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Collective Exercises – Long Division

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Golden beads – 50 unit beads and a supply of tens, hundreds, and thousands.
Most of the hundreds and thousands will be wooden.
Number cards – 1 large set 1 to 9000; three small sets 1 to 3000.
One large tray with a dish for units.
Three small trays each with a small dish.
Several rugs.
Blue, green, and red bows/necklaces. 


Long Division 
  1. Invite three children to the lesson. 
  2. Ask the child to set up the materials the same way they did with division.  
  3. “Today we are going to divide by a larger number” use a number that is larger than 9, such as 12. 
  4. Place a number on the large tray with the large cards. 
  5. Wait for the children to bring that number of beads then verify it.  
  6. Show the children the blue, green and red necklaces. 
  7. “We are going to divide this number by 12. But we don’t have 12 people here, do we?” 
  8. “What we’ll have to do is ask one of you to get a number of beads that is enough for 10 people.” 
  9. Hand a green necklace to two children so that they each have their own. 
  10. “This green necklace means you get beads for just one person.” 
  11. Hand a blue necklace to the other child. 
  12. “This blue necklace means that you get 10 times what they get, because remember, you are getting beads for 10 people.” 
  13. Find 9 children that are free and invite them to stand shoulder to shoulder with each other, and the child with the blue necklace, to visually demonstrate what 10 people looks like and how big the number might be. 
  14. Begin to distribute accordingly, 2,000 for the child with the blue necklace, 200 for each child with the green necklaces. “Remember, you are going to get ten times less.” 
  15. 100 for the child with the blue necklace, 10 for each child with the green necklaces. 
  16. 1 ten for the child with the blue necklace, 1 unit for each child with the green necklaces.  
  17. “Alright, let’s count our beads and then get the cards that are the same number.” 
  18. “What are your numbers?” 
  19. “Oh my, Nic, what a big number you have! But that’s not all yours, we have to divide it for 10 people!” 
  20. Show the child the 10 green trays that are on the math shelf. 
  21. Ask the children to roll out rugs on the floor for the 10 trays. 
  22. Ask the children to proceed by exchanging the larger categories for smaller categories to be evenly divided on 10 trays. Such as a thousand cube exchanged for 10 hundreds.  
  23. The child distributes the beads to the 10 trays.  
  24. Ask the child to take one of the 10 trays for himself. 
  25. Ask the child to count how many he has on his green tray and replace his old cards from his other math tray with new ones that reflect his new amount.  
  26. Repeat the concluding process as with the previous division lessons: “This is the number we started with” say the number, “divided by 12 people, and this is what each person got” say the number. “What one person gets is the answer!”


Work independently.  


To reinforce the functions of the decimal system, and to show how the quantities are distributed in long division, but in the end the answer is how much one receives.  
To reinforce how to exchange from one category to another. 

Control of Error

Purpose and process are more important than the correct answer. 


5 to 6

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