Learning Objectives
o Discussthe language, symbols and conventions of
mathematics.
o Explain the nature of mathematics as a language.
o Acknowledge that mathematics is a useful
language.
o Compare and contrast expression and sentences.
o Identify and discuss the four basic concepts in
mathematical language.
o Perform operations on mathematical expressions
correctly.
3.
Topic Outline
I. Characteristicsof Mathematical Language
II. Expression versus Sentences
III.Conventions in the Mathematical
Language
IV. Four Basic Concepts
V. Elementary Logic
VI. Formality
What is alanguage?
Language (n.): a
systematic means of
communicating ideas or
feelings by the use of
conventional symbols,
sounds, or marks having
understood meaning
What is alanguage?
∀
∃
∴
𝒙 , 𝖦 𝒑 𝒙 , න
𝒇(𝒙) ,
sum, product, integral
‘for every”
“there exists”
“therefore”
8.
Mathematical Language
Mathematical languageis the system used to communicate
mathematical ideas.
It consists of some natural language using technical terms
(mathematical terms) and grammatical conventions that are
uncommon to mathematical discourse, supplemented by a highly
specialized symbolic notation for mathematical formulas.
Mathematical notation used for formulas has its own grammar
and shared by mathematicians anywhere in the globe.
Mathematical language is being precise, concise, and powerful.
10.
The following arecommonly used in the
order of operations:
Symbol Meaning Example
+ Add 3 + 7 =10
- Subtract 5 – 2 = 3
× Multiply 4 × 3 = 12
÷ Divide 20 ÷ 5 = 4
11.
The following arecommonly used in the order of
operations:
Symbol Meaning Example
/ Divide 20/5 = 4
π pi A = πr²
ꝏ infinity is endless
ꝏ
= equals 1 + 1 = 2
Approximately
equal to
π 3.14
Not equal to π 2
12.
The following arecommonly used in the order of
operations:
Symbol Meaning Example
Less than, less than
or equal
2 3
Greater than,
greater than or
equal
5 1
Square root
(radical)
2
degrees 20
therefore A = B B = A
13.
Phrase
a group ofwords that expresses a
concept
Sentenc
e
a group of words that are put
together to mean
something
14.
Mathematical Sentence
Sentence (ormathematical sentence)
– a statement about two expressions,
either using numbers, variables, or a
combination of both.
Uses symbols or words like equals,
greater than, or less than.
It is a correct arrangement of
mathematical symbols that states a
complete thought and can be
determined whether it’s true, false,
sometimes true/sometimes false.
Expressio
na group ofnumber or variable
with or without mathematical
operation
Equatio
n
a group of number or variable
with or without mathematical
operation
separated by an equal sign
18.
Mathematical Expressions
consist ofterms. The terms is
separated from other terms
with either plus or minus
signs. A single term may
contain an expression in
parentheses or other
grouping symbols.
English words tomathematics
English phrase/sentence Mathematical symbols
Product of two numbers 𝐴 × 𝐵 or
𝐴𝐵
Three more than twice a number 2𝑥 + 3
Two less than half a number is 15. 1
𝑦 − 2 = 15
2
The sum of three distinct numbers is at
least 10.
𝑥 + 𝑦 + 𝑧 ≥ 10
He owns at most eight cars. 𝐶 ≤ 8
The price of the house increased by 8%. 𝑃𝑛𝑒𝑤 = 𝑃𝑜𝑙𝑑 + 0.08
𝑃𝑜𝑙𝑑
Each kid gets one-eighth of the cake. 1
𝐾 =
𝐶
8
25.
Expression or sentence?
Classify.
(1)The product of two numbers
(2) The sum of three integers is greater than 11.
(3) Half of the sum of 23 and 88
(4) The sum of two numbers is half their product.
(5) 2𝑥 − 3
(6) 𝑥 = 1
(7) 𝑥 +
3𝑦
2
(8) 𝑥 + 2𝑥 + 3𝑥 + 4𝑥
+ 5𝑥
26.
a. Precise (ableto make very fine
distinctions)
Example. The use of
mathematical symbol is only done
based on its meaning and purpose.
Like + means add, - means
subtract × multiply and ÷ means
divide.
27.
b. Concise (ableto say things
briefly)
Example. The long English
sentence can be shortened using
mathematical symbols. Eight plus
two equals ten which means 8 + 2
= 10.
28.
b. Concise (ableto say things
briefly)
Example.
3 x 3 x 3 x 3 x 3
𝟑
𝟓
3 to the power of 5
29.
c. Powerful (ableto 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.
