Children as young as two start recognizing the significance of what we call a specific number and the value of that number. In our home, we started by telling the kids to use two hands when they carried something and counting the hands they had holding it, “one hand, two hands.” It didn’t take long before they understood. Preschool age children don’t struggle with concepts so much as abstractions. If you can present information in a concrete way, they’ll catch on. In Montessori, after the children have started associating numerals to specific values, the next step, whether it’s in preschool or kindergarten, is showing them the values in different places in numbers with multiple digits.
The first step to this work is introducing the different parts of it. A single bead indicates one unit. Present the bead and tell the child that it is one unit and show him the corresponding card with a one on it and then place it below the bead and to the right of the child.
Now, count out ten beads verbally, one at a time: one unit, two units, three units… and pull out a string of beads that indicates one-ten. (You can also count each bead on the ten) Now pull out the card that says “10” on it and place it below the one-ten, just to the left of the one unit, and put the 10 beads away that demonstrated that 10 units is the same as one ten.
Count out ten tens one at a time: one ten, two tens, three tens… and line the strings up next to each other so they make a square. Put a bead hundred square over the top of the strings so the squares are lined up with each other. Explain that 10 tens is the same as one hundred. Pull out the card that says “100” and put it below the hundred square just to the left of the ten card and put the 10 strings of ten away.
Count out ten hundreds one at a time: one hundred, two hundreds, three hundreds… and place them on top of each other so they make a cube. Place the thousand cube next to the hundreds and let the child investigate them both so they can see that 10 hundreds is the same as one thousand. Pull out the thousand card and place it below the thousand cube to the left of the hundred square.
We normally lay out works from left to right in the order we do them, because that is the direction we read. The reason we don’t with math is that, we read from thousands down to ones, and not the other way around. Don’t worry: the child doesn’t understand the theory behind how works are laid out, so they aren’t confused. Just accept as a teacher that this work is demonstrated backwards from the others and let it go.
Because the ideas are shown in a concrete way with only loose ties to the arabic numerals, kids are quickly able to internalize the tens, hundreds and thousands. This way when they start learning addition, they can go immediately to 4 digits because in their heads whether it’s four digits or one digit, it’s the same principle.