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Problem Solving Strategies
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- Pre-Algebra
More Problem-Solving Strategies: Look for a Pattern
- January 24, 2014
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One of the problem-solving strategies that is often used in math is to look for a pattern. Often when exploring problems, the student can notice a relationship between numbers. This relationship can help to solve the problem by shortening the number of steps it takes to get to a solution.
Step 1: Make a Table
The first step to look for a pattern is to make a table showing the relationships that are there. For example, suppose the problem were to find the next three numbers in the series 2, 4, 6, 8. They are related in a simple way, such that 2 +2 is 4 +2 is 6 +2 is 8. In order to extend the pattern, 8 +2 is 10, +2 is 12 +2 is 14. Therefore, the next three numbers are 10, 12, and 14.
Step 2: Find the Relationship Between Numbers
In the previous example, the relationship was very simple, as the pattern was the set of the first 7 even numbers. Each number in the series was separated by the same distance. Suppose the relationship weren’t quite as simple. This time, the numbers in the sequence are 1, 5, 14, 30, and 55. What are the next 3 numbers in the series? 1 +4 is 5 +9 is 14 +16 is 30 +25 is 55. The numbers aren’t even the same distance from one another.
Step 3: Make a Prediction
What do these numbers have in common? After finding a pattern, it’s possible to predict what the next numbers will be. Those differences 1, 4, 9, 16, and 25, have a pattern in themselves. They are the first 5 squared numbers, as 1 2 is 1, 2 2 is 4, 3 2 is 9, 4 2 is 16, and 5 2 is 25. So the next difference might be 6 2 or 36, and 55 + 36 = 91. The next squared number will be 7 2 , or 49, and 91 +49 = 140. The next squared number will be 8 2 or 64, and 140 + 64 = 204.
Step 4: Check the Answer
The sequence with the next three numbers is 1, 5, 14, 30, 55, 91, 140, and 204. The pattern fits in every step of the sequence. If the numbers were added carefully, it would be easy to check each one, as 1 + 4 is 5, 5 + 9 is 14, 14 + 16 is 30, 30 + 25 is 55, 55 + 36 is 91, 91 + 49 is 140, and 140 + 64 is 204. The next squared number would be 81 (9 2 ), and 204 + 81 is 285.
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Jul 4, 2021 • Download as PPTX, PDF •. 7 likes • 9,062 views. E. EFREN ARCHIDE. This presentation presents three common sequences-the Arithmetic sequence, the Geometric sequence and the Fibonacci sequence. Education. 1 of 12. Download now. Problem Solving with Patterns - Download as a PDF or view online for free.
1 of 26. Download now. Download to read offline. Mathematics in the Modern World Lecture 1. 1. Chapter 1: Nature of Mathematics Section 1.1 Patterns and Numbers in Nature and the World Anna Clarice M. Yanday Pangasinan State University August, 2018. 2.
Mathematics in the Modern World (Patterns and Sequences).pptx - Download as a PDF or view online for free. ... This ppt gives information about 1.principle of least square. 2.fitting of straight line. ... POLYA'S PROBLEM SOLVING TECHNIQUE • Understand the Problem • Devise a Plan • Carry out the Plan • Look Back
In this video you will learn to apply problem solving with patterns. References: Aufmann, R. (2018). Mathematics in the Modern World. Rex Publishing. Manil...
However, it is important to note that Polya's stages are flexible and not to be taken literally in linear order. To Polya, problem solving was a major theme of doing mathematics and "teaching students to think" was of primary importance. "How to think" is a theme that underlies much of genuine inquiry and problem solving in mathematics.
LEC 1 MMW - Lectures - Midterms coverage of Mathematics in the Modern World; Problem SET 1 Patterns AND Sequence ... It has its own rules, form, symbols, etc. It is amazing that the language of Math can be understood anywhere around the world! In this Chapter, Problem Solving and Reasoning, you will see Math as a tool that sharpens one's ...
Mathematics in the Modern World Lesson 1: Mathematics in Our. AI Homework Help. Expert Help. Study Resources. ... -A process of thinking -A set of problem-solving tools - An art -A language Numbers, Symbols, Operations, Sets, Notation, ... Patterns and Numbers in Nature Types of Patterns -Logical Pattern.
1 Mathematics in the Modern World Richard M. Oco, MAEM (Instructor) 2 Time: 5:30pm-7:00pm Day: Tuesday ... Download ppt "Mathematics in the Modern World" Similar presentations ... EXAMPLE 6 Solve a multi-step problem Job Earnings You have two summer jobs at a youth center. You earn $8 per hour teaching basketball and $10 per hour.
Download ppt "Problem Solving Strategies". Polya's Four-Step Model George Polya has had an important influence on problem solving in mathematics education. He noted that good problem solvers tend to forget the details and focus on the structure of the problem, while poor problem solvers do the opposite. Four-Step Process: 1.
Mathematics in the Modern World - Free download as Powerpoint Presentation (.ppt), PDF File (.pdf), Text File (.txt) or view presentation slides online. This document discusses patterns in nature and mathematics in the modern world. It begins with two quotes about the relationship between nature and mathematics. It then outlines five learning outcomes related to identifying patterns ...
Education. 1 of 10. Download now. Mathematics in the modern world. 1. This course deals with the nature of mathematics, appreciation of its practical, intellectual and aesthetic dimensions and applications of mathematical tools in daily life. The course begins with an introduction to the nature of mathematics as an exploration of patterns (in ...
MATHEMATICS-IN-THE-MODERN-WORLD.pptx - Free download as Powerpoint Presentation (.ppt / .pptx), PDF File (.pdf), Text File (.txt) or view presentation slides online. Scribd is the world's largest social reading and publishing site.
Use different types of reasoning to justify statements and arguments made about mathematics and mathematical concepts; 2. Write clear and logical proofs; 3. Solve problems involving patterns and recreational problems involving Polya's 4steps; 4. Organize one's methods and approaches for proving and solving problems.
Step 1: Make a Table. The first step to look for a pattern is to make a table showing the relationships that are there. For example, suppose the problem were to find the next three numbers in the series 2, 4, 6, 8. They are related in a simple way, such that 2 +2 is 4 +2 is 6 +2 is 8. In order to extend the pattern, 8 +2 is 10, +2 is 12 +2 is 14.
MMW Chap 3 Problem Solving and Reasoning - Free download as Powerpoint Presentation (.ppt / .pptx), PDF File (.pdf), Text File (.txt) or view presentation slides online.
PROBLEM SOLVING. Objectives: After going through this module, you are expected to: (1) Use different types of reasoning to justify statements and arguments. (2) Solve problems involving patterns and problems following Polya's Strategy. (3) Organize methods and approaches for solving problems. Inductive and Deductive Reasoning Inductive Reasoning
View ppt 07 Mathematics in the Modern World.pdf from BSIT 111 at AMA Computer University - Quezon City. MATHEMATICS IN THE MODERN WORLD Imelda B. Antonio Mary Hope H. Gravoso PROBLEM SOLVING ... • Draw a diagram. Polya's Problem Solving Strategy 3. Carry out the plan Once a plan has been devised it must be carried out. Polya's Problem Solving ...
Mathematics-in-the-modern-world.pptx - Free download as Powerpoint Presentation (.ppt / .pptx), PDF File (.pdf), Text File (.txt) or view presentation slides online. This document discusses the nature of mathematics. It states that mathematics is partly invented through early human representations of quantities, but also partly discovered through theorems like the Pythagorean theorem.
Download now. 1. Mathematics in our World. 2. Mathematics is … a set of problem- solving tools a language an art a study of patterns a process of thinking "Mathematics is the alphabet with which God has written the universe.". - Galileo Galilei. 3. The elephant and the blind men.
Mathematics in the Modern World - Free download as PDF File (.pdf), Text File (.txt) or read online for free. 1) Patterns are regular, repeated, or recurring forms found everywhere from nature to manmade designs. Studying patterns helps identify relationships and make predictions. 2) Symmetries are a type of pattern where different sides of something are alike, such as line or bilateral ...
mathematics in the modern world - Free download as Word Doc (.doc / .docx), PDF File (.pdf), Text File (.txt) or read online for free. 1. The document discusses patterns found in nature and how mathematics is used to describe them. It provides examples of symmetry, fractals, spirals, and the Fibonacci sequence, which are all common patterns seen in plants, animals, weather, and other natural ...