Mathematical Language PDF

Mathematical Language Characteristics and Conventions in the Mathematical Language Mathematical Language Characteristics and Conventions in the Mathematical Language Characteristics of Mathematical Language 1. Precise 2. Concise 3. Powerful Characteristics of Math...

Mathematical Language Characteristics and Conventions in the Mathematical Language Mathematical Language Characteristics and Conventions in the Mathematical Language Characteristics of Mathematical Language 1. Precise 2. Concise 3. Powerful Characteristics of Mathematical Language 1. Precise 2. Concise 3. Powerful Vocabulary Vs. Sentences Every language has its vocabulary, and its rules for combining these words into complete thoughts. Importance of Mathematical Language Comprehension Development of Mathematics Proficiency Better Communication Vocabulary Vs. Sentences Every language has its vocabulary, and its rules for combining these words into complete thoughts. Importance of Mathematical Language Comprehension Development of Mathematics Proficiency Better Communication Natural and Mathematical Language Nouns in Mathematics could be fixed things such as numbers, or expressions with numbers Verbs could be equal sign “=“, or inequalities “” Pronouns could be variables Natural and Mathematical Language Nouns in Mathematics could be fixed things such as numbers, or expressions with numbers Verbs could be equal sign “=“, or inequalities “” Pronouns could be variables Expressions and Sentences A Mathematical Sentence expresses a complete mathematical thought about the relation of a mathematical object to another mathematical object. 6(x + 4) 3x + 4 = y (6 - k)/ 12 x + 2x = 3x 11m + 7 x–1=0 Expressions and Sentences A Mathematical Sentence expresses a complete mathematical thought about the relation of a mathematical object to another mathematical object. 6(x + 4) 3x + 4 = y (6 - k)/ 12 x + 2x = 3x 11m + 7 x–1=0 Conventions in mathematics, some commonly used symbols, its meaning and example Basic Operations and Relational Symbols Basic Operations and Relational Symbols Sets of Numbers Translating Words into Symbols 1. The sum of a and b 2. The product of x and y 3. The sum of x and the difference of y and z 4. The product of x and the sum of y and z 5. Six less than twice a number is forty five. 6. A number minus seven yields ten. 7. A total of six and some number 8. Twelve added to a number 9. Eight times a number is forty-eight. Translating Symbols into Words 1. x (y + z) 2. xy + xz 3. (x + z) + (y - z) Four Basic Sets, Functions, Relations, Concepts and Binary Operations Sets and Subsets Use of the word “set” as a formal mathematical term was introduced in 1879 by Georg Cantor. For most mathematical purposes we can think of a set intuitively, as Cantor did, simply as a collection of elements. A set is a collection of well-defined objects. Sets Examples: A set of counting numbers from 1 to 10. A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A= {x/x ⋲ N1, x