Math

1. MATHEMATICS AS A
LANGUAGE
Mathematics in the Modern World

3. Wait! Before we talk about “MATH”
Lets PLAY A GAME!

4. …just a game
of what’s
next!!!
Ooopss…

5. ANSWE
R:
WHAT’S NEXT?

6. 1 ∗ 1 = 1
11 ∗ 11 = 121
111 ∗ 111 = 12,321
1,111 ∗ 1,111 = 1,234,321
11,111 ∗ 11,111 = 123,454,321
111,111 ∗ 111,111 = ? ? ? ?
WHAT’S NEXT?
ANSWE
R: 12,345,654,321

7. WHAT’S NEXT?
1
3
15
7
31
ANSWE
R:
1 = 21
− 1
3 = 22
− 1
7 = 23
− 1
15 = 24
− 1
31 = 25
− 1
IS THIS THE
ONLY EXPLANATION?

8. WHAT’S NEXT?
ANSWE
R:

9. WHAT’S THE
PATTERN IN
THE GIVEN
SET OF
EQUATIONS
?

10. LETS
BEGIN!

11. How did you learn
your native
language?
(Filipino/Chinese
English/Japanese
Korean…)

12. MATHEMATICS AS LANGUAGE
A LANGUAGE is a systematic means of
communicating by the use of sound or conventional
symbols. It is the code we all use to express
ourselves and communicate to others.

13. Components of a language:
Vocabulary of symbols or words
Grammar or rules of how these symbols are used
Community of people who use and understand
these symbols
Range of meanings that can be communicated
with these symbols.

14. • ENGLISH LANGUAGE
• Symbols: English Letters
• Vowels and Consonants
• Words
• Phrases
• Sentences
MATHEMATICAL LANGUAGE
Symbols: English Letters/ Arabic
Numerals
Variables and Constants
Term
Algebraic Expressions
Mathematical statements:
Equations, Inequalities, etc

15. ELEMENTS OF THE
MATHEMATICAL LANGUAGE
0123456789
±×÷ ∞ =≠ ~ <≥≤∓≅
≡ ∀
4
∪ ∩ ∅ % ∃ ∄ ∈
∋ 𝛼 𝛽 𝛾 𝛿 𝜀 𝜖 𝜃 𝜗 𝜋 𝜇 𝜌 𝜎 𝜏 𝜑 𝜔

16. •The Language of Mathematics was designed so
we can write about:
1. Things like Numbers, Sets, Functions, etc.
2. What we Do with those things (add, subtract,
multiply, divide, join together, etc.)

17. SYMBOLS
Mathematics uses symbols instead of words:
There are the 10 digits: 0, 1, 2, ... 9
There are symbols for operations: +, −, ×, /, ...
And symbols that "stand in" for values: x, y, ...
And many special symbols: π, =, <, ≤, ...

18. LETTER CONVENTIONS
• Often (but not always) letters have special uses:
• Those are not rules, but they are often used that way.
Examples What they usually mean
Start of the alphabet: a, b, c, ... constants (fixed values)
From i to n: i, j, k, l, m, n Positive integers (for counting)
End of the alphabet: ... x, y, z variables (unknowns)

19. Example:
y = ax + b
•People will assume that a and b are fixed values,
•And that x is the one that changes, which in turn
makes y change.

20. NOUNS, VERBS, SENTENCES
• Even though we don't use the words "noun", "verb", or
"pronoun" in Mathematics, you can imagine
these similarities to English:
Nouns could be fixed things, such as numbers, or
expressions with numbers:
The Verb could be the equals sign "=", or
an inequality like < or >
15 2(3-1/2) 42

21. NOUNS, VERBS, SENTENCES
Pronouns (things like it, he, you, etc.) could be variables
like x or y:
And they could be put together into a Sentence like this:
3x + 7 = 22
5x-7 xy2 -3/x