**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 three-part lesson, to be taught when the child can discriminate the different dimensions without hesitation.

Block A: short- tall

Block B: thick -thin

Block C: shallow-deep (sockets)

Block D: large-small

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 three-part 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 hand-eye co-ordination
- 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 three-part 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:**

“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

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