SMALL BEAD FRAMES
…small bead frame, corresponding form
…a golden unit bead, 10-bar, 100-square, 1000-cube
…2 green beads (from the unit division board)
Introduce the child to the concept of hierarchy with an analogy: i.e. the social organization differentiates one person from the next. The same thing happens in the beads, These 4 beads could be units of the simple class or units of the thousands depending on their position.
These three colors, green, blue, and red are repeated in each class in the same sequence. Only their position will differentiate them.
Isolate two green loose beads. How many are there? 2 On the frame isolate one unit and one thousand bead. Here I also have two green beads, but I can’t call them just ‘2 green beads.’ The one at the top has the value of one; the bead on the lower wire has the value of 1000. The position makes the difference.
The absolute value is the value of the unit independent of its position (the number of beads on the wire). The relative value is the value of a digit when its relative position is taken into consideration.
The History of The Abacus
Relate the story of the abacus: A bead frame like this is used by children all over to learn to count. It is a very, very old instrument, that was used by the Chinese as far back as 500 BC. They called it ‘swan-pan’. The Japanese caught on to the idea, but they called it ‘soro-ban.’ The Russians learned about it and began to use it in their country, calling it ‘s-ciot’, which means calculator. Around 1812 there were French prisoners in Russia who learned about the abacus. When he was released he brought the idea back to France. This knowledge spread rapidly around Europe and to America.
Studies have shown that this design originated long, long ago. People made little grooves in the sand and placed little pebbles into the grooves. Each groove was like one of our wires, and the pebbles were like our beads.
Introduction to the materials
Our bead frame has four wires; the first three are equal distances from one another, and between the third and fourth there is a greater distance. This space separates the simple class from the class of thousands. On the right side we see these two classes indicated by two different colors. There are ten beads on each wire. The number on the left side of the frame indicate the value of each bead on that wire. Here it says 1, so each bead has the value of one… and so on to 1000.
On this form the same situation is repeated. Turn the bead frame on its side to demonstrate the corresponding colors, names of classes, and the space to divide the classes, which has been replaced by a comma.
Passage from sensorial to symbolic representation
Isolate the golden bead, and ask the child to identify its value; one unit. Isolate one green unit bead on the right side of the frame. This green bead is also one unit. Each bead on this row is a unit.
Isolate the ten-bar, and ask the child to identify its value; ten. This blue bead also has the value of ten. Each one of the beads on this row is worth ten units. Continue in the same way with the square and the cube.
By means of the three period lesson: have the child match the corresponding quantities, i.e. Give me 100. The child gives the square. Now show me 100 on the frame, or pointing to a particular bead: What is this? The child names it and gets the corresponding golden bead material.
To check the child’s comprehension, isolate one unit bead and one thousand bead. These two beads are both green: do they have the same value? Why?