2023-09-15T12:38:30+03:00[Europe/Moscow] en true <p>logic</p>, <p>reasoning</p>, <p>inductive or deductive</p>, <p><strong><em><u>not </u></em></strong><u>the study of persuasion</u> and manipulative manipulative rhetorical devices</p><p>successful argument’ does not mean persuasive argument</p>, <p>Human fallibility and manipulative rhetoric</p>, <p>T</p>, <p>1. Inductive reasoning</p><p>2. Deductive reasoning</p>, <p>inductive</p>, <p>deductive</p>, <p>inductive reasoning uses <u>patterns </u>to arrive at a conclusion (conjecture) </p><p></p><p>deductive reasoning uses <u>facts, rules</u>, definitions or properties to arrive at a conclusion</p>, <p>30 degrees, deductive</p>, <p>shade at lower left, inductive</p>, <p>deductive</p>, <p>inductive</p>, <p>inductive</p>, <p>inductive</p>, <p>deductive</p>, <p>inductive</p>, <p>1. 452. no, the tsunami height would be negative and height can never be negative3. minimum is 7.4 wherein the max tsunami height is 14. inductive</p>, <p>Not always true. If x = 0, the result is not equal to 1.</p>, <p>not true</p>, <p>the number is a multiple of 5</p>, <p>1. sequence</p><p></p><p>2. terms of sequence</p>, <p>𝐹<sub>8</sub> = 21</p><p>𝐹<sub>10 </sub>= 55</p>, <p>Binet's formula</p>, <p>Pascal's triangle</p>, <p>1. ones2. counting numbers3. triangular numbers4. marbles&nbsp;</p>, <p>1. 12. 33. 64. 105. 15</p>, <p>1. 12. 43. 104. 205. 35</p>, <p>2<sup>n</sup></p><p></p><p>2<sup>10 </sup>= 1024</p>, <p>1. = π‘₯<sup>6</sup> + 6π‘₯<sup>5</sup>𝑦 + 15π‘₯<sup>4</sup>𝑦<sup>2</sup> + 20π‘₯<sup>3</sup>𝑦<sup>3 </sup>+ 15π‘₯<sup>2</sup>𝑦 <sup>4</sup> + 6π‘₯𝑦<sup>5</sup> + 𝑦<sup>6</sup></p><p></p><p>2. = π‘₯<sup>7</sup> - 7π‘₯<sup>6</sup>𝑦 + 21π‘₯<sup>5</sup>𝑦<sup>2</sup> - 35π‘₯<sup>4</sup>𝑦<sup>3 </sup>+ 35π‘₯<sup>3</sup>𝑦<sup>4</sup> - 21π‘₯<sup>2</sup>𝑦 <sup>5</sup> + 7π‘₯𝑦<sup>6</sup> - 𝑦<sup>7</sup></p><p></p><p>3. = 1(π‘₯) <sup>4</sup>(βˆ’2)<sup>0</sup> + 4(π‘₯)<sup>3</sup>(βˆ’2) + 6(π‘₯)<sup>2</sup>(βˆ’2)<sup>2</sup> + 4(x)(βˆ’2)<sup>3</sup> + 1(π‘₯)<sup>0</sup>(βˆ’2)<sup>4</sup> </p><p></p><p>= (π‘₯)<sup>4</sup> βˆ’ 8(π‘₯)<sup>3 </sup>+ 24(π‘₯)<sup>2</sup> βˆ’ 32π‘₯ + 16</p><p>= π‘₯<sup>4</sup> βˆ’ 8π‘₯<sup>3</sup> + 24π‘₯<sup>2</sup> βˆ’ 32π‘₯ + 16</p>, <p>TRUE</p>, <p>George Polya</p><p></p><p>father of problem-solving</p>, <p>How to Solve It</p>, <p>1. Understand the problem</p><p>2. Devise a plan</p><p>3. Carry out the plan</p><p>4. Review the solution</p>, <p>b</p>, <p>b</p>, <p>b</p>, <p>b</p>, <p>d</p>, <p>- listing, tabulating- drawing a diagram- guessing then proving if your answers (guesses)</p>, <p>a</p>, <p>c</p>, <p>1024 ways</p><p></p><p>2<sup>10</sup> = 1024</p>, <p>Thus, there are tourists who made a side trip to HK</p>, <p>1. Modulo</p><p>2. congruent</p>, <p>1. modulus</p><p>2. congruence</p><p>3. Aufmann</p>, <p>Wednesday</p>, <p>Saturday</p> flashcards

[MMW] Problem solving & reasoning

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  • logic

    science of correct reasoning

  • reasoning

    The drawing of inferences or conclusions

  • inductive or deductive

    provlem solivng and reasoning reasoning can either be...

  • not the study of persuasion and manipulative manipulative rhetorical devices

    successful argument’ does not mean persuasive argument

    provlem solivng and reasoning logic is not...

  • Human fallibility and manipulative rhetoric

    ____ and ____ led people to accept poor reasoning and reject good reasoning

  • T

    T OR F: In a successful argument if the premises are true, then the conclusion is either guaranteed to be true or likely to be true.

  • 1. Inductive reasoning

    2. Deductive reasoning

    1. ______ is the process of reaching a general conclusion by examining specific examples.

    2. ______ is the process of reaching a conclusion by applying general assumptions, procedures, or principles.

  • arrangement of inductive reasoning vs deductive reasoning (pyramid)

  • inductive vs deductive reasoning formula

  • inductive

    INDUCTIVE OR DEDUCTIVE REASONING?You are a good student.

    You get all 90+.

    Therefore, your friends must get all 90+ too.

  • deductive

    INDUCTIVE OR DEDUCTIVE REASONING?Ninety percent of humans are right-handed.

    Edryshe is human, therefore Edryshe is right-handed

  • inductive reasoning uses patterns to arrive at a conclusion (conjecture)

    deductive reasoning uses facts, rules, definitions or properties to arrive at a conclusion

    what inductive reasoning use vs deductive reasoning use

  • 30 degrees, deductive

    INDUCTIVE OR DEDUCTIVE REASONING?identify angle x as well

    INDUCTIVE OR DEDUCTIVE REASONING?identify angle x as well

  • shade at lower left, inductive

    INDUCTIVE OR DEDUCTIVE REASONING?"

    INDUCTIVE OR DEDUCTIVE REASONING?"

  • deductive

    INDUCTIVE OR DEDUCTIVE REASONING?

    All oranges are fruits.

    All fruits grow on trees.

    Therefore, all oranges grow on trees.

  • inductive

    INDUCTIVE OR DEDUCTIVE REASONING?

    Diding hails from Visayas and Visayans are accented in their mother tongue when they speak English.

    Therefore, Diding is accented.

  • inductive

    INDUCTIVE OR DEDUCTIVE REASONING?

    1, 1, 2, 3, 5, 8 . . .

  • inductive

    INDUCTIVE OR DEDUCTIVE REASONING?

    6, 13, 20, 27, ...

  • deductive

    INDUCTIVE OR DEDUCTIVE REASONING?The sum of two odd integers is an even

    m and n are odd integers

    Thus, m + n is even.

  • inductive

    INDUCTIVE OR DEDUCTIVE REASONING?

    3 + 5 = 8, 7 + 11 = 18, and 9 + 21 = 30

    Therefore, the sum of two odd integers is even.

  • 1. 452. no, the tsunami height would be negative and height can never be negative3. minimum is 7.4 wherein the max tsunami height is 14. inductive

    INDUCTIVE OR DEDUCTIVE REASONING?1. If the earthquake magnitude is 8.5, how high (in meters) can the tsunami be?2. Can a tsunami occur when the earthquake magnitude is less than 7? Why?3. What is the earthquake magnitude where the start of the max tsunami height can be determined?4. inductive or deductive reasoning?

    INDUCTIVE OR DEDUCTIVE REASONING?

    1. If the earthquake magnitude is 8.5, how high (in meters) can the tsunami be?

    2. Can a tsunami occur when the earthquake magnitude is less than 7? Why?

    3. What is the earthquake magnitude where the start of the max tsunami height can be determined?

    4. inductive or deductive reasoning?

  • Not always true. If x = 0, the result is not equal to 1.

    ANSWER THE PROBLEM BY INDUCTIVE REASONINGProve that the following is not true or not always true.

    ANSWER THE PROBLEM BY INDUCTIVE REASONING

    Prove that the following is not true or not always true.

  • not true

    ANSWER THE PROBLEM BY INDUCTIVE REASONINGProve that the following is not true or not always true.

    ANSWER THE PROBLEM BY INDUCTIVE REASONING

    Prove that the following is not true or not always true.

  • the number is a multiple of 5

    ANSWER THE PROBLEM BY DEDUCTIVE REASONING

    Consider the following procedure:

    Pick a number.

    Multiply the number by 10, add 8 to the product, divide the number by 2, and subtract by 4.

  • 1. sequence

    2. terms of sequence

    1. _____ an ordered list of numbers

    2. the numbers seperated by commas are called the _____

  • 𝐹8 = 21

    𝐹10 = 55

    PROBLEM SOLVING WITH PATTERNSFind the 𝐹8 π‘Žπ‘›π‘‘ 𝐹10

  • Binet's formula

    Binet's formula

    what formula is used to identify large fibonacci numbers.

    state the formula

  • provlem solivng and reasoning USING BINET'S FORMULAFind the:1. 20th fibonacci number2. 50th fibonacci number

  • Pascal's triangle

    Pascal's triangle

    what is the triangular arrangement of numbers that gives the coefficients in the expansion of any binomial expression.

  • 1. ones2. counting numbers3. triangular numbers4. marbles 

    where the arrows are pointed

    where the arrows are pointed

  • 1. 12. 33. 64. 105. 15

    1. 12. 33. 64. 105. 15

    identify the number of dots for the to create ff triangle pattern1. 12. 23. 34. 45. 5

  • 1. 12. 43. 104. 205. 35

    1. 12. 43. 104. 205. 35

    identify the number of marbles are needed for a stack of a certain height 1. height=12. height=23. height=34. height=45. height=5

  • 2n210 = 1024

    2n

    210 = 1024

    formula to get the sum of the row of pascal's triangle

    210 = ?

  • use pascal's triangle as a guide to get the expansion of the ff algebraic expressions:

    1. (a+b)02. (a+b)13. (a+b)2 

    1. (a+b)32. (a+b)43. (a+b)5 

  • 1. = π‘₯6 + 6π‘₯5𝑦 + 15π‘₯4𝑦2 + 20π‘₯3𝑦3 + 15π‘₯2𝑦 4 + 6π‘₯𝑦5 + 𝑦6

    2. = π‘₯7 - 7π‘₯6𝑦 + 21π‘₯5𝑦2 - 35π‘₯4𝑦3 + 35π‘₯3𝑦4 - 21π‘₯2𝑦 5 + 7π‘₯𝑦6 - 𝑦7

    3. = 1(π‘₯) 4(βˆ’2)0 + 4(π‘₯)3(βˆ’2) + 6(π‘₯)2(βˆ’2)2 + 4(x)(βˆ’2)3 + 1(π‘₯)0(βˆ’2)4

    = (π‘₯)4 βˆ’ 8(π‘₯)3 + 24(π‘₯)2 βˆ’ 32π‘₯ + 16

    = π‘₯4 βˆ’ 8π‘₯3 + 24π‘₯2 βˆ’ 32π‘₯ + 16

    USING PASCAL'S TRIANGLE AS A GUIDE, EXPAND THE FF ALGEBRAIC EXPRESSIONS:1. (x+y)62. (x-y)73. (x-2)4

  • TRUE

    TRUE

    T OR F: Can fibonacci numbers can be found in pascal's triangle?

  • George Polya

    father of problem-solving

    He is one of the recent mathematicians who outlined a strategy for solving problems from virtually any discipline

    What is he also known for?

  • How to Solve It

    In his book, β€œ____”, he wrote: β€œA great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest; but it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and triumph of discovery.

  • 1. Understand the problem

    2. Devise a plan

    3. Carry out the plan

    4. Review the solution

    Steps in polya's problem-strategy

  • b

    This part of the problem-solving is sometimes (if not always) neglecteda. Carry out the planb. Understand the problemc. Review the solutiond. Devise a plan

  • b

    In order to solve a problem, one must first know what is being asked, and what information or data can be extracted from what is given.a. Carry out the planb. Understand the problemc. Review the solutiond. Devise a plan

  • b

    You can state the problem in your own words.a. Carry out the planb. Understand the problemc. Review the solutiond. Devise a plan

  • b

    problem solving and reasoning You can state the problem in your own wordsa. Carry out the planb. Understand the problemc. Review the solutiond. Devise a plan

  • d

    Listening, tabulating are some of the strategies to solve a problema. Carry out the planb. Understand the problemc. Review the solutiond. Devise a plan

  • - listing, tabulating- drawing a diagram- guessing then proving if your answers (guesses)

    types of strategies to solve the problem

  • a

    provlem solivng and reasoning "Implementing the strategy chosen (in the second step) until the problem is solved.

    a. Carry out the planb. Understand the problemc. Review the solutiond. Devise a plan

  • c

    Counter checking if your answers are correcta. Carry out the planb. Understand the problemc. Review the solutiond. Devise a plan

  • 1024 ways

    210 = 1024

    APPLICATION OF POLYA'S STRATEGYA quiz consists of ten TRUE or FALSE questions. How many possible ways can a student answer the quiz?

  • Thus, there are tourists who made a side trip to HK

    Thus, there are tourists who made a side trip to HK

    APPLICATION OF POLYA'S STRATEGYAn agency charged P15,000 for a 3-day and 2-night tour in Macau and P20,000 for the same tour with a side trip to Hong Kong. Ten persons joined the trip, which enable them to collect P170,000.

    How many tourists made a side trip to Hong Kong?

    Let x = tourist visiting Macao y = tourist visiting Macao with a side trip to Hong Kong

  • 1. Modulo

    2. congruent

    _____ is when two integers a and b are said to be ______modulo n, within being a natural number, if π‘Žβˆ’π‘ 𝑛 is an integer. In this case, we write π‘Ž ≑ π‘π‘šπ‘œπ‘‘ 𝑛.

    The number n is called the modulus. The statement π‘Ž ≑ π‘π‘šπ‘œπ‘‘ 𝑛 is called a congruence, (Aufmann, 2015).

  • 1. modulus

    2. congruence

    3. Aufmann

    Two integers a and b are said to be congruent modulo n, within being a natural number, if π‘Žβˆ’π‘ 𝑛 is an integer. In this case, we write π‘Ž ≑ π‘π‘šπ‘œπ‘‘ 𝑛.

    The number n is called the _____. The statement π‘Ž ≑ π‘π‘šπ‘œπ‘‘ 𝑛 is called a _____, (_____, 2015).

  • Wednesday

    Wednesday

    MODULOFinding a Day of the Week.

    In 2017, Venus’ birthday fell on a Saturday, June 3. On what day of the week does her birthday fall in 2020? (Note that 2020 is a leap year).

  • Saturday

    Saturday

    MODULOFinding a Day of the Week.

    In 2020, Venus’ birthday fell on a Wednesday, June 3. On what day of the week does her birthday fall in 2017? (Note that 2020 is a leap year).