The National Library of Virtual Manipulatives (NLVM) is a website that houses a goldmine of visual models and interactive virtual manipulatives for mathematics instruction.  The library began as a project in 1999 with support from the National Science Foundation and was developed at Utah State University. It has since undergone numerous revisions and additions and presently contains over 100 virtual manipulatives. The manipulatives are available in English, French, and Spanish. To use the manipulatives you must have a Java enabled web browser.

The organization of the website is very user friendly and extremely easy to navigate. The home page consists of a simple table with suggested grade bands heading each column and a math content area heading each row.

Each section contains an alphabetized list of the manipulatives available along with a small picture of what each manipulative looks like and a short description of its purpose.

For each virtual manipulative there are simple directions to help parents, teachers, and students to understand the purpose and functionality of the manipulative. Once you open a virtual manipulative, you will see these options at the top of the screen – “Parent/Teacher”, “Instructions” and sometimes “Activities”.

In these tabs you will find:

• Clear instructions on how the virtual manipulative works
• Key mathematical concepts and relationships explored
• Suggestions for activities or lesson plans (with lesson objectives, extensions, suggestions for formative assessment, cross references)
• Built in answer check

Some manipulatives also contain extra activities that are intended for independent practice or group activities. An integral component of these supplementary activities is a process of reflection where students are asked to describe, analyze, and extend their thinking which can be accomplished in group discussions or by writing in math journals.

This resource can be used for adult education students at all levels to develop algebraic thinking, build conceptual understanding, and develop problem solving skills. You’ll find as you explore the site that many of the virtual manipulatives are repeated across several grade bands, suggesting that it is not particularly the grade band that teachers should be focusing when choosing manipulatives they would like to use with their students. Thus, a suggestion here would be for teachers to first browse the manipulatives in the Pre-K-2 grade band, choose one to try with students, and then move forward as they assess student understanding of foundational concepts.

Be sure to check out the numerous fraction manipulatives! You’ll find them in the Number and Operations section and they provide lots of opportunities for your students to visualize, manipulate, and gain conceptual understanding of what fractions really mean. Once accomplished, be sure to check out Fractions – Adding as well as Fractions – Rectangle Multiplication. Note: Make sure that students have already explored and understand the concept of whole number multiplication, using Rectangle Multiplication, before moving onto fractions.

If you are fortunate enough to have a SMARTboard in your classroom, you can use the suggested lesson plans as a way to engage students and involve the whole class in an interactive lesson. In addition to a virtual delivery of some of the more traditional manipulatives that you might already be familiar with, such as a geoboard, pattern blocks, and play money, you’ll find algebra balance scales, a function machine, graphing tools, measurement tools, and manipulatives that explore patterns. Some of these can be used as stand-alone lessons while others would work well as an interactive supplement to your current lessons.

Another way the SMARTboard would work well is to have one of the manipulatives ready-and-waiting as a warm up activity as students filter into the classroom.  Recommended here would be one of the more self-directed activities such as:

Circle 99, Coin Problem, Color Patterns, Peg Puzzle, or Fifteen Puzzle.

If you do not have internet access in your classroom, the NLVM Application is available for individual or multi-station purchase.

Overall, this is an effective and engaging resource to use as we align our mathematics instruction with Common Core State Standards and as we work to deepen our students, and our own, understanding of mathematical concepts and ideas.