Montessori AMI Primary Guide
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Numbers through Ten
  Number Rods
  Sandpaper Numbers
  Number Rods and Cards
  Spindle Boxes
  Concept of Zero
  Cards and Counters
  Memory Game
Decimal System
  Introduction to quantity
  Formation of Numbers
  Stamp Game
  Dot Game
  Word Problems
Linear & Skip Counting
  Teens: Quanity
  Teens: Symbol
  Tens: Association
  Linear Counting
  Skip Counting
  Number Roll
Tables of Arithmetic
  Addition Snake Game
  Strip Board - exercises
  Addition Strip Board
  Addition Charts
  Substraction Snake Game
  Substraction Strip Board
  Substraction Charts
  Multiplication Bead
  Multiplication Board
  Multiplication Charts
  Unit Division Board
  Division Charts
Passage to Abstraction
  Small Bead Frame
  Wooden Hierarchical Material
  Large Bead Frame
  Racks and Tubes

Dot Game


- Squared paper inserted into a frame of ground glass or slate with columns headed 1, 10, 100, 1,000, and 10,000. The columns are divided into small squares so that there are ten in each horizontal row. At the foot of each column are two spaces, the upper one for carrying figures, the lower one for the result. There is a blank column at the right side where the problem to be done is written.
- A good lead pencil
- A purple or orange pencil
- A ruler


Stage A

  1. Invite a child to come and work with you. Introduce him to the new paper and have him bring it over to the table.
  2. Show the child the different columns on the paper and introduce the child to the new number of 10,000.
  3. Tell the child you are going to write and addition problem and write one on the right side of the grid.
  4. Have the child choose at least three more 4-digit numbers.
  5. Once all add-ins have been written, draw a line with the ruler and write in a plus sign.
  6. Look at the first number and write a dot in the units column for each unit in the first number.
  7. Repeat for the tens, hundreds and thousands.
  8. Repeat for each add-in until the whole grid is filled with the appropriate amount of dots.
  9. Then count the first row of dots in the units from left to right. When you get to ten dots, cross it out and make an orange dot in the first bottom large square. As you do so, say: “This represents one ten.”
  10. Continue counting the units in this same way. (Crossing off each ten units and marking with an orange dot.)
  11. Write the number of units left in the second bottom square.
  12. Look at how many orange dots you have in the units column. Mark that amount in a number in the tens column. Tell the child, “I am carrying over 2 tens.”
  13. Also place two orange dots next to the last pencil dot in the tens column.
  14. Repeat in this way for the tens column, the thousand, and the 10 thousand columns. Always carrying over what needs to be.
  15. Read the answer with the child, emphasizing the ten-thousand number. E.g. Thirty-two thousand, one hundred and fifty two.
  16. Have the child write the answer under the problem one the right side of the paper and show the child where we place the comma to separate the thousands.
  17. Read the whole problem with the child.


See pdf for a Dot Game Stage A complete

Stage B
This is to be done in the same way as in Stage A, but this time have the child make the dots for all of the units, then all of the tens, then all of the hundreds, and then all of the thousands. This is to be done from the top unit to the bottom unit.

See diagram for a Dot Game Stage B in progress.


The child can work alone, creating his own addition problems and finding the answers as he was shown.

This work can be done after the Stamp Game in Addition.


- To give the child further understanding of addition in the decimal System and to give him a sense of an ability to work with large numbers.
- To emphasize the fact that in each catergory, there are never combinations that come to more than 9, so that it is just as easy to add tens of thousands together as it is units.
- The making of tens focuses on the child’s attention on the process of carrying.
- To further familiarize the child with the different categories.
- A first abstraction in the decimal System.

Control of Error
The directress. It is not the exactness of the result that is sought, but what has been stated as the direct purpose.

4 1/2 years onwards

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