Math Manipulatives

Concrete Representation, Physical Models, Card sort

UDL 2.5 UDL 5.2

Manipulatives are physical objects that aid understanding of mathematical concepts or processes by allowing students to physically explore or demonstrate the concept or process. The use of manipulatives provides a way for students to learn concepts in a developmentally-appropriate, hands-on, experiential way. Mathematical manipulatives are typically used in the first step of introducing new mathematical concepts.

Implementation Tips

Number Lines
For students who need support when adding and subtracting positive and negative numbers, a number line can be provided.
When teaching the value of coins, use actual coins to represent values (e.g. A nickel is equal to 5 pennies. A quarter is equal to five nickels.).
Additional Support
If a student is a visual learner, use manipulatives to support answering math problems (e.g. counters for adding/subtractions, fraction strips, base ten blocks,etc.)


1:1 Correspondence with Manipulatives
When introducing addition, teachers can have students count items representing the numbers to be counted.
Fraction Strips
Teachers can use fraction strips to demonstrate parts of a whole.
Base 10 Blocks
Base 10 blocks can be used to conceptually demonstrate place value and regrouping.
Math Card Sorts
Teachers can put mathematical information (e.g. definitions, graphs, equations, etc.) on cards so that students can physically sort and organize information.

Related Strategies