Mathematical-Language-and-Symbols.pdf lesson 1

This will help students to understand mathematical language and symbols. Summary of Lesson 1: Mathematical Language and Symbols
1. Introduction to Mathematical Language

Importance of Language in Mathematics: Just like any other language, mathematics has its own vocabulary and grammar. Understanding this language is crucial for grasping mathematical concepts.
Precision and Conciseness: Mathematical language is designed to be precise and concise, allowing complex ideas to be expressed clearly and efficiently.
2. Vocabulary of Mathematics

Mathematical Nouns: These are the names given to mathematical objects, such as numbers, variables, sets, and functions. For example, in the expression ( x + y = z ), ( x ), ( y ), and ( z ) are mathematical nouns.
Mathematical Sentences: These are complete thoughts or statements in mathematics, often involving relationships between nouns. For example, equations and inequalities are mathematical sentences.
3. Symbols and Notation

Common Symbols: The lesson covers various symbols used in mathematics, such as ( + ) for addition, ( - ) for subtraction, ( \times ) for multiplication, and ( \div ) for division. It also includes symbols for equality (( = )), inequality (( \neq )), and more complex operations like integrals (( \int )) and derivatives (( \frac{d}{dx} )).
Greek Letters: Many mathematical symbols are derived from Greek letters, such as ( \alpha ), ( \beta ), ( \gamma ), and ( \delta ). These are often used to represent constants, variables, and specific functions.
4. Translating Words into Symbols

Word Problems: The lesson emphasizes the importance of translating word problems into mathematical symbols and equations. This skill is essential for solving real-world problems using mathematics.
Practice Examples: Various examples are provided to practice translating sentences into mathematical expressions. For instance, “the sum of a number and five” can be translated to ( x + 5 ).
5. Syntax and Structure

Order of Operations: The lesson reviews the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Proper Notation: Emphasis is placed on using proper notation to avoid ambiguity. For example, the expression ( 3 + 4 \times 2 ) should be interpreted as ( 3 + (4 \times 2) ), not ( (3 + 4) \times 2 ).
6. Practice and Application

Exercises: The lesson includes exercises to reinforce the concepts learned. These exercises help students practice translating words into symbols, using proper notation, and solving equations.
Real-World Applications: Examples of how mathematical language and symbols are used in various fields, such as engineering, physics, and economics, are provided to show the practical importance of these skills.

1. MATHEMATICS IN
THE MODERN
WORLD

2. MOUNT CARMEL COLLEGE OF ESCALANTE INC.
RENE L. GELOGO, LPT, MED-MATH
INSTRUCTOR

14. EXAMPLE:
Mathematical Expressions:
1.The sum of a number and five
2.3x + 4y
3. Twice a number plus two
Mathematical Sentences:
1.The sum of a number and five is 10.
2.3x + 4y = 12
3. Twice a number plus two equals 14.

20. GENERAL INSTRUCTIONS: Copy and Answer on a One-whole
yellow pad. Write all your answers next line after each item (See
Example Below). Erasures or any tampering on your answer is Not
Allowed.
1. Twice a number is not more than seven.
Ans: 2x ≤ 7
George Y. Bogart BSED 1-EnglishDate: 9/4/2024
ACTIVITY 1: Expression or Sentence
1. Twice a number is not more than seven.
Ans: Bogart
ACTIVITY 2: Open or Closed Sentence
1. Twice a number is not more than seven.
Ans: Open
ACTIVITY 3: Translating phrases to Mathematical
sentence or expression.
For the proceeding Activities, please read and understand
Each instructionsindicatedtherein.
Mathematics in the Modern World

21. ACTIVITY 1:
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7.� = 1
8.�+
3
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9.�
2
+3�=8
10.3�
4
+2�
3
−4�
2
+5�−1
EXPRESSION or SENTENCE
Directions: Write your 1
st
Name if it is a Mathematical
Expression and your Surname if it is a Mathematical
Sentence.

22. ACTIVITY 2:
1.Four is a Prime number.
2.2x + 10 = 30.
3.The cube root of 8 is 2.
4.2(3 + 4) = 2 x 7.
5.The product of a number and 2 is equal to 18.
6.Seven minus 12 equals 5.
7.15 = 3x – 6.
8.The square root of 9x is 3.
9.One-half of 50 is the square of 5.
10. A number added to 12 is equal to 24.
OPEN OR CLOSED SENTENCE
Directions: Write your Surname if the sentence is
OPEN and your 1
st
Name if it is CLOSED. For those
Closed sentence, Identify if it is True or False.

23. ACTIVITY 3:
1.The difference of Five and a number
2.Negative thirteen decreased by 3 times a number
3.Eleven subtracted from a number
4.Twice a number, decreased by 58
5.Five times the sum of a number “n” and -23
6.Six more than a number is 20.
7.Three times a number yields five more than twice the
same number.
8.The quotient of a number and seven, minus three, is
four.
9.The product of a number and eight is at least 12.
10.The sum of a number and two is at most 24.
TRANSLATING PHRASES TO
MATHEMATICAL SENTENCE
OR EXPRESSION.
Directions: Translate the following English phrases or
sentences into Mathematical Sentence or Expression.
Use only variable x if needed.