Presentation of the Decimal System
Golden Bead Material or Base Ten Material
Age 3 and up
A child usually has done the number rods, number rods and numerals, the spindle box, and numerals and counters i.e. the child can count quantities up to 10.
Introduce the names and quantity proportions.
Introduces counting that brings the child to higher numbers.
The introduction uses sensorial approach in that the different bead material can be differentiated in depth, weight and quantity.
Finally, this brings counting to higher numbers.
Shows exponents with 10^0 (units) being points:
This pattern continues throughout the number system.
For example, 10 cubes in a line make 10,000, 100 cubes in a square make 100,000, 1000 cubes made in a giant cube make 1,000,000.
You can make giant cube and repeat the pattern to get any natural number.
Materials needed for the following exercises;
(You can use a small egg cup for ones (units), a bigger container for tens, hundreds, and thousand.)
To Make Materials:
To make the bead materials for this lesson you will need about 2000 golden beads (7 or 8 mm) and wire. (I used plastic beads that are very shinny and pretty with wild wire (copper jewelry wire)-they turned out great!) I used 18-gauge wire and about 8-mm beads (with predrilled holes). If you want to make it out of glass beads it might be cheaper to buy the materials from a Montessori supplier. Set aside 10 bead units.
Cut about 3 1/2 inches of wire. Loop and secure with needle nose pliers or tweezers at one end and string on 10 golden beads. Secure the end with a loop and squeeze with pliers. Make 199 ten-bead bars. Put 9 ten golden bead bars aside. Put aside the 10 bead bar units (ones). Take the rest of the 190 ten bead bars. Take 10 golden bead bars and lay them flat like a square. Thread the 10 bars together with wire at the top and bottom. Tuck in the wires securely. When finished, set aside 9 sets of the 100 bead squares. Take the last 10 one hundred bead squares and stand them on end. Thread them together with wire, well tucked in again. The loops should all be on 2 sides together. You may have to hot glue the 100's together to keep the square together or thread the beads through plastic needle point mesh.
Easy method to make material:
You can print off the golden bead template and make the 10 bars, 100 squares, and 1000 cube glue on light wood or durable cardboard.
Introduce each bead member (1,10,100,1000) with the three period lesson. Hint: You can make the introduction easier by introducing 1 and 10 the first day, then add a new bead member each day-100 then 1000.
Take one golden bead unit, one ten golden bead bar, one hundred golden bead square, and one thousand golden bead cube on a felt lined tray to the table.
(When presenting the material lay out the quantities as you would numbers place for 1000, 100, 10, 1- i.e. cube, square, bar and unit.)
Show your child the one bead unit and say, "This is one." (The child will know this!) Let your child hold and feel the bead. Next, introduce the ten gold bead bar, and say, "This is ten." (Again the child will probably know this is 10) Again, the child can hold be ten gold bead bar and count the beads. Show the 100 square and tell your child, "This is one hundred." Let him count the 10 gold bead bars in the square to find out it is made of 10 gold bead bars.
Lastly, Show your child the thousand cube, and say it is called one thousand. Count with your child to show him or her that ten hundred are one thousand.
Let your child hold and compare the bead systems. Usually, the heavy cube gets the best response with, "This is heavy!"
Ask your child if he or she can show you, 1, 10, 100, 1000. Mix up the quantities several times and ask in random order the quantities, such as 10, 1, 1000, and 100.
Ask the name of the quantities, 1,10,100, and 1000.
If the child wants to count instead of you, that's great! Sometimes, an inventive child will take the singe bead and count out the 10 bead bar. Then take the ten bead bar and count out the hundred square, and finally, take the 100 square and place it on top of each one hundred square of the 1000 cube and count out 10 hundreds.
Age 4 to 4 1/2
Presentation: Take the material on a tray to your child's table and spread a felt mat on the table. Put out the unit beads, one at a time, letting your child count them. Make a straight line as if you were making a ten bar. When your child reaches nine say if you had more golden bead it would make 10. Take away the nine beads and replace them with a 10 golden bead bar. If this is simple for your child you can say, "If you had 1 more bead, how many would you have?"
Next, count out the nine ten gold bead bars one by one with your child. Put the tens side by side as if making the hundred square. When the nine bars have been counted again explain, "if you had one more there would be one hundred." Take away the tens and replace with a hundred square.
Lastly, count the hundred squares with your child one by one. Place the squares on top of each other as if making a thousand cube. After all nine squares have been counted say, "if there was one more hundred that would make 10 hundreds. 10 hundreds make one thousand." Take away the hundred squares and replace them with the thousand cube.
Count the thousands with your child one by one. Place the cubes in a line. After all nine cubes have been counted, say, "if we had one more cube it would make 10 thousand.
You can make more thousand cubes for your child as needed. Later on you can introduce one million this way.
Let the child do the exercises on his or her own.
Age: 4 1/2 to 5 1/2 Fetching Game You can do this with one child or a small group of children. Purpose: To reinforce the name of the quantities with the actual gold bead material.
Presentation: Small Group exercise (3 to 4 children.) The golden bead materials, now including the wooden hundred squares and thousand-cubes are arranged on a table with the units on the right and thousands on the left. Each child takes a tray. The teacher asks the child to bring a quantity from one group hierarchy. 'Bring me 3 hundreds' or "Bring me 5 tens." As each child returns with the quantity, the child identifies it, and the teacher and child count it together. Have the child put the quantity back in the proper place. Repeat often over the following days.
Gradually ask for more complicated amounts until your child can bring four number groups at once - (1 thousand, 5 hundreds, 4 tens and 3 units)
Age-4 1/2 and older Purpose: Present written symbols of numbers for the gold bead materials-units, tens, hundreds, and thousands. Gives understanding of the make up of the decimal system.
Purpose: To learn the names of hundred and thousand in association to their respective quantity.
Material: A set of large number cards on which is written the numbers 1 through 9000.
(You can get card stock from any office supply store and print out the numbers.)
A box or container to store the numbers.
Presentation: Show the 1 number card, the 10 number card, the 100 number card, and the 1000 number card to your child. Your child will be able to tell you the numbers 1 and 10. Tell your child the names of "hundred" and "thousand". Teach these numbers using the 3 period lesson. Mix up several times.
Purpose: Child places the number symbols in order from longest to shortest
Take all the cards and count with your child. Start with the units, and count, "1, 2, 3, 4,5, 6,7,8,9" Put the numbers in order on the right side of the working area. Lay out the tens next, "ten, two tens, three tens, four tens, 5 tens, up to 9 tens". Next lay out and count, " 1 hundred, 2 hundred, 3 hundred," up to 9 hundred
* Easier Exercise: Use only the 1000 card and put away the cards 2000 to 9000.
Introduce the 2000 through 9000 after the easier lesson is mastered.
Fetching Number Card Game (You can do this with a small group of children -Make sure they have done exercises 1 and 2) Children spread out the cards so the numbers can be seen clearly. Take turns asking each child to fetch a card- "Bring me 200." As this gets easier ask, Bring me 100 and 9 units" then later- Bring me 300, 6 tens, and four units
Lastly, put the numbers in proper order, from longest cards (l000's) to shortest cards (units)
Give the child a card and have them tell you what the number is.
Purpose: Associate the numbers and quantities up to 9000.
Age: 4 1/2 to 5 1/2 and upwards
9 Golden Beads, 9 ten golden bead bars, 9 hundred golden bead squares, and 9 golden thousand cubes. (You can use representations of these units) 2 table areas Mat
Presentation: Have the children lay out the cards in four columns as shown below:
The golden bead material is laid out similarly on another table in the same order as the numbers. (1000's on left, 100's next, 10's next, and units on right side)
1. Show your child a card and ask him or her to fetch the corresponding quantity. "Can you find this with the golden beads?"
2. Check the beads on a mat. Put the card back and ask your child to put back the beads.
3. Repeat this exercise over following days.
4. When your child is ready, take several cards out, show your child the card one at a time. For example, take out the 100 card, 50 card, and 3 card. Ask your child to fetch the beads.
5. When your child brings the beads, check the quantity and put the cards on top of each other with the longest at the bottom. Hold the cards together, and tap down on the unit end on the table. The cards are now level and read 153.
6. Say, "one hundred fifty three"
7. At this point you introduce the sequin boards. Until your child may have been calling fifty, "five tens". This usually instills interest in the new name and all the sequin boards can be taught.
Reverse Exercise of "Banking Game" Put various quantities of bead material on the children's trays and ask the children to bring the cards that correspond.