The Geometry Cabinet

Note: As with the other material, the most contrasting plane figures should always be chosen for the presentation. The more contrasting the material, the easier it is for the child to discriminate

Material Description : A wooden cabinet with six drawers plus a presentation tray containing thirty three plane figures: the “insets” and their corresponding “frame”. The bottom of the drawers and the tray are painted in the same colour blue as the insets. Each plane figure is fitted with a knob.

o Presentation tray - with six wooden tablets.o The drawers contain various figures: curvilinear triangle, ellipse, oval,

quatrefoil.o Quadrilaterals: rhombus, right angled trapezium, isosceles trapezium,

parallelogram, acute angled scalene triangle. These figures are referred to as right angled trapezoid and isosceles trapezoid (in American English).

o Six circles decreasing in diameter from 10cm to 5 cm.o Rectangles: one square and five rectangles, the bases vary from 10cm to

5cm, while the height remain constant.o Seven triangles: equilateral, acute angled isosceles, right angled isosceles,

obtuse angled isosceles, right angled scalene, obtuse angled scalene and acute angled scalene.

o Regular polygons: pentagon, hexagon, heptagon, octagon, nonagon, decagon.

Display : The drawers can be kept in a row on a collapsible shelf in the veranda.

Presentation : At the shelf, remove the circle, square and the equilateral triangle from their

respective places in the geometry cabinet and fit them in the demonstration tray. Keep them separated by means of the wooden tablets.

Lift out one of the figures (say the square) holding it by the knob with the thumb and two fingers of the left hand.

Feel around the edges of the square, with a natural continuous movement using the index and middle finger, starting at one point closest to oneself and in clockwise direction.

Place the square on the wooden tablet and feel around the cut out part of the empty frame an anti-clockwise direction.

Fit the square back in place. Do the same for the circle and the triangle. Remove the three insets and place on the mat at random. Ask the children to feel the insets and the cut out part of the frame. Replace it into its corresponding frame. After the first three, other shapes maybe added to the demonstration tray e.g.

pentagon, rhombus, ellipse. In this way the child can be introduced to a variety of shapes chosen from different drawers over a period of time.

Exercises :1. Own activity as shown in presentation2. The child works with each drawer individually3. The child works with two drawers together4. Gradually more drawers are added until he can work with the full cabinet.

Note : The procedure reflects the essential Montessori Principal of going from contrast to similarities and then gradation. Each drawer is taken separately to show the type of gradation, i.e. difference in grades of the same figure e.g. triangle, circle, square (special case), polygons.

Language : To be taught by the Three Period Lesson. Language can be introduced when they can distinguish each shape easily. This is generally done with cards preliminarily.

Control of Error : Built in the material.

Direct Aim :1. Discrimination of figure – provide the child with the key to orient himself

with and within the world of shapes2. Enhancement of visual memory

3. To help the child to become aware of the fundamental geometrical shapes by means of his visual and kinesthetic senses, there by becoming sensitive to various shapes in general.

Indirect Aim :1. Preparation for the study of mathematics – geometry2. Preparation of the hand for writing

Age at Presentation : Three to four and a half years.

Games 1. Reverse pairing at random. Put indicator in one cut out and the child finds

its pair.2. Reverse pairing at random. As memory exercise 1. Two mat game - same

as exercise 1 except insets are placed far on another mat.3. Reverse pairing at random. As memory exercise 2. Same as exercise 1,

except the insets are placed at different places.4. Reverse pairing in succession. As memory exercise 2. Same as exercise 1,

except indicator is placed in succession.5. Reverse pairing in succession. As memory exercise 1. Same as exercise 4,

except insets are placed far on the mat.6. Reverse pairing in succession. As memory exercise 2. Same as exercise 4,

except insets are placed at different places.

Note: The below grading games are only possible for the drawers of the rectangles, polygons and circles where there is gradation)

7. Grading with frame close by – mix insets and let the child guide them on mat and check with the frame.

8. Grading with frame far - same as memory exercise 7, except the frame is kept far away from view.

The two exercises that is possible with any material with grading, as follows:

9. The child will grade the insets. Then ask the child to close their eyes. Remove one inset from its place and remove the gap. Place the removed inset on the mat. Ask the child to open their eyes and find the position of the removed inset.

10.Same as memory exercise 9, except you hide the inset which you remove.

Geometric Cards

Material Description : Three sets of cards, matching each figure in the Geometry Cabinet. First set with figures completely filled in; second set with figures in thick outline; third set with figures in thin outline. Each set is arranged in random.

Note : For the presentation and exercises with the geometric cards it’s not necessary for the cards and cabinet to be at a great distance from one another, since these activities are not for the helping of the memorisation.

Presentation : (first set only)Find the shape: Choose a few cards of contrasting shapes. Place it in a pile on the mat. Take the first card, look at it and leave it on the mat. Go to the cabinet to find the corresponding shape. Superimpose the shape on the card. Continue in this way for the rest of the cards. Gradually, more and more cards are added until the whole set is given.

Find the cards: Take a few contrasting shapes on the tray. Place on the mat at random. Show the child a shape. Invite the child to find the appropriate card from the set. Continue in this way for the rest of the shapes.

Note : The number of shapes or cards used depends on the ability of the child.

Exercises :1. Child works through all as presentation2. Later introduced to the second set of cards (those with thick outline) and

works through them as described above.3. Finally he can be introduced to the third set (those with the thin outline) in

the same way.

Language : No language given with cards. He learns names with shapes.

Control of Error : None.

Age at Presentation : Following the work with the shapes in the Geometry Cabinet.

Games Two floor mats, the drawers and the cards (two children can work together)1. On a floor mat, layout the three sets of cards belonging to particular sets of

figure(s). The drawers with corresponding insets are taken to the other floor mat. Take a shape, let the child feel it and leave it on the mat. Go to the other mat and bring the three corresponding cards. Superimpose the shape on the cards one after the other. The cards are replaced and the game continues. The directress uses her discretion as to the number of drawers used.Note: This game becomes more challenging as more cards and figures are added. Until all the drawers and all sets of card are used at the same time.

2. All three sets are laid at random. All drawers are placed on another mat at a distance. The directress intentionally hides one card; the child must discover which one is missing by placing on each one.

3. CardsPlay the second game without use of control and the child finds out which one is missing (the child first use the filled in cards only if necessary).

Note:1. Here the child uses the figures, taking in impressions sensorially. Later in

the elementary, the child gets that the triangle is the constructor, the square is the measurer and the circle is the calculator

2. The triangle is the first figure we can get by using the minimum number of sides. The triangle means three angles, so it has three sides. Equilateral is the most perfect of all the triangles and that’s why it is added in the presentation tray. If we add one more side to the triangle then we get a quadrilateral. The square is the most perfect quadrilateral and if we add an infinite number of sides we get a circle.

3. Looking across all the Montessori material, one finds an underlying principal:

a. What is perfect is offered firstb. What is most familiar is offered firstc. Contrast are given first, to gain the impressions of the qualities

4. An upright posture is very important when tracing the figures because we want the child to experience shape with touch and not with pressure. The child gets two impressions:

a. When he traces the solid figuresb. When he traces the space it occupies in the frame.

With an upright body the child gets the impression that the movement is from the shoulder.

5. Graceful movement and control is very important for the child, thus when you present start with the corner closest to you.

6. Do not count the sides when doing the polygons as that is not the purpose here.

Rough and Smooth Tablets

Material Description :Box 1 - gradation of roughness

o Five pairs of rough tablets of the same gradations as Touch Board C

Box 2 – gradation of smoothnesso Five pairs of smooth tablets of the same gradations as Touch Board C

Note: Sensitise fingers before beginning

PresentationPairing

Bring the material to the table One of each pair is removed from the box and placed at random on the table The directress feels a tablet lightly with the eyes closed and gives it to the

child Continue in this way until all the tablets have been felt Start with contrasting textures so that the child becomes aware of the

difference Remove the other tablets from the box and place at random to one side Isolate one tablet from one of the sets, feel it with eyes closed and find its

pair from among the tablets of the other set When the match has been found, place pair on one side Isolate another tablet and find its match in the same way Continue until all the pairs have been matched Open the eyes, the difference in shade and in the “grain” of the sandpaper

will reveal a mistake if made. Fix all the tablets. Invite the child to pair with his eyes closed

Exercises :1. As in the presentation, the child can do all the five pairs with his eyes closed2. Grading: bring the material to the table, one of each pair of tablets is

removed from the boxes and placed at random. Use the blindfold or close eyes. Find the roughest tablet and place it aside. From the remaining tablets, find the roughest one and place it next to the first tablet. Feel both of them and invite the child to do the same. Find the roughest among the remaining tablets and place next to the other two. Feel all three of them. Continue in this way, until all the tablets have been graded. Open the eyes

and remove from the box to grade this set in the same way. The child can use the set graded by the directress as a control.

Note: the same procedure for pairing and grading are used for Box 23. At a later stage the child may grade and pair at the same time (this applies to

boxes 1 and 2)

Language : Comparatives and Superlatives of “rough”.

Comparatives and Superlatives of “smooth”.

Control of Error : In the material the difference in the colour and the grain in the sandpaper.

Direct Aim : Refinement of the tactile sense to discriminate the fine distinction between “rough” and “smooth” (blindfold will help the child focus on one sense)

Indirect Aim : To help the child prepare indirectly for writing.

Age at Presentation : Three and a half years.

Games 1. Two mat game – Unroll two mats on floor on the opposite sides of the room.

Place one of each pair of tablets at random on one of the mats. Choose the roughest tablet and carry it on to the other mat. Invite one of the children to find and choose the roughest tablet and carry to the other mat and so on until all the tablets have been taken across.

2. Language games - a) Unroll two mats at opposite ends of the room. Place one of each pair

of tablets at random on one of the mats. Choose one tablet and bring it to the other mat. Ask one child to go bring the tablet that is “rougher” and bring to the mat. The game continues until all tablets are brought.

b) The same can be done finding a “smoother” one.

3.a) As a refinement of the game the child might be asked to bring a tablet

that is “next rougher”b) The child is asked to bring the tablet that is “next smoother”

4. Group Activity – each child takes a tablet and hides it behind his back. Then they place them one by one in order of gradation

5. The exercises possible for all grading.

The Fabrics

Material Description :o Box 1 – Fabrics of great contrast differing in texture and colour but of the

same size (eight to ten pairs)

o Box 2 - Fabrics more similar in texture and colour and of the same size (eight to ten pairs)

Note: 1. The fabric should be changed every so often to maintain interest of the child

and offer him greater experience2. The hands should be washed and sensitised3. The fabrics should be hemmed, cleaned and well pressed

Presentation :Box 1

Bring the material to the chowki. Remove from the box a few contrasting pairs of fabrics (say three). Close eyes and feel each pair by gently rubbing the fabric between the

thumb and fingertips. Having felt one of the fabrics, pass it to the child to feel. Encourage him to do so with eyes closed. Proceed now to pair the fabrics. When a pair is found, it should be given to the child to feel. Mix the fabrics on the chowki and invite the child to pair them using a

blindfold. Continue to add more fabrics from Box 1 as and when appropriate.

Box 2 Presented in the same way as Box 1.

Exercises : For both Box 1 and Box 2 – as the presentation with all fabrics.

Language : After sufficient experience, the names of the fabrics maybe given.

Control of Error : In the material; the colour, design and texture of the fabrics.

Direct Aim : Further refinement of the tactile.

Age at Presentation : Three and a half years.

Note: Recommended that in Box 1, fabrics used are natural e.g. silk, wool, cotton, linen, loin cloth, gauze, satin, velvet etc

Discrimination of Grains(Stereognostic trays, sorting grains, bag of coins)

Stereognostic Trays

Material Description : We have three bags made of attractive plain colours, washable cotton material, all have string or ribbon arrangements for opening or closing the bags. They should all be uniform in colour. Outside each bag there is an embroidered number in succession. The embroidery should match the bag.

o Bag 1 - In this bag there are 20 small geometric solids, 10 prisms and 10 cubes, made of wood. They should be modest in dimensions and not too different.

o Bag 2 - A mixture of two types of small buttons, which have the same shape but are slightly different in size, in two different colours.

o Bag 3 - A mixture of two types of beads, which vary in their shape and colour.

On the shelf nearby have two or three trays, each with a large bowl and two smaller bowls, or alternatively a tray with indentations. The larger bowl should be in the centre and the smaller ones on the sides. The tray can be of any material, e.g. wood, glass, metal, etc.

Presentation :Bag 1

Present this on a working mat. Ask the child to open the bag and take out the pieces one by one. Put them on the mat randomly after feeling one prism and one cube. Now put on the blindfold and bring any one solid in front. Then feel the other solids and find the identical one to the one isolated. Sort them on top on either side of the mat. Do one then let the child do the rest.

Bag 2 / Bag 3 Let the child bring the bag. Ask the child to empty the contents of the bag into the larger bowl of the

tray.

The adult puts on the blindfold and takes any one button or bead. Feel its shape and size by putting it on the palm of the left hand and feeling

it with the right hand. Then put it in one of the smaller bowls. Now feel one of the other type and put it in the other smaller bowl, thus

sorting them out by feeling them. You do two or three and then let the child do the rest. The child will then do the other bag in the same way.

Control of Error : The child will look visually.

Direct Aim : Refinement of the stereognostic sense.

Age at Presentation : Three years, after the stereognostic activities of the Geometric Solids.

Footnote :1. Before using the grain, begin with exercises. Dr Montessori describes this is

The Discovery of the Child (page 164). She suggests 12 small prisms and cubes, and also little balls or coins. After this, things that are small and closely related can be given, e.g. seeds and rice

2. Stereognostic is not just using the fingertips but involves using the whole hand. In Italian the word for this is “Palpare” which means to touch and grasp with the hand and not just the fingertips

Sorting Grains

Material Description : There are five bags all having draw strings or ribbon arrangement to open and close them.

o Bag Four (After the stereognostic bags) - This bag contains two types of seeds, 15 to 20, which are slightly different in shape and colour, e.g. ellipsoid shape and kidney shape.

o Bag Five - A mixture of two types of seeds (lentils), which have the same shape and same size but the texture is different. One has a smooth surface and one has a rough surface, e.g. pepper and peas.

o Bag Six - A mixture of whole and split dal (double convex and concave), 15 to 20 of each, differing in thickness and form.

o Bag Seven - A mixture of 16 to 20 of each grain of wheat and rice. They should be well selected so they are not broken. Both of them are thick and long, but the wheat has a dividing ridge.

o Bag Eight - A mixture of coins of your currency in pairs. The latest in use in your country: Rs 1, 50, 25, 20, 10. Sew a coin outside the bag.

Number all of the bags with embroidery or applique. Along with these bags on the shelf, have the sorting trays and blindfold.

Note:You could have the following trays instead of the above material:

1. A tray with four saucers, three filled with different grains such as peas, beans, cloves, etc. (6 or 7 of each) and one empty saucer

2. A tray with four saucers, three filled with different grains which are much smaller and finer than the ones in tray one, e.g. rice, moong, beans, lentils or still finer grains, and one empty saucer

IntroductionBring bag four and the blindfold

1. First familiarise the child with the contents2. Feel each one by putting it on the palm of your hand and rolling it between

your fingertips3. Invite the child to feel each one and keep them in the two small bowls

Presentation : Using the blindfold sort one or two of them and let the child do the rest The child will inspect

Exercises : The child will do bags 5, 6 and 7 in the same way.

Footnote : For the trays the child mixes 3 grains and sorts them. One of each type can be left in the respective bowl as a control.

Bag of Coins

Presentation : Let the child feel each coin individually, showing the different aspects and

feeling around it on each side Thoroughly feel it Then put the coins in the bag and let the child match the different ones He can do it first by looking and then by using the blindfold Later give the value of the coins

Note : When there are more grains in the tray then sort accordingly in the saucers, in the same way as if you give the full trays.

Language : No specific terms.

The names of the seeds or grains should be introduced.

Control of Error : In the difference of colours and shapes of the seeds or grains.

Direct Aim : Refinement of the stereognostic sense.

Age at Presentation : Three and a half to four years.