For many people, the mention of math manipulatives calls to mind using marbles for counting or craft sticks tied in bundles of 10 to illustrate place value. Once such elementary concepts have been learned, the role of hands-on math tools may be less clear.

Educators have discovered, however, that using manipulatives well helps students of all ages to learn new concepts and deepen understanding. Using manipulatives effectively also increases retention of mastered concepts.

The most effective math manipulatives are visually simple and consistently used throughout a curriculum. Extra, visually-rich detail, such as that found on play money, on objects featuring licensed characters, or in small plastic animals, can significantly distract students from the concept they are trying to learn. The manipulatives that are most helpful to students have been carefully designed to bridge the gap between concrete and abstract concepts.

Math Manipulatives for Everyone

Here are some of the advanced math concepts that can be demonstrated with appropriate manipulatives:

• Operations with fractions
• Operations with decimals
• Area, volume, and surface area
• Operations with negative and positive numbers
• Exponents
• Square roots
• Place value in algebraic equations
• Ratios
• Algebraic properties
• Polynomial factoring
• Operations with polynomials
• Solving equations

Even adults who have taken advanced math courses can be astonished to see algebra concepts so clearly represented with place-value blocks or algebra tiles. For example, we may know that x² = x ⋅ x, but can we visualize it? Do we truly understand what x² + 5x + 6 actually represents?

As a homeschooling family begins to incorporate manipulatives into an older student’s math experience, the parents’ involvement and positive attitude are crucial to success. Some specific considerations and tips include:

4 Math Manipulatives Tips for Parents

1) Model With Your Student

Model with your student how to use the manipulatives to understand a specific concept.

2) Use What You Need

Use manipulatives only as much as an individual student needs. Otherwise older students may get bored and frustrated.

3) Demonstrate Mastery

Use manipulatives to have students demonstrate mastery of a lesson’s concepts and skills. Doing so successfully shows understanding rather than the ability to follow a rote procedure.

4) Represent Abstract Ideas

Represent abstract ideas with manipulatives to help students articulate their thought process when explaining a concept. If needed, the instructor can then guide the student toward a better process.

Math-U-See Manipulatives App

You may be familiar with the Math-U-See manipulatives, which provide a foundation for many mathematical concepts. They include integer blocks, fraction overlays, and algebra/decimal inserts. Did you know that Math-U-See also offers an app on multiple platforms that features all the manipulatives in an easy-to-use format? The app is a wonderful tool for families on the go who want their math lessons to be more portable.

You can learn more here.

Further Reading

David T. Willingham wrote a fascinating article for American Educator titled “Do Manipulatives Help Students Learn?” in 2017. You can read it here.