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Cylinder Blocks
Material Description:
Four wooden blocks containing ten cylinders of different sizes, with knobs, each fitting into it’s respective hole.
Block A: Each cylinder has the same diameter, they decrease in height successively from tall to short. They differ in one dimension, height
Block B: Each cylinder has the same height, decreasing in diameter successively from thick to thin. They differ in two dimensions, width and length
Block C: Each cylinder has a diminishing diameter and an increasing height. They differ inversely in three dimensions
Block D: Each cylinder has both a diminishing diameter and height. They differ regularly in three dimensions
How to hold:
Hold the block with the hands, grasping firmly at either end.
Display
 On furniture, either decreasing or increasing in complexity, depending how the furniture is organised so that the child is attracted to either Block B or D first
Presentation:
 Place the block on the table or working mat, grasp the knobs of the cylinder with the right thumb, index and middle finger
 Remove the extremes first, placing them in front of their respective sockets
 Then take the second largest and begin placing the cylinders at random
 To replace them, begin with the extremes, then, looking at the child randomly select the next cylinder and look at it’s base and around the side of it and look at all the sockets, then review at the cylinder and look back at the sockets similar to it, finally look at the cylinder again and align it with the appropriate socket, turning it to compare the cylinders base with the socket
 Align the cylinder directly over the socket and slowly push it all the way down.
Exercises:
 When the child knows the material fully use two blocks together, placing them at right angles and mixing the cylinders from both blocks together.
 Use three blocks together, placing them in a triangle and mixing the cylinders from all the blocks together in the space between the blocks.
 Use all four blocks together, placing them in a square and mixing the cylinders from all the blocks together in the space between the blocks.
Language:
To be covered in the threepart lesson, to be taught when the child can discriminate the different dimensions without hesitation.
Block A: short tall
Block B: thick thin
Block C: shallowdeep (sockets)
Block D: largesmall
For all: Comparatives and superlatives
Criteria of Perfection (Control of Error):
 This lies within the material itself
Direct Aim:
 Visual discrimination of dimensions
Indirect Aims:
 Muscular preparation for writing; how to hold a pen
 Refinement of voluntary movement; fitting cylinder in one precise movement
 Preparation of Mathematical Mind;
 The drive towards accurate observation
 The motivation to create order out of chaos
 The ability to perceive patters of relationship leading to abstraction and use of imagination
Age at Presentation:
Three years
Games (Further Exercises):
 Indicate a specific socket and ask the child to choose the corresponding cylinder
 To be shown when two or three children knows the language and exercise well, let the children repeat the exercise above with a greater distance between the randomly assorted cylinders and sockets.
The Pink Tower
Material Description:
Ten pink cubes, differing in size progressively from one cm^{3} to ten cm^{3}. They vary in three dimensions: the smallest is one cm^{3}, the next larger one is 2 cm^{3}, going up to ten cm^{3}.
How to hold:
Hold each cube, one at a time across the top with thumb and index. Larger cubes may be supported by the left hand. To give sensation of breadth and weight.
Display
On specific furniture, displayed prominently in the centre of the room
Presentation:
 Place the cubes directly from the furniture, randomly on the working mat as above
 Take the ten cm^{3} and place it separately from the others
 Look for and take the nine cm^{3} after a series of looking
 Place it centrally on the ten cm^{3} in one movement, if the positioning is imperfect lift the cube and replace
 Inspect all the sides
 Continue until complete – you can choose move one cube to put two similar cubes close together on the mat to compare
 When complete invite the child to look at the tower from above and walk around the tower, clockwise
 To dismantle take apart piece by piece and place at random
 Invite the child to repeat
Exercises:
 When the child knows the material fully, rebuild tower so that one corner and two vertices are aligned, lowering each cube and slightly pushing to the lower ones edge, invite the child to look as before
 Variation: Take the one cm^{3} and fit it on the ledge of thetwo cm^{3 }and each successive one.
Language:
To be covered in the threepart lesson, to be taught when the child can discriminate the different dimensions without hesitation.
“Large””Small”, comparatives and superlatives
Criteria of Perfection (Control of Error):
 In the child’s own ability to discriminate dimension
Direct Aim:
 Visual discrimination of dimensions
Indirect Aim:
 Refinement of voluntary movement; fitting cubes one on top of the other in one precise movement
 Refinement of handeye coordination
 Muscular education of grip
Age at Presentation:
Three to three and a half years
Games (Further Exercises):
 To be shown when two or three children knows the language and exercise well, place one mat at either end of the room, indicate one cube and ask the child to bring one an increment large or smaller from the other mat
Footnote:
The dimensions in this exercise correspond to the Cylinder Block C and D
The Brown Stair
Material Description:
Ten prisms, brown in colour, measuring (in centimetres) 1x1x20, 2x2x20, 3x3x20, until 10x10x20. They progressively increase in size in the algebraic series in the second power, each vary in two dimensions, height and width, representing 1^{2}, 2^{2}, 3^{2}
How to hold:
Hold each prism, one at a time across the breadth with thumb and index. Thicker prisms may be supported by the left hand. To give sensation of breadth and weight.
Display
On specific furniture, displayed so the child sees that the length of each prism is the same.
Presentation:
 Place the prisms directly from the furniture, randomly on the working mat as above
 Take the 10x10x20 and place it separately from the others
 Look for and take the 9x9x20 after a series of looks, place it in front of the 10x10x20
 Place it ensuring that the sides are even by running the hands along the square faces
 Inspect all the sides
 Continue until complete
 When complete invite the child to look at the stair straight on and from the sides
 To dismantle take apart piece by piece and place at random
 Invite the child to repeat
Exercises:
 Variation: Take the 1x1x20 and fit it on the ledge of the2x2x20and each successive one.
Language:
To be covered in the threepart lesson, to be taught when the child can discriminate the different dimensions without hesitation.
“Thick””thin”, comparatives and superlatives
Criteria of Perfection (Control of Error):
 In the child’s own ability to discriminate dimension
Direct Aim:
 Visual discrimination of dimensions
Indirect Aim:
 Refinement of voluntary movement; fitting prisms in one precise movement
 Muscular education of grip
 Preparation of Mathematical Mind
 Preparation for Mathematics
Age at Presentation:
Three to three and a half years
Games (Further Exercises):
 To be shown when two or three children knows the language and exercise well, place one mat at either end of the room, indicate one prism and ask the child to bring one an increment large or smaller from the other mat
Footnote:
The dimensions in this exercise correspond to the Cylinder Block B
The Red Rods
Material Description:
Ten red rods, they each vary in one dimensions, length. The shortest is 10centimetres long and they progressively increase by ten centimetres at a time until the final rod which measures on metre.
How to hold:
Hold each rod, one at a time across the width, with thumb and index. Thicker rods may be supported by the left hand. To give sensation of breadth and weight.
Display
On specific furniture, displayed low so that the child incidentally develops an internal sense of one metre and ten centimetre increments.
Presentation:
 Place the rods directly from the furniture, randomly on the working mat as above, ensuring that they are not parallel
 Take the one metre and place it separately from the others, trace its length with the fingers
 Look for and take the 90 cm after a series of looks, place it in front of the one metre rod, making sure the left ends are even and tracing its length with the fingers
 Continue until complete
 When complete invite the child to look at the rods straight on and from the sides
 To dismantle take apart piece by piece and place at random
 Invite the child to repeat
Exercises:
 Variation: Take the 10 cm rod and fit it to the right end of the 20 cm rod and each successive one.
Language:
To be covered in the threepart lesson, to be taught when the child can discriminate the different dimensions without hesitation.
“Long””Short”, comparatives and superlatives
Criteria of Perfection (Control of Error):
 In the child’s own ability to discriminate dimension
Direct Aim:
 Visual discrimination of dimensions
 Muscular memory of length
Indirect Aim:
 Preparation for Mathematics
 Knowledge of one metre length
Age at Presentation:
Three and a half years
Games (Further Exercises):
 To be shown when two or three children knows the language and exercise well, place one mat at either end of the room, take the one metre rod and ask the child to bring one an increment smaller from the other mat
Footnote:
The dimensions in this exercise correspond to the Cylinder Block A