar triangles through combining sides and angles
 Coin Tossing – exploring probability concepts through simulating repeated coin tosses
 Stick or Switch – investigating probabilities of sticking with a decision or switching

High School Math Website
The interactive math on this website for high school is broken down into grades 912. Some of the interactive math topics found includes:


 Fibonacci Numbers – exploring the Fibonacci sequence and the golden ratio
 Rational Numbers Triangle – exploring a triangular array which contains every positive rational number exactly one time
 Pentominoes – using the 12 pentomino combinations to solve problems
 Great Circle – using a 3D globe to visualize and measure the shortest path between two points on the globe
 Transformations – interacting with and seeing the result of a rotation transformation
 Whammy Awards – using different voting schemes to cause contradictory outcomes

Math Website Requirements and Standards
The NLVM works with all web browsers for either PC or Mac. The browser must have Java Applets, which can be easily downloaded if not on the computer. This website is funded by grants from the National Science Foundation and complies with all Math Standards.
An additional website, An Interactive K12 Math Website provides online resources to support interactive math activities to the Illuminations website.