In the early grades, it’s not uncommon to see math manipulatives used daily in the classroom. Teachers pull out connecting cubes, counters, base ten blocks, and more—tools that help students build a concrete understanding of math concepts. Whether they’re exploring different ways to make 10 or practicing addition, these hands-on tools support their thinking in meaningful ways.
This follows the CRA model—Concrete, Representational, Abstract. We start with the concrete, like manipulatives. Once students have a solid grasp of the concept, we move into the representational, such as drawings or visual models. Finally, we introduce the abstract, using numbers and symbols alone. For example:
- Concrete: Use connecting cubes to model 5 + 3
- Representational: Draw 5 circles and 3 more
- Abstract: Solve 5 + 3 = 8
But here’s what I’ve been thinking about lately: why do we often abandon manipulatives once students move into the upper grades?
Sure, by fourth or fifth grade, many students no longer need cubes for basic addition and subtraction. At that point, they’ve likely mastered those foundational skills and can work abstractly. But what about when we introduce new, more complex concepts—like volume in upper elementary or integers in middle school?
Volume is a great example. It’s a tough concept to grasp without something physical to hold or build. Yet so often, we hand students a formula and expect them to just “get it.” What if we instead gave them time to build with cubes, experiment, and see what volume means before jumping into the numbers?
The same goes for concepts like negative numbers. A number line or clothesline math activity can help students visualize and understand the relationships between positive and negative values. Why skip that step?
All this has me wondering: Is it a time issue? A training issue? Have we simply forgotten how powerful manipulatives can be for older students, too?
I’d love to hear your thoughts.
Do you use manipulatives in your classroom? What grade do you teach? What concepts do you use them for?
Let’s keep the conversation going—and keep math meaningful at every grade level.
Nowa Techie 
I don’t know if this was necessarily a conscious decision by educators, sometimes these frozen accidents happen where everybody does something one way, because that’s the way it’s been done before. At the same time, I think there is this false notion that “mature” math only involves numbers. But the best scientists and mathematicians in the world still play with things like manipulatives.
I love the image of Watson and Crick building the model of DNA, or the story of Linus Pauling playing with folding pieces of paper while sick in bed (which led to the story of the alpha helix).
I mostly teach elementary schoolers, but am strongly supportive of using manipulatives in higher grades! I think using manipulatives creates such memorable conceptual experiences that stay with people a lot longer than “formulas”.
I agree, I don’t think this was a conscious decision by educators. I think part of the fall out of focusing so much on state testing is a result of trying to get to the finish line as quickly as possible. Again, nothing against educators it’s a broken part of the system.