Lower School Blog: Math Progression in Primary

Lower School Blog: Math Progression in Primary

Your child is exposed to mathematical concepts such as time, schedule, money, sharing things, calculating measurements, page numbers in books, estimations, etc. on a daily basis. In some cases, math encounters are concrete (e.g. I have two strawberries. I added one so now I have three strawberries), but to a young child, math is not as simple as it sounds. Children draw on their everyday interactions with the physical world to give meaning to abstract concepts, and it is through these sensorial experiences that we see the enrichment and development of a child’s mathematical mind. 

Using scientific and well-designed Montessori math materials, Primary children will begin to crave and understand the concepts of exactness, quantity, size, sequence, and pattern. These materials give a solid impression, enriching the child’s perception of the world and the significance of arithmetic. 

At the Primary level, we categorize math lessons into six different groups to help students conceptualize and establish a progression with numbers and build a strong foundation for exploring later mathematical concepts.

Group 1 - Concept of Numbers 1-10

This group provides the basis of our number system, and we introduce numbers (1-10) together.  We want the children to absorb and feel comfortable with the sense of quantity before introducing the symbols.  

Group 2 - The Decimal System 

Once the child understands the concept of one through ten, they will begin the famous lessons with the Golden Beads as an introduction to the Decimal System (units, tens, hundreds, and thousands). These materials are efficiently and geometrically presented to show relationships among themselves; for example, a bead is a sphere, a ten is a line, a hundred is a square, and a thousand is a cube. With these groups, operations are dramatized to show how they work, giving the child their first sensory experience with addition, subtraction, multiplication, and division. 

Group 3 - Teens and Tens

It’s all about counting! With this group, we focus on the quantity and symbol of numbers within the category of teens and tens. We concentrate on the proper names of numbers between 10 and 20 and the same for 10, 20, 30, 40, and so on. At this point, we no longer say “two tens and three units,” but instead say “twenty-three,” so that the child learns to incorporate the proper language. Children also have the opportunity to count to 1000, when they previously had only counted to 10. 

Group 4 - Memorization

After extensive work with sensorial math materials such as the snake game for addition and subtraction, multiplication with the bead boards or the unit division board, the students now understand the process of all operations, and it is time to memorize facts! Young children appreciate the repetitive nature of the math chart materials, which offer plenty of opportunities to practice and learn.

Group 5 - Passage to Abstraction

Passage of Abstraction refers to the ability to calculate with paper and pencil based on your knowledge of facts. By now, all children have a lot of math experience, and all materials in this group will use all of their knowledge. Many of these lessons are given at the Lower Elementary level, and they serve as an excellent transition for the children moving up. 

Group 6 - Fractions

This group serves as another transitional material for the children, and provides a solid opportunity to experience numbers when talking about the parts of a whole. Children may also experience operations with fractions. 

With every lesson group, we see the growth of the child’s mathematical mind. As children progress through each level, they not only gain a greater understanding of concrete and abstract math operations, but increased clarity of the world in which we all live. 


Claudia Caihuara

Primary Guide, Mulberry Community

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