problem solving with patterns mathematics in the modern world

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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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Mathematics in the modern world / Ethel Cecille Baltazar, Carmelita Ragasa, Justina Evangelista.

• Baltazar, Ethel Cecille M [author]
• Ragasa, Carmelita [author]
• Evangelista, Justina [author]
• 9789719810728 (pbk.)
• Mathematics
• Mathematics -- Popular works
• QA39.3 B21 2018
• Click here to view the table of contents
• Holdings ( 3 )
• Title notes ( 6 )

Includes bibliographical references and index.

Preface -- Chapter 1: The nature of mathematics -- Chapter 2: Mathematical language and symbols -- Chapter 3: Problem solving and reasoning -- Chapter 4: The statistical tools -- Chapter 5: The mathematical of graphs -- Chapter 6: Apportionment and voting -- Chapter 7: The mathematics of patterns and symmetries -- Chapter 8: The beauty of codes -- Chapter 9: Linear programming -- Chapter 10: Mathematical system -- References -- Index -- The authors.

"What is mathematics? Where can it be found? What is it for? What is it about? How is it done? Who uses it? These are just some of the essential questions that Mathematics in the Modern World aims to answer. The book covers the mandated topics and some of the elective ones which are all organized in a logical fashion. In particular, topics include the nature of mathematics, mathematical language and symbols, problem solving and reasoning, statistical tools, graphs, apportionment and voting, patterns and symmetries, coding, linear programming, and mathematical system. Written in a lucid manner, the book will surely enable students to understand not only the concepts presented but more importantly their application to everyday lives. Finally, it offers a wide array of exercises designed to reinforce lessons, introduce topics, and recognize and celebrate the place of mathematics in the modern world."--Back cover.

Fund 164 C&E Publishing, Inc. Purchased 01/08/2021 78739 PNR PHP 375.00 2020-11-467 2021-1-0061 copy 1

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It contains both radial and bilateral symmetry.

These are numbers that are used to measure the number of elements in a given set.

It is a declarative statement that is true or false but not both.

Proposition

Preposition

Disjunction

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Contradiction

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Biconditional

Conditional

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It is the main component of logic in mathematics.

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Two sets, say A and B, are said to be joint sets if they are mutually exclusive.

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True, at all situations

True, but there are exemptions

False, at all situations

False, but there are exemptions

It is the set of all elements under discussion.

In union of sets, elements are not repeated in a set.

It is the value of the golden ratio.

An example of non-reflexive relation statement.

is the father of

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Ordered Pair

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For some x, P(x)

None of these

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some planets are not terrestrial

all planets are not terrestrial

M is an invertible marix. Therefore,

all matrices are invertible

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some matrices are not invertible

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if p then q

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Given f(t) = t 2 − t and h(x) = 3x + 2, evaluate f(h(1)).

What is the next letter in the series; A, D, I, L?

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Find the 30th term of the arithmetic sequence, 10, 7, 4...

In a town of 605 people, 285 people eat hamburger and 212 people eat pizza and 127 people eat chicken, 20 people eat hamburger and chicken, 29 people eat hamburger and pizza and 35 people eat pizza and chicken. 50 people does not eat any of these foods and 15 people eat all kinds of foods. How many people eat one food?

Illustrate using a venn diagram the relationship between cabbage, food and vegetable.

Select from four alternative diagrams, the one that best illustrates the relationship among the three classes : Dove , Aviary, Dogs

What is the next pattern?

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