A topic about mathematical language topic.pptx

Mathematical Language a complete guide

1. Characteristics and Convention of Mathematical Language Mathematics in the Modern World

2. And the system used to communicate mathematical ideas is called mathematical language. Language is a system of communication used by a particular community that can either be or . It is a way of transforming information and meaning.

3. A mathematical language uses , instead of , to communicate mathematical

4. Characteristics of Mathematical Language

5. Characteristics of the language of mathematics 9+3=12 The sum of nine plus three is twelve Precise Concise Powerful

6. Precise Concise Powerful Every symbol and term has a unique meaning Example: The symbol π always represents 3.1416 …, never any other value. Uses minimal symbols to represent complex ideas. Example: Instead of saying “ the sum of a number and five is equal to ten ,” we write 𝑥+5=10 Can describe abstract and real-world situations. Example: 𝐸=𝑚𝑐2 describes the relationship between energy, mass, and the speed of light.

7. The language of mathematics can be learned but requires the needed to learn any foreign language. Math is considered a language . Hence, the and organization to form equations are the same in every country of the

8. Conventions in the Mathematical Language

9. A Mathematical Convention is a , , ,notation, or usage which is generally agreed upon by mathematicians.

10. Mathematical symbols -is a figure or a combination of figures that is used to represent a mathematical object.

11. Numbers Operation symbols Relation symbols Grouping symbols Variables 0, 1, 2,… +, -, *, ÷ =, ≠, <, ≤, >, ≥ ( ), [ ], { } x, y, n, A, V represent quantity; Nouns in the alphabet act as connectives in math sentences for comparison, act as Verbs to associate groups of numbers and operators letters to represent quantities; act as Pronouns

12. A is a symbol commonly represented by any that may assume various values.

13. For instance, the phrase “a number” is sometimes expressed as variable x, a, b, or any other n in the English alphabet.

14. How to translate English phrase to Mathematical phrase and vice versa? Verbal Phrases: The sum of a number and seven. Twice a number decreased by three. The product of five and a number. A number divided by eight. Four more than three times a number . Mathematical Expressions: x+7 2x−3 5x 3x +4  

15. Expression vs. Sentence

16. Feature Mathematical Expression Mathematical Sentence Definition A combination of numbers, variables, and operation symbols without a relation symbol (=, <, >, etc.). A statement that expresses a complete idea and includes a relation symbol (=, <, >, ≥, ≤). Key Components Numbers, variables, operation symbols (+, −, ×, ÷), but no equal or inequality sign . Numbers, variables, operation symbols, and a relation symbol that makes it a complete statement. Completeness It is incomplete because it does not make a statement or comparison. It is complete because it makes a statement that can be true or false. Examples 4a−7b Feature Mathematical Expression Mathematical Sentence Definition A combination of numbers, variables, and operation symbols without a relation symbol (=, <, >, etc.). A statement that expresses a complete idea and includes a relation symbol (=, <, >, ≥, ≤). Key Components Numbers, variables, operation symbols (+, −, ×, ÷), but no equal or inequality sign . Numbers, variables, operation symbols, and a relation symbol that makes it a complete statement. Completeness It is incomplete because it does not make a statement or comparison. It is complete because it makes a statement that can be true or false. Examples 4a−7b

17. Activity 3. Test I. Mathematical Sentence / Mathematical Expression / Neither

18. Activity 3. Test II. Translate each phrase into mathematical expression. Use a few variables as possible. 1.) the difference of 8a and 3, to the 6th power 2.) 5 minus m to the 8th 3.) the quantity 2 minus 71m, squared 4.) the quotient of 7 and d squared 5.) 10 times the sum 2 plus k

19. 1 . Mathematical sentence 2. Mathematical sentence: 3. Mathematical expression 4. Neither 5. Mathematical sentence : Mathematical Sentence / Mathematical Expression / Neither

20. 6. Mathematical sentence 7. Neither 8. Mathematical sentence 9. Mathematical sentence 10. Mathematical expression Mathematical Sentence / Mathematical Expression / Neither

21. Translate each phrase into mathematical expression. Use a few variables as possible. 1.) the difference of 8a and 3, to the 6th power (8a- 3) 6 2.) 5 minus m to the 8th 5-m 8 3.) the quantity 2 minus 71m, squared (2 - 71m) 2 4.) the quotient of 7 and d squared 𝟕/d 2 5.) 10 times the sum 2 plus k 10 (2 + k)