Virtual Manipulatives: Powerful Tools to Build Conceptual Understanding in Mathematics
In order to develop every student’s mathematical proficiency, leaders and teachers must systematically integrate the use of concrete and virtual manipulatives into classroom instruction at all grade levels (NCSM, 2013). Virtual manipulatives can be used as a part of the Concrete-Representational-Abstract (C-R-A) learning cycle. These manipulatives are important tools for teacher modeling and demonstration, and provide students access to manipulatives both inside and outside of the school day via computers and other mobile devices (NCSM, 2013).
Here’s a sample of virtual manipulatives that are available for teachers and students:
Math Learning Center Apps are free virtual manipulative apps that are available in two or more versions: a web app for all modern browsers, and downloadable versions for specific operating systems and devices (such as Apple iOS for iPad).
Illuminations Interactives from the National Council of Teachers of Mathematics (NCTM) contain virtual manipulatives and applets identified by grade band. Apps for mobile devices are also among interactives.
Houghton Mifflin Harcourt iTools contain virtual manipulatives with activities for the following: counters, base-ten blocks, number lines, number charts, graphs, fractions, geometry, measurement, algebra, and probability.
Glencoe/McGraw-Hill virtual manipulatives include a series of commonly used manipulatives. It also includes game boards, story boards, various grids, graph formats and number lines. Tools include a ruler, protractor, timer, stopwatch, straight line tool, pen, color options, text boxes, and more.
National Council of Supervisors of Mathematics. (2013). Improving student achievement in mathematics by using manipulatives with classroom instruction. Retrieved from mathedleadership.org
Enhanced Scope and Sequence
The SOL Enhanced Scope and Sequence (ESS) was created by a team of general and special educators and VDOE personnel. ESS provides teachers across the state with differentiated lessons that are aligned with the essential knowledge and skills found in the Curriculum Framework at VDOE. The ESS is organized by content areas (i.e. Mathematics, English, History and Social Science, Science), and can be accessed at the Virginia Department of Education Standards of Learning.
Virginia Department of Education Instructional Resources
- The Standards and SOL-based Instructional Resources
- Math ESS Lessons
- English ESS Lessons
- Science and Social Studies ESS Lessons
Suggestions for Communicating With and About People with Disabilities at the CDC.
Virginia Department of Education Mathematics Resources
- Tests and Sample Item Sets Released in Spring 2014 (Grade 3, Grade 4, and Grade 5)
- VDOE Mathematics Resources
- Algebra Readiness Inventory Curriculum Companion
- Web Tour of the ARI Curriculum Companion
- Mathematics Word Wall Cards
- VDOE Guidelines for Educating Students with Specific Learning Disabilities in Math
T-TAC Online Math Resources
Additional Mathematics Sites of Interest
Fluency Without Fear by Jo Boaler (activities to develop Number Sense and Number Facts)
Watch this NCETM video of a teacher using multiple representations for multiplication. (This teacher works in a school where 3 x 4 is interpreted as 3 + 3 + 3 + 3). It is a good example of how to support the conceptual understanding of multiplication facts and its importance as students develop fact fluency.
Quantiles Framework Resources
- Quantiles Teacher Assistant and Quantiles Math Skills Database Search
- Web Tour of the Quantiles Framework Tools
Newly Added Resources
At the National Center on Intensive Instruction website, you can find examples of instructional plans that intensify fraction instruction. You can download the plans and print-based representations (manipulatives) at the links below.