Mathematics in the Lower Elementary classroom is an extension of the groundwork that was laid down in the Primary classroom. By this point, most students are familiar with the teens (11 – 19), the decimal system (units, tens, hundreds, thousands) and basic operations such as addition, subtraction, multiplication and division.

By this stage the children are recording their work on paper, although many won’t be able to solve the same problems if asked to work with paper and pencil alone without the visual aid of the Montessori materials. The concrete Montessori materials make it possible for the child to see and understand, slowly internalizing each concept until it becomes fixed and clear in his mind.

The entire purpose of the Montessori Math curriculum is to make the abstract concrete, until the child can close his eyes and visualize mathematical processes at work. Step by step, the materials become less concrete and more symbolic. Montessori uses a wide range of parallel materials and exercises to help the child extend his knowledge and gradually memorize the basic math facts that every one of us is expected to know.

Students often work with numbers into the thousands, hundred thousands, and millions as they practice the basic operations. Using such large numbers with increasingly abstract materials enhances their reasoning skills, memory and executive function skills, in addition to the completion of mathematical problems. By third grade, students are using a calculator to check the work of a classmate.


The subject of geometry is often not taught in public school until high school. In Montessori schools, students have been exposed to geometric concepts since the age of three. This exposure continues in the Lower Elementary classroom to include further work with the geometric solids, work with fractions, angles, triangles, quadrilaterals and other polygons including circles. There are many materials in the classroom that help students visualize these concepts, laying a strong foundation for the more advanced abstract work they will do in the Upper Elementary classroom, high school and college.