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.

I’d seen this resource before, but I appreciate the reminder to take a second look. I’ve been thinking about algebra lately and so I went straight to the algebra tiles manipulative. Again, I had seen this tool for teaching multiplication of binomials and factoring of polynomials, but I didn’t really understand it. The manipulative was a great way to gain a concrete understanding of multiplication two binomials, (x+2) and (y+3), for example. The visual manipulative requires that all the pieces fit correctly, so you get feedback from the form of the tool that will you check to see if you understand.

I was wowed by the task of factoring polynomials with algebra tiles. I’m still getting comfortable with polynomials myself, so I really liked the practice. Using the tool, I was able to factor 2x^2 + 4xy +3x +6y into (2x +3) and (x + 2y) in 15 seconds flat! I’m proud of myself.

http://nlvm.usu.edu/en/nav/frames_asid_189_g_2_t_2.html?open=activities&from=topic_t_2.html (algebra tiles)

I also really liked the teacher/parent instructions on the manipulative pages. Under algebra tiles, I found:

“Use of this manipulative may make more sense if students understand how to represent multiplication and division of whole numbers or rational numbers as rectangular arrays. (See, for example: Rectangular Multiplication and Rectangular Multiplication of Fractions manipulatives)”

So, this led all me back to Patricia’s recommendation. I think it would be really interesting to look at Rectangular Multiplication with a class, then maybe Rectangular Multiplication of Fractions and then finally the Algebra Tiles. All three lay a good conceptual framework for multiplication (and area for that matter).

http://nlvm.usu.edu/en/nav/frames_asid_192_g_1_t_1.html (Multiplication)

http://nlvm.usu.edu/en/nav/frames_asid_194_g_2_t_1.html?from=topic_t_1.html (fractions)

Loved idea of using of multiple tools to learn number sense.