# Using Online Technology to Teach Math Skills to K-12 Students

The National Library of Virtual Manipulatives (NLVM) for mathematics has been online for about 10 years. It provides web-based 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 hand-in-hand 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, PreK-2 and 3-5. Some of the interactive math topics found includes:

• 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

• 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 ninety-nine
• 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 6-8. 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 9-12. 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 K-12 Math Website provides online resources to support interactive math activities to the Illuminations website.