Introduction to quantity

Materials 1
- A tray containing 1 golden bead unit, 1 golden ten-bar, 1 golden hundred square and 1 thousand cube.
- A small mat for the table.

Presentation 1
1. Invite a child to come and work with you. Bring him to the shelf, name the lesson and have him bring the material over to the shelf. 2. Have him unroll the small mat onto the table.
3. Take the unit, feel it, and name it. “This is a unit.” 4. Give it to the child to feel and name it.
5. Have him place it on the right side of the small mat.
6. Repeat for the ten-bar.
7. When the child places it onto the small mat, count the beads. 8. Place the ten-bar vertically to the left of the unit.
9. Repeat for the hundred square.
10. Lay it on the mat to the left of the ten-bar.
11. Use the ten-bar to count how many tens are in the hundred. 12. Repeat for the thousand cube.
13. Place it to the left of the hundred square and use the hundred to count how many hundreds are in a thousand. 14. Do a Three-Period Lesson for them.
15. End the 2nd Period with the categories in the correct order: (from left to right) thousand, hundred, ten, unit. 16. For the 3rd Period, point to each category and ask the child to name it. 17. Show the child how to put the material away, making sure the beads are placed in the correct order on the tray. Materials 2

- A mat
- A supply box with unit beads, ten-bars, hundred square and thousand cube with beads drawn on them. - A tray as in Presention 1
- A tray with a dish on it.
Presentation 2 
1. Invite a child to come and work with you. Have him bring the material over to the table. 2. Have him unroll a mat and have him bring over the material. 3. Compair the material in the box to the mterial that is on the tray that was used in Presentation1. This will show the child that units and tens are the same. 4. Take out a hundred from the box and comapir it to the hundred on the tray. 5. Tell the child that the hundred on the tray is made of beads but the hundred in the box has beads drawn on it. But explain that they are still both hundreds. 6. Put the hundred from the box at the top of the mat.

7. Repeat and discuss for the thousand.
8. Place the thousand from the box above the hundred at the top of the mat. 9. Take the material out of the box and set it up as shown :

This mat is called the Supply May
10. Have the child bring over a small mat and place it far away from the supply mat. 11. Have him also bring over a tray with a small dish on it and have him place it onto the small mat. 12. Sit next to the small mat with the child.

13. Ask the child for a precise amount of units, such as 5 units. 14. Have the child go over to the supply mat with the tray and count out 5 units. Have him place these units into the dish on the tray. If needed, go with the child. 15. Have the child bring the material over to the small mat and have him count it to check. 16. Repeat by giving the child other amounts to get, such as : 4 tens, or 7 hundreds, or 5 thousands. 17. After some time, you place an amount of material onto the tray and have the child count to tell you how much there is. 18. Repeat this until the child seems comfortable with this exercise. 19. When the child can work well with one catergory, introduce two categories  such as 4 units ans 2 tens. Continue like this for three categories and then four categories. Purpose

Direct
To introduce the child to the concept of the decimal system. To make the child familiar with the names and relative sizes of the categories To help the child with the difference in bulk between e.g. 6 units and 6 thousands. Control of Error

The directress and the child’s own knowledge 

Age
4 – 4 1/2 years

Symbols

Materials
- A box containing 4 sets of cards:
1 set for units – 1 to 9 in green symbols
1 set for tens – 10 to 90 in blue symbols
1 set for hundreds – 100 to 900 in red symbols
1 set for thousands – 1000 in green symbols
- A mat
Presentation
1. Invite a child to come and work with you.
2. Have him unroll a mat and have him bring over the material to the mats. 3. Put the box of cards on the lower part of the mat.
4. Take out the card for 1 and ask the child what it is.
5. Take out the card written 10 and ask the child what it is. 6. Notice how many zeros are in the number 10.
7. Take out the card written 100 and name it.
8. Notice how many zeros 100 has.
9. Take out the card written 1000 and name it. Notice the zeros. 10. Also notice the colors of the cards.
11. Do a Three-Period lesson for 1, 10, 100, 1000.
12. Place card 1 at the top right of the mat.
13. Take out the unit cards and place card 2 under card 1.
14. Have the child name card 2.
15. Repeat for all of the unit cards (the child can do this). 16. Repeat for the 10’s by placing them in a column to the right of the units. 17. Repeat for the and 100’s and 1000’s cards. Always making the column to the right of the preceding cards.   18. Do a Three Period Lesson. Each time, as how many zeros are in the number. 19. Have the child collect the cards.

20. Mix them and place them randomly in their correct columns. 21. Have the child pick up one column at a time (beginning with the unit cards) and replacing them in the column in order. 22. Have the child repeat for the other three columns.

23. Each time the child replaces the cards in order, have him say what it is. For example, “1 unit” for 1, or “3 tens” for 30, or “8 hundreds” for 800, or “5 thousands” for 5000, etc. 24. Once all of the cards have been lain out, have the child count, using the decimal quantity: 1 unit, 2 units, 3 units, etc. 25. Repeat for the tens, hundreds and thousands.

26. Each time, asking how many zeros there are.
27. Once done, have the child put the material away.
Purpose
Direct
To acquaint the child with the written symbols for the
quantities/categories of the decimal system.
Control of Error
The directress and the child’s own knowledge 

Age
4 – 4 1/2 years

Formation of Numbers

Materials
- The supply of limited golden bead materials
- The large cards to 1000
- Trays for participating children
- Two mats

.

Presentation
Invite a child to come with you. Have him unroll two mats and bring the material to one mat. Place a small mat between the two larger mats and place the tray onto the smaler mat. Have the child put out the unit beads in a vertical row from 1 to 9 from the top of one of the large mats. Have the child put out the ten-bars to the left of the unit beads in a vertical row, the hundred squares to the left of the ten-bars, and the 1000 cube to the left of the hundred squares. Have the child place the large cards 1 – 1000  (only 1000) on the other large mat as in the Introduction to Symbols exercise.

Choose a card from the layout and give it to the child for him to put it on his tray. Ask the child to go and get the amount of beads written on the card. The child should take his try with the card on it to the mat with the beads and collect the correct amount of beads. Have the child place the beads onto the samller mat and count to check. Have the child replace the material from his tray and repeat by giving him another card. Repeat this a few times.

After some time, reverse the activity by giving the child an amount of beads. Have him count the beads and then go get the corresponding card to match the number of beads. Check the child’s work with him.

Have the child replace the material from his tray and repeat. Once the child seems to understnad, give him two cards such as 20 and 3. Have the child name then: 2 tens and 3 units.
Have the child go to the mat and collect the correct amount of beads. When he comes back to the small mat, check his work.
Repeat using the hundred cards and the one thousand card.
After a while, reverse the activity by giving the child an amount of beads to which he must find the correct corresponding card. Begin with one catergory (such as units). Later move one to two adjacent catergories (such as units and tens), three adjacent categories, and four adjacent categories. Then non adjacent categories.  

Show how to correctly place the cards 
Have the child bring over (for example) 1426 in beads.
Have the child bring over the corresponding cards.
Place the 400 card on top of the 1000 card with both of their left sides lining up. Place the 20 ontop in a similar manner and then the 6.
Pick up the cards by holding then from the side near the far left. Rotate them up vertically clockwise. Slide the numbers down to the lower side. Place the cards back onto the mat and then number you have created is 1426. Read it saying: 1 thousand, 4 hundred, 2 tens, and 6 units. Have the child repeat it with you.

Read it again but this time saying: one-thousand, four hundred and twenty-six. Read it again with the child.
Have the child replace the material back onto the correct mats and repeat. Direct
To make the child familiar with the different categories of numbers, especially with regard to reading the symbols. To give the child the wording of large numbers

Indirect
For the hierarchy of numbers, that is, that while the significant figure are always from 1 to 9, it is the place they occupy in the complex number which gives them the importance of 1, 10, 100 or 1000. For the fact that in a large number made up of two or more categories, the zero merely shows an empty place. That is, that one of the categories is lacking (in 1065, for instance, the hundreds are missing). For the fact that only 9 of each category are necessary to form any number. Control of Error

If the directress perceives any slip, then she should ask the child to read out the symbol and count ever the quantity of beads which he has brought. This will make him aware of his mistakes.  Age

4 1/2 years
Changing

Materials
- Supply box
- A mat
Presentation
1. Invite the child to come and work with you.
2. Have him unroll a mat and have him bring the supply box over to it. 3. Have the child set out the material on the mat as in the Supply Mat. 4. Have the child count out the units and place then in a vertical line. 5. When he gets to ten units, show him how it looks just like the ten-bar. 6. Have the child continue in this manner, each time noticing the look alike to the ten-bar. 7. Continue until there are no more units. Look at the remaining units that cannot be formed into a ten-bar and ask the child if there are enough units to create a ten-bar. Ask the child why this is so. 8. Have him count how many ten-bars he had made by using the units. 9. Have him then count the ten-bars and place them side by side. 10. When he has counted ten ten-bars, notice how it looks just like the hundred square. 11. Repeat until all of the ten-bars have been used. If there are some ten-bars left over, ask the child if there are enough to make a hundred square. Discuss why with the child. 12. Have the child count how many hundred squares he made by using the ten-bars. 13. Then have the child count the hundred squares by stacking them on top of each other. 14. When the child reaches 10 hundreds, discuss how this looks like the thousand cube. 15. Repeat until there are no more hundred squares. If there are any left over that cannot be made into a thou...

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