Montessori Exercises

Pink Tower

Description of Materials

• Ten pink wooden cubes varying in size from one cubic centimetre to one cubic decimetre
• A floor mat

Objectives

• To develop the child’s visual and muscular perception of dimension in judging sizes
• To develop the child’s co-ordination of movement and fine motor control
• To prepare the child, indirectly, for mathematics by giving the child experiences in comparison, grading and seriation with the cube
• To give the child basic language- important in mathematics

Control of Error

If the tower is incorrectly built it may fall down and this will act as control of error. However, if the child makes only a slight error, the teacher should not intervene, but wait for the child to correct his error. It may be necessary for the teacher to present the material again at a later stage.

Language

• Large, small
• Large, larger, largest
• Small, smaller, smallest
• Larger than, smaller than
• As large as, as small as
• Big, little,etc.

Approximate Age

From 2 ½ years onwards.

Presentation 1

• This is an individual exercise which is done on the floor on a floor mat. (Note : Work cycle to be observed)
• The teacher first shows the child how to carry the cubes to the floor mat :
• For the first four cubes starting from the smallest, we use the first 3 fingers to grasp each cube over the top and place it randomly on the floor mat.
• From the 4th cube to the 7th cube, we may use one whole hand to bring each cube to the mat.
• As for the last three cubes, if it is too big for the child to hold with one whole hand, then they may use both hands to carry it to the mat, by balancing the bottom of the cube with the palm of the other hand.
• All the cubes are placed at random on the floor mat.
• Teacher then shows how to build a tower :
  • Starts with the largest cube and place the next largest cube centrally on the previous one. Teacher may show how to build the first 3 cubes and then select the next largest cube and invites the child to place that cube on the previous one.
  • Allow the child to do the last piece of cube by himself.
  • When the tower is completed, invites the child to view it from the top.
  • When the presentation is completed, teacher then shows how to remove the cubes, starting from the cube at the top and placing it on the mat.
  • Teacher shows for the first two cubes and then invites the child to remove the rest.
  • To place the cubes back to its shelves, we begin by taking the largest cube.

Exercise 1

The child may choose to build the Pink Tower.

Note:

• The cubes have the advantage that any two successive cubes vary in three dimensions, length, width and height, thus making their difference in size reasonably obvious to children. Easy beginnings are never a waste of time when they help to establish basic ideas and here it may be useful to build a tower from :
  • The three or four smallest cubes.
  • The three largest cubes.
  • The three successive cubes from the middle.
  • With slow or special needs children, five cubes can be used, made up of every other cube.
• The most difficult of the blocks to place in position is the smallest, which is 3/8″ on each side. The child’s arm has to be quite steady to place this small object on the center of the next largest block and requires close attention and obvious efforts in performing this task
• By holding the first few cubes with the thumb, index and middle fingers , i.e. the ‘pincer grip’ will prepare the child for holding the pencil later when learning how to write.
• After making repeated use of the cubes, a child’s hand finally adopts automatically the precise position necessary to cover the top dimension of the cube. In other words, a child develops a muscular memory for define graduations of space.

Presentation 2

When the child is ready, i.e. the child is competent at building the complete tower by placing one cube centrally on another, we then tells the child, “We are going to build the tower in a slightly different way”

• Teacher shows how to build the complete tower which has two flat walls all the way up.
• When the tower is completed, teacher takes the smallest piece of cube and says, “Now we are going to slide the smallest cube along the side”. Teacher then slides the smallest cube along the steps of the tower from the bottom to the top and finally placing that piece of cube on the top.
• Teacher may do the Three Period Lesson with the biggest and smallest cube – “This is big” ; “This is small”

Notes:

• By building the tower in the way shown in the second presentation allows the child to see that the smallest cube has some relationship to the others as it will “fit” anywhere on any of the steps of the tower when we slide the cube along the steps of the tower from the bottom to the top.
• Another aspect of the material is that the smallest cube is the centimeter cube, or cubic centimeter, and the largest contains a thousand of these (the litre). The child will meet these ideas very much later, but handling the cubes at this present stage should contribute to a most useful experimental foundation.

Extension

• Instead of building it vertically up, we may build it horizontally, laying the cubes on the floor mat. Teacher may show how to build the first 3 cubes and then allow the child to proceed with the rest of the cubes.
• Play a game with the children. This can be done in a group. Select 3 different sized cubes and lay them on the table. Teacher make a request, for e.g. ‘Bring me the largest cube’, ‘Bring me the smallest cube’ or the teacher selects a cube and then says ‘Bring me a larger cube than this’,…etc. The child will have to bring the cube required to the teacher.
• May also be built as a spiral.
• Invite the child to make a two dimensional representations of the tower. Firstly, prepare some ready cut squares from pink paper or card which matches the dimension of the cubes. Place these in a basket. Invite the child to first build the pink tower and then make a picture of the tower by gluing the squares onto a piece of paper.

Number Rods

Description of Materials

• Montessori Number Rods.
• Large felt mat for floor exercise.

Objectives

• To introduce the child to fix quantity.
• To introduce the child to counting from 1 to 10 using whole quantities, e.g. 2 as a whole.
• To make the child aware of the sequence of numbers 1 to 10.
• To make the child aware of the quantitative relationship between numbers, e.g. 2 is more than 1 and 3 is more than 2, etc.
• To make the child aware of the concept of numbers as an aggregate of 1’s (e.g. the child can check this by counting the rods)
• To introduce the verbal number names and their quantity from 1-10.

Control of Error

• If the stair is correctly built the child will be able to name the rods from one to ten in the correct order. If the stair is built incorrectly, the stair will not be a smooth ascending stair, so visually, the child could see that it was not built correctly.

Language

• One, two, three to ten.

Approximate age

3 and above.

Presentation 1

• Teacher invites the child to the shelf and introduces her to the Number Rods. Teacher invites the child to select a working place on the floor and then show the child how to bring the materials to the working place.
• Teacher shows how to lay out the floor mat.
• Teacher places the rods at random on the mat.
• Teacher shows the child how to build the stairs with the first three rods. Then she invites the child to continue building the rest.
• When completed, teacher takes the first 3 rods and go through “The Three Period Lesson” and introduces the names “one, two, three” in association with the quantities one, two, three.

The First Period

She points to the first rod and say ,”This is one. (The teacher encourages the child to repeat the name after her and says, ‘Can you say one?“) She then points to the second rod and say, “This is two.” And then to the third rod and say “This is three”

The Second Period

Teacher then says to the child “Show me 1” and the child will probably point to the first rod. “Show me 2” and so on.

The Third Period

Teacher jumbles up the rods and place at random on the table. She then points to any one rods and say ‘What is this?” and the child answer. She repeats for the other two rods.

• When exercise is completed, the teacher shows the child how to place the Number Rods back to its original place on the shelf and explain to the child that the materials must be returned to its place so that others may work on it. He may work on the material anytime he wishes to on his own.

Additional Note:

• Gradually, the child will learn up to 10 with the introduction of three rods at a time with one rod from the previous lesson and two new ones, for e.g. One, two, three in the first lesson and then three, four, five in the second lesson and so on till ten. If the child forgets some of them, use the Three Period Lesson to teach him again. Remember to count slowly.

Individual Exercise

The child can take the number rods anytime he wishes to build and count the rods up to ten.

Extension

• Instead of building the stair the method shown above, we can also build them in a graph format as shown in fig. 1.5.
• Play a game. Ask the child to close their eyes. Teacher takes away one rod. Ask child to open their eyes and find which is missing

The Spindle Box

Description of Materials

• A wooden box with ten compartments. The numerals 0 to 9 written at the back of the box.
• 45spindles
  Note : The difference between the Number Rods and the Spindle Box is

• With the Number Rods, the quantity is fixed and the numerals are loose
• With the Spindle Box, the numerals are fixed and the quantities are loose.
• Zero is introduced.

Objectives

• To give the child further practice in associating each numeral with the right number situation.
• To introduce the number and concept of 0.

Control of Error

• There are exactly 45 spindles for the box. The child places the number of spindles associated with the numerals at the back of the box and when he reaches 9, if he finds too many or too few spindles to be placed into the compartment, then he will know that he had make a mistake and he can check his work and correct his error.

Language

0, 1 to 9

Approximate Age

3 and above.

Presentation

• Teacher invites the child to the shelf and introduces her to the Spindle box. Teacher invites the child to select a working place on the table and then shows the child how to carry the materials to the selected working place.
• Teacher place the materials on the table. Teacher points and read the numbers at the back on the box, starting from 0 to 9 and the child repeats after her.
• Teacher and child remove all the spindles from the compartment and place them in front of the box on the table.
• Teacher takes one spindle, grab hold of it in the left hand and say “1”. Then, she places it in the compartment numbered 1. She repeats the same for 2 and 3.
• Teacher encourages the child to carry on with the rest of the spindles
• When child finishes, the teacher points to the compartment numbered 0 and say “0 means nothing, so we do not place any spindles in this compartment.”
• When the exercise is completed, teacher shows the child how to place the materials back to its original place on the shelf. Teacher explains to the child that the materials must be returned to its place so that others may work on it and that he may work on the materials anytime he wishes to, on his own.

Extension

• Place all the spindles correctly in the Spindle Box except perhaps 2 compartments. Invite the child to spot the mistake. The child will have to count and check each compartment to find the mistake.
• Invite the child to close their eyes. Place a bundle of spindles in their hand. They may use both hands. Ask them to feel and count the spindles and to tell you how many they have in their hands. By closing their eyes and depending on just their feeling of the spindles, it gives them a better feel of the quantity they have in their hand as the number increased.

Variation

To give the child further practice in associating each numeral with the right number situations and to reinforce the concept of zero.

• “Can you clap for me 5 times? “
• “Can you come to me 0 times ?”
• “Can you stamp your feet 3 times ?”