Material
- Cabinet of cubes, squares and chains, ranging from 2 to 10, including the unit bead.
- Chain of 2 -green, with corresponding labels in green, marked 1, 2, then 4, 6, 8.
- Chain of 3-pink,with corresponding labels in pink, marked 1, 2, 3,then 6, 9, 12….. 27.
- Chain of 4-yellow,with corresponding labels in yellow, marked 1, 2, 3, 4,then 8, 12, 16,…..etc.
- Chain of 5-light blue, with corresponding labels in blue, marked 1, 2, 3, 4, 5,then 10, 15, 20,…..etc.
- Chain of 6-lilac,with corresponding labels in lilac, marked 1, 2, 3, 4, 5, 6,then 12, 18,…..etc.
- Chain of 7-white,with corresponding labels in white,marked 1, 2, 3, 4, 5, 6, 7,then 14, 21,…..etc.
- Chain of 8-brown,with corresponding labels in brown,marked 1, 2, 3, 4, 5, 6, 7, 8, then 16, 24,…..etc.
- Chain of 9-dark blue, with corresponding labels in dark blue, marked 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 27,…..etc.
Exercise 1: Squares and chains
- Start with the short chain of 5. On a mat on the table.
- Take the square of 5, and fold the short chain of 5 beside it: they are equal.
- Count and unfold the chain.
- The first bar, as before, is marked individually, and after that, every 5 beads. The markers are pale blue, to match the color of the beads.
- When they have been counted and marked, the child counts the markers, saying ‘5, 10, 15, 20, and 25.’
- The square of 5 has been counted.
Exercise 2: Cubes, squares and chains
Material
- The long chain of 5 is now introduced. The child must be shown how to carry the chain.
- Also used are: another set of blue tickets, 5 squares of 5 and the cube of 5.
Exercise
- Lay out the chain in lengths of 5. What have we got? 5 squares of 5.
- Lay out 5 squares of 5 correspondingly.
- Now, pile up the 5 squares, and what do we have now? The cube of 5.
- Place the cube of 5 beside it.
- If we want to find out how many units there are in the cube of 5, we have to count the long chain of 5 (as we have seen now, it is the same as the cube of 5).
- If possible, lay it out full length on a mat on the floor. It gives a sensorial impression of length. Otherwise it can be laid out on a mat on the table, in a spiral form or pentagon form, or some other shape that allows one to still see the patterns or groups.
- The labels are laid out, face upwards, on another mat, either at random or in order.
- The beads are counted individually, the labeling is done in the usual way.
- The child should take as active a part in the presentation as possible.
- When 25 is reached (the square of 5) a square of 5 is placed opposite. Repeat at 50, 75, and so on.
- The child counts the chain by the labels, 5, 10, 15, 20, etc.
- The children like to see how many times the short chain fits into the long chain.
Additional Exercises the children discover by themselves or to which they are guided.
- They compare the short chains with the long chains without counting.
- They compare the short chains with each other, and place the corresponding square beside each chain.
- They lay out long chains beside each other.
- They compare the cubes to the Pink Tower.
- Comparison to Geometric cabinet. They lay out the short chains in forms in comparison to their numbers (i.e. in a triangle-3, square-4, pentagon-5, hexagon-6, heptagon-7, octagon-8, nonagon-9, and decagon-10, and compare them with the geometric cabinet tray of polygons.