Direct Aim
The aim of the early exercises with this frame has already been stated with the small bead frame. Here the child is helped to form a concept of long multiplication.
Point of Interest
The activity involved.
Control of Error
There is no automatic control.
Age of Interest
About 71/2 years.
Material
- This frame is similar to the small bead frame, but here there are 7 wires and on this frame we can count up to 1,000,000. Here again one bead is equivalent to the whole amount of the beads on the bar above, e.g. one blue bead (10,000) is equal to 10 green beads (1,000). With this frame the hierarchy of numbers is stressed very clearly. There is the repetition of color within the categories and there is a larger space between the hundreds and thousands, hundreds of thousands and the millions. In the first group there are; units – green,
tens of units-blue, hundreds of units-red, In the second group there are units of thousands – green, tens of thousands-blue, hundreds of thousands-red, and finally units of millions – green.
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With this apparatus there is a special lined paper that is used. See the sample. The sets are clearly divided. When writing large numbers, we use commas to separate the groups, e.g. 7,278,482. Also, write the number directly over the appropriate colored line. This helps the child to associate the units, colors, and numbers.
Note: It is advisable that the children should have worked with the advanced bead material dealing with the hierarchy of number. Also, they can do work with a large divided mat or whiteboard with a large red line dividing the sets, and loose beads and symbols.
Introductory Presentation
Discuss the symbolism of the frame – how the green beads stand for units -then we have units of thousands, units of millions, etc. Ask ‘Can you show me the tens of thousands?’, etc. Compare this frame with the small bead frame.
Exercises
They are similar to those done with the Small Bead Frame. Every bead should be counted and recorded. The teacher should discuss the placing of the digits with the child. The symbols always range from 1 to 9, but it is the place they occupy that is important.
The child should use a divided mat, a quantity of loose symbols from 1 to 9 and use these with the frame, i.e. without mixing the categories–e.g. move 5 tens of thousands from left to right on the Bead Frame and place the symbol ‘5’ in the appropriate position on the Divided Mat.
Later he can use the Divided Mat alone. He has now got used to using the zeros, without which a symbol, say ‘8’, might not portray the quantity he wishes to show. This further enriches his concept of zero.
Meanwhile he continues with the exercises as for the Small Bead Frame. Encourage him to read any numbers he has made, e.g. 6,989,224 as 6 millions, 9 hundred and eighty-nine thousands, 2 hundred and twenty-four.
The early work with this frame should go on for weeks. It is actually intended mainly for long multiplication, so don’t keep him on addition and subtraction for too long.
Addition
He can be given a dynamic problem from the very beginning. For example,
3,125,481
2,035,468
2,117,533 +
He records his answer on the special paper and does the addition the same way as he did before with the Small Bead Frame.
Subtraction
Worked in the same way as with the Small Bead Frame.
Multiplication
1. The child can do short multiplication at first, but do not delay before introducing him to long multiplication. It is important to remember what the child should know and be able to do before starting the long multiplication, as there is a lot of mental work involved.
- He must be familiar with the relationship of the categories and be able to move freely from one to the next.
- He should be able to convert numbers easily, e.g. 36 thousands means the same as 3 tens of thousands and 6 thousands.
- He must be very familiar with his tables, and
- with the multiplication by 10 and 100. (The color of the beads will guide him.)
He should be given fairly simple sums at first, e.g.
4,596
x 28
(Do not include huņdreds in the multiplier till later.)
Write down the sum on the special bead frame paper. Analyse the sum with the child. Then explain that ‘We are going to multiply by 8 first, then by 20. 20=2 tens, so we multiply 4,596 by 10. ‘How do we do that? By adding a nought: 45,960 by 2’.
As the child does the two short multiplications he writes down their products. Then, to get the final result of 4,596×28, he adds the two products, which gives him 128,688. Later the child can be given sums containing hundreds in the multiplier. Stress that to multiply by 100 you add two noughts.