(2)

• Modeling and Formulating


  Creating appropriate representations and relationships to mathematize the original problem
• Transforming and manipulating


  Changing the mathematical form in which a problem is originally expressed to equivalent forms that represent solutions
• Inferring


  Applying derived solutions to the original problem situation, and interpreting and generalizing the result in that light (double checking)
• Communicating


  Reporting what has been learned about a problem to a specified audience
• Multivariate Expressions


  Expressions having more than one variable
• Multivariate Expressions


  • 5xy + 9x - 12
  • 31abc
  • 9y / 3x
• Natural Language Phrases


  Group of words that has NO complete thought
• Characteristics of Mathematical Language

  • Mathematics is about ideas - relationships, quantities, processes, measurements, reasoning and so on
• Mathematical expressions


  Consists of terms. A term of a mathematical expression is separated from other terms with either a plus (+) or minus sign (-)
• Algebraic Expression


  A quantity which contains numbers and variables
• Parts of an Algebraic Expression

  • Literal coefficient (the variable, represents the unknown and makes use of letters)
  • Numerical coefficient (The number with the variable)
  • Constant (Any single number)
• Monomial


  A mathematical expression containing only 1 term
• Monomial


  • 7xyz
  • 21(x-8)
• Binomial


  A mathematical expression containing two (2) terms
• Binomial


  • 3x + 4
  • 5x + 12y
• Trinomial


  A mathematical expression containing three (3) terms
• Trinomial


  • x^2 + 2xy + y^2
  • 2x + 2(x+y) - 36
• Polynomial


  A mathematical expression containing more than two terms
• Polynomial

  • 2x^3 + y^2 + x - 6
• Mathematical Sentences


  Combines two mathematical expressions using a comparison operator
• Equation


  A mathematical equation containing the equal sign (=)
• Equation


  • 3x + 2 = 18
• Inequality


  A mathematical equation containing the inequality signs ( ≠, <, >, ≤, ≥ )
• Inequality


  • 16y > 20
• Open Sentence


  It uses variables, meaning that it is not known whether or not the mathematical sentence is true or false
• Open Sentence


  • 2xy < 3y
  • 18w > 16.5
  • 3(m+n) = 100
  • 8ab - c = 1
  • x + y = 5
• Closed Sentence


  A mathematical sentence that is known to be either true or false
• True Closed Sentence


  • 3(m+n) = 3m + 3n
  • 251/2 = 5
  • 2(x + y) = 2x + 2y
  • 18(2) > 16.5
  • 3 (m+n) = (m+n) + (m+n) + (m+n)
• False Closed Sentence


  • 9 is an even number
  • 4+4 = 5
  • 10 - 1 = 8
  • 6 - 6 = 1
  • The square root of 4 is 1
  • x + 2x + 3x = 10x
• Context


  Refers to the particular topics being studied and it is important to understand the context to understand mathematical symbols
• Convention


  A technique used by mathematicians, engineers, scientists in which each particular symbol has particular meaning
• Convention


  • The Greek letter π (pi) is used to represent the number 3.14159
  • We often use ɑ (alpha), β (beta), and θ (theta) to represent angles
  • The Greek capital letter Σ (sigma) is frequently used to represent the summation of several numbers