Manipulative Mathematics


Manipulatives give students concrete models of abstract mathematical concepts. Students using manipulatives develop conceptual understanding of arithmetic and algebraic topics and procedures because they see how and why the mathematical procedures work.

We created Manipulative Mathematics activities for those topics where our experience teaching at Santa Ana College shows that developmental mathematics students have little understanding of mathematical concepts and tend to rely on poorly memorized procedures.  The concrete manipulative activities help students visualize and understand the abstract arithmetic and algebraic concepts.

We have sets of manipulatives, such as color chips, fraction pieces, algebra tiles, geoboards, and more, in our classrooms. Our college students use them to model and learn about mathematical procedures.  The degree to which we use  manipulatives varies according to the needs of each class.  Instead of lecturing on a topic, we guide our students through an activity in class to promote discovery learning. Later, we refer to the concrete activities when working examples on the board or answering student questions. We have heard many “ahas” from students who finally understand, for example, how to work with fractions or signed numbers.  You can read comments from some of our students by clicking here.

We created a series of Manipulative Mathematics packets to serve as resources for teachers who would like to use manipulatives to help their students develop conceptual understanding of arithmetic and algebraic topics.  Each packet includes one or more activities related to a common mathematical topic. Each activity includes an instructor page, student worksheet, and extra practice problems.

  • The instructor page lists the resources needed, and gives information about the purpose of the activity and detailed directions for use in class. A link to an online source of virtual manipulatives similar to the physical ones used in the activity is provided on the instructor page of most activities.
  • The student worksheet is a step-by-step developmental progression of questions leading students to discover a mathematical property or algorithm through the use of manipulatives.
  • The extra practice problems reinforce the results of the student worksheet.

Use the link below to see the full set of Manipulative Mathematics Activity Worksheets.

Teacher training videos giving guidance on the use of all the manipulatives in the Manipulative Mathematics activities can be viewed at this link:  Manipulative Mathematics Teacher Training Videos.

The target user of  Manipulative Mathematics activities is a community college teacher of Developmental Mathematics. High school and middle school teachers may want to consider using Manipulative Mathematics activities in their mathematics classes. The activities could also benefit anyone who would like a clearer understanding of basic algebraic concepts.


Manipulative Mathematics links:
Activity Worksheets

Teacher Training Videos
Links to Virtual Manipulatives




15 responses to Manipulative Mathematics

  1. Cindy Fry


    I am new to teaching middle/high school math and am interested in your materials. Would you please make these available to me so that I may use them in our math classes?

    Thank you,


    • MaryAnne

      Cindy, you should be able to view and download our materials directly from the website. If you do use them in your math classes, please let us know.

  2. Tam'ra Kerch

    I am teaching Foundations of Algebra to 9th graders and would love access to your Manipulative packets if possible. I have taught developmental math to college students and see the value of teaching this course prior to college entrance. Thanks much!

  3. Suwanda Coffey

    I have been reading the information on your website and it has been interesting. My state has recently created a course that sounds very much like your course. I work as a math mentor to teachers & would love to review your course materials. Will you provide access to me?

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