Sunday, April 27, 2008

The Stamp Game - Addition

The stamp game is a wonderful tool for learning and reinforcing knowledge of the four operations: addition, subtraction, multiplication and division. This post will discuss and describe simple addition work with the stamp game.

I was lucky enough to attend the International Montessori Conference in Paris in 2001. It was a wonderful experience. It would take a post dedicated to the conference itself to articulate the impact that it had on me and my future as a Montessori teacher.

Many of the Montessori materials from the first Casa were on display. The originial color tablets were included. They were in fact made from embroidery floss (individual colors) wrapped on small cards that you can actually still buy at JoAnn Fabrics. The stamp game, I am sure you can now guess, was created from duplicates of postage stamps with values that represented ones, tens, hundreds and thousands. I saw some of these materials again in the ongoing Montessori Centennial museum show in San Francisco a year ago. If you ever get a chance to see any of these materials jump at it. For me, they connect me to the source; the ideas and materials behind their creation.

The stamp game has stamp sized flat, wooden squares that come in three colors: green, red and blue. The question is sometimes asked - "Why isn't there a fourth color for thousands?" I will tell you the answer here. One, ten and hundred are in the simple family. One thousand, ten thousand and hundred thousand are in the thousand family. One thousand is represented by green as it is the ones of the thousand family. The other very important point to remember is that children in the Montessori classroom learn math via the decimal system. They are counting up to ten. Quantities more than ten are converted into tens, hundreds or thousands. I will explain more later. So they learn math via the decimal system plus language. The success a child has with the math materials is dependent on their knowledge and memory of the terms ones (units), hundreds, thousands, ten thousands, hundred thousands - etc.

This is an addition problem placed by a child on the table. The green stamps in the foreground are ones (units). In the background the green stamps are the thousands. This problem reads as follows: 3,245 + 2,312 (*Note: the comma written in the quantity - ex. 2,312 is denoting the separation between the two families: simple and thousands). The child has laid out the first quantity and then placed a ruler under that first amount. Beneath the ruler she has placed the second quantity.

Now the child has removed the ruler leaving the two quantities, still separate, on the table.

The child now moves the second quantity up to join the first. Addition is two smaller quantities joining to make one larger quantity. The operation addition is based on gathering behavior - getting more - as is multiplication. Division is an equal distribution operation.

The child counts the number of stamps starting at the last stamp and moving up the vertical row towards the box. They then note the answer on their sheet. I have laminated cards with problems written on them that children independently copy onto stamp equation paper. These papers are color coded. The spaces for ones are green, tens blue, hundreds red and thousands green. Prior to the child independently copying static or dynamic math equations, I write them so as to ensure that the child 1. sees where to place the numbers for each quantity 2. that the answer does not either include a zero or requires carrying over - yet.

Above: Stamp Game paper. These fifteen boxes are cut into individual ones and kept on the shelf next to the Stamp Game itself.

Carrying over is very easy with the stamp game material if the child has worked with the golden bead materials, the teens and ten boards. Say the child is doing this problem - 2, 467 + 1,325. They place the first number on the table, then the ruler, then the second number. They remove the ruler and join the two quantities. Counting up towards the box, the child counts to ten (as there will be twelve one (unit) stamps). Once the child has counted ten ones, they slide them away from the rest of the ones and turn them into the "bank" - which is the box with the remaining stamps in it. They turn ten ones (units) in for one ten stamp. They then place this additional ten stamp below the vertical row of the already placed tens. They count the remaining ones and note the quantity on their problem paper. They continue counting the remaining quantities and noting their results until they have completed the problem. Note: if the child hesitates when they see more than ten ones (or other quantities) remind them that "ten ones equals one ten." Once in a while you will see a child write 12 in the single box denoted for ones on the problem sheet. Again, remind them to write only one number in each box and that they need to go to the bank.

There are skittles included in the stamp game. They are used for division work and I will discuss and explain this in another post.

1 comment:

melissa joanne said...

The stamp game was not presented in my training and I never saw it before it this year. My new school has it, some of the children are ready for it, and based on this post it seems like a very valuable material.

I brought it home to study it along with this post and make sure I fully understand and am comfortable with the presentation.

I am struggling with some minor details. Would you be willing to describe to me the theory behind separating the quantities with a ruler initially, and later counting the sum beginning at the bottom as opposed to the top of each vertical row?