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Collective Exercises – Short 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. 
1 set of small number cards 1 to 9 for the divisor.  


Static, Short Division 
  1. Invite three children to the lesson. 
  2. Ask the child to set up the materials, everything the same as you would with addition, but we are using the small number cards again that we used before for multiplication, this time for division. 
  3. Ask the children to bring their math trays to the large rug.
  4. “I bet the golden beads are pretty easy now. Well, I have a new challenge for you. It’s called division. Division means we share a number into smaller numbers, and the smaller numbers are all the same, they are equal.” 
  5. “If there is anything left, we don’t share what’s left.” 
  6. Place the large number cards on the large tray and ask the children to get the beads, for example, 6963. 
  7. Once they return, verify the beads.  
  8. Place the large number cards in the right corner of the rug. 
  9. Begin to divide the beads from the large tray to the children’s three trays, by starting with the thousands (largest category). 
  10. Place one thousands cube on each child’s tray, so that each child has one cube. 
  11.  Then place the other thousands cube on each child’s tray, so that each child now has two cubes.  
  12. Ask the children to count what number they each have. 
  13. “Two thousands! Right! Go get that number from your rugs and put it on your thousands.” 
  14. Repeat this process for the other categories, going from hundreds, to tens, to units (largest to smallest because it is division). 
  15. Once the children have all their number cards, ask them to put them together to see what number they each have.  
  16. Ask the children to place their number cards in the right top corner of the rug. 
  17. “Lizette has 2321, Berna has 2321, and Madhu has 2321.”  
  18. “How many people did we share the number with? That’s right, 3 people!” 
  19. “There is another way to write this!” 
  20. Flip two sets of cards over and take the 3 card from the division rug. 
  21. Place the 3 to the right of the large number cards 6963. 
  22. Place one of the child’s 2321 card set to the right of the 3. 
  23. “This number, 6963, shared 3 times, is 2321!” 
  24. Continue this process until the children tire, then clean up.  
Dynamic, Short Division 
  1. Invite children to the lesson.  
  2. Repeat the same process as static division, except this time, your large number cards must result in exchanging larger categories for smaller categories, with a number such as 6438. 
  3. “We’re going to division again, but this time we are going to use exchanging too. Remember, if there is any left over, it stays on the tray and no one gets it, because sometimes the number can’t be shared all the way.”  
  4. After the children bring the beads and verify them, the thousands are distributed.  
  5. The children count them and place their small number card 2000 on the thousands cubes. 
  6. 400 can be divided 3 times, so each child gets 100, but leaves 100 left over. 
  7. Ask the children to place their small number card 100 on their hundreds. 
  8. Ask a child “What can you exchange this 100 for? 10 tens, right!” 
  9. Count to verify what the child brought and continue this process with the rest of the categories.  
  10. Finish the lesson in the same way as static short division.  


Work independently.  


To gain a sensorial impression of division, which is the sharing of quantities equally, one category at a time, and finding that the answer is the amount that one gets.  
To further understand the decimal system, and to reinforce the process of exchanging. 

Control of Error

 Purpose and process are more important than the correct answer. 


5 to 5 1/2


Words such as dividend, divisor, and quotient can be mentioned casually. 

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