National Standard in Mathematics

Introduction

In this Paper the national standards of the mathematical education of the students of grade 9th will be discussed in details. We will analyze and observe multiple teaching strategies and the concepts and topics that the students of the described level should adapt competently to move ahead in their academic path. We will also discuss the weaknesses and issues and how they should be handling to maximize the learning effect and outcome for the students.

Discussion

Understand patterns, relations, and functions  

Grades 9 Expectations: It is expected that the 9th graders should

generalize patterns using explicitly defined and recursively defined functions;

understand relations and functions and select, convert flexibly among, and use various representations for them;

Analyze functions of one variable by investigating rates of change and able to analyze them analytically representing them in appropriate manner.

Understand and perform transformations such as arithmetically combining, composing, and inverting commonly used functions.

Represent and analyze mathematical situations and structures using algebraic symbols

Grades 9 Expectations: In grades 3-5all students should

understand the meaning of equivalent forms of expressions, equations, inequalities, and relations;

Write equivalent forms of equations, inequalities, and systems of equations and solve simple problems with fluency either verbally or with paper and pencil.

Use mathematical models to represent and understand quantitative relationships  

Grades 9th Expectations: It is expected that the 9th graders should

identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships;

Use symbolic expressions, to represent relationships arising from various contexts; representing which quantity is less or greater than the second one, less than or equal to.

Draw reasonable conclusions about a situation being expressed.

Measurement

Understand measurable attributes of objects and the units, systems, and processes of measurement  

Grades 9th Expectations: It is expected that the 9th graders should

Make decisions about units and scales that are appropriate for problem situations involving measurement.

 

Apply appropriate techniques, tools, and formulas to determine measurements.  

Grades 9th Expectations: It is expected that the 9th graders should

Understand and use formulas for the volume, area and surface area of geometric figures, including circles, rectangles, squares and triangles.

Use unit analysis to check measurement computations.

Understand patterns, relations, and functions

The students of grade 9 should be able to analyze and investigative the geometric and numerical patterns.

Understand patterns, relations, and functions

The students of grade 9 should be able to analyze and investigative the geometric and numerical patterns and should be able to represent them in the mathematical form either in words or symbolically.

They should become mature enough to analyze the hierarchy of pattern and how it is varying, able to tabulate this information in a systematic way and use the standards and generalizations that were made for the expressions of mathematical problems. As an example a teacher can ask the student of his class to describe briefly the pattern of “increasing the number of squares” as shown in the figure 1 and can express them in the form of mathematical sentences. The students should be encouraged to predict the result of the continuation of the pattern verbally as it will further enhanced the analytical ...