Problem Solving With and Without Mathematics

Problem Solving With and Without Mathematics An Idiot’s Guide To The Idiots Inside All Of Us, For Business and Everything Else Hopefully, this text and picture book will always be an e-book and a free book, until it becomes a video … book. Multimedia versions … with multiple dimensions … even more welcome … © 2016 Gain Knowledge Group. All Rights Reserved.

Created In Some Particular Order By: Albina Serikova, Adilet Smagulov, Aleksei Kunchenko, Alimzhan Mukhitbek, Alyona Li, Azhdar Janaev, Dawon Park, Eun Pyo Hong, Gleb Gadelshin, Hae Young Yun, Jaemyong Chang, Jungaye Jeong, Kainar Kaharman, Kihun Kang, Kristina Arjakova, Kyojin Shin, Navruzbek Mirzaev, Oleg Tyo, Shekhroz Bakhriddinov, Shukhrat Ergashov, Su Bin Lim, SunWoo Park, Timothy David Christian, Turlan Zhanessenov, Yerlan Alpysbayev, Zeyu Zhong, Zhang Yihai, Ravi Kashyap … Acknowledgements: Inputs from the following members was instrumental in establishing and developing this new course: Kyun-Hwa Kim, Andrew Isaak, Tom Steinberger, Xiangcai Meng, Kushal Sharma, Joshua Park, Nurmukhammad Yusupov, Chia-Hsing Huang and Jerman Rose. We could not have undertaken this mission in such a short duration without the help and support of all SolBridge Students / Staff / Faculty Members and all our loved ones …

Created For: Please check the title to see if this E-Book is for you. Created @: SolBridge

International School of Business

[Does it matter where this {E-Book} is from and from whom??? If it works for you, take it and use it … But before you do that … you first need to download it … as you try out … these techniques … in your own … laboratory … brain bakery … mind farm … Remember, where you get … buns and brains … mind the farm (s), which is (are) a lot more fun !!!] © 2016 Gain Knowledge Group. All Rights Reserved.

Topics for Discussion

– Earth Year … Nudge … The Forgotten His-Story … Beauty & (Love )The Beast …

– Inner Fish … Man the Van … Babysitting Complexity … Super Man / IQ Man …

– Cosmic Comic Business … The Bigger Problem … Why Problem Solving? …

– Thanksgiving … Mind The Final Frontier … Baby / Puppy … Flow Charts …

– Subconsciously Conscious or Consciously Unconscious … Success / Failure …

– Nonsense & Non-sense … The Luck Factor … Math Anxiety … Right / Wrong …

– A Technique for Producing Ideas … Transcendental Exponential (… Monsters) …

– Numbers are Prime … Matrices … Sinking Titanic By Induction … Logarithms …

– Being a Human Being … Pure Perception … Albert Einstein … Brain or Belly …

– Survival Senses … Involvement Quotient … Acres & Acres of Diamonds …

– Weed Problems … Smoking Ethics … Does Size Matter … Mars versus Venus …

– Thought Reading … Space Bending … W&@$ Holes !!! Sleeping Like A Koala …

– The Problem Solvers‘ Non-Hypocritic Hippocratic Oath. © 2016 Gain Knowledge Group. All Rights Reserved.

3

Introduction We consider the essential elements of problem solving that will be useful from a business perspective in addition to being applicable to other areas of life. The discussion (each week) revolves around certain well-known problems from real life scenarios and a demonstration of how trial and error techniques have been used to solve these problems. We then pick simple mathematical tools that be applied to solve these problems. The idea is to understand how the intuition that all of us possess can be developed and elegant solutions can be obtained by applying simple mathematical results. The goal is to introduce to everyone (and help them develop an appreciation of) some basic mathematical techniques that can be useful towards the solving of real life problems. This course is being offered as an elective. This course (set of discussions) is meant to be completely self-contained and all the required concepts will be introduced and developed in the class (sections below). We will learn how to solve problems and we will learn about decision making and human behavior so that the solution techniques can be applied to business and everyday problems. There will be topics covered from many fields including: marketing, psychology, operations, management, finance, literature, artificial intelligence, mathematics, economics, physics, biology, etc. The prescribed textbooks and reading material are meant to illustrate techniques regarding how problems can be solved and to develop a good understanding of the environment in which these problems operate including the agents related to these problems. We also look at how problems are created in many situations, which can then be a business opportunity. Hence, the textbooks are about problem solving and people from a business perspective, which is the field of behavioral economics. The essential requirement for reading this course is to have curiosity and a willingness to participate in the exercises with the objective of trying to find solutions independently. This course is open to people from all disciplines. The only mathematical skill required for this course is familiarity with addition. At the end of this course, students (almost everyone in society if we define students as someone that wants to continue learning) will: 1.Understand the importance of trial and error in solving problems. 2.Develop an appreciation of simple mathematical tools that can complement the intuition behind solving business problems. 3.Develop the ability to approach new problems and come up new tools that might be necessary, on their own. Comprehend how new problems keep arising in real life situations as old problems are solved and the importance of human behavior in the creation and solution of many problems. (An unintended consequence might be starting to believe that mathematics can become simple with minimal effort to understand the steps and the notation). 4.Develop an appreciation of behavioral economics, which illustrates how the beliefs of agents can have a great influence on how any social system operates. 5.Develop the skills to apply these techniques to business situations. © 2016 Gain Knowledge Group. All Rights Reserved.

Earth Year

© 2016 Gain Knowledge Group. All Rights Reserved.

Inner Fish • “Take the entire 4.5-billion-year history of the earth and scale it down to a single year, with January 1 being the origin of the earth and midnight on December 31 being the present. Until June, the only organisms were single-celled microbes, such as algae, bacteria, and amoebae. The first animal with a head did not appear until October. The first human appears on December 31. We, like all the animals and plants that have ever lived, are recent crashers at the party of life on earth.” • ― Neil Shubin, Your Inner Fish: A Journey Into the 3.5-Billion-Year History of the Human Body © 2016 Gain Knowledge Group. All Rights Reserved.

Seem Familiar


Seem Somewhat Less Familiar


A Nudge • Thaler and co-author Cass Sunstein define it as a choice “that alters people’s behavior in a predictable way without forbidding any options or significantly changing their economic incentives.” • The important thing about nudges? They're not mandates. Nudges don't attempt to make it impossible to do the wrong thing, but rather they make it easier to do the right thing. • This same principle can be applied to any number of other choices, big and small, that people make in the course of their lives. To nudge people to save for retirement, you can automatically enroll them in a 401(k) plan when they start a new job. To nudge people into using less energy, you can show them how much electricity they consume relative to their neighbors. To nudge them toward better eating habits, make the healthy food options easier to reach in cafeterias. © 2016 Gain Knowledge Group. All Rights Reserved.

Baby / Puppy


What? Where? When? Why? • • • •

What did the puppy say? Where did this story happen? When did this story happen? Why ... ?


Conscious and Sub-Conscious • Who we are? • Amma / Appa

• Does Sophia (First Robot Citizen of Saudi Arabia) have a SubConscious? • Wonderful that Sophia and her like will be around more … • If we are Consciously Unconscious, • If we are Sub-Consciously Unconscious, • If we are Consciously Conscious, – Then we can do a lot … but can we do more …

• If the Sub-Conscious becomes Conscious then …


Problem Types • Simplistic: Who is the president of USA? • Deterministic: What is the area of the land on which SolBridge is built? • Random: Who will be the next president of the USA? • Indeterminate: Should the US continue with its trade policy? • What should be the ideal age for retirement?


Risky Sports • • • • • • • •

Motorcycle Racing Horse Racing Sky Diving Mountain Climbing Boxing Scuba Diving American College Football Hang Gliding


Risky Sports --- Ranked • • • • • • • •

Boxing American College Football Motorcycle Racing Scuba Diving Mountain Climbing Hang Gliding Sky Diving Horse Racing


Mind Expansion … Problem Solving is similar to Walking, Talking …? Success and Failure … Does not matter what you did in other courses. All the material is completely self contained. It helps to know some techniques but we should be open to other avenues… Why Problem Solving? Why Anything? © 2016 Gain Knowledge Group. All Rights Reserved.

Thanksgiving “Problems may not seem good on the surface; but where there are problems there are opportunities …” Who are the problems creators then? Who is doing the problem maintenance? How do we thank them? Also let us keep in mind that it is easy (relatively easier, perhaps) to create and even maintain problems, but solving them takes a lot of effort and skill …


Problems and Profits … “Problems may not seem good on the surface; but where there are problems there are opportunities …” The space of Business Problems can be bigger than all other problems since … In Business, we need to solve problems and then make profits on top of that. This makes it the bigger problem … © 2016 Gain Knowledge Group. All Rights Reserved.

Space Walking or Writing?

“Which is harder?”


The Space Pen … Paul C. Fisher and his company, the Fisher Pen Company, reportedly invested $1 million to create what is now commonly known as the space pen. Pencils may not have been the best choice anyway. The tips flaked and broke off, drifting in microgravity where they could potentially harm an astronaut or equipment. And pencils are flammable--a quality NASA wanted to avoid in onboard objects after the Apollo 1 fire. Unlike most ballpoint pens, Fisher's pen does not rely on gravity to get the ink flowing. The cartridge is instead pressurized with nitrogen at 35 pounds per square inch. This pressure pushes the ink toward the tungsten carbide ball at the pen's tip. The ink, too, differs from that of other pens. Fisher used ink that stays a gel-like solid until the movement of the ballpoint turns it into a fluid. The pressurized nitrogen also prevents air from mixing with the ink so it cannot evaporate or oxidize. What should be the cost of such a pen?


Space: The Final Frontier? When did man travel to space for the first time?


Space: The Timeline …


Space Explorers …


The Forgotten History Wan decided to take advantage of China's advanced rocket and fireworks technology to launch himself into outer space. He supposedly had a chair built with forty-seven rockets attached. On the day of lift-off, Wan, splendidly attired, climbed into his rocket chair and forty seven servants lit the fuses and then hastily ran for cover. There was a huge explosion. When the smoke cleared, Wan and the chair were gone, and was said never to have been seen again


Why is His-Story Forgotten? If His-Story is not relevant to our story, why do We care? So perhaps, the real way to learn history is through stories that pass on the message in a way such that it is connected to our everyday lives, not by timelines and dates.


Mind: The Final Frontier? The forgotten heroes. The fallen angels … What we can do? Why we need to do it? The “How to do it?” will follow along … Any achievement has to first happen in our imagination.


What? Watt?First Steam Engine?

A model of a beam engine featuring James Watt's parallel linkage for double action.[1


In 1781 Scottish engineer James Watt patented a steam engine that produced continuous rotary motion.[5] Watt's tenhorsepower engines enabled a wide range of manufacturing machinery to be powered. The engines could be sited anywhere that water and coal or wood fuel could be obtained. By 1883, engines that could provide 10,000 hp had become feasible.[6] The stationary steam engine was a key component of the Industrial Revolution, allowing factories to locate where water power was unavailable. The atmospheric engines of Newcomen and Watt were large compared to the amount of power they produced, but high-pressure steam engines were light enough to be applied to vehicles such as traction engines and railway locomotives

Watt Not !!! Steam ejected tangentially from nozzles caused a pivoted ball to rotate. Its thermal efficiency was low. This suggests that the conversion of steam pressure into mechanical movement was known in Roman Egypt in the 1st century. Heron also devised a machine that used air heated in an altar fire to displace a quantity of water from a closed vessel. The weight of the water was made to pull a hidden rope to operate temple doors.[4][5] Some historians have conflated the two inventions to assert, incorrectly, that the aeolipile was capable of useful work

The earliest known rudimentary steam engine and reaction steam turbine, the aeolipile, is described by a mathematician and engineer named Heron of Alexandria (Heron) in 1st century Roman Egypt, as recorded in his manuscript Spiritalia seu Pneumatica © 2016 Gain Knowledge Group. All Rights Reserved.

A TECHNIQUE FOR PRODUCING IDEAS


29


Eureka … The exclamation 'Eureka!' is attributed to the ancient Greek scholar Archimedes. He reportedly proclaimed "Eureka! Eureka!" after he had stepped into a bath and noticed that the water level rose, whereupon he suddenly understood that the volume of water displaced must be equal to the volume of the part of his body he had submerged. (This relation is not what is known as Archimedes' principle—that deals with the upthrust experienced by a body immersed in a fluid.[2][3]) He then realized that the volume of irregular objects could be measured with precision, a previously intractable problem. He is said to have been so eager to share his discovery that he leapt out of his bathtub and ran naked through the streets of Syracuse. Archimedes' insight led to the solution of a problem posed by Hiero of Syracuse, on how to assess the purity of an irregular golden votive crown; he had given his goldsmith the pure gold to be used, and correctly suspected he had been cheated by the goldsmith removing gold and adding the same weight of silver. Equipment for weighing objects with a fair amount of precision already existed, and now that Archimedes could also measure volume, their ratio would give the object's density, an important indicator of purity (as gold is nearly twice as dense as silver and has significantly greater weight for the same volume of matter at standard temperatures and pressure). © 2016 Gain Knowledge Group. All Rights Reserved.

Good News … The creation of ideas is a process, not an accident. What we think of as Intuition is a series of steps that can be taught and repeated. The quality of ideas though is the result of all our life experiences … What we can do is make the most of our natural gifts and environmental upbringing. © 2016 Gain Knowledge Group. All Rights Reserved.

Background… Book written in the 1940s James Young was approached by someone who asked how he gets ideas … It seemed like a funny and naïve question … Do ideas just appear on the surface of the mind? Just like an island of Coral (Atoll) pops out of the sea. The formula for ideas is so simple to state, that few who hear it will really believe it. While simple to state, it requires rigorous thinking and habits to follow it, so even people who accept it do not apply it.


The Pareto theory


Types of people by Pareto

Speculator


Rentier

The speculator according to Pareto

◉ ◉ ◉ ◉ ◉

Speculative type of person Constantly pre-occupied with the possibilities of new combinations Not only the business enterprisers and also political, diplomatic reconstructions.


The rentier according to Pareto

◉ ◉ ◉ ◉

Stockholder Steady-going Unimaginative Conserving people

Training the mind What are the means of developing it?

Train the Mind in the Methods and Grasp the General principles

◉ Idea is a new combination of old elements, nothing more nor less ◉ The ability to make new combinations is important ◉ The ability to see relationships or connections …

Five Steps for producing ideas

◉ ◉ ◉ ◉ ◉

Gather raw material The mental digestive process Gestate Gaze up at the new idea Grow your idea


1. Gather

◉ ◉ ◉ ◉ ◉ ◉ ◉ ◉

Gather raw material Two kinds: Specific and general Specific to your product/expert/industry Can you describe the difference between two cab drivers you have met recently? What can be said about a new soap advertisement you have to create? Combination of specific knowledge with general knowledge about life and events. Gathering general materials is the continuous process of being interesting in everything. Gathering materials: Part of it is current; part of it is life-long

Kaleidoscope

◉ ◉ ◉ ◉ ◉

Is an instrument which used for getting new models -Little pieces of colored glass -Geometrical designs -Possibilities for new and striking combinations The construction of an idea is the construction of a new pattern in this kaleidoscopic world in which we live. ◉ What happens if we have more colored glass?

Practical suggestions for the first step

◉ ◉ ◉ ◉ ◉ ◉ ◉

Card-index method -get 3x5 ruled white cards -write in them all specific information Storing up method -indexing and cross-indexing Google Drive Ex: The famous scrapbooks of Sherlock Holmes

In solving a problem of this sort, the grand thing is to be able to reason backwards. That is a very useful accomplishment, and a very easy one, but people do not practice it much. — Sherlock Holmes, in Sir Arthur Conan Doyle's

2. The mental digestive process

◉ Move the combination around like a puzzle ◉ See if and how the pieces fit together ◉ Partial ideas will come first. Put them down on paper. Never mind how crazy they seem. Look to put the pieces of the puzzle together. Don’t give up. ◉ This is also when people zoom off: Get absent minded.

3. Gestate

◉ This happens entirely in your head, so.. ◉ Create “white space” for your mind to do its work. ◉ Plan times to unplug. ◉ Take walks, listen to music, watch a movie?, play video games, do a lot of relaxing activities. ◉ Whatever stimulates your emotions and imagination. ◉ Sherlock Holmes would drop everything and head to a concert with Watson.

4. Gaze up at the new idea ○ The new idea will appear “out of nowhere” ○ Recognize it, gaze upon it, inspect it closely, don’t change it too quickly. ○ “This is the way ideas come: after you have stopped straining for them, and have passed through a period of rest and relaxation from the search”-Yuoung ○ Remember Archimedes in the bathtub … ○

5. Grow your idea (the final stage) ○ It may not be as perfect as it seemed when it first appeared ○ This is where good ideas often get lost ○ Be patient ○ Submit your idea for criticism and critique.

Lastly ○ Remember: Words are Ideas too!!!. ○ Someone tried reading a dictionary and said he could not get a hang of the story simply missed the point: namely it is a collection of very short stories.

THE LUCK FACTOR


50

Good and Bad Fortune … • A ten-year scientific study into the nature of luck has revealed that, to a large extent, • People make their own good and bad fortune. The results also show that it is • Possible to enhance the amount of luck that people encounter in their lives. • Can we accept this?


Buffet(t) on the Street … • The man did indeed turn out to be Warren Buffett, and the chance meeting proved highly fortuitous because about a year later Buffett agreed to buy Helzberg’s chain of stores. • And all because Helzberg just happened to be walking by as a woman called out Buffett’s name on a street corner in New York.


Chance … • “Some of the most important determinants of life paths often arise through the most trivial of circumstances.” • Lucky charms, amulets, and talismans have been found in virtually all civilizations throughout recorded history. • Touching (“knocking on”) wood dates back to pagan rituals that were designed to elicit the help of benign and powerful tree gods. • The number thirteen is seen as unlucky because there were thirteen people at Christ's last supper. • When a ladder is propped up against a wall it forms a natural triangle which used to be seen as symbolic of the Holy Trinity. • To walk under the ladder would break the Trinity and therefore bring ill fortune. © 2016 Gain Knowledge Group. All Rights Reserved.

A little bit of… • Lady Luck in our lives … • Why Luck is referred to as a Lady will need another book, but is briefly discussed in the section, “Being a Human Being” … • Throughout history, people have recognized that good and bad luck can transform lives. A few seconds of ill fortune can lay waste years of striving, and moments of good luck can save an enormous amount of hard work • Coin Toss and Black / White Cat


What would Sherlock Holmes Do? • Investigate … • Advertisements calling for exceptionally lucky or unlucky people. • 400 participants; the youngest eighteen, a student, the oldest eighty-four, a retired accountant. • Patricia, twenty-seven, has experienced bad luck throughout much of her life. A few years ago, she started to work as cabin crew for an airline, and quickly gained a reputation as being accident-prone and a bad omen. One of her first flights had to make an unplanned stopover because some passengers had become drunk and abusive. Another of Patricia’s flights was struck by lightning, and just weeks later a third flight was forced to make an emergency landing. © 2016 Gain Knowledge Group. All Rights Reserved.

Thoughts and Behavior • Responsible for much of our fortune? • Lucky people generate their own good fortune via four basic principles. They are skilled at creating and noticing chance opportunities, make lucky decisions by listening to their intuition, create self-fulfilling prophesies via positive expectations, and adopt a resilient attitude that transforms bad luck into good. • I gave both lucky and unlucky people a newspaper, and asked them to look through it and tell me how many photographs were inside. On average, the unlucky people took about two minutes to count the photographs whereas the lucky people took just seconds. Why? Because the second page of the newspaper contained the message “Stop counting – There are 43 photographs in this newspaper.” This message took up half of the page and was written in type that was over two inches high. © 2016 Gain Knowledge Group. All Rights Reserved.

Anxious … Tense … • Anxiety disrupts people’s ability to notice the unexpected • People were asked to watch a moving dot in the center of a computer screen. Without warning, large dots would occasionally be flashed at the edges of the screen. Nearly all participants noticed these large dots. The experiment was then repeated with a second group of people, who were offered a large financial reward for accurately watching the center dot. This time, people were far more anxious about the whole situation. They became very focused on the center dot and over a third of them missed the large dots when they appeared on the screen.

• The harder they looked, the less they saw … • Unlucky people go to parties intent on finding their perfect partner and so miss opportunities to make good friends. They look through newspapers determined to find certain type of job advertisements and as a result miss other types of jobs. • Lucky people are more relaxed and open, and therefore see what is there rather than just what they are looking for. © 2016 Gain Knowledge Group. All Rights Reserved.

Randomness to Luck • Lucky participants went to considerable lengths to introduce variety and change into their lives. • One person noticed that noticed that whenever he went to a party, he tended to talk to the same type of people. To help disrupt this routine, and make life more fun, he thinks of a color before he arrives at the party and then chooses to only speak to people wearing that color of clothing at the party! • Collecting apples from an orchard


Bronze or Silver in the Olympics • Which one do you think makes a person more happy? • Bank Robbery!!! You get shot in the arm. Is this lucky or unlucky?


All in the Mind … • Lucky people tend to imagine spontaneously how the bad luck they encounter could have been worse and, in doing so, they feel much better about themselves and their lives. This, in turn, helps keep their expectations about the future high, and, increases the likelihood of them continuing to live a lucky life.


Luck School … • Series of experiments examining whether people’s luck can be enhanced by getting them to think and behave like a lucky person • Met up with participants on a one-to-one basis, and asked them to complete standard questionnaires measuring their luck and how satisfied they were with six major areas of their life. • Described the four main principles of luck, explained how lucky people used these to create good fortune in their lives, and described simple techniques designed to help them think and behave like a lucky person • Eighty percent of people were now happier, more satisfied with their lives, and, perhaps most important of all, luckier. Unlucky people had become lucky, and lucky people had become even luckier.


Positive Skepticism • Skepticism can play a positive role in people’s lives. The research is not simply about debunking superstitious thinking and behavior. Instead, it is about encouraging people to move away from a magical way of thinking and toward a more rational view of luck


TOOLS AND TECHNIQUES


63

Sense and Non-Sense • I walked to the bank. No one was there. It was Tuesday. A woman spoke to me in a Foreign Language. I dropped a camera and when, I stooped to pick it up, the music began. It has been a long war. But my children were safe.


Sense and Sensible .. • The end of World War II had just been declared. I was in a little French town on my way to a bank. That Tuesday happened to be a French national holiday, so the bank was closed. A French woman, celebrating the armistice, handed me her camera and asked me to take a photograph of her and her husband. I accidentally dropped the camera, at which point the French Marseillaise began playing from a loud speaker in the center of the town. I was touched with emotion. My two sons had fought with American forces. It has been a long war, but they were safe.


Major Factors and Issues • Car Accident • Factors are situations that can cause the problem. • Issues are derived from the factors.


Three Techniques • Problem Restatement • Pros and Cons • Convergent / Divergent Thinking


Problem Restatement -- Pitfalls • Water Bed Anecdote • Consider from whose viewpoint the problem is originating. Who are the stake holders? • No Focus --- Too Vague or Broad (What should we do about computers in the classroom?) • Focus is misdirected --- Definition is too narrow. Grades are slipping. How can we get him to study harder? • Assumption Driven --- How can we make people aware of our product? • Solution Driven --- How can we persuade government to reduce prison overcrowding?


Problem Restatement --- Tools • Paraphrase (Rewrite question with other words to have same meaning). How can we limit congestion on the roads? • 180 Degrees (How can we encourage people to attend the Business Plan competition?) • Broaden the Focus (Change Jobs or Have Job Security?) • Redirect the Focus (Boost Sales or Cut Costs?) • Ask “Why” we want to solve this problem?


PIP…. The Star is above the plus * + The Star is above the plus + *


Positive is Preferable … Experiments have shown that humans take longer to process a negative thought than a positive one. When we try to verify something, we assume it is true and match it against facts. If they match we stop. If it is false, we take extra steps to revise our assumptions.


Man the Van !!! • In teams of three of four: • Your Business is a Frozen Foods Business. (Feel Free to Consider other Products) • One person is head of Sales and Delivery • One person is CEO • One person is CAO (head of budgeting, finance etc) • One person is head of Operations • Discuss whether your business needs a new van or a truck?


Pros and Cons 1. List all the Pros 2. List all the Cons 3. Review and Consolidate the Cons, Merging and Eliminating 4. Neutralize as many Cons as Possible 5. Compare the Pros and Unalterable Cons 6. Pick one Option


Six Steps Example – One: Pros Truck is better than van because: 1.Has three to four times the load capacity of van. 2.Can handle expected growth in sales? 3.Advertising on truck will be more effective than on a van.


Six Steps Example – Two: Cons

Truck is worse than van because: 1.Gets less mileage per gallon of fuel 2.Maintenance and repair are more costly 3.Purchase price is three times greater 4.Fuel costs are greater 5.Is wasteful because truck might not always be filled to capacity 6.Is more difficult to drive: More accidents and more damage to the vehicle; More difficult to find and keep qualified drivers 7.Liability is greater (costs when payments need to be made) 8.Insurance is more costly 9.State and local taxes are greater [registration / licensing] 10.Competitors are expanding their delivery fleet with vans © 2016 Gain Knowledge Group. All Rights Reserved.

Six Steps Example – Three Review / Consolidate / Merge / Eliminate Truck is worse than van because: Gets less mileage per gallon of fuel Fuel costs are greater •Liability is greater (costs when payments need to be made) •Insurance is more costly 1.Competitors are expanding their delivery fleet with vans


Six Steps Example – Four (Neutralize) Truck is worse than van because: 1.Gets less mileage per gallon of fuel 2.Maintenance and repair are more costly Design delivery routes that are more cost effective

3.Purchase price is three times greater 4.State and local taxes are greater [registration / licensing] It has greater capacity; it is more efficient and profitable

5.Is wasteful because truck might not always be filled to capacity. Design better usage pattern and delivery routes.

6.Is more difficult to drive: More accidents and more damage to the vehicle; More difficult to find and keep qualified drivers No Fix

7.Liability is greater (costs when payments need to be made) No Fix © 2016 Gain Knowledge Group. All Rights Reserved.

Six Steps Example – One: Pros

Van Pros: 1.Gets more mileage per gallon of fuel 2.Maintenance and repair are less costly 3.Purchase price is one third of Truck 4.Is less difficult to drive: Less accidents and less damage to the vehicle; Less difficult to find and keep qualified drivers 5.Insurance is less costly 6.State and local taxes are lesser [registration / licensing]


Six Steps Example – Two: Cons Van Cons: 1.Has only third or fourth the load capacity of Truck. 2.Cannot handle expected growth in sales? 3.Advertising on van will be less effective than on a Truck.


Six Steps Example – Three Nothing to Review / Consolidate / Merge / Eliminate for Van Pros and Cons


Six Steps Example – Four: Neutralize Van Cons: 1.Has only third or fourth the load capacity of Truck. No Fix

2.Cannot handle expected growth in sales? No Fix

3.Advertising on van will be less effective than on a Truck. No Fix


Status Quo Pros: 1. No need for additional funds for purchase 2. No additional tax payments 3. No additional maintenance and repair costs 4. No need to hire skilled driver Cons: 1. Deliveries are falling ever further behind sales. Nothing to Review / Consolidate / Merge / Eliminate No Fix for the Cons: Deliveries are falling ever further behind sales.


Work Force 1. Should your new company have a work force made of only part-time or full-time employees? 2. You want to open a new restaurant. How could you choose a location for your restaurant?


Convergent and Divergent • We are focusing in one Factor • We are still collecting other Factors


Convergent and Divergent • • • •

The more ideas the better Build one idea upon another Wacky ideas are okay Don’t evaluate ideas (just yet)


Bicycle Marks


FLOW CHARTS


87

One Ball with Different Weight Find Ball with Different Weight

Put Three / Three in Each Pan

Check the Weight

same

different

same

Check the Weight

Replace Other Three to Right Pan

There is no Problem

different

Pick Three from Right Pan

Pick Three from Right Pan.

Remove / Add Three to Other Pan Was right Pan Heavier Check the Weight

No

Put Two From Right Pan into Each Pan. Keep Third On Standby

Yes Check the Weight

Put Two From Right Pan into Each Pan. Keep Third On Standby

?

Third Ball is Lighter Than All Nine

different same Check the Weight

Third Ball is Heavier Than All Nine

different


same

Ball in Heavier Pan is Heavier Than All Nine

Ball in Lighter Pan is Lighter Than All Nine

?

One Ball … (Continued) same

Check the weight

There is no problem

different Pan is heavier

Pick 3 balls Yes

Put 2 from pan in each pan, without 3rd same

Put 2 from right pan different Ball is heavier than all 9

No

Check the weight

3rd ball is lighter than all 9

different Check the weight

Ball is lighter than all 9

same

3rd ball is heavier than all 9 © 2016 Gain Knowledge Group. All Rights Reserved.

89

A

B

C

D

E

Find ball with different weight

Pick 2 groups

F

G

H

I

It means this one (I) is heavier

same

1. Make 3 groups with 3 balls each (A to C, D to F, G to I)

different Check the weight 1 vs 1

Know which ball is heavier than all 9 (I)

same Means group #3 has heavier ball

Check the weight

different

same Check the weight

One side is heavier

1 vs 1

Know (D) the heaviest ball

different

Know (D) the heaviest ball © 2016 Gain Knowledge Group. All Rights Reserved.

90

Don’t Worry Be Happy …


More Space …


Pictures And No Words A Picture is a Thousand Words…


More Tire Marks … No More


Choice of Produce


Parents on Facebook


Finding a Video on YouTube


Is Number “N” Even or Odd?


Flow Chart for Factorial


Flow Chart to Find all Prime Numbers till N


MATH ANXIETY: WHAT, WHO, WHY AND HOW? © 2016 Gain Knowledge Group. All Rights Reserved.

101

What is It? • For people with math anxiety, opening a math textbook or even entering a math classroom can trigger a negative emotional response, but it does not stop there. Activities such as reading a cash register receipt can send those with math anxiety into a panic. Math anxiety is an adverse emotional reaction to math or the prospect of doing math • Despite normal performance in most thinking and reasoning tasks, people with math anxiety perform poorly when numerical information is involved. • Is Math anxiety simply a proxy for low math ability?


Maybe !!! But Mostly Not !!! • Yet low math ability is not the entire explanation for why math anxiety and poor math performance co-occur. It has been shown that people’s anxiety about doing math – over and above their actual math ability – is an impediment to math achievement • When faced with a math task, math anxious individuals tend to worry about the situation and its consequences. These worries compromise cognitive resources, such as working memory, a short-term system involved in the regulation and control of information relevant to the task at hand. When the ability of working memory to maintain task focus is disrupted, math performance often suffers


Who? When? Why? • Progress in understanding how math anxiety relates to math performance. • Determining who is most likely to develop math anxiety, “when they will develop it, and why?” is essential for gaining a full understanding of the math anxiety phenomenon and its role in math achievement.


The First Years … • Elementary school years are critical for learning basic mathematical skills. • Until recently the dominant view among educators and researchers alike was that math anxiety only arose in the context of complex mathematics (e.g. algebra) and thus was not present in young children. • Math anxiety was thought to develop in junior high school. • Children as young as first grade report varying levels of anxiety about math, which is inversely related to their math achievement. • This anxiety is also associated with a distinct pattern of neural activity in brain regions (amygdala) associated with negative emotions and numerical computations © 2016 Gain Knowledge Group. All Rights Reserved.

With and Without … • All of you noticed the “Without Mathematics” • Most teachers are also anxious about teaching mathematics!!! • Female students of highly math anxious female teachers (>90% of elementary teachers in the USA are female) who tended to endorse the stereotype that ‘boys are good at math, girls at reading”


How about Adults? • In adults, math anxiety is associated with deficits in one or more of the fundamental building blocks of mathematics. • For example, adults who are math anxious are worse than their non-anxious peers at counting objects, at deciding which of two numbers represents a larger quantity, and at mentally rotating 3D objects • People who are unfamiliar with a particular domain are often easily swayed by negative emotions. They pick up on social cues that highlight math in negative terms.


The Cure !!! • Bolstering basic numerical and spatial processing skills may help to reduce the likelihood of developing math anxiety. • Early identification of at-risk students (coupled with targeted exercises designed to boost their basic mathematical competencies and regulate their potential anxieties) may help to prevent children from developing math anxiety in the first place. • Regulation of the negativity associated with math situations may increase math success, even for those individuals who are chronically math anxious • When simply anticipating an upcoming math task, math anxious individuals who show activation in a frontoparietal network known to be involved in the control of negative emotions perform nearly as well as their non-anxious counterparts on a difficult math test. © 2016 Gain Knowledge Group. All Rights Reserved.

Write about Your Emotions • Writing is thought to alleviate the burden that negative thoughts place on working memory by affording people an opportunity to re-evaluate the stressful experience in a manner that reduces the necessity to worry altogether • Test anxious high school students write about their worries prior to an upcoming final exam boosted their scores from B– to B+ (even after taking into account grades across the school year) • Simply telling students that physiological responses often associated with anxious reactions (e.g. sweaty palms, rapid heartbeat; frustration and confusion) are beneficial for thinking and reasoning can improve test performance in stressful situations. • Viewing a math test as a challenge rather than a threat, the better, not worse, is their performance © 2016 Gain Knowledge Group. All Rights Reserved.

Solution … Most (All ) Problems

• Get rid of the anxiety, the problem will take care of itself … • By ignoring the powerful role that anxiety plays in mathematical situations, we are overlooking an important piece of the equation in terms of understanding how people learn and perform mathematics.


NUMBERS: RATIONAL OR IRRATIONAL


111

Write Flow Chart to Find Factorial • N!=N*(N-1)*…1 • Computers can only multiple two numbers at a time.


Square Root of a Number • Create Algorithm to find square root of a number. • n*n=m


Square Root of a Number • You have a 3 and a 5 litre water container, each container has no markings except for that which gives you it's total volume. You also have a running tap. You must use the containers and the tap in such away as to exactly measure out 4 litres of water. How is this done? Can you generalise the form of your answer?


NUMBERS: PRIME OR NOT PRIME


115

Square Root two is Irrational?


Prime Divisible by 24

• If p is a prime number bigger than3, then (p^2 – 1) is divisible by 24.


Show Not Prime or Composite

• N^4 + 4^n, n >1


Find all such Primes

• Find all prime numbers p such that 2p+1 is a perfect square.


Find all Prime Numbers