Virtual Mathematics Manipulatives by the National Library of Virtual Manipulatives

PBWorks Wiki Page by Kelsey Odom

**What is the National Library of Virtual Manipulatives?**

Powered by Utah State University and the National Science Foundation, the National Library of Virtual Manipulatives (NLVM) is a website that boasts a collection of manipulatives for mathematics. All that is needed for students to access these virtual manipulatives is a computer with internet access.

(Above is a picture of the NLVM homepage. Notice the link for the "Base Blocks" virtual manipulative. http://nlvm.usu.edu/en/nav/grade_g_2.html)

**What are Base Blocks? **

Base Blocks are physical representations of numbers. Each individual block represents “one.” Depending on the Base System being used, the individual blocks can be clustered so that place value becomes a clear and easy-to-explain concept. The most common types of Base Blocks are Base 10 Blocks because they correlate with our number system.

(Above are pictures of Base 10 Blocks. On the left are the actual manipulatives while the picture on the right shows the virtual manipulatives. http://2.bp.blogspot.com/_7FZSsh37jk8/TI-1eAMsJ_I/AAAAAAAABFo/B8PPOSqFoQ8/s1600/Base+10+blocks.jpg and http://nlvm.usu.edu/en/nav/frames_asid_152_g_2_t_1.html?from=grade_g_2.html)

Click here to view a short video explaining Base Blocks as they work in the Base 10 System. We are familiar with the Base 10 System (because that is our number system). However, there are other Base Systems as well. The Base 5 System is commonly taught is elementary school classrooms. Please click on this link to read a detailed explanation of how Base Blocks work in the Base 5 System.

(Above are pictures of Base 5 Blocks. On the left are the actual manipulatives while the picture on the right shows the virtual manipulatives. http://www.snow.edu/jonathanb/Courses/Math2010/base5blocks_1.jpg and http://nlvm.usu.edu/en/nav/frames_asid_152_g_2_t_1.html?from=grade_g_2.html)

**How do the NLVM Base Blocks work?**

The NLVM website contains Base Blocks as virtual manipulatives. These mathematics tools can be accessed by clicking on the “Base Blocks” link on the NLVM homepage or by simply clicking here.

(Above is a picture of the NLVM homepage. The blue arrow points to the access point for the Base Blocks. http://nlvm.usu.edu/en/nav/grade_g_2.html)

(Above is a picture of the Base Blocks virtual manipulative from the NLVM website. http://nlvm.usu.edu/en/nav/frames_asid_152_g_2_t_1.html?from=grade_g_2.html)

Based on the provided background information about Base Blocks, the NLVM virtual manipulatives can be used in mathematics lessons to illustrate the concept of place value. The number of times a student clicks on the units, longs, flats and blocks at the top of the page causes the screen to show that many units, longs, flats and blocks. For example, if a student wanted to show the number 2,135 using the manipulatives he/she would click the units button five times, the longs button three times, the flats button once and the blocks button twice. The number on the right hand side of the screen denotes the numerical value of the manipulatives. There is also a helpful instructions page that can be accessed by clicking on the button in the top right-hand corner of the page.

(Above is a labeled picture that helps show how the NLVM Base Blocks virtual manipulatives work. http://nlvm.usu.edu/en/nav/frames_asid_152_g_2_t_1.html?from=grade_g_2.html)

In the bottom right-hand corner of the Base Blocks page is a button that reads, “Show a Problem.” Clicking on this button yields a prompt in the center of the right-hand margin. This feature can be used for students in their practice using the Base Blocks manipulatives.

(Above are two pictures showing how to queue the practice problems within the NLVM Base Blocks virtual manipulatives. http://nlvm.usu.edu/en/nav/frames_asid_152_g_2_t_1.html?from=grade_g_2.html)

As students become more advanced, more columns can be added to the manipulative page. Students can also extend the page to start working on their understanding of place values after a decimal point.

(Above is a picture showing how to add decimal places and additional columns to the manipulative page. http://nlvm.usu.edu/en/nav/frames_asid_152_g_2_t_1.html?from=grade_g_2.html)

On the page, there is a place to switch what Base System the manipulatives represent. To switch to the Base 5 System the down arrow may be pushed once. Now five units equal a long, five longs equal a flat and five flats equal a block. Gaining an understanding of other Base Systems causes students to better understand the Base 10 System. This online mathematics tool helps students grasp number theory concepts such as place value, borrowing and decimals.

(Above is a picture illustrating how to change the Base System of the manipulative page. http://nlvm.usu.edu/en/nav/frames_asid_152_g_2_t_1.html?from=grade_g_2.html)

**What are three lesson ideas that incorporate the NLVM Base Blocks?**

Lesson Plan One: To ease into using the NLVM Base Blocks virtual manipulatives, it is a good idea to start students off with the practice of using the blocks to represent different numbers. Follow the link below to some worksheets that will allow students to become familiar with the online mathematics tool while recording their discoveries with pencil and paper. The NLVM Base Blocks should be incorporated into this lesson as the visual represention of place values. A student should take a number from the worksheet and build the corresponding value with the virtual Base Blocks. This lesson is a great way for a teacher to gadge student understanding of the virtual manipulatives.Lesson Plan Two: Once students are comfortable with the NLVM Base Blocks virtual manipulatives, playing a team-oriented game is a fun way for them to demonstrate their understandings of place values. Follow the link below to a lesson idea that will cause students to work in teams to slove place value problems. The NLVM Base Blocks must be incorporated as the method of communication in this place value game. Students must work together to solve place value problems relavent to everyday life.

Lesson Plan Three: When students are ready to think about numbers in different bases, it is time to implement the lesson plan found at the link below. It is important that students skip the first few slides of the lesson plan presentation about different colored chips. The directions about using diffeerent chips are irrelavent since students are using the NLVM Base Blocks virtual manipulatives (that they are already familiar with) when solving problems throughtout the course of this lesson. However, the remaining slides cause students to solve problems using the Base 5 System that relate to real-life. The slides even give students hints in order to help them solve the problems! This lesson serves as a good introduction to elementary-level number theory and will lead to students having broader understandings of adding, subtracting and borrowing in our familiar Base 10 System. This lesson plan culminates a unit in which students have worked with the NLVM Base Blocks virtual manipulatives and have develop an understanding of number theory principles relevant to elementary school curriculum. This lesson shows that students have not only learned how to use an online mathematics tool, they have learned how to use technology to solve problems that they face on a daily basis.

**Thank you for your interest in Base Blocks virtual manipulatives by the National Library of Virtual Manipulatives. Happy Learning and Teaching! **

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