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NCTM Math Standards 5-8

 

 

enc4.gif (4101 bytes)NCTM Math Standards 5-8                                        

STANDARD 1: MATHEMATICS AS PROBLEM SOLVING Examples of Problem Solving

 

In grades 5-8, the study of mathematics should emphasize problem solving so that students can--

Focus

Problem solving should be the central focus of the mathematics curriculum. As such, it is a primary goal of all mathematics instruction and an integral part of all mathematical activity. Problem solving is not a distinct topic but a process that should permeate the entire program and provide the context in which concepts and skills can be learned.

 

 

 

 

enc4.gif (4101 bytes)NCTM Math Standards 5-8                    

STANDARD 2: MATHEMATICS AS COMMUNICATION Examples of Communication

 

In grades 5-8, the study of mathematics should include opportunities to communicate so that students can--

Focus

The use of mathematics in other disciplines has increased dramatically, largely because of its power to represent and communicate ideas concisely. Society's increasing use of technology requires that students learn both to communicate with computers and to make use of their own individual power as a medium of communication. The ability to read, write, listen, think creatively, and communicate about problems will develop and deepen students' understanding of mathematics.

 

 

enc4.gif (4101 bytes)NCTM Math Standards 5-8                                             

STANDARD 3: MATHEMATICS AS REASONING Examples of Reasoning

In grades 5-8, reasoning shall permeate the mathematics curriculum so that students can--

Focus

Reasoning is fundamental to the knowing and doing of mathematics. Although most disciplines have standards of evaluation by which new theories or discoveries are judged, nowhere are these standards as explicit and well formulated as they are in mathematics. Conjecturing and demonstrating the logical validity of conjectures are the essence of the creative act of doing mathematics. To give more students access to mathematics as a powerful way of making sense of the world, it is essential that an emphasis on reasoning pervade all mathematical activity. Students need a great deal of time and many experiences to develop their ability to construct valid arguments in problem settings and evaluate the arguments of others.

 

 

 

enc4.gif (4101 bytes)NCTM Math Standards 5-8                                              

STANDARD 4: MATHEMATICAL CONNECTIONS Examples of Connections

 

In grades 5-8, the mathematics curriculum should include the investigation of mathematical connections so that students can--

Focus

For many students, mathematics in the middle grades has far too often simply repeated or extended much of the computational work covered in the earlier grades. The intent of this standard is to help students broaden their perspective, to view mathematics as an integrated whole rather than as an isolated set of topics, and to acknowledge its relevance and usefulness both in and out of school. Mathematics instruction at the 5-8 level should prepare students for expanded and deeper study in high school through exploration of the interconnections among mathematical ideas.

 

 

 

 

enc4.gif (4101 bytes)NCTM Math Standards 5-8                              

 

STANDARD 5: NUMBER AND NUMBER RELATIONSHIPS Examples of Number Relations

 

In grades 5-8, the mathematics curriculum should include the continued development of number and number relationships so that students can--

Focus

The use of concise symbols and language to represent numbers is a significant historical and practical development. In the middle school years, students come to recognize that numbers have multiple representations, so the development of concepts for fractions, ratios, decimals, and percents and the idea of multiple representations of these numbers need special attention and emphasis. The ability to generate, read, use, and appreciate multiple representations of the same quantity is a critical step in learning to understand and do mathematics.

 

 

 

enc4.gif (4101 bytes)NCTM Math Standards 5-8                                         

STANDARD 6: NUMBER SYSTEMS AND NUMBER THEORY Examples of  Number Sense, Concepts, and Operations

 

In grades 5-8, the mathematics curriculum should include the study of number systems and number theory so that students can--

Focus

The central theme of this standard is the underlying structure of mathematics, which bonds its many individual facets into a useful, interesting, and logical whole. Instruction in grades 5-8 typically devotes a great deal of time to helping students master a myriad of details but pays scant attention to how these individual facets fit together. It is the intent of this standard that students should come to understand and appreciate mathematics as a coherent body of knowledge rather than a vast, perhaps bewildering, collection of isolated facts and rules. Understanding this structure promotes students' efficiency in investigating the arithmetic of fractions, decimals, integers, and rationals through the unity of common ideas. It also offers insights into how the whole number system is extended to the rational number system and beyond. It improves problem-solving capability by providing a better perspective of arithmetic operations.

 

 

 

 

enc4.gif (4101 bytes)NCTM Math Standards 5-8                                  

 

STANDARD 7: COMPUTATION AND ESTIMATION Examples of Estimation

In grades 5-8, the mathematics curriculum should develop the concepts underlying computation and estimation in various contexts so that students can--

Focus

Although computation is vital in this information age, technology has drastically changed the methods by which we compute. Whereas inexpensive calculators execute routine computations accurately and quickly and computers execute more complex computations with ease, many current mathematics programs focus on traditional paper-and-pencil algorithms. This standard prepares students to select and use appropriate mental, paper-and-pencil, calculator, and computer methods.

 

 

 

 

enc4.gif (4101 bytes)NCTM Math Standards 5-8                        

 

STANDARD 8: PATTERNS AND FUNCTIONS  Examples of Patterns and Functions

 In grades 5-8, the mathematics curriculum should include explorations of patterns and functions so that students can--

Focus

One of the central themes of mathematics is the study of patterns and functions. This study requires students to recognize, describe, and generalize patterns and build mathematical models to predict the behavior of real-world phenomena that exhibit the observed pattern. The widespread occurrence of regular and chaotic pattern behavior makes the study of patterns and functions important. Exploring patterns helps students develop mathematical power and instills in them an appreciation for the beauty of mathematics.

 

 

 

enc4.gif (4101 bytes)NCTM Math Standards 5-8                                  

STANDARD 9: ALGEBRA

Examples of Algebra 

In grades 5-8, the mathematics curriculum should include explorations of algebraic concepts and processes so that students can-

Focus

The middle school mathematics curriculum is, in many ways, a bridge between the concrete elementary school curriculum and the more formal mathematics curriculum of the high school. One critical transition is that between arithmetic and algebra. It is thus essential that in grades 5-8, students explore algebraic concepts in an informal way to build a foundation for the subsequent formal study of algebra. Such informal explorations should emphasize physical models, data, graphs, and other mathematical representations rather than facility with formal algebraic manipulation. Students should be taught to generalize number patterns to model, represent, or describe observed physical patterns, regularities, and problems. These informal explorations of algebraic concepts should help students to gain confidence in their ability to abstract relationships from contextual information and use a variety of representations to describe those relationships.

 

 

 

 

enc4.gif (4101 bytes)NCTM Math Standards 5-8                                 

 

STANDARD 10: STATISTICS Examples of Statistics

In grades 5-8, the mathematics curriculum should include exploration of statistics in real-world situations so that students can--

Focus

In this age of information and technology, an ever-increasing need exists to understand how information is processed and translated into usable knowledge. Because of society's expanding use of data for prediction and decision making, it is important that students develop an understanding of the concepts and processes used in analyzing data. A knowledge of statistics is necessary if students are to become intelligent consumers who can make critical and informed decisions.

 

 

 

enc4.gif (4101 bytes)NCTM Math Standards 5-8                            

 

STANDARD 11: PROBABILITY Examples of Probability

In grades 5-8, the mathematics curriculum should include explorations of probability in real-world situations so that students can--

Focus

Probability theory is the underpinning of the modern world. Current research in both the physical and social sciences cannot be understood without it. Today's politics, tomorrow's weather report and next week's satellites all depend on it. (Huff and Geise 1959)

An understanding of probability and the related area of statistics is essential to being an informed citizen. Often we read statements such as, "There is a 20 percent chance of rain or snow today." "The odds are three to two that the Cats will win the championship." "The probability of winning the grand prize in the state lottery is 1 in 7 240 000." Students in the middle grades have an intense interest in the notions of fairness and the chances of winning games. The study of probability develops concepts and methods for investigating such situations. These methods allow students to make predictions when uncertainty exists and to make sense of claims that they see and hear.

 

 

 

 

enc4.gif (4101 bytes)NCTM Math Standards 5-8                      

STANDARD 12: GEOMETRY Examples of Geometry and Spatial Sense

              In grades 5-8, the mathematics curriculum should include the study of the geometry of one, two, and three dimensions in a variety of situations so that students can--

Focus: 

Geometry is grasping space . . . that space in which the child lives, breathes and moves. The space that the child must learn to know, explore, conquer, in order to live, breathe and move better in it. (Freudenthal 1973, p. 403).

The study of geometry helps students represent and make sense of the world. Geometric models provide a perspective from which students can analyze and solve problems, and geometric interpretations can help make an abstract (symbolic) representation more easily understood. Many ideas about number and measurement arise from attempts to quantify real-world objects that can be viewed geometrically. For example, the use of area models provides an interpretation for much of the arithmetic of decimals, fractions, ratios, proportions, and percents.

 

 

 

enc4.gif (4101 bytes)NCTM Math Standards 5-8                         

STANDARD 13: MEASUREMENT Examples of Measurement

 

In grades 5-8, the mathematics curriculum should include extensive concrete experiences using measurement so that students can--

Focus

Measurement activities can and should require a dynamic interaction between students and their environment. Students encounter measurement ideas both in and out of school, in such areas as architecture, art, science, commercial design, sports, cooking, shopping, and map reading. The study of measurement shows the usefulness and practical applications of mathematics, and students' need to communicate about various measurements highlights the importance of standard units and common measurement systems.

 


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Updated: March 12, 2004