Further Materials

# Knobless Cylinders

This is one of the last sensorial materials to be presented since it is not specifically to discriminate dimensions but a way to discover the relationships between cylinders of the four series

Material Description:

Four boxes each containing a set of cylinders with the dimensions of the four cylinder blocks.

• Each set is a specific colour
• Set A is blue, differing in one dimension – height

• Set B is red, differing in two dimensions – width and breadth

• Set C is green and Set D is yellow, they both differ in all three dimensions, though Set C does so inversely and Set D regularly.

Presentation:

• Bring Sets C and D to a mat or large table, in either case cover the surface in felt
• Open the cylinders from Set C, the green ones and place them at random
• Grade them in either direction, mix and invite the child to repeat
• Grade Set D, the yellow ones, this time do not mix
• Take Set C and place them in front of Set D, in order of the same diameter
• Let the child inspect the rows from both ends
• Mix and grade Set C in order of height, bring Set D in front and arrange in order of same height
• Let the child see the relationship further by superimposing one set onto the other in the four ways

Exercises:

• As in the presentation
• Either the yellow set with the red set or the green set and red set, till both combinations have been tried
• Introduce the blue ones, Set A last with any of the others, as it differs in only one dimension
• Let the child three explore all sets together
• Let the child explore all four sets together
• The child may discover ways other than laterally to build and make a tower, each set will produce a different form – Set A will make the tallest tower, do this on a mat.
• Two Mat Game – Put the Set C on mat and the others on a different mat, show the child one yellow cylinder and ask her to find some that are similar (height, diameter, or both).  If you give the second largest she can find one of each set that are the same diameter and may build the tower. Let two children work together isolating a different set and comparing them with the others.

Language:

None

Criteria of Perfection (Control of Error):

• In the child’s ability

Direct Aim:

• To observe and compare different sets with each other

Indirect Aim:

• To develop a clearer understanding of dimensions and their interplay

Age at Presentation:

Four and a half to five years

Footnote:

The Knobless Cylinders are the culmination of discrimination, to use them the child must be able to know how to sort and grade each series and use her powers of discrimination compare differences and similarities.  The movement of the cylinder pre-empts calculus, by asking the child to make connections, decisions and make connections.  To show this mental movements are used.

While being a very attractive activity it should not be presented until at least four and a half years as the discoveries it can lead to require greater understanding of dimensions, colours and a more mature kinaesthetic appreciation than a younger child can apply.

By comparing all four sets the child will find the following partial pairs;

Set A and Set C have one identical pair, while the rest differ in either height or diameter

Set A and Set D have one identical pair, while the rest differ in either height or diameter

Set C and Set D have cylinders which are identical in height

Set A has cylinders with the same diameter as the seventh one in each other set

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