Dynamic addition, using the stamp game, is another step on the way towards memorization and abstract pencil and paper work for Montessori students.
Learning Addition and Subtraction: Definition of Terms and Materials
Dynamic addition is that which involves "carrying the one" or exchanging, because the sum of two numbers is greater than 10. Children learn the concept of carrying, as they literally carry stamps to exchange them.
The stamp game consists of a box of tiles, known as stamps. One set of green stamps is labeled with a 1. The blue set of stamps is labeled with a 10. The red set of stamps is labeled with a 100. A second set of green stamps is labeled with 1000. These colors correspond with the color scheme on the numeral cards that label quantities.
Also present in the box are round chips that represent zero in a quantity. Skittles, which resemble red, blue, and green game pawns, will not be used in this lesson.
Learning Addition and Subtraction: Purpose of Dynamic Addition with the Stamp Game
The stamp game directly corresponds to the golden bead material. It is just more abstract, yet concretely demonstrates the addition process to young children. "Carrying" the stamps to exchange is a concrete way to "carry the one" when adding sums greater than ten. It prepares the child for pencil and paper work, and memorization of addition facts.
Prior Learning Required for Dynamic Addition with the Stamp Game
Children need to be familiar with the decimal system, prior to using the stamp game. They will gain this through creating quantities, the bank game, and the forty-five layout.
They should have already done dynamic addition with the golden bead materials (linked below), to understand the process. They also should have had a presentation of static addition with the stamp game, to demonstrate an understanding of the abstract stamps.
Required Materials for Dynamic Addition with the Stamp Game
- Work rug (some children may prefer to work at a table)
- Stamp game
- Two sets of small numeral cards
- Set of large numeral cards
Learning Addition and Subtraction: The Montessori Presentation of Dynamic Addition with the Stamp Game
- Invite the child to come to a lesson on dynamic addition with the stamp game.
- Ask the child to create two different quantities with the stamps. These quantities should have at least one opportunity for exchanging, or "carrying the one", such as 5716 and 3478. Then the child should label each quantity with the small numeral cards.
- Mix all of the stamps in the middle of the work area. Sort them in columns of 1000s, 100s, 10s, and 1s, with the thousands on the left, and the ones on the right.
- Start counting the ones. When you get to ten say, "I have 10. I can exchange these for a 10 stamp." Return the ten 1s to the box, and add a 10 stamp to the 10s column. Finish counting the 1s, and label them with a large card, in this case a 4.
- Repeat the process with the 10s, 100s, and 1000s, exchanging when necessary.
- When all of the stamps have been counted and labeled, set up the numeral cards with the proper signs to form the equation: 5716 + 3478 = 9194.
Independent Follow-Up Work with the Stamp Game
The child may now independently create equations to solve with the stamp game. Encourage her to write them down, using a grid to ensure proper lining up of numerals. Collect these equations in a booklet.
Try equations with smaller numerals, such as 259 + 987, or 53 + 82. Try equations with a 0.