Tuesday, May 18, 2010

Montessori Math: Decimal System

After single digit numbers are mastered, it is time to move onto work with the decimal system and the golden bead material. I have seen a few lists that put teens and tens work after 0-10, but most of the Montessori resources I've read recommend decimal system first. I thought this was a little strange at first, but it actually makes sense.

The first step is to learn the terminology and get a sensorial feel for the numbers. The child is shown a golden bead unit, ten bar, hundred square and thousand cube. He is taught the names and that ten of one equals the next biggest. Note: Unlike everything else, which is done left to right, in these presentations you work right to left. Units are on the right, then tens to the left of that and so on, because that it the way numbers are laid out.

Once the child is familiar with the tangible versions, he is introduced to the symbols with the number cards. The cards are introduced in a similar way to the beads. Then the relationship between the two is shown.

Eventually the child is shown how to make numbers with the golden bead material and the number cards. In the beginning you give him number cards and have him find the corresponding beads. When he is good at that, you give him groups of beads and have him find the right cards. For example, he might have a thousand cube, three hundred squares, four ten bars and seven units. He would find the 1000, 300, 40 and 7 cards, then stack them all up to make 1347. For now, the number is read: One thousand, three hundred, four tens, seven units.

When he is comfortable making numbers with the beads and cards, he is shown progressively how to use them in each of the four basic arithmetic operations. He doesn't memorize anything at this point. It is all concrete work meant to give him a strong impression that will benefit him down the road. Other activities, like the stamp game, compliment and give more practice with the operations and exchanges.

The teens and tens are started around the same point, when the child is comfortable working the golden beads and cards and making the big numbers. The teens and tens activities clarify terminology as well as help the child understand the counting sequence beyond ten, and they are done parallel to the golden bead work, so the child is learning more than one thing at a time in the math area at this point. Here is a good post about the teens board, the first activity in the teens and tens sequence.

Previous posts in this series:
In the Beginning
Sensorial Bead Material


Nicole said...

Nice post! I hadn't realized that the units went on the left - I'll make sure to do it correctly this week when Short Pants and I work with the beads - thanks.

Karen said...

So nice your post!!thanks for taking time to explain it!!! So interesting... I will presented soon!!!

Thank you!!

The girl who painted trees said...

Thank you for taking the time to explain this!