Mathematics in the Modern World - Problem Solving and Reasoning

Vocabulary flashcards covering the terminology and methods of problem solving and reasoning from the GE013 Mathematics in the Modern World course.

GE013

The course code for Mathematics in the Modern World, a 3-unit course at ASIA TECHNOLOGICAL SCHOOL OF SCIENCE AND ARTS (ASIATECH).

Mathematics in the Modern World

A course that deals with the nature of mathematics, its practical, intellectual, and aesthetic dimensions, and the application of mathematical tools in daily life.

The Nature of Mathematics

A core topic in the course outline that includes patterns and numbers in nature, the Fibonacci Sequence, and the behavior of nature.

Mathematical Language and Symbols

A topic covering characteristics of mathematical language, expressions vs. sentences, conventions, basic concepts, and elementary logic.

Inductive and Deductive Reasoning

Types of reasoning used to justify statements and arguments made about mathematics and mathematical concepts.

Polya's Four Steps in Problem Solving

A structured strategy for solving problems consisting of: 1. Understand the Problem, 2. Devise a Plan, 3. Carry Out the Plan, and 4. Look Back.

Step 1: Understand the Problem

The stage of problem solving where you read the question carefully several times and identify what is being sought (e.g., letting $x$ represent a number).

Step 2: Devise a Plan

The stage where you choose a strategy, such as making an organized list of all possible orders or translating a verbal problem mathematically into an equation.

Step 3: Carry Out the Plan

The stage where the chosen strategy is executed, such as listing specific game outcomes (WWW, WLWW, etc.) or solving an equation algebraically.

Step 4: Look Back

The final stage where you check the results for duplications, ensure all possibilities are included, and verify that the answer (e.g., area of $1,350$) matches the given conditions.

NCAA Best of Five Series Example

A problem demonstrating that there are exactly $10$ different ways a team can winning a championship decided by a best of five series.

Example 2 Algebraic Equation

The mathematical translation of the problem 'Two times the sum of a number and 3 is equal to thrice the number plus 4,' represented as $2(x + 3) = 3x + 4$.

Area of a Rectangle Formula

The formula $A = lw$ used in problem solving to find dimensions when given the area and a relationship between length and width.

Example 3 Dimensions

A rectangular table with a width of $30$ inches and a length of $45$ inches ($15$ inches more than its width), resulting in an area of $1,350$ square inches.