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

Unit Division Board


- The unit division board
- 9 green skittles
- A box with 81 green beads
- Printed division slips


  1. Show the child the material and have him bring it to the table.
  2. Look at the board with the child. Show him all the places for the beads.
  3. Show him the numbers at the top of the boards and tell him that they are the dividend.
  4. Tell him the numbers on the side will be the answer.
  5. Write 27 ¸ 9 = on squared paper.
  6. Begin by telling the child the two rules: the answer cannot be larger than 9 and the remainder cannot be equal to or larger than the divisor.
  7. Place 27 green beads into the glass bowl.
  8. Ask the child how many times will we give 27 out. (9)
  9. Place 9 green skittles along the top of the board.
  10. Give each skittle a bead until there are no beads left.
  11. See below for the equation in progress:

    montessori, table of arithmetics, unit division board table of aithmetics, unit division board
    Table of division

  12. Say, “27 ¸ 9 is 3”. Point to the 3 along the vertical side of the board.
  13. Have the child write in the answer to the equation.
  14. Have him replace the beads into the bowl.
  15. Ask the child how many beads we have in the bowl. (27)
  16. Tell him as you write the next part of the equation on the second line of paper, “27 ¸ 8 =”
  17. Have him do this equation as he had just done the last.
  18. Have him write the answer with the remainder.
  19. Read the whole equation with the child.
  20. Tell the child that there is something special about the remainder: “We can have a remainder as long as it is smaller than the dividend.”
  21. Repeat as above for 27 ¸ 6 =
  22. After the child has written the answer and the remainder check to see if the remainder is smaller than the dividend.
  23. Repeat in this way for the entire sheet of paper.
  24. When you reach 27 ¸ 2, your remainder will be bigger than the dividend. Point this out to the child and then cross out the entire equation because: “We can never have a remainder that is the same or bigger than the dividend.”



  1. Write 81 ¸ 9 =
  2. Have the child count 81 beads into the glass bowl and place nine skittles at the top of the board.
  3. Have the child do this equation as written above.
  4. Read the finished equation out loud with the child.
  5. Then write: 81 ¸ 8 =
  6. Have the child do this equation and write in the remainder.
  7. Look with the child at the remainder and notice that it is bigger than the dividend.
  8. Cross off the whole equation.
  9. Repeat for 81 ¸ 7 =
  10. Repeat for 81 ¸ 6 =
  11. Look at the last three crossed off equations and wonder out loud: “I wonder if the others will also have a remainder larger than the dividend?”
  12. The child should notice that the remainder gets bigger and bigger as the dividend gets smaller and smaller.
  13. Decide together that because of this pattern, only 81 ¸ 9 works.
  14. You can finish this presentation here.

On the same day or at a later date repeat this work for 80 ¸ 9 through 1, 79 ¸ 9 through 1, 78 ¸ 9 through 1, etc…

For the first few sets of work, clear the board after each equation.

Once the child understands that each equation is a new and different equation, you do not need to clear the board after each equation.

The child can work as shown in the presentation. Once the child
has done all the equations on all of the slips, re-read the equations. Underline in red the equations with no remainder. The child can then record all of the equations with no remainder on the squared paper.


To familiarize the child with the various ways in which numbers may be divided.

Control of Error
Division Chart 1

5 1/2 - 6 years

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