**The 1st Aim**

To deepen students’ understanding of basic concepts and principles, laws about diagrams and to make students master how to treat and express mathematically, and moreover, to make them develope their abilities to consider the phenomena mathematically. And knowing pleasure of mathematical activities and the appreciation of mathematical view and thinking, to make students foster attitude to make use of them by themselves.

**The 2nd Each grade’s objects and contents**

**[The 1st grade]**

1 Object

(1) To deepen students’ understanding of concepts of number by extending numbers into positive ones and negative ones. And not only understanding of significance to use the letter and the meaning of equation, but to make students express and treat the relation and laws among numbers generally and briefly.

(2)To deepen students’ intuitive view and thinking through their observation and operation and experiment about plane figures and space figures, and moreover, to make them foster the basis to cosider the things logically.

(3)Through searching concrete phenomena, not only to deepen students’ view and thinking of proportion and inverse proportion, but also to make them foster the basis to express and consider the relation among numbers, quantities.

2 Contents

A Number and Formula

(1)To make students understand positive number and negative number through their activities in the concrete situations and to make them enabe to calculate four operations.

*konowing neccesity of negative number and understanding the meaning of positive number and negative number.

*understanding the meaning of four operations of positive number and negative number, and calculating simple ones.

(2)Not only to make students foster the ability to express the relation and the law using the letters and reading the meaning of formula, but also to make them enable to calculate a formula used the letters.

*understanding the significance to use the letter.

*knowing how to express multiplication and division in a formula used the letters.

*calculating addition and subtraction of simple linear expression.

(3)To make students understand equation and to make them enable to use equations with one unknown and of the first degree.

*understanding equation and the meaning of the letter and solution in it.

*finding out the property of equality and knowing that equation can be solved on the basis of it.

*solving simple equations with one unknown and of the first degree.

[Terminology and Symbol]

natural number, code, absolute value, term, coefficient, <, >, <=, >=

**[The 2nd grade]**

**1 Aim**

(1) To make students develope the ability to calculate and transform according to the purpose with formula used the letters, and moreover, to make them understand simultaneous linear equations with two unknowns and foster the ability to use it.

(2) To deepen students’ understanding of the properties about basic plane diagrams through observation,operation and experiment, and moreover, to make them understand the significance and the method of mathematical inference in consideration of the properties of diagrams, and also to make them foster the ability to express the process of inferencs.

(3) To make students understand linear function through searching concrete phenomena, and moreover, to make them foster the ability to find out functional relationship and express it, and also to consider it. And through observation and experiment with concrete phenomena, to make students foster the basis of probabilistic thinking.

2 Contents

**A Number and Formula **

(1) To make students develope the ability to find the relationship of quantity whithin phenomena and to make use of it , expressing as the formula used the letters.

*Being able to calculate simple polynomial addition and subtraction, and to calculate simple monomial multiplication and division.

*understanding of being able to utilize literal expressions in order to catch quantity and the relationship of quantities. *transforming simple formula according to the purpose.

(2) To make students understand simultaneous linear equations with two unknowns and be able to use them.

*understanding of linear equations with two unknowns and the meaning of its solution.

* understanding of simultaneous linear equations with two unknowns and the meaning of its solution, and moreover, being able to solve simple simultaneous linear equations with two unknowns and use them.

[ Terminology and Symbol]

similar term

**B Diagram**

(1) Through students’ observation, operation and experiment, to make them find the properties of basic plane diagrams and unable to ascertain them on the basis of the properties of parallel lines.

*understanding the properties of parallel lines and angle, and on the basis of them, ascertaining the properties of diagrams.

*knowing that they can find out the properties of polygon’s angles on the basis of the properties of pallel lines and triangle’s angles.

(2) To make students ascertain the properties of plane diagrams on the basis of congruent conditions about triangle and to make them foster the ability to consider them logically.

*understanding the significance and method of proof.

*understanding the congruent conditions of triangle, and on the basis of them, ascertaining the properties of triangles and parallelograms.

*finding out the relationship between angle of circumference and central angle, and moreover, knowing that it can be ascertained logically for them.

[ Terminology and Symbol]

vertically opposite angle, internal angle, external angle, difinition, proof, =-(congruence)

**C Relationship of number and quantity**

(1) Taking two quantities out from concrete phenomena, to make students understand linear function, and moreover, to make them foster the ability to find functional relationship, to express them, and to consider them.

*knowing that there are some phenomena that can be caught using linear function.

*understanding the ratio of values that linear function attains and the features of graph, and moreover, making use of linear function.

*being able to read linear equations with two unknowns as the formula expressing function.

(2) To make students understand probability through their observation and experiment with concrete phenomena.

*being able to arrange the cases orderly that could be occurred.

*understanding the meaning of probability expressing the degree that ambiguous phenomena could be occurred, and being able to get probability on the simple cases.

**[The 3rd Grade]**

**1 Aim**

(1) To make students understand square root of number and to deepen their understanding of the concept of number more and more. And, not only to improve students’ abilities to calculate according to the purpose and to change the formulas, but also to make them understand secondary equation and make use of the formulas efficiently.

(2) To make students understand similarity of diagrams and Pythagorean thorem through their observation, operation and experiment, and moreover, to make them develop their abilities to utilize them in considering the properties of diagrams and metric. And to develop their abilities to consider the diagrams forseeing logically and express it.

(3)Through searching concrete phenomena, not only to make students understand the function y=ax^{2}, but also to develop their abilities to find out functional relationship among them and to express and consider them.

**2 Contents**

**A Number and Formula**

(1) To make students understand square root of positive numbers and to make them be able to use it.

*understanding of necessity of square root and meaning of it.

*calculating the simple formulas including square root.

(2) About simple polynomials used the letters, not only to make students expand formulas and factorize them, but also to make them be able to change the formulas according to the purpose.

*calculating multiplication of monomial by polynomial, and division of polynomial by monomial.

*calculating simple linear formulas ,and expanding and factorizing the formulas using the following formulas.

(a+b)^{2}=a^{2}+2ab+b^{2}

(a-b)^{2}=a^{2}-2ab+b^{2}

(a+b)(a-b)=a^{2}-b^{2}

(x+a)(x+b)=x^{2}+(a+b)x+ab

(3)To make students understand quadratic equation and use it.

*knowing necessity of quadratic equation and the meaning of the solution.

*being able to solute simple quadratic equations and making use of them.

[ Terminology and Symbol ]

radical sign, prime, factor, root

**B Diagram**

(1) To make students ascertain the properties of diagrams on the basis of similarity conditions about triangle, and to develop their abilities to consider them logically and express them.

*understanding of sililarity about diagrams and ascertaining the propereties of diagrams logically, using similarity conditions about triangle.

*finding out the ratios of parallel lines and segments and ascertainning them.

*making use of the thinking of similarity.

(2) To make students understand Pythagorean theorem and use it.

*finding out Pythagorean theorem and knowing that it can be proved.

*understanding of the meaning of Pythagorean theorem and making use of it.

[ Terminology and Symbol ]

infinity

**C Relationship of Number and Quantity**

(1)Taking out two quantities from concrete phenomena, through searching their changing and mapping, to make students understand function y=ax^{2}, and also to develop students’ability to find out functional relationship and express and consider them.

*knowing that there might be phenomena that can be catched as function y=ax^{2}.

*understanding the feature of the graph of function y=ax^{2} and the ratio of change attaining values of the function.

It took the long time for me to translate this article into English. I do not know whether this work will be useful for you. May your work be blessed!! (2.26.2000)