In the struggle to teach math to first and second graders, the real enemy is Piaget's stages of development. The simple truth is that teachers have to find a way to present relatively abstract mathematical ideas to children who haven't yet developed much capacity for abstract thought. The solution is simple: find a way to represent those abstract ideas in a tangible, concrete manner that kids can see and touch. Base 10 blocks are a powerful tool for doing just that.
Overcoming Abstraction
It's no great trick to teach most elementary school kids to count. Many (probably most) can do that when they show up at school. And they certainly know the difference between one cookie and three cookies. Teaching them the names of our ten numerals usually isn't that complex a task, either. But when it comes time to cross the line from single digit numbers to using our numerals to represent more complex values, like eleven or two-fifths, mathematical ideas start to become a little muddier in the first and second grade brain...
In his or her mind a child may ask you, why is 11 worth more than 8, when eight is a bigger number than either of the two "ones" in eleven? It's even bigger than the two ones added together? Does that make sense? And you expect me to believe that 2/5 has less value than 1, even though both 2 and 5 have more value than 1...?
Of course, most first graders can't articulate their objections that clearly. They just know it has suddenly become (for some of them, at least) confusing.
Intro to Base 10 Block
Base 10 blocks (see image 1), like many other math manipulatives, allow children to see and touch the ideas they are being asked to cope with in math class. Base 10 blocks usually come in four sizes. There is the cube which represents a value of 1. The "long" is a block that looks like 10 of the cubes glued together; it represents a value of 10, and the kids can count 10 of the individual cube blocks on a long. The "flat" is a block that looks like 10 of the "longs" glued together; it represents a value of 100, and the kids can count the 10 "longs" on a "flat." Finally, there is the "block" - the size of 10 of the "flats" laid on top of each other. The "block" represents a value of 1,000.
The first time you use base 10 blocks it is a good idea to simply allow the children to examine them and compare them. Discuss them - their sizes and how they relate to each other. Practice counting them in order to allow the children to become comfortable with the fine motor skills required for using the blocks.
Representing Numbers with Blocks
When the children become comfortable with using the blocks, you can begin teaching them to build representations of numbers with the blocks. Many teachers create a place value mat that the kids can lay on their work surface. The mat should have columns that are four to six inches wide and are labeled "ones," "tens," "hundreds," and "thousands." Students learn to always put cubes in the "ones" column, longs in the "tens" column, flats in the "hundreds" column, and blocks in the "thousands" column. After that has been mastered, they are introduced to the basic rule of base 10 counting - you can't have more than nine pieces in any particular column. If you get more than that, you have to go back to the storage bin and trade your ten cubes in for a long, or your ten longs in for a flat...
Children should be allowed to use the blocks regularly. The initial goal is to develop the skill of representing numbers - like 37 (image 2), or even bigger numbers like 1,232 (image 3). Maybe the mats eventually disappear; maybe as a teacher you'll decide you want to keep using them. Once the children have mastered building numbers with their blocks, you're ready to use the base 10 blocks to teach operations - like addition and subtraction.
Greg Cruey - Greg Cruey is an educator and journalist. He works as an educational interventionist specializing in a small, rural school in Central ...
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