Verbal and problem solving
There are two steps to solving math word problems:
1. Translate the wording into a numeric equation
that combines smaller "expressions"
2. Solve the equation!
Suggestions:
* Read the problem entirely
Get a feel for the whole problem
* List information and the variables you identify
Attach units of measure to the variables (gallons, miles, inches, etc.) * Define what answer you need,
as well as its units of measure
* Work in an organized manner
Working clearly will help you think clearly
* Draw and label all graphs and pictures clearly
* Note or explain each step of your process;
this will help you track variables and remember their meanings * Look for the "key" words (above)
Certain words indicate certain mathematical operations:
Math expressions (examples):
after you review the keywords, test yourself
addition: 5+x| subtraction: 5-x|
multiplication: 5*x; 5x| division: 5 ÷ x; 5/x|
Exercise: ("mouse over" the block for answer)|
Key words for addition +
increased by; more than; combined together; total of; sum; added to| What is the sum of 8 and y?| 8 + y|
Express the number (x) of apples
increased by two| x + 2|
Express the total weight of
Alphie the dog (x) and Cyrus the cat (y)| x + y|
Key words for Subtraction -
less than, fewer than, reduced by, decreased by, difference of| What is four less than y| y - 4|
What is nine less than a number (y)| y - 9|
What if the number (x) of pizzas
was reduced by 6?| x - 6|
What is the difference of my weight (x)
and your weight (y)| x - y|
Key words for multiplication * x or integers next to each other (5y, xy): of, times, multiplied by|
What is y multiplied by 13| 13y or 13 * y|
Three runners averaged "y" minutes.
Express their total running time:| 3y|
I drive my car at 55 miles per hour.
How far will I go in "x" hours?| 55x|
Key words for division ÷ /
per, a; out of; ratio of,...

...be learned comprehensively and with much depth. The twin goals of mathematics in the basic education levels, K-10 are Critical Thinking and ProblemSolving. We adopt the definition of critical thinking by Scriven and Paul (1987): Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action. On the other hand, we define ProblemSolving in mathematics using Polya’s (1945 & 1962) definition: Mathematical problemsolving is finding a way around a difficulty, around an obstacle, and finding a solution to a problem that is unknown. These two goals are to be achieved with an organized and rigorous curriculum content, a well-defined set of high-level skills and processes, desirable values and attitudes, and appropriate tools, recognizing as well the different contexts of Filipino learners. There are five content areas in the curriculum, as adopted from the framework prepared by MATHTED & SEI (2010): Numbers and Number Sense, Measurement, Geometry, Patterns and Algebra, and Probability and Statistics. The specific skills and processes to be developed are: Knowing and Understanding; Estimating, Computing and Solving; Visualizing and...

...Chapter 1
THE PROBLEM AND ITS BACKGROUND
Introduction
The history of science and math are interrelated. The people who shaped science are also important in mathematics. As in science, the early history of mathematics is sketchy. We know that the lunar and solar cycles were counted by the Babylonians and Egyptians in an organized fashion. Early Indian mathematicians are credited with many astronomical observations as well as the beginning of algebra. The use of decimals and numbers with 9 figures and a zero are also attributed to the Indians. Their work spread to the Arabic nations, where the term Arabic numbers (compared to Roman numerals) first emerged.
The Chinese are credited with the inventions of spills and abacus, which are both counting machines. Multiplications tables were used at least from the 6th century BC. Chinese mathematics was used for the solutions of practical problems in engineering and business. Although the Chinese had advanced algebra, western scholars seemingly were ignorant of much of this work.
Starting in the 6th century BC, Greek mathematicians documented many discoveries in geometry. The Greeks' conception of numbers as the elements of all things and of the heavens made mathematical relationships a respected field of study. The philosophy of Pythagoras, Plato and Aristotle reflected the almost "god-like" respect the Greeks gave to the interrelationship of numbers with the universe.
Mathematics is a...

...Problem-Solving
Despite what folks accomplish as a profession or where they exist, most folks use the majority of their waking hours, at a workplace or at home, tackling situations. Most situations people challenge are little, some are substantial and complex, yet they need to be settled in a tasteful manner. There are a few definitions of a situation or how one individual may distinguish a situation. A situation is a chance for development. A situation may be a true break, the stroke of fortunes, chance thumping, an opportunity to get out of the groove of the ordinary and greatly improve the situation. A situation is the contrast between an individual present state and an individual objective state. A situation can come about because of revamped learning or supposing. At the point that a person knows where they are and where they need to be, they have a situation to fathom in getting to their objective. A situation comes about because of the acknowledgment of a present defective and the credence in the probability of a preferred fate. The function of this paper will explain the different approaches to the study of problem-solving. Explain the role of insight and creativity in the problemsolving process, analyze the dynamics of problem representation and problem solution and analyze the function of reasoning, judgment, and decision making in the...

...In my efforts to solve a problem I have often begun by identifying the one issue that affects me and focus on the individual tasks that led to the problem attempting to use logical and critical thinking. I have hit upon the realization that this focus works well with simpler problems that need immediate clarification but it has proven appropriate that problems that are more difficult and require a more long-term and elaborate answer requires the use of a Systems Thinking approach. My failure to seek broad, long-term solutions has me stamping out grass fires while my house burns down. I have adopted Daniel Aronson ideas on systems thinking to aid in keeping “the big picture” when developing solutions.
Critical and creative thinking processes are required when solvingproblems using systems thinking but I see the concentration shift from breaking down and examining individual tasks to studying how various system tasks shape both that system and the other systems in which it interacts.
When using systems thinking, essential in arriving to an amicable and effective end state are the realizations that must be shared by the solution seekers. To which all players must realize that their roles affect other stakeholders and the desired outcome. Each seeker should study how past solutions have added to a problem and therefore any steps to correct a current problem...

...ProblemSolving
Younger Sibling Problems
Younger siblings can be a problem that will lead to a bigger problem, your parents being angry at you for never being home. My younger brothers, CJ and Colin, are obnoxious and very annoying. CJ is six years younger than me and Colin is eight years younger than me. You wouldn’t think that they would be a problem to me since there is such an age difference between us, but they are. Since my brothers annoy me I am rarely home; my parents get angry with me for it, but there is not much I can do when both of my brothers get on my nerves; most of the time they do it at the same time. A big problem for me is that my brothers annoy me so much that I have to leave and go somewhere that does not involve my brothers, which causes my parents to be mad at me.
CJ, the older brother, is so mouthy. He always has something to say to me when I try talk to him; most of the time it is not nice, it is usually something rude. It seems like he was raised not to be respectful, but he wasn’t raised that way. For example, one day I asked him nicely to grab my cellphone and his reply was “why don’t you get up and get it yourself, both of your legs work, right?” I do not know why he acts the way he does, but it gets on my nerves. CJ and I always argue about everything. For instance, when I am in the living room watching TV he will try to play the Xbox, but I...

...Decision-Making & ProblemSolving
“Thinking is any mental activity that helps formulate or solve a problem, make a decision, or fulfill a desire to understand. It is a searching for answers, a reaching for meaning.” –Vincent Ryan Ruggiero
* Develop evidence to support views
* Analyze situations carefully
* Discuss subjects in an organized way
* Predict the consequences of actions
* Weigh alternatives
* Generate and organize ideas
* Form and apply concepts
* Design systematic plans of action
A 5 Step ProblemSolving Strategy
1. Specify the problem – the first step to solving a problem is to identify it as specifically as possible. It involves evaluating the present state and determining how it differs from the goal state.
2. Analyze the problem - analyzing the problem involves learning as much as you can about it. It may be necessary to look beyond the obvious, surface situation, to stretch your imagination and reach for more creative options.
* seek other perspectives (ask other people there opinion)
* be flexible in your analysis
* consider various strands of impact
* brainstorm about all possibilities and implications (use some brainstorm activities)
* Research problems for which you lack complete information. Get help.
3....

...Technology
ProblemSolving
Objectives
Outline the steps in problemsolving
Decompose a simple problem into its significant parts
Understand the variables, constants and data types used when solvingproblems on a computer.
Explain and develop algorithms
Represent algorithms in pseudocode or flowcharts
Topics to be covered
ProblemSolving
The Processing Cycle
Defining Diagrams
Algorithms
Pseudocode
Flowcharts
ProblemSolving
We are faced with different types of problems in our everyday life. Every problem requires a solution to resolve it. There maybe more than one solution to a problem.
Problem-solving involves identifying, analyzing and resolving problems using logic, reasoning skills and analytical skills.
A problem is a discrepancy between what is required and what exists. Problem can be simple or complex depending on its nature. A single-task problem is usually a relatively simple problem, whereas a multi-task problem is usually more complex and may require more resources to solve.
A solution is a procedure consisting of a set of instructions that, if followed in order, achieve the required result.
Problem...

...about generational differences in workplaces. Firstly, causes, which are the lack of understanding probably due to biases, common attitudes and tools of communication worth an in-depth investigation, followed by consequences of the problem, that is confusion, mistanding, and even confilcits of each other. Ultimately, solutions of the problem due to generational differences in a workplace will be delineated.
Communication is the conveying of ideas together with absorbing one’s opinions (Sinclair, 2001). ‘We have two ears and one mouth so that we can listen twice as much as we speak’ – to communicate effectively, we should put effort into listening to and thus understanding each other (Epictetus). However, an effective communication is exactly what is lacking between different generations, which is one of the major problems in a workplace.
First of all, generations do not understand one another well probably due to each’s biases against the others: the idea that the older generations are stubborn and reluctant to accept new opinions is deep-rooted among Gen Y-ers, the younger generations, while Gen X-ers, the older generations deem that the youngsters nowadays are lackadaisical. What must not be overlooked is that the mass media has worsened the problem by developing terms like “70s’”, “80s’” and “90s’” that encompass stereotypical and generalizing qualities regarding each group, causing even greater prejudice...