Math in Block Play, Pt. 1

posted by David Banzer

As a preschool teacher, the block area was my favorite area in my classroom and I spent a good portion of my time working with preschoolers as they built with blocks. Unit blocks specifically have enormous value in their use in the preschool classroom. Once children are familiar with the qualities of these blocks, they can create elaborate constructions, typically based in daily experiences, and used for representational purposes. These constructions and representations, both final products and the process of building, have huge potential for teaching and learning early mathematics.

Blocks are a very constructive material. Their dimensions are set and cannot be changed, unlike creating with clay or play dough. Typical wooden blocks also allow children to build with creativity as they are not bound to blocks needing to fit together a specific way, such as with Legos which interlock and must be in a specific position. This allows children to build with an infinite number of possible constructions.

Unit blocks are inherently mathematical. The standard unit block, a rectangle block or rectangular prism, can be seen as the base of the unit block system. Two half-unit blocks, square face blocks, laid lengthwise make up the same dimensions of a unit block. Triangle-faced blocks likewise can be put together to equal a standard unit block. These equalities are the basis of algebraic thinking, where equal parts are compared, as well as an understanding of geometry and number operations.


We can see these visually in the photos above. While young children may happen upon these relationships, it is our role as adults and educators of children to understand the mathematical implications of blocks and know how to support children’s mathematical learning through block play. Let’s examine the photo below.


A group of children created this during free choice time in a preschool classroom. What do you see in this photo? What math concepts do you think these children may have been explicitly or implicitly exploring? How do you think they constructed this? Why do you think they constructed this?

At first glance, it may appear that these children were randomly building, putting blocks together without a plan. However, upon a closer examination, we begin to see patterns of construction. These children were building their neighborhood in Chicago. We can see a roadway at the bottom, with triangle blocks representing cars on a bridge. Above the roadway, we see rows of buildings. There are shorter buildings and taller buildings, buildings with short triangular roofs and some with steep, tall sloping roofs. We can imagine the mathematical language that the children were using with each other, and the mathematical language that the preschool teacher was using to support mathematical learning. How many buildings do we need in the neighborhood? Let’s add a short house next to the tall building! There’s not enough cars on the road, we need more! How many cars should there be? How many buildings fit on this street? How many more triangle blocks do we need? We have a long rectangle block on the side of the road, do we need more blocks for the other side of the street? How many short rectangle blocks do we need to have the same length as the longest rectangle block?

All of these questions, responses, and statements focus on mathematical knowledge. Children can explore number sense and operations by adding and removing blocks, and by counting and quantifying the blocks in portions of their constructions. They can explore geometry by putting shapes together to create other shapes and by understanding what three-dimensional shapes are called. Algebraic thinking can be explored as children see equalities and inequalities in their constructions. They can represent objects in the real world and can plan and recreate their experiences. This re-creation of their experience can utilize mathematical thinking by educators prompting questions about these experiences, such as, “How tall was the building?”

In the next few blog posts, I will be further exploring math in block play. In the meantime, get out some blocks and play! Blocks are fun for all ages. Test out your own understanding of math concepts in your own block play.

David Banzer, M.Ed.

David Banzer, M.Ed., is a doctoral student focusing on early math teaching and learning at the University of Illinois at Chicago. He received his B.S. in psychology from Seattle University in 2004 and his M.Ed. in early childhood education from the University of Illinois at Chicago in 2011. After working as a preschool teacher at Erie Neighborhood House from 2008 to 2015, he began serving in his current position as education coordinator for the social service agency. Banzer is also interested in helping early childhood professionals develop their own math abilities—along with a greater awareness of how young children develop mathematical thinking skills. He has created and facilitated a series of professional development programs focused on math and technology in the early childhood classroom and presented at conferences throughout the state of Illinois. He is passionate about early math because it lays the foundation for future academic success. "Math is everywhere in the world," Banzer observes, "and children can explore math in everything that they do."

Read more posts by David Banzer, M.Ed.

5 Replies to “Math in Block Play, Pt. 1”

  1. Block area is on the most popular centers in our classroom. After currently taking a mathematics training and focusing on spatial relationships and shapes I may add more options to our block area to create more shapes, patterns, etc. Great article!

  2. The block area has always been my favorite.
    The things children can build are limitless!
    The worse thing is…someone always comes and knocks it down. 🙁
    I’ve begun to recognize the sneer..

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