1.9.2: Exercise 1.9

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    MAKING CONNECTIONS TO THE COLLABORATION

    (1) Which of the following was one of the main mathematical ideas of the collaboration?

    (i) A percentage is calculated by dividing one number by another number.

    (ii) Smoking is a major health problem in the United States and China.

    (iii) A percentage is a comparison of two numbers. To understand the meaning of a percentage, it is important to know what two quantities are being compared.

    (iv) The percentage of students who are parents is the same as the percentage of parents who are students.

    DEVELOPING SKILLS AND UNDERSTANDING

    (2) Data from the National Center for Education Statistics (NCES)30 provides a statistical snapshot of the proportion of bachelor’s degrees conferred in different fields of study in 2019-20. A total of approximately 2,000,000 awarded degrees were included in the study. The table below displays the total number of students who majored in each of the following fields of study.

    Field of Study

    Number of Students who Majored in Field

    Percentage of Students who Majored in Field

    Psychology

    120,000

    (i)

    Social Sciences/History

    161,200

    (ii)

    Biology/Biomedical Sciences

    126,600

    (iii)

    Computer/Information Science

    97,000

    (iv)

    Engineering

    128,300

    (v)

    Visual and Performing Arts

    92,300

    (vi)

    Business

    387,900

    (vii)

    Health Professions

    257,300

    (viii)

    Communication/Journalism

    91,800

    (ix)

    (a) Complete the table (i) to (ix) by filling in the percentages of students who majored in each field of study. Round to one decimal place where necessary.

    (b) What was the most popular major in 2019–20?

    (i) Engineering

    (ii) Business

    (iii) Health Professions

    (iv) Psychology

    (c) Fill in the blanks to complete the following statements.

    (i) About ________ out of every 100 students in 2019–20 majored in the most popular field.

    (ii) About ________ out of every 1,000 students in 2019–20 majored in the most popular field.

    (3) Select the answer(s) that correctly complete the statement from the list below: A New York Times story reported that 10% of male high school dropouts are in jail or detention centers.31 According to this statistic, about ________ in every ________ male high school dropouts is (are) in jail or juvenile detention. There may be more than one correct answer.

    (i) 1 in every 10

    (ii) 1 in every 10%

    (iii) 0.1 in every 100

    (iv) 1 in every 100

    (v) 10 in every 100

    (4) A teacher has collected data on the grades his students received in his morning and afternoon classes. The following tables show two different ways to represent the same data as percentages.

    Table 1

     

    Grade A

    Grade B

    Grade C

    Grade D

    Grade F

    Morning Class

    12.5%

    25.0%

    37.5%

    6.3%

    18.7%

    Afternoon Class

    14.3%

    20.0%

    37.1%

    8.6%

    20.0%

    Table 2

     

    Grade A

    Grade B

    Grade C

    Grade D

    Grade F

    Morning Class

    44.4%

    53.3%

    48.0%

    40.0%

    46.2%

    Afternoon Class

    55.6%

    46.7%

    52.0%

    60.0%

    53.8%

    (a) Which table could be used to answer the following question: What percentage of the students who received an “A” is in the morning class?

    (b) Which table could be used to answer the following question: What percentage of the students in the morning class received an “A”?

    (c) What are the reference values in Table 1?

    (i) The number of students in a certain class.

    (ii) The number of students who earned a certain grade.

    (iii) The number of students in a certain class who earned a certain grade.

    (iv) The total number of students in both classes.

    (d) What are the reference values in Table 2?

    (i) The number of students in a certain class.

    (ii) The number of students who earned a certain grade.

    (iii) The number of students in a certain class who earned a certain grade.

    (iv) The total number of students in both classes.

    MAKING CONNECTIONS ACROSS THE COURSE

    (5) Congratulations! You won a lottery prize and have a taxable income of $1,025,400. Use the table below to answer the following questions.

    Taxable Income

    Tax

    $0–$9,950

    10% of taxable income

    $9,951–$40,525

    $995.00 plus 12% of excess over $9,950

    $40,526–$86,375

    $4,664.00 plus 22% of excess over $40,525

    $86,376–$164,925

    $14,751.00 plus 24% of excess over $86,375

    $164,926–$209,425

    $33,603.00 plus 32% of excess over $164,925

    $209,426–$523,600

    $47,843.00 plus 35% of excess over $209,425

    $523,601 plus

    $157,804.25 plus 37% of excess over $523,600

    (a) How much tax will you pay on your winnings? Round to the nearest dollar.

    (b) Which of the following expressions can be used to calculate the tax?

    (i) $1,025,400 – 0.37($501,800 – $157,804.25)

    (ii) 0.37 + $501,800($1,025,400 – $157,804.25)

    (iii) ($1,025,400 + $157,804.25) – ($523,600 × 0.37)

    (iv) $157,804.25 + 0.37($1,025,400 – $523,600)

    (v) $1,025,400 – 0.37($1,025,400 – $523,600)

    After Exercise 1.8 (survey)

    The work phase of regulating your learning includes checking your understanding. One of the ways to do this is by asking yourself: “Can I explain this to someone?” Check your understanding by reading Question 5(b) from Exercise 1.8 and explaining the answer below. In this question, you considered how much tax you would pay on lottery winnings of $1,025,400.

    Write your explanation below.

    _______________________________________

    30 https://nces.ed.gov/programs/coe/indicator/cta

    31 http://www.nytimes.com/2009/10/09/education/09dropout.html?_r=0

    This page titled 1.9.2: Exercise 1.9 was last modified on Wed, 15 May 2024 07:37:45 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Carnegie Math Pathways (WestEd) .