MMW-CHAPTER-2.pptx major in Elementary Education

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1. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) MATHEMATICS in the MODERN WORLD INTRODUCTION: INSTRUCTOR: RHEA C. GATON

2. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) Chapter 2: MATHEMATICAL LANGUAGE AND SYMBOLS The Language, Symbols, Syntax and Rules of Matematics

3. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) The language of mathematics is the system used by mathematicians to communicate mathematical ideas among themselves. This language consists of a substrate of some natural language (for example English) using technical terms and grammatical conventions that are peculiar to mathematical discourse, supplemented by a highly specialized symbolic notation for mathematical formulas.

4. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) Mathematics as a language has symbols to express a formula or to represent a constant. It has syntax to make the expression well-formed to make the characters and symbols clear and valid that do not violate the rules.

5. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations, and other aspects of logical syntax. A mathematical concept is independent of the symbol chosen to represent it. In short, convention dictates the meaning

6. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) The language of mathematics makes it easy to express the kinds of symbols, syntax and rules that mathematicians like to do and characterized by the following:

7. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) PRECISE (able to make very fine distinctions) Example. The use of mathematical symbol is only done based on its meaning and purpose. Like means add, means subtract, x multiply and + means divide.

8. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) B. CONCISE (able to say things briefly) Example: The long English sentence can be shortened using mathematical symbols. Eight plus two equals ten which means 8+2 = 10.

9. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) C. POWERFUL (able to express complex thoughts with relative ease) Example. The application of critical thinking and problem solving skill requires the comprehension, analysis and reasoning to obtain the correct solution.

10. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) Writing Mathematical Language as an Expression or Sentence

11. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. It is a correct arrangement of mathematical symbols used to represent a mathematical object of interest. An expression does not state a complete thought; it does not make sense to ask if an expression is true or false.

12. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) The most common expression types are numbers, sets, and functions. Numbers have lots of different names: for example, the expressions: 5 2+3 10/2 (6-2)+1 all look different but are all just different names for the same number. This simple idea that numbers have lots of different names is extremely important in mathematics.

13. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) The basic syntax for entering mathematical formulas or expressions in the system enables you to quickly enter expressions using 2-D notation. The most common mistake is to forget the parentheses "( )". For example, the expression: 1/(x+1) is different from 1/x+1 which the system interprets as (1/x)+1.

14. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) Examples:The use of expressions ranges from the simple to complex: 8x-5 (linear polynomial) (quadratic polynomial) (rational fraction)  

15. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) On the other hand, a mathematical sentence is the analogue of an English sentence; it is a correct arrangement of mathematical symbols that a complete thought. Sentences have verbs. In the mathematical sentence ‘3+4=7’ the verb is =.

16. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) A sentence can be (always) true, (always) false, or sometimes true/sometimes false. For example, the sentence 1+2=3 is true. The sentence -1+2=4 is false. The sentence x=2 is sometimes true/sometimes false: it is true when x is 2, and false otherwise. The sentence x+3=3+x is (always) true, no matter what number is chosen for x.

17. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) Mathematical Convention

18. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) A mathematical convention is a fact, name, notation, or usage which is generally agreed upon by mathematicians. For instance, the fact that one evaluates multiplication before addition in the expression (2+3) x 4 is merely conventional. There is nothing inherently significant about of operations. Mathematicians abide by conventions in order to allow other mathematicians to understand what they write without constantly having to redefine basic terms.

19. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) The following symbols are commonly used in the order of operations:

20. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) Perform Operations on Mathematical Expressions Correctly

21. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) In simplifying mathematical expressions, the following order of operations is one critical point to observe. Order of operations is the hierarchy of mathematical operations. It is the set of rules that determines which operations should be done before or after others.

22. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) Before, we used to have the MDAS, that stands for Multiplication, Division, Addition and Subtraction. It was changed to use PEMDAS which means Parentheses, Exponents, Multiplication and Division and Addition and Subtraction. But now, most scientific calculators follow BODMAS, that is Brackets, Order, Division and Multiplication, Addition and Subtraction.

23. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) The order of operations or BODMAS/PEMDAS is merely a set of rules that prioritize the sequence of operations starting from the most important to the least important. STEP 1. Do as much as you can to simplify everything inside the parenthesis first. STEP 2. Simplify every exponential number in the numerical expression. STEP 3. Multiply and divide whichever comes first, from left to right. STEP 4. Add and subtract whichever comes first, from left to right.