Module Overview
... In Grade 6, students formed a conceptual understanding of integers through the use of the number line, absolute value, and opposites and extended their understanding to include the ordering and comparing of rational numbers (6.NS.C.5, 6.NS.C.6, 6.NS.C.7). This module uses the Integer Game: a card ga ...
... In Grade 6, students formed a conceptual understanding of integers through the use of the number line, absolute value, and opposites and extended their understanding to include the ordering and comparing of rational numbers (6.NS.C.5, 6.NS.C.6, 6.NS.C.7). This module uses the Integer Game: a card ga ...
Grade 7 Math Module 2 Overview
... In Grade 6, students formed a conceptual understanding of integers through the use of the number line, absolute value, and opposites and extended their understanding to include the ordering and comparing of rational numbers (6.NS.C.5, 6.NS.C.6, 6.NS.C.7). This module uses the Integer Game: a card ga ...
... In Grade 6, students formed a conceptual understanding of integers through the use of the number line, absolute value, and opposites and extended their understanding to include the ordering and comparing of rational numbers (6.NS.C.5, 6.NS.C.6, 6.NS.C.7). This module uses the Integer Game: a card ga ...
prime numbers as potential pseudo
... that we have 333 possible primes for every thousand. But when you start to cut of the composite ones this number decreases exponentially. The first thousand (5 to 1005) has 166 primes; the second thousand (1005 to 2005) has 136 primes, and so on. After 120 thousands (120000) there are, only, 70 poss ...
... that we have 333 possible primes for every thousand. But when you start to cut of the composite ones this number decreases exponentially. The first thousand (5 to 1005) has 166 primes; the second thousand (1005 to 2005) has 136 primes, and so on. After 120 thousands (120000) there are, only, 70 poss ...
Grades 2,3,and 4 outcomes
... 2 B9: model and perform the addition of two 2-digit numbers, with and without regrouping 2 B10: model and perform the subtraction of two 2-digit numbers, with and without regrouping 2 B11: estimate the sum or difference to two 2-digit numbers 2 B12: use technology to solve problems involving sums or ...
... 2 B9: model and perform the addition of two 2-digit numbers, with and without regrouping 2 B10: model and perform the subtraction of two 2-digit numbers, with and without regrouping 2 B11: estimate the sum or difference to two 2-digit numbers 2 B12: use technology to solve problems involving sums or ...
Disk Based Hash Tables and Quantified Numbers
... For the past decades, one of the bottlenecks which holds back the time a computational process takes to complete are the clock cycles taken to get the data from memory storage to CPU registers to perform the necessary logical or arithmetical operation plus the cycles taken to put the result back to ...
... For the past decades, one of the bottlenecks which holds back the time a computational process takes to complete are the clock cycles taken to get the data from memory storage to CPU registers to perform the necessary logical or arithmetical operation plus the cycles taken to put the result back to ...
Surreal number
In mathematics, the surreal number system is an arithmetic continuum containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surreals share many properties with the reals, including a total order ≤ and the usual arithmetic operations (addition, subtraction, multiplication, and division); as such, they form an ordered field. (Strictly speaking, the surreals are not a set, but a proper class.) If formulated in Von Neumann–Bernays–Gödel set theory, the surreal numbers are the largest possible ordered field; all other ordered fields, such as the rationals, the reals, the rational functions, the Levi-Civita field, the superreal numbers, and the hyperreal numbers, can be realized as subfields of the surreals. It has also been shown (in Von Neumann–Bernays–Gödel set theory) that the maximal class hyperreal field is isomorphic to the maximal class surreal field; in theories without the axiom of global choice, this need not be the case, and in such theories it is not necessarily true that the surreals are the largest ordered field. The surreals also contain all transfinite ordinal numbers; the arithmetic on them is given by the natural operations.In 1907 Hahn introduced Hahn series as a generalization of formal power series, and Hausdorff introduced certain ordered sets called ηα-sets for ordinals α and asked if it was possible to find a compatible ordered group or field structure. In 1962 Alling used a modified form of Hahn series to construct such ordered fields associated to certain ordinals α, and taking α to be the class of all ordinals in his construction gives a class that is an ordered field isomorphic to the surreal numbers.Research on the go endgame by John Horton Conway led to a simpler definition and construction of the surreal numbers. Conway's construction was introduced in Donald Knuth's 1974 book Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness. In his book, which takes the form of a dialogue, Knuth coined the term surreal numbers for what Conway had called simply numbers. Conway later adopted Knuth's term, and used surreals for analyzing games in his 1976 book On Numbers and Games.