Arithmetic is a branch of mathematics that consists of the study of numbers, especially concerning the properties of the traditional operations on them—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. Arithmetic is an elementary part of number theory, and number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra, geometry, and analysis. The terms arithmetic and higher arithmetic were used until the beginning of the 20th century as synonyms for number theory, and are sometimes still used to refer to a wider part of number theory.
Backgammon is one of the oldest known board games. Its history can be traced back nearly 5,000 years to archaeological discoveries in Jiroft, modern-day Iran. It is a two-player game where each player has fifteen pieces that move between twenty-four triangles (points) according to the roll of two dice. The objective of the game is to be first to bear off, i.e. move all fifteen checkers off the board. Backgammon is a member of the tables family of games, one of the oldest classes of board games.
In computing, floating-point arithmetic (FP) is arithmetic using formulaic representation of real numbers as an approximation to support a trade-off between range and precision. For this reason, floating-point computation is often used in systems with very small and very large real numbers that require fast processing times. In general, a floating-point number is represented approximately with a fixed number of significant digits and scaled using an exponent in some fixed base; the base for the scaling is normally two, ten, or sixteen. A number that can be represented exactly is of the following form:
In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values. Integers are commonly represented in a computer as a group of binary digits (bits). The size of the grouping varies so the set of integer sizes available varies between different types of computers. Computer hardware nearly always provides a way to represent a processor register or memory address as an integer.
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called numerals; for example, "5" is a numeral that represents the number five. As only a relatively small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system, which allows for the representation of any number using a combination of ten fundamental numeric symbols, called digits. In addition to their use in counting and measuring, numerals are often used for labels, for ordering, and for codes. In common usage, a numeral is not clearly distinguished from the number that it represents.
A computer number format is the internal representation of numeric values in digital device hardware and software, such as in programmable computers and calculators. Numerical values are stored as groupings of bits, such as bytes and words. The encoding between numerical values and bit patterns is chosen for convenience of the operation of the computer; the encoding used by the computer's instruction set generally requires conversion for external use, such as for printing and display. Different types of processors may have different internal representations of numerical values and different conventions are used for integer and real numbers. Most calculations are carried out with number formats that fit into a processor register, but some software systems allow representation of arbitrarily large numbers using multiple words of memory.
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" (one).
New Mathematics or New Math was a dramatic change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries and elsewhere, during the 1950s–1970s. Curriculum topics and teaching practices were changed in the U.S. shortly after the Sputnik crisis. The goal was to boost students' science education and mathematical skill to meet the technological threat of Soviet engineers, reputedly highly skilled mathematicians.
In computing, signed number representations are required to encode negative numbers in binary number systems.
Principles and Standards for School Mathematics (PSSM) are guidelines produced by the National Council of Teachers of Mathematics (NCTM) in 2000, setting forth recommendations for mathematics educators. They form a national vision for preschool through twelfth grade mathematics education in the US and Canada. It is the primary model for standards-based mathematics.
Elementary mathematics consists of mathematics topics frequently taught at the primary or secondary school levels.
In mathematics, 0.999... denotes the repeating decimal consisting of an unending sequence of 9s after the decimal point. This repeating decimal represents the smallest number no less than every decimal number in the sequence. This number is equal to 1. In other words, "0.999..." and "1" represent the same number. There are many ways of showing this equality, from intuitive arguments to mathematically rigorous proofs. The technique used depends on the target audience, background assumptions, historical context, and preferred development of the real numbers, the system within which 0.999... is commonly defined.
The School Mathematics Project arose in the United Kingdom as part of the new mathematics educational movement of the 1960s. It is a developer of mathematics textbooks for secondary schools, formerly based in Southampton in the UK.
The ProgramByDesign project is an outreach effort of the PLT research group. The goal is to train college faculty, high school teachers, and possibly even middle school teachers, in programming and computing.
Core-Plus Mathematics is a high school mathematics program consisting of a four-year series of print and digital student textbooks and supporting materials for teachers, developed by the Core-Plus Mathematics Project (CPMP) at Western Michigan University, with funding from the National Science Foundation. Development of the program started in 1992. The first edition, entitled Contemporary Mathematics in Context: A Unified Approach, was completed in 1995. The third edition, entitled Core-Plus Mathematics: Contemporary Mathematics in Context, was published by McGraw-Hill Education in 2015.
Investigations in Numbers, Data, and Space is a K–5 mathematics curriculum, developed at TERC in Cambridge, Massachusetts, United States. The curriculum is often referred to as Investigations or simply TERC. Patterned after the NCTM standards for mathematics, it is among the most widely used of the new reform mathematics curricula. As opposed to referring to textbooks and having teachers impose methods for solving arithmetic problems, the TERC program uses a constructivist approach that encourages students to develop their own understanding of mathematics. The curriculum underwent a major revision in 2005–2007.
Connected Mathematics is a comprehensive mathematics program intended for U.S. students in grades 6-8. The curriculum design, text materials for students, and supporting resources for teachers were created and have been progressively refined by the Connected Mathematics Project (CMP) at Michigan State University with advice and contributions from many mathematics teachers, curriculum developers, mathematicians, and mathematics education researchers.
In mathematics education, a representation is a way of encoding an idea or a relationship, and can be both internal and external. Thus multiple representations are ways to symbolize, to describe and to refer to the same mathematical entity. They are used to understand, to develop, and to communicate different mathematical features of the same object or operation, as well as connections between different properties. Multiple representations include graphs and diagrams, tables and grids, formulas, symbols, words, gestures, software code, videos, concrete models, physical and virtual manipulatives, pictures, and sounds. Representations are thinking tools for doing mathematics.
The Secondary School Mathematics Curriculum Improvement Study (SSMCIS) was the name of an American mathematics education program that stood for both the name of a curriculum and the name of the project that was responsible for developing curriculum materials. It is considered part of the second round of initiatives in the "New Math" movement of the 1960s. The program was led by Howard F. Fehr, a professor at Columbia University Teachers College.
Frédérique Papy-Lenger was a Belgian mathematician and mathematics educator active in the New Math movement of the 1960s and 1970s.
