Select Page

1. Home
2. Knowledge Base
3. Mathematics
4. Decimal System

#### 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.

#### Presentation

1. Invite three children to the lesson.
2. Show the children the small number cards and the small blue work rugs.
3. Ask the children to lay out two large rugs at a distance from each other.
4. Place the large math tray in the middle of the rug.
5. Ask the children to place the large number cards on one the other large rug, in formation.
6. Ask the children to unroll their blue math rugs near the large rug that has the large number cards on it.
7. Ask the children to place the small number cards on their work rugs, in formation.
8. Ask each child to bring their own math tray to their small rugs.
9. One child at a time, put four cards from the child’s small rug – one of each category – in random spots on the tray, such as 2000, 400, 10, 5.
10. Ask the child to get that number in beads on the tray, and bring them to the rug with the large tray.
11. Repeat this process for all three children with their own numbers, such as 1000, 200, 60, 1, and 3000, 200, 20, 1.
12. Once all children are at the rug with their beads on their trays, verify their number by counting the beads, one child at a time.
13. After you verify that the child has brought the correct number of beads, ask the child to place his beads on the large tray, be sure to point out the dish for unit beads.
14. Repeat for all three children.
15. Lift the whole tray up, to dramatize how big the number is when the beads are added up together.
16. Ask one child to choose what category he wants to count. Have him count all the beads in that category and to place that category in a group at the top of the large rug.
17. Ask the child to find the large number card that matches the number of beads, and ask him to place it on top of the group of beads.
18. When a child is about to place beads in a group on the rug, make sure that they are placed in a proper, orderly spot, thousands on the left, then hundreds, then tens, then units on the right.
19. Repeat this process for each child.
20. With four categories, and three children, you can count the last remaining category together as a group.
21. Once all the categories are on the rug, are counted, and matched with a large number card, ask each child to pick up his or her small number cards from his or her tray and place the cards on top of each other, so that each child has four cards stacked, aligned to the left.
22. Ask, or wait for, the children to slide the cards to the right, revealing their four digit numbers.
23. Ask them to place their four digit numbers in the top right corner of the rug.
24. Point at each four digit number and say who brought that number.
25. Stack the large number cards on top of one another, aligned left, then slide them to the right to reveal the large four digit number.
26. “2415, and 1261, and 3221 make 6897!”
27. “We put all the beads together, and we got an even bigger number! It is called addition, we just did addition!”
28. Repeat this process until the children tire, then clean up.
1. Repeat the same process as static addition, however, after combining the beads, the procedure changes.
3. Once the child counts ten unit beads, kindly ask the child to stop counting.
4. “Ten unit beads is the same as what? That’s right! One ten!”
5. “Can you place these ten unit beads in the dish and exchange them for a ten?”
6. Go with the child and ask him to count the units as he place them back in the units box.
7. Walk back to the rug with him.
8. Ask the child to place the ten in the group with the other tens.
9. Ask the child to finish counting the unit beads and to find the matching large number card.
10. Ask him to place the large number card on the group of unit beads.
11. Repeat this process for the other categories, assisting the children exchanging when necessary.
12. Complete the process in the same way as static addition.

#### Exercises

Work independently.

#### Purpose

To gain a sensorial impression of the nature of addition.
To see the function of the decimal system.
To understand the process of exchanging, from a lower hierarchy to a higher one.

#### Control of Error

Purpose and process are more important than the correct answer.

4 1/2

#### Notes

You can have a dish for the tens category as well, which helps keep the beads organized.
The children aren’t told about “plus” yet, they will learn that soon.