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Mathematics as a Language

Mathematics is the language in which God has written the universe.” – Galileo Galilei

Having a common language will facilitate communication and result to clear information. Mathematics has its own language which for some people make it difficult to understand. This lesson will help you understand Math and its composition as a language.


Objectives

At the end of this lesson, the student must be able to:

  • classify the characteristics of mathematical language;
  • identify the elements of mathematical language;
  • differentiate expressions from sentences; and
  • express math expressions using correct conventions.


Pre-Test

For each question, choose the best answer. The answer key is below.

  1. Which of the following is a mathematical sentence?
    • 1/2
    • y=2
    • >1
    • -5
  2. Which is written in the most conventional way?
    • 2cab
    • abc2
    • 2abc
    • ab2c

Answer Key

  1. y=2
  2. 2abc

Characteristics of Math as a Language

Numbers are used to rate a performance (from elementary even in post graduate school). But why not words to describe performance? The following characteristics of Math will tell you the idea why.

  1. Precise – exact
  2. Concise – brief; not too wordy; straight to the point
  3. Powerful – express complex thoughts with relative ease; a tool in discovery

Example:

You got a score of 50 out of 100.

  • Precision – 50/100 (exact)
  • Concise – the quality of your performance was described briefly as 50/100. The 50/100 summarized getting half of the test items correctly and getting the other half incorrectly
  • Powerful – the 50/100 suggests the need for improvement and reflected the lack of readiness before the exam

Elements of Mathematical Language

If in English, the nouns are usually the subjects, and so with Math! Numbers are the “core” of mathematics such as describing their patterns, their characteristics and everything about them. Pronouns are used to substitute a for a person or a thing. In Math we use the variables for unknown values. The action words or the verbs are the operations which direct us what to do with the numbers.

mathematics-as-a-language

Expression vs. Sentence

Mathematical Expression – does not express a complete thought; incomplete.

Sentence – states complete thought using mathematical symbols <,>,=,≠ in between two or more elements.

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mathematics-as-a-language

Mathematical Conventions

Mathematical Convention is a fact, name, usage or notation which is generally agreed upon by mathematicians.

The expression below sparked arguments on whether the answer is 1 or 16.

mathematics-as-a-language

Clearly, there is ambiguity or confusion and does not satisfy one of the characteristics of math such as being precise. The problem does not convey a clear message. One (1) is not equal to 16. Thus, writing the expression that way such as is not conventional and incorrect. It could have been written as either:

mathematics-as-a-language

Then it will yield to 1 and 16, respectively.

  • PEMDAS – Order of operation (Parenthesis, Exponent, Multiplication or Division, Addition or Subtraction)

Note:

M or D (whichever comes first from left to right)

A or S (whichever comes first from left to right)

  • When using variables, use dot instead of . If there will be no confusion, the symbol may be dropped.

8∙y = 8y

a∙b∙c=abc

  • It is conventional to write the constant first before the variables. The variables must be in alphabetical order.

t∙s∙9 = 9st

Activity

  1. Give examples of mathematical expressions and mathematical sentences (5 each).
  2. Identify which characteristic(s) of Math as a language is/are depicted in each item and explain why.
Baking

Baking

Vaccine

Vaccine

Self-assessment:

For each question, choose the best answer. The answer key is below.

  1. Which is a mathematical sentence?
    • > 1
    • 1/2
    • x=y
    • = -1
  2. Express √3x in the most conventional way
    • x√3
    • √3x
    • x/√3
    • √3/x
  3. Express z∙y∙5∙a in the most conventional way.
    • yz5a
    • ayz5
    • 5ayz
    • 5yza

Answer Key

  1. x=y
  2. √3x
  3. 5ayz

Comments

David from West Midlands, England on September 28, 2020:

Thank you for the explanations. I enjoyed reading them.

Domingo T. Obniala Jr. on September 27, 2020:

Present

Mark christian Herrera on September 27, 2020:

Thank you ma'am

Ma. Elaine Ecal on September 27, 2020:

Thank you po mam

LOUIE LOCRIDA on September 27, 2020:

THANKS MADAM

Charles Justine rosal on September 27, 2020:

Thank you

Paul gayanes on September 27, 2020:

Thank you po madam

John Rey Barcebal on September 27, 2020:

Thank you mam

Tuscano jomar on September 27, 2020:

Mathematical expression

Y+7

2m

5k/3

4g-2k

5-L

Mathematical sentences

5+5=10

5x2=10

5√20

5x+5x=10x

25-5=20

Baking

Because baking use mathematical sentences and mathematical expressions

VIN EISEN GARCIA on September 27, 2020:

Thank you po madam!

Joana on September 27, 2020:

Thankyou for your good activity ma'am ❣️