Math can feel like an abstract and overwhelming subject for children with math learning differences. The key to unlocking their understanding often lies in making math concepts tangible and concrete. By using manipulatives—hands-on tools that children can touch, move, and experiment with—you can bridge the gap between abstract ideas and real-world understanding. Here are my go-to manipulatives for teaching the basics of numbers and the number system.

Cuisenaire Rods
Cuisenaire Rods are colorful blocks of varying lengths that help children visualize relationships between numbers. They’re excellent for teaching addition, subtraction, multiplication, and fractions. By physically arranging and comparing the rods, children can develop a deeper sense of number magnitude and relationships.
Number Track
A number track is a simplified number line, often used with counters or markers. It’s perfect for helping children understand sequencing, addition, subtraction, and even skip counting. The visual and interactive nature of a number track makes it easier for children to see how numbers relate to one another.
Base Ten Frames
Base ten frames are grids that visually represent numbers using counters. They’re especially useful for teaching place value and building a foundational understanding of our base-10 number system. Children can manipulate the counters to see how numbers are grouped into tens and ones.
Craft Sticks and Elastics
Sometimes, the simplest tools are the most effective. Bundling craft sticks with elastics into groups of tens and leaving singles loose can help children grasp the concept of place value. They can physically group and regroup the sticks to perform addition or subtraction operations.
Rekenrek
The rekenrek, or arithmetic rack, is a counting frame with beads arranged in rows of ten. It’s an intuitive tool for teaching number sense, subitizing (recognizing quantities without counting), and basic arithmetic operations. The dual color scheme of the beads provides a clear visual distinction that aids comprehension.
Base Ten Blocks
Base ten blocks are a staple for teaching place value, addition, subtraction, and even multiplication. The blocks come in different sizes to represent units, tens, hundreds, and thousands. Children can physically build numbers and break them apart to understand the concept of regrouping.
Dice
Dice are versatile tools that can be used for countless math games and activities. From simple number recognition and counting to more complex addition, subtraction, and multiplication exercises, dice add an element of fun and randomness that keeps children engaged.
Fraction Cubes
Fraction cubes make the often tricky concept of fractions more accessible. These manipulatives allow children to compare fractions visually, see how they combine to form whole numbers, and explore equivalencies. They’re particularly helpful for teaching addition and subtraction of fractions.
Real Money
Using real coins and bills introduces children to the practical application of math. Money manipulatives are excellent for teaching counting, addition, subtraction, and the concept of decimals. Children can practice making change and budgeting, which ties math to everyday life.
Gear Clock
Understanding time can be challenging for many children, but a gear clock makes it easier. By manipulating the hands on the clock, children can see the relationship between hours and minutes. This hands-on approach helps demystify the concept of telling time and understanding intervals.
Final Thoughts
Making math concrete through manipulatives not only aids understanding but also builds confidence and enjoyment in learning. These tools help children engage with math in a hands-on way, transforming abstract concepts into tangible learning experiences. Whether you’re a teacher, tutor, or parent, incorporating these manipulatives into your math instruction can make a world of difference for children with math learning differences.
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