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    MMW - 12.4.19 Activity - Polya - A2 - Mirasol

    Uploaded by

    Elle Kate
    1. The document discusses examples solved using Polya's four-step problem solving strategy of understanding the problem, devising a plan, carrying out the plan, and looking back. The examples include counting possible outcomes of wins and losses in games, using proportions to calculate a person's height based on measurements of their face, and determining how many tourists took a side trip using financial information. 2. Further examples include finding the value of i^173 using patterns in exponents of i, finding the last digit of a sum by using patterns in last digits of exponential terms, and calculating the day of the week someone was born given they were born a certain number of days before another person's birthday.

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    MMW - 12.4.19 Activity - Polya - A2 - Mirasol

    Uploaded by

    Elle Kate
    567 views5 pages
    1. The document discusses examples solved using Polya's four-step problem solving strategy of understanding the problem, devising a plan, carrying out the plan, and looking back. The examples include counting possible outcomes of wins and losses in games, using proportions to calculate a person's height based on measurements of their face, and determining how many tourists took a side trip using financial information. 2. Further examples include finding the value of i^173 using patterns in exponents of i, finding the last digit of a sum by using patterns in last digits of exponential terms, and calculating the day of the week someone was born given they were born a certain number of days before another person's birthday.

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    MMW - 12.4.19 ACTIVITY - POLYA - A2 - MIRASOL.docx

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    1. The document discusses examples solved using Polya's four-step problem solving strategy of understanding the problem, devising a plan, carrying out the plan, and looking back. The examples include counting possible outcomes of wins and losses in games, using proportions to calculate a person's height based on measurements of their face, and determining how many tourists took a side trip using financial information. 2. Further examples include finding the value of i^173 using patterns in exponents of i, finding the last digit of a sum by using patterns in last digits of exponential terms, and calculating the day of the week someone was born given they were born a certain number of days before another person's birthday.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    567 views5 pages

    MMW - 12.4.19 Activity - Polya - A2 - Mirasol

    Uploaded by

    Elle Kate
    1. The document discusses examples solved using Polya's four-step problem solving strategy of understanding the problem, devising a plan, carrying out the plan, and looking back. The examples include counting possible outcomes of wins and losses in games, using proportions to calculate a person's height based on measurements of their face, and determining how many tourists took a side trip using financial information. 2. Further examples include finding the value of i^173 using patterns in exponents of i, finding the last digit of a sum by using patterns in last digits of exponential terms, and calculating the day of the week someone was born given they were born a certain number of days before another person's birthday.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    of 5

    MATHEMATICS IN THE MODERN WORLD – A2

    APPLICATION OF POLYA’S STRATEGY


    1. The GSM basketball team won three out of their last six games. In how many different orders
    could they have attained three wins and three losses in six games?
    a. Understand the Problem (Analysis)
    GSM Team
    Wins – 3 | Loses – 3
    Number of Games: 6
    b. Devise a Plan (Planning)
    nCr = n!/(n-r)!r!
    Let:
    n = Number of games
    r = the number of wins or loses which are 6 and 3 respectively.

    c. Carry out the Plan (Implementation)


    6!
    6C3 =
    ( 6−3 ) ! 3 !
    6C3 = 20
    d. Look back (Reflection)
    720 number of games
    = 20 ✔
    ( 6−3 ) 3 !

    2. Leonardo da Vinci was a famous artist during renaissance period. He wrote in his notebook that
    “from the top to the bottom of the chin is the sixth part of the face, and it is fifty-fourth part of
    the man.” Suppose the distance from top to bottom of the chin is 1.2 inches. Using Leonardo da
    Vinci’s measurement, find the height of the person.
    a. Understand the Problem (Analysis)
    Top to Bottom of the chin > 6th part of his face > 54th part of his total height
    b. Device a Plan
    1 d
    =
    x h
    Let:
    x = 54th of the man’s total height
    d = 1.2 the distance from the top to bottom of the chin
    h = height of the man
    c. Carry out the Plan
    1 1.2
    MIRASOL, ELIZA KATE B.

    =
    54 h
    h=54 x 1.2
    h = 64. 8
    d. Look Back
    1 1.2
    =
    54 64.8
    64.8=64.8

    1
    MATHEMATICS IN THE MODERN WORLD – A2

    3. An agency charged P 15 000 for a 3-day and 2-night tour in Macau and P 20 000 for the same
    tour with a side trip to Hongkong. Ten persons joined the trip, which enable them to collect P
    170 000. How many tourists made a side trip to Hongkong?
    a. Understand the Problem
    P 15, 000 – if same tour
    P 20, 000 – if same tour but with a side trip to Hong Kong
    P 170, 000 – collected money of the 10 persons who joined the trip
    b. Devise a Plan
    Let:
    y = the number of tourists who made a side trip to Hong Kong
    10 = number of people who joined the trip
    10 – y = number of tourists with the same tour but without a side trip to Hong Kong
    (Same tour with a side trip to Hong Kong) y + (same tour) (10 – y) = collected money
    c. Carry out the Plan
    20, 000y + 15,000 (10 – y) = 170, 000
    20, 000y + 15, 000 – 15, 000y = 170, 000
    5, 000y = 20, 000
    y=4
    d. Look Back
    Tourists that joined the Tourists who did not joined the
    side Trip side trip
    Tourist 1 = 20, 000 Tourist 5 = 15, 000
    Tourist 2 = 20, 000 Tourist 6 = 15, 000
    Tourist 3 = 20, 000 Tourist 7 = 15, 000
    Tourist 4 = 20, 000 Tourist 8 = 15, 000
    Tourist 9 = 15, 000
    Tourist 10 = 15, 000

    Total 1 = 80, 000 Total 2 = 90, 000

    Grand total = Total 1 + Total 2


    = 80, 000 + 90, 000
    = 170, 000
     Therefore, Collected money ( 170, 000) is equal to the total money from the tourists who joined
    MIRASOL, ELIZA KATE B.

    the side trip and the tourist who did not.


     There are only 4 tourists who joined the tour with a side trip in Hong Kong.

    2
    MATHEMATICS IN THE MODERN WORLD – A2

    Continuation from book - Page 105


    1. In the complex number system, i 1=i; i 2=−1 ; i 3=−i ;i 4=1 ; i5 =i, … Find i 173.

    a. Understand the problem


    To find i 173 with the given the complex number system.
    b. Devise a Plan

    Exponent of i Equivalent
    1 i
    2 -1
    3 −i
    4 1
    5 i
    6 -1

    Based on the table, there are values repeating after a period of 4. Using this, we can
    divide 173 by 4, then compare the remainder to the table.

    c. Carry Out the Plan


    173
    =43 with remainder of 1. This means that i 173 =i1 =i
    4

    d. Look Back
    By using modulo operations,
    173 mod 4 = 1 mod 4 ✔
    ∴ the answer is correct MIRASOL, ELIZA KATE B.

    3
    MATHEMATICS IN THE MODERN WORLD – A2

    e. Find the last digit of the sum: 32018 + 4 2018

    a. Understand the Problem

    Find the last digit of the sum of two numbers raised by an exponent

    b. Devise a Plan

    n Last Digit of 3n Last Digit of 4 n


    1 3 4
    2 9 6
    3 7 4
    4 1 6
    5 3 4
    With accordance to the table, there is a pattern that can be observed. The last
    digit of 3n repeats after a period of 4. However, the last digit of 4 n repeats after a
    period of 2. With this, we divide the exponent by 4 and 2, the compare them to the
    table of 3n and 4 n respectively.

    c. Carry Out the Plan

    2018
    =504 remainder of 2. This means that 32018 =32=9.
    4

    2018
    =1009. There is no remainder, then the exponent is equal to the period for 4 n.
    2
    This means that 4 2018 =4 2=16 . Thus, the last digit is 6.
    Finding the sum of the two, 9 + 6 = 15
    MIRASOL, ELIZA KATE B.

    d. Look Back
    Using Modulo operations,
    2018 mod 4 = 2 mod 4
    2018 mod 2 = 0 mod 2 = 2 mod 2 ✔
    ∴ the answer is correct.

    4
    MATHEMATICS IN THE MODERN WORLD – A2

    e. Yan was born exactly 78 days before Dong was born. If Dong was born on a Monday,
    what day was Yan born?

    a. Understand the Problem


    Yan| x= 78 days y=? Dong |x=? y=Monday

    b. Devise a Plan

    Considered that today is Monday, then exactly 7 days ago is also a Monday knowing that
    a week has 7 days. Through this, we can find the nearest multiple of 7 from 78 and working
    backwards from there can be applied to reach the exact day that we are trying to find.
    c. Carry Out the Plan

    Days from Dong’s Birth Day


    77 Monday
    78 Sunday
    79 Saturday
    80 Friday
    81 Thursday
    82 Wednesday
    83 Tuesday
    Based on the table, 78 days from when Dong was born is a Sunday. Therefore,
    Yan was born on a Sunday.

    d. Look Back
    MIRASOL, ELIZA KATE B.

    It would be always a Sunday, 78 days before a Monday. For example, if today is


    June 4, which is a Monday, then 78 days ago was March 18, which was a
    Sunday. Therefore, the answer is correct. ✔

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