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# Collective Exercises – Subtraction

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5. Collective Exercises – Subtraction

#### Material

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 9000 for the answer.

#### Presentation

##### Static Subtraction
1. Invite one child to the lesson.
2. Ask the child to set up the materials, everything the same as you would with addition, but this time you are also including a set of small number cards 1 – 9000, from the subtraction box.
3. Show the child the subtraction box and ask him to place these cards in formation on a blue math rug.
4. Place the large cards on the large math tray that was previously used for putting the beads together.
5. “Can you get this number of beads and put them on this tray? I know it’s different, but I have something new to show you!”
6. Wait for the child to bring the large tray back to the rug with the beads.
7. Verify what he brought by counting it.
8. Go with the child to his blue rug which is at a distance.
9. Pick up small number cards from his rug and place them on his math tray.
10. “I’m going to put some numbers on your tray, but don’t go get this amount. Just bring your tray to the rug. We’re going to use this number in a different way.”
13. “I have so many beads. Would you like some beads? I bet you would!”
14. Ask the child to read the first category of his number, units.
15. Ask the child to take that number of beads from your tray and put it on his tray.
16. Continue this process for each category.
17. After all categories are accounted for, ask the child to put his cards together and then place the new number on the rug.
18. Point to your large cards “This is how many beads I had” and say the number.
19. “This is how many beads you took away from me” read the number.
20. “Now I have a different number. Let’s find out what that number is.”
22. After the child counts the first category, units, ask the child to use the small numbers from the subtraction box that have been laid out on the other small blue math rug. Ask him to use this for the other categories too.
23. Ask the child to put the number together.
24. Place the new number on the rug below the other two numbers.
25. Repeat “this is how many beads I had” followed by the number, “and this is how many beads you took away from me” follow by the number, “and now my new number is…” followed by the new number.
26. “When you have a number, and take away from it, it’s called subtraction. You just did subtraction!
##### Dynamic Subtraction
1. Invite one child to the lesson.
2. Repeat the same process as before, but this time use a number that requires exchanging a larger category for a smaller category, such as 4238 on large cards and 3164 on small cards.
3. When it comes to trying to figure out how to take 4 units away from 3, say “Oh! Looks like we need more units. We don’t have enough here, but I know where we can get some.”
4. “Go to the storefront and exchange this ten for ten units.”
5. “Alright, now we have enough!”
6. Continue and complete the lesson as you would with static subtraction.
##### Dynamic Subtraction (2 children)
1. Repeat the process the same as before, with a number such as 6647.
2. After the children gather the beads on the large tray and you verify them, place their small number cards randomly on their trays, that make numbers such as 3153, and 3363.
4.  Ask the first child to read the first category of his number, units.
5. Ask the child to take that number of beads from your tray and put it on his tray.
6. Continue this process for each category until the child finishes.
7. Ask the child to put his number together and place it under the large card number, 3153.
8. Count the beads that are remaining on the large tray to arrive at the new number.
9. Flip over the original large numbers so that they are face down. Move them to the side and say “I don’t have this number anymore.”
10. Put the new number made of large number cards in the old numbers place.
11. “This is my new number. 3494.”
12. “But we’re not done yet, you need beads too!”
13. Repeat the process with the second child the same as the first child.
14. Once the child takes his beads, ask him to place his cards below the first child’s cards on the rug.
15. “Now I have a different number! Can you count the beads on the large tray?”
16. Flip over the second set of large number cards so that they are face down too, and put them to the side.
17. Use the small subtraction numbers for the final sum of beads that remain on the large tray.
18.  “Let’s go back to where we started.” Flip over the original large cards.
19. “I had 6647, Emily took away 3153 beads, and Nic took away 3362 beads. My new number is 132!

#### Exercises

Work independently.

#### Purpose

To gain a sensorial impression of subtraction.
When quantities are taken away from a larger number, what is left is less than the original.
To further understand the decimal system.
To further understand the role of exchanging when you take one of a larger category to get 10 of a smaller category.

#### Control of Error

Purpose and process are more important than the correct answer.

4 1/2 to 5

#### Notes

With independent work, the children will inevitably need guidance as they will eventually run into negatives.