2. Bring the bead presentation tray containing 1 unit, 10 bar, 100 square, 1000 cube to the rug. Later add to these materials the 100 and 1000 chains.
3. As the child progresses with each stage the materials needed will be noted. There is no formal presentation with these sensorial experiences.
4. The various stages can be done with the children individually or in small groups.
5. The children should have worked with the initial bead presentation and the short bead stair and be very familiar with the sensorial materials.
1000 cube 100 square 10 bar 1 unit
a. Directress points to the 1 unit bead, saying "one"
Directress points to the 10 bar saying, "ten" and then counting it out
Directress points to the 100 square saying, "One hundred" and then counting, "ten, twenty, thirty, forty, fifty, sixty, etc. to one hundred"
Directress points to the 1000 cube saying "one thousand" and then counting it out, "one hundred, two hundred, three hundred, four hundred, five hundred, six hundred, etc. to one thousand"
b. Next, Directress places the unit bead by each bead in the ten bar counting it out again. Then she places the ten bar, superimposed, over each ten-bar of the 100 square and counts it out. Lastly she places the hundred square in the same manner over each 100 square in the 1000 cube, counting it out as before.
c. Directress asks child, "How many units are there in a 10 bar?", "How many ten bars in one 100 square?", "How many one hundred squares in one 1000 cube?"
1000 cube 100 square 10 bar 1 unit
Under the above layout place the following bead materials:
1000 chain 100 chain 10 bar 1 unit
(laid out vertically) (vertically)
a. See if the child notices any similarity in these layouts. Are they the same?
b. Directress: "Can you bring me something in the math area that would also represent units?"
Child could bring:
* shortest number rod
* another unit bead
* 1 red bead
* numeral one
* one spindle
* one counter, etc.
c. Directress: "Can you bring me something else in the math area that would also represent ten?"
Child could bring to the rug:
* longest number rod
* another ten bar
* numeral ten
* ten spindles
* ten fractions parts, etc.
d. Directress: "Can you bring me something else in the math area that would also represent 100?"
Child repeats above process.
e. Directress: "Can you bring me something else in the math area that would represent 1000?"
Child repeats above process.
f. After this stage is completed the child or children return the materials they brought to their appropriate place.
g. Same process is used here except the child or children are asked to bring the Directress materials in the same quantities from other areas of the classroom. After this stage is complete the children return the materials to their appropriate place.
Going across the top of the rug, right to left, place the following short bead stair beads: 9 bead bar, 8 bead bar, 7 bead bar, 6 bead bar,..... to 1 red bead.
a. Child counts each bead bar as it is being placed on the rug beginning with the one red bead saying, "one".
Two green beads- "one, two"
Three peach beads- "one, two, three"
Four yellow beads- "one, two, three, four"
Five light blue beads- "one, two, three, four, five"
Continue in this manner through nine
b. Below the above layout place in a vertical line below the appropriate beads the square chains: 9 chain (vertical), 8 chain, 7 chain, etc. to 1 redbead.
Beginning with the red bead the Directress places the individual bead bars next to the appropriate sections of the square chains. This is to show the child the relationship of the materials together and how many individual bars are used to make a particular chain. After placing the bead bars next to the appropriate sections of the square chain return the bead bars to the top of the rug.
c. Repeat above process but place the total layout in a horizontal manner.
1 red bead 1 red bead 2 green bead bar 2 green square chain 3 peach bead bar 3 peach square chain 4 yellow bead bar 4 yellow square chain 5 light blue bead bar 5 light blue square chain 6 violet bead bar 6 violet square chain 7 white bead bar 7 white square chain 8 brown bead bar 8 brown square chain 9 dark blue bead bar 9 dark blue square chain 10 golden bar 100 golden chain
Going across the top of the rug, right to left, place the bead bars 1-9, underneath the bead bars (vertically) the square chains and underneath the square chains the squares.
a. Let the child or children observe this layout for a while. Does he notice any similarities? How are these chains to the squares related?
Directress then takes each bead bar and places it next to the appropriate sections of the square chains (as in Stage III, b). She then returns the beads to the top of the rug.
b. Directress then folds each square chain, beginning with two, to form the square below. Place the squares next to the folded up chains.
Place the squares on top of the folded chains.
Return the bead bars to the box.
c. Place the folded square chains across the top of the rug but now left to right from 1 to 100. Place the squares below this in the appropriate place. Place the squares in the Square of Pythagorean below this. Let the child observe the color relationship.
Superimpose the squares (beads) on top of one another beginning with the 100 square, square of nine, square of eight, etc. to 1. Repeat this with the Square of Pythagorean.
d. Let the children later discover if there is any relationship of size between the following:
* bead squares to the squares in the square of Pythagorean
* either of the above to the cubes in the pink tower
* either of the above to the broad stair
* matching the colors to color box 2
Materials: Colored bead squares, colored bead cubes, rugs.
g. Across the top of the rug, right to left, lay out the squares from 100 to 1 and below place the cubes.
100 square
9
square 8
square 7
square 6
square etc. to 1 red bead 1000
cube 9
cube 8
cube 7
cube 6
cube etc. to 1 red bead
a. Let child observe this new layout. Does he see any similarities? Is there any relationship?
Beginning with 1 show the child how many squares are represented in each appropriate cube. After each is shown replace the square to its appropriate place on the rug. In doing this superimpose the square directly over each square in the cube, counting it out (e.g. the square and cube of five). "This is the square of five", "This is the cube of five." Placing the square of five over the squares in the cube, count it out, "one, two, three, four, five." Repeat this procedure all the way through.
b. Layout as before but this time layout all of the squares in a vertical manner from left to right. Place the cubes underneath each appropriate row of squares. Let the child observe this pattern.
Beginning with the 1 bead place it next to the other red bead.
Stack up the squares of two to form the cube of two.
Stack up the squares of three to form the cube of three.
Stack up the squares of four to form the cube of four.
Continue in this manner all the way through 1000.
c. Repeat the above steps in (b) in a horizontal manner.
d. Beginning with the 1000 cube, build the cubes vertically to form a tower, superimposing one cube on top of another.
Materials: Colored bead cubes and cube chains, rugs. Later bead squares.
Across the top of the rug, right to left, place the colored bead cubes.
1000 cube 9 cube 8 cube 7 cube 6 cube...... etc. to 1 red bead
In a vertical manner under each appropriate cube place the cube chain.
1000 chain 9 8 7 6 5 chain, ...etc.
a. Let child observe the layout. Does he see any similarity?
Directress then may say, "There is one bead here and one bead here", "There are eight beads here" (pointing to the cube of 2) and "There are eight beads in this chain", "There are 27 beads in this cube" (3) and "There are 27 beads in this chain"
Repeat this process all the way through to 1000 showing first the number of beads in the cube and then in the chain.
* Chain of 4-64
* Chain of 5-125
* Chain of 7-343
* Chain of 8-512
* Chain of 9-729
* Chain of 10-1000
Layout all the cube chains, left to right, across the top of the rug but vertically. Below each of the chains layout all of the colored squares vertically under the appropriate cubes.
Fold up each length of the cube chain to form each square and then place the square next to it. Repeat this process all the way through to 1000. When completed place the squares directly on top of the folded chains.
c. Could repeat b in a horizontal manner also.
Materials: Colored square chains, colored cube chains, rugs. Later short bead stair added.
Across the top of a rug, right to left, place the square chains vertically. Below this, in the same manner, place the cube chains.
a. Let the child or children observe this pattern. Place the 1 red bead next to the other red bead (moving it down). Continue in this manner placing each of the colored square chains next to each appropriate section of the cube chains from 2 through 1000. Child can count how many square chains there are in a cube chain. Leave the square chains at the end of the cube chains.
b. Layout all of the bead bars across the top of the rug (vertically) from left to right. To the right of the bead bars place the square chains. To the right of the square chains place the cube chains. Let child observe the work.
c. Layout as before in b. At the end of each square chain place one square and at the end of each cube place a cube. Let the child observe this pattern.
Making of booklets for the bead bars, square chains, squares or cubes, fewof the shorter cube chains. Directress should make a model booklet for eachmaterial and include the appropriate language within it.
a. Child takes a booklet to a rug with the bead material that corresponds to the booklet. He relates the knowledge of the booklet to the materials.
b. Later on the child may begin to make his own booklets or draw his own bead materials on white paper.
* colored bead bars book first
* squares
* cubes
* square chains --- on large piece of paper
* cube chains --- on large piece of paper
Materials: Colored square chains, rug.
a. Place all of the square chains in a vertical manner on the rug, right to left.
Move down the one red bead
Move down the bead chain of 2 (leave in a vertical line)
Move the peach chain down and form in a triangle
Move the yellow chain down and form a square
Move the light blue chain down and form a pentagon
Move the violet chain down and form a hexagon
Move the white chain down and form a heptagon
Move the brown chain down and form an octagon
Move the dark blue chain down and form a nonagon
Move the 100 chain down and form a decagon
b. After forming the above Directress points to the third chain (forms a triangle) and asks the child, "Can you find something in the geometric cabinet that looks like this?"
Repeat this with each figure formed.
Child places geometric figure on the rug next to the beads.
* With the red and green beads any straight line figure will do.
* This is a great activity and is enjoyed by every child.
Materials: Colored square chains, rug.
a. Layout all of the square chains in the same manner as in Stage IX. Beginning with the two chain place it in the middle of the rug in an upside down V. Taking each chain, in turn, place it on the outside of the previous chain in like manner until all of the chains are in the proper place. When completed, put the 1 red bead in the center.
Materials: As above plus cube chains.
a. Layout the cube chains as before. Beginning with the third chain (peach), have three children holding it in order to form a triangle. Each child in turn counts the side he is holding and then the chain is placed on the rug.
b. Repeat with the four chain (making a square) but add another child. Repeat with the five chain (making a pentagon) but add another child. Repeat this procedure through the ten or 1000 chain, thus having ten children.
c. When the chains are laid out on the rug as above (geometric forms), suggest to the children that they might find these forms in the geometric cabinet. have the children find these forms in the cabinet and bring the geometric insets to the rug and place by the appropriate beads. Return material when through.
d. Layout the cube chains in the shapes as in b and place inside the same shapes with the square chains. Let children observe work when completed.
Materials: Short bead stair, square chains, cube chains, rugs.
a. Lay out the short bead stair on the rug in a vertical manner. Leave a space and then lay out the square chains in the same way. Leave another space and lay out the cube chains in the same way.
* This shows the child the progression of different relationships between units, squares, and cubes.
Give the children lots of sensorial practice with the short bead stair, square and cube chains, etc. before he actually counts them. When the child gets to the point where he is counting, put out all the square chains and one square which represents each chain. The child can count chains 1-6 in any order and then 7-10 or 100. Later on the Directress adds the cube chains, cubes, and the rest of the squares to the bead cabinet. The children are encouraged to count the shorter cube chains before he does the longer ones. The child is probably in his late second year or early third year in Montessori when counting the square chains and older for the cube chains (S to 6).
2. When the child counts the chains the control is in the Directress or the tickets.