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



- As for addition, but all small cards are laid out to 9000.

Static Division

  1. Have three children come and work with you.
  2. Have them set up the material.
  3. Bring over the directress tray to the supply mat and ask for 9 units, 3 ten, 9 hundred, and 3 thousand.
  4. Bring the tray back over to the mat.
  5. Ask the first child to count the units and to then bring the card over for 9 units.
  6. Ask the next child to count the tens and to then bring over the card.
  7. Repeat for the hundreds and thousands.
  8. Ask one child to place all of the cards together and as a group, read out 9 units, 3 ten, 9 hundred, 3 thousand.
  9. Super-impose the cards.
  10. Tell them that you want to give them all some of your beads and you want to be fair and give them each the same amount.
  11. Say that in division, we always start with the thousands.
  12. Start by giving each child 1 thousand. Say, “I don’t have any more thousands to give.”
  13. Have each child count how many thousands they have to check if each child has the same amount of thousands.
  14. Have the children go over to their card mat and get the card for 1 thousand.
  15. Repeat for the hundreds. They should all have 3 hundreds.
  16. Repeat for the tens. They should all have 1 ten.
  17. Repeat for the units. They should all have 3 units.
  18. Emphasis that you gave each of them the same amount. “Did you get the same amount?”
  19. Have each child place his cards together and read out loud the number the child has.
  20. Place the large cards at the top left of the mat.
  21. Say that because they each have the same amount, you only need one of their cards.
  22. Discuss that because there are three children, you gave each one of them the same amount, to three children.
  23. Take out a 3 from your small dish and place it to the left of the large cards.
  24. Then place one of the children’s cards to the right of the 3.
  25. Then, out loud, and as you point to each number say, “3939 divided by 3 is 1313.”


Dynamic Division

  1. Begin by telling the children that division is different than the other operations. We must start with the thousands.
  2. Move over to the supply tray and ask each child in turn to place 6 units, 2 tens, 5 hundreds, and 4 thousands onto the directress tray.
  3. Give each child 1 thousand and have them get the card.
  4. Have a child exchange the last thousand for 10 hundreds.
  5. Give each child 1 thousand until they all have 5 hundreds.
  6. Look at the 2 tens and notice that you cannot give each child a ten. Ask one child to exchange a ten for 10 units.
  7. Ask another child to do the same for the other ten.
  8. Count all of the units. (26)
  9. Give each child a unit until they all have 8 units. Discuss Have then get the correct cards.
  10. Have them place their cards together and read what each child has.
  11. Notice how they all have the same number.
  12. Lay out all of the children’s cards under the large cards.
  13. Read 4526 divided by 3 is 1508.
  14. Look at the remaining units and say, “But we have a remainder of 2. Place the two units in the dish to the right of 1508.
  15. Reread: “4526 divided by 3 is 1508 with a remainder of 2.”

Long Division

  1. Bring the directress tray over to the supply mat with the children.
  2. Ask for 2568 in material.
  3. Bring the tray back over to the working mat with the children.
  4. Count out the numbers of each and ask the children to bring the corresponding cards over.
  5. Tell the children that today we are not going to divide by 3 as we have been. We will be dividing by 12. Show the fact that one child is going to represent the tens by giving the first child a blue ribbon and the two other children a green ribbon because they represent units.
  6. Ask the first child to go ask nine of their friends if they would come over for just a moment.
  7. Count them all (including the first child) and say that because these nine children all have to go back to work, the first child will represent them all.
  8. Give the first child the thousand block and give the other two children each 1 hundred because “the first child represents ten people so he has ten times as many hundreds.”
  9. Give the other thousand to the first child and each of the other children a hundred square. Have them get the cards.
  10. Give the first child a hundred square and the other two children a ten bar.
  11. Have then get the appropriate cards.
  12. Repeat in this way until all of the beads have been shared appropriately.
  13. Have each child count what they have and choose the correct cards to show the number: 2140, 214, 214.
  14. Roll out the long red mat and have the first child re-invite his nine friends to sit behind the red mat.
  15. Discuss how you want to give each of their friends some of your beads but you can’t because you only have 2 thousands.
  16. Divide the 2140 by ten, exchanging when necessary.
  17. Once it has been divided equally among himself and his nine friends, have him count what he has and have him choose the new correct cards for what he has left on his tray: 214
  18. Look at the two other children sitting next to this first child and notice that they too have 214.
  19. Then look at the nine friends and check if they all have 214. Say, “You all have the same amount!”
  20. Then place 12 (explain because you are dividing the total by 12 people) to the right of the large cards reading 2568 and 214 to the right of the 12.
  21. Read out loud: 2568 divided by 12 is 214.
  22. Excuse the nine friends and have the three children replace the material.


Short Division
To give the impression of the nature of division. Here a large quantity is divided into a number of smaller equal quantities.

Long Division
To show the child how the quantities are distributed in long division. He learns how the divisor is always grouped and how the answer is always the share of one person.

Control of Error
The directress verifies at first. Then she shows that if all the smaller numbers that were taken away are added together, they should amount to the original number.

4 1/2 - 5 years

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