Chapter 2 Problem Solving Chapter 2 Problem Solving
Chapter 2 Problem Solving Chapter 2: Problem Solving 1
Problem Solving How To Solve It Chapter 2 Problem Solving 2
Problem Solving Process q Phase 1: Understanding the problem q Phase 2: Devising a plan q Phase 3: Carrying out the plan q Phase 4: Looking back Chapter 2 Problem Solving Process 3
1: Understanding the problem q What is the unknown? What are the data? q What is the condition? Is it possible to satisfy the condition? Is the condition sufficient to determine the unknown? q Draw a figure. Introduce suitable notation. Chapter 2 Phase 1: Understanding the problem 4
2: Devising a plan q How you seen the problem before? Do you know a related problem? q Look at the unknown. Think of a problem having the same or similar unknown. q Split the problem into smaller sub-problems. q If you can’t solve it, solve a more general version, or a special case, or part of it. Chapter 2 Phase 2: Devising a plan 5
3: Carrying out the plan q Carry out your plan of the solution. Check each step. q Can you see clearly that the step is correct? q Can you prove that it is correct? Chapter 2 Phase 3: Carrying out the plan 6
4: Looking back q Can you check the result? q Can you derive the result differently? q Can you use the result, or the method, for some other problem? Chapter 2 Phase 4: Looking back 7
Area of circle q What is the data? Side of square = 2 a q What is the unknown? Area of circle, C. 2 a q What is the condition? If radius r is known, C can be calculated. q How to obtain r? Chapter 2 Area of circle 8
Area of circle q Pythagoras’ theorem a r r 2 = 2 * a 2 a q Area of circle C = * r 2 = * 2 * a 2 Chapter 2 Area of circle 9
Pascal’s triangle 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 Chapter 2 n. C k Pascal's triangle = n! / (k! * (n-k)!) 10
NE-paths q To find number of NE-paths between any two points. C A Chapter 2 NE-paths 11
Creative thinking Most new discoveries are suddenly-seen things that were always there. A new idea is a light that illuminates presences while simply had no form for us before the light fell on them. Susan Langer Chapter 2 Creative thinking 12
Creative thinking Myths q Creativity requires genius q You have to be odd q Creative thinking isn’t rigorous, but uses simple processes Chapter 2 Creative thinking 13
Homework Try exercises behind chapter 2. Chapter 2 Homework 14
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