Introducing the binary system in grades four to six

1973 ◽  
Vol 20 (3) ◽  
pp. 182-183
Author(s):  
Jan Unenge
Keyword(s):  
Binary System ◽  
Elementary Mathematics ◽  
Place Value ◽  
Decimal System ◽  
Mathematics Program

The teaching of place value is one of the most important—and possibly the most interesting—parts of the elementary mathematics program. You can show the children how you get another name for the number seven if you count in fives. And children will better understand what happens when you go from nine to ten and from ninetynine to one hundred in the decimal system if you discuss different bases with them. I have used the following technique for teaching the binary system in grades four to six.

In the classroom: Binary can be F-U-N

1963 ◽  
Vol 10 (6) ◽  
pp. 354-355
Author(s):  
Marion E. Ochsenhirt ◽  
Mary M. Wedemeyer
Keyword(s):  
Binary System ◽  
Place Value ◽  
Seventh Grade ◽  
Educational Value ◽  
Decimal System ◽  
The North ◽  
New Situation ◽  
Modern Mathematics

The seventh-grade students of the North Hills Joint Schools have found that there is fun as well as educational value in using the binary system. As all teachers of modern mathematics know, one of the main reasons for teaching the binary system is that the pattern for place value in this system is identical to that of the traditional decimal system. Developing the pattern in an entirely new situation gives the student a better understanding of the decimal system.

Non-standard methods for converting numbers from one number system to another

2020 ◽  
Vol 1 (9) ◽  
pp. 28-30
Author(s):  
D. M. Zlatopolski
Keyword(s):  
Binary System ◽  
Maximum Degree ◽  
Number System ◽  
Binary Form ◽  
Binary Number ◽  
Standard Methods ◽  
Optimal Variant ◽  
Decimal System ◽  
Large Numbers ◽  
Independent Work

The article describes a number of little-known methods for translating natural numbers from one number system to another. The first is a method for converting large numbers from the decimal system to the binary system, based on multiple divisions of a given number and all intermediate quotients by 64 (or another number equal to 2n ), followed by writing the last quotient and the resulting remainders in binary form. Then two methods of mutual translation of decimal and binary numbers are described, based on the so-called «Horner scheme». An optimal variant of converting numbers into the binary number system by the method of division by 2 is also given. In conclusion, a fragment of a manuscript from the beginning of the late 16th — early 17th centuries is published with translation into the binary system by the method of highlighting the maximum degree of number 2. Assignments for independent work of students are offered.

The Effects of Studying Decimal and Nondecimal Numeration Systems on Mathematical Understanding, Retention, and Transfer

1970 ◽  
Vol 1 (3) ◽  
pp. 162-172
Author(s):  
Richard C. Diedrich ◽  
Vincent J. Glennon
Keyword(s):  
Multivariate Analysis ◽  
Mathematical Understanding ◽  
Analysis Of Covariance ◽  
Value Systems ◽  
Place Value ◽  
Decimal System ◽  
Statistical Procedures ◽  
System 2 ◽  
Grade Groups ◽  
Numeration Systems

What are the effects of studying 1, 3, or 5 place-value systems of numeration? Each of 3 experimental 4th grade groups received 30 minutes of instruction for 9 consecutive school days. A 4th group served as control. Statistical procedures included multivariate analysis of covariance. The results suggest: for the group under consideration (1) a study of the decimal system alone tends to be just as effective as a study of 3 or 5 systems in promoting understanding of the decimal system; (2) a study of either 3 or 5 place-value systems of numeration appears to be more effective than a study of the decimal system alone in promoting understanding of the general principles of place-value systems of numeration.

Research of EAN-13 Barcode Identification Based on Unitary Decimalization

2013 ◽  
Vol 303-306 ◽  
pp. 611-616
Author(s):  
Cai Hong Ding ◽  
Chuang Zhang ◽  
Yan Zhu Yang
Keyword(s):  
Binary System ◽  
Averaging Method ◽  
Decimal System ◽  
Image Identification ◽  
Similar Line ◽  
The Times

This paper has put forward a decimal system based on binary system for representing figures of barcode image. Different with traditional distance of similar line unitary method, this paper invents the unitary decimalize method for EAN-13 image identification. Counting and sorting the times of the number that appears when scan the image to calculate the width of unit bar not use the averaging method, which has the same identification effect but more simple and effective. At last make the corresponding program to verify the method, the result shows this method performs well. It is not only suitable to the horizontal positive-going or reversed-going barcode image but also to the oblique barcode image.

Things you can try: Using functional bulletin boards in elementary mathematics

1972 ◽  
Vol 19 (6) ◽  
pp. 467-471
Author(s):  
William E. Schall
Keyword(s):  
New York ◽  
Elementary School ◽  
Elementary Mathematics ◽  
School Science ◽  
Bulletin Board ◽  
Visual Aids ◽  
Elementary School Science ◽  
Bulletin Boards ◽  
Mathematics Program ◽  
Intelligent Planning

Visual aids—films, still pictures, models, bulletin boards, and so on—are among the most useful tools in education, but they do not teach without intelligent planning and use (Glenn O. Blough and Albert J. Hugget, Elementary School Science and How to Teach It [New York: Dryden Press, 1957], pp. 33–34). Bulletin boards can play an important role in today's mathematics program. However, a bulletin board, if it is to be successful in achieving its purpose, must gain and be worthy of the class's attention.

An additive numeral system related to place value

1965 ◽  
Vol 12 (3) ◽  
pp. 212-215
Author(s):  
Goldie E. Vitt
Keyword(s):  
Young Children ◽  
Learning Experiences ◽  
Place Value ◽  
Decimal System ◽  
Conventional Methods

The concepts relating to place value in our decimal system involve what are probably some of the most difficult learning experiences that the primary child encounters. While many young children are able to tell “how many ones,” ”how many tens,” “how many hundreds” in a numeral, the teacher sometimes has reason to suspect that this skill is a superficial one, and that many conventional methods of presenting material intended to teach place value do not promote real internalization of the concepts involved or provide realistic mean for evaluation of learnings.

Mathematics in Egypt

2018 ◽  
pp. 48-60
Author(s):  
Annette Imhausen
Keyword(s):  
Number System ◽  
Place Value ◽  
High Status ◽  
Decimal System ◽  
Unit Fractions ◽  
Essential Tool ◽  
Mathematical Texts

This chapter studies Egyptian mathematics, an essential tool to administer resources, from the invention of the script and number system, ca 3000 bce. Egyptian writing was a tool restricted to the elites. Their number system was a decimal system without positional (place-value) notation. Their concept of unit fractions, as the inverses of integers, was fundamentally different from ours; other fractional values were expressed as a sum of unit fractions. The few surviving mathematical texts contain a collection of problems or tables to aid in calculations, or actual worked calculations, or a mixture of these. Some scribes had high status, based explicitly on the numerate activity of calculating taxes owed and work produced. Later Egyptian mathematics displays Mesopotamian influences.

The Egyptian Number System

2016 ◽  
Author(s):  
Annette Imhausen
Keyword(s):  
Number System ◽  
Decimal Place ◽  
Place Value ◽  
Decimal System ◽  
Absolute Value ◽  
Ancient Egyptian ◽  
System P ◽  
The Absolute ◽  
The Individual

This chapter describes the ancient Egyptian number system. The system can be described in modern terminology as a decimal system without positional (place-value) notation. The basis of the number system was 10 (hence decimal system), but unlike our decimal place-value notation using the ten numerics 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, in which the absolute value is determined by its position within the number (e.g., in the number 125, the absolute value of 1 is 1 × 102, the absolute value of 2 is 2 × 101, and the absolute value of 5 is 5 × 100), the Egyptian system used individual symbols for each power of 10. Although there is no information about the choice of the individual signs for the respective values, some of them seem plausible choices. The most basic, the simple stroke to represent a unit, is used not only in Egypt but also in a variety of other cultures, possibly originating from marks on a tally stick.

Aligning traditional with new mathematics

1964 ◽  
Vol 11 (1) ◽  
pp. 23-27
Author(s):  
Sister Ann Jude Lynch
Keyword(s):  
Elementary Mathematics ◽  
New Methods ◽  
New Concepts ◽  
Mathematics Program ◽  
Teaching Area

The chief challenge in elementary mathematics today is the gradual adjusting to the new methods and ideas while still retaining much that is traditional. My problem has been how to continue to use a textbook that is a moderately traditional one while moving into that teaching area that involves the new concepts in mathematics. After much frustrated planning, I remembered a famous cliché used by one of our old-time Supervisors of Schools. “You do not teach a text, you teach a child.” The next step was to move to the question of how to teach these children some of the necessary concepts inherent in the new mathematics program while concomitantly using the traditional text.

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