An example of a teacher guidance item.

To the teacher:

1. This " Bridges" workbook is the second in a series of two workbooks:
Using Base Ten Blocks for Numbers up to 1,000
Using Discs for Numbers up to 10,000
2. The two workbooks can be incorporated in the chapter "The decimal structure: introduction, acquaintance, addition and subtraction" of the main sequence (3rd grade):
"Using Surfaces for Numbers Up To 1,000" is a readiness workbook and has to be taught before the chapter itself.
"Using Discs for Numbers Up To 10,000" is a supplement workbook and has to be taught after working with the scattered colored discs and before working with the discs on the abacus.
3. The workbook is intended for children who have difficulties with understanding the decimal structure of numbers, especially the operations of exchanging performed while adding and subtracting numbers. The diagnosis in the workbook is designed for locating such difficulties and directing the child to the appropriate activities in the workbook.
The workbook is also intended for students who have difficulties with mental addition and subtraction exercises based on the decimal structure of numbers. The workbook contains special activities that deal with this subject.
4. In the main sequence, the decimal structure of multi-digit numbers (up to 10,000) is learned using scattered colored discs, according to the rule "1 to 3" (one blue disc equals 3 yellow discs, 1 green disc equals 3 blue discs, and 1 white disc equals 3 green discs).
This " Bridges " workbook contains activities for acquaintance with the decimal structure of multi-digit numbers (up to 10,000) using the rule "1 to 10" (one blue disc equals 10 yellow discs, 1 green disc equals 10 blue discs, and 1 white disc equals 10 green discs).
The main goals of these activities are:
- Make the child understand that the exchange operations do not change the value of the quantity. Such understanding is acquired through comparing the "value of the pile of discs" before and after the exchange operations. The value of a pile of discs is measured by the number of yellow discs one gets after all possible changing operations have been done.
- Bring the child to make a connection between different "worlds":
a. Between addition and subtraction operations he has performed before and these operations as performed on multi-digit numbers.
b. Between operations on numbers and operations on discs.
c. Between operations on discs and operations on surfaces.
5. In addition to the decimal structure of numbers, the workbook presents gradually the sequence of numbers between 1,000 and 10,000, and deals with addition and subtraction operations on these numbers, performed with a model, as a basis for performing mental calculations.


* from the introduction to the workbook "Using Discs for Numbers up to 10,000"