Children enter a sensitive

Children enter a sensitive period for math learning around age 4-5 once they are comfortable with counting numbers 1-10. We begin teaching numbers beyond 10 including the teens, tens, linear and skip counting using materials like the square bead chain. 

 

At the same time, we are also giving children a concrete understanding of the decimal system using the Bank Game. First we introduce the thousands cube (a cube made up of 1,000 gold beads) and hundreds square (a square made up of 100 gold beads) to children and make sure they can connect a written numeral with the correct number of cubes, squares, bars, and units.  Once they are comfortable with this material we add in the four operations, addition, multiplication, subtraction and division.  

 

Berlin and Zachary, both five years old, are working with the Bank Game. Starting with addition, we give two children numbers, asking them to get the corresponding beads, add them together, and count them. Then we ask both Berlin and Zachary to get the same number (for example 2,432) they add them together and count the total, just as they did in addition but this time we use the language “2,432 two times is how much?” Then we move to subtraction and division. 

 

After children have mastered this, we teach children about exchanging. For example, 10 units can be exchanged for a 10 bead bar, 10 bead bars can be exchanged for a hundreds bar.  In this way, Montessori gives a very real, hands-on approach to abstract, complex concepts so that children truly understand what they mean. As children gain fluency and comfort in understanding they will drop the hands-on material and start working only with the written symbols on paper.