Problem
    15.1
    Topic 15: Circle Graphs
    for use before
    Data Distributions
    Investigation 1
    Circle graphs, or pie charts, show data by the percent of a quantity divided
    into several categories. A circle graph always represents all (100%) of
    the data.
    A. The circle graph shows the
    vacation choices for 200 middle
    school students.
    1. What percent of the students like to
    go to a theme park on a vacation?
    2. Of the 200 students, how many
    students preferred to go to
    the beach on their vacation?
    3. Of the 200 students, how many students like
    to go camping or to the mountains? Explain.
    B. Nate goes to Westville Middle School. He
    wants to make a circle graph to represent
    the three grades of his school.
    1. Nate knows that 50%, or one half, of a circle
    is a straight line. How many degrees are there
    in a straight line?
    2. Multiply the percent of students in the eighth grade
    by 360 to find the central angle for that piece of the circle.
    3. Find the central angle for each of the other two grades.
    4. Use a compass and protractor to draw a circle graph.
    5. Label each sector with the appropriate grade
    and percent.
    6
    7
    8
    33%
    42%
    25%
    Grade
    Percent of
    students
    camping
    15%
    theme
    park
    32%
    beach
    26%
    mountains
    7%
    visiting
    relatives
    20%
    17%
    28%
    25%
    30%
    Exercises
    1. The circle graph shows the size of the businesses in Westville that have
    made a decision to “Go Green.”
    a. What percent of the businesses that decided to “Go Green” were
    small?
    b. There are 170 businesses that participated. How many medium-
    sized businesses decided to “Go Green?”
    2. a. Make a circle graph for the table of data.
    b. Make a circle graph for the table of data.
    c. Determine the actual number for each color group.
    4. Explain how a circle graph represents data differently from a bar or
    line graph.
    green
    purple
    pink
    blue
    red
    26%
    13%
    12%
    30%
    19%
    Favorite
    color
    Percent of
    students
    Steel
    Anderson
    Payne
    Johnson
    Harmon
    Martin
    20
    38
    28
    36
    42
    36
    Homeroom
    Teacher
    Number of
    students
    Small
    13%
    Large
    48%
    Medium
    39%
    Topic 15: Circle Graphs
    Guided Instruction
    Mathematical Goals
    • Read and organize data in circle graphs.
    Vocabulary
    •
    circle graph
    Materials
    •
    compass
    •
    protractor
    At a Glance
    Because circle graphs depend on fractions, percents, and central angles of a
    circle, you should review the connections between these topics.
    Start with a clock as a point of reference.
    •
    A clock is a circle divided into segments by numbers. How many
    segments are on a clock face?
    (12)
    •
    What fractional part of the entire clock face is each segment?
    •
    What fractional part of the circle is between 12 and 3?
    •
    How do you write as a percent?
    (25%)
    •
    If one clock hand is on the 12 and the other is on the 3, what is the name
    of the angle that is formed in the center of the clock face?
    (right angle)
    •
    How many degrees are in a right angle?
    (90?)
    Continue relating to 25% to 90? to establish the understanding of
    representing percents within a circle.
    If it has been a while since the students have used a compass and/or a
    protractor, you may need to give them an opportunity to practice drawing
    circles and central angles.
    Let the students work in pairs. It would be a good idea to check each
    student’s work at Question B, part 2. If any student has an incorrect answer
    to this question, they will need assistance finding the central angles.
    Summarize with questions like:
    •
    When would you use a circle graph to display data?
    (When you want to
    see how each part compares to the whole.)
    •
    How is the data expressed?
    (percents)
    •
    What do you need to find before you can display the data in the circle
    graph?
    (the central angle)
    •
    How can you find a central angle?
    (by multiplying the percent by 360?)
    You will find additional work on circle graphs in the grade 6 unit
    Data
    About Us.
    1
    4
    1
    4
    Q
    3
    12
    , or
    1
    4
    R
    Q
    1
    12
    R
    PACING
    1 day
    ACE Assignment Guide
    for Topic 15
    Core
    1–3
    Answers to Topic 15
    Problem 15.1
    A. 1.
    32%
    2.
    52
    3.
    44 students; Explanations may vary.
    Sample: I added the 7% of the Mountains
    to the 15% of Camping for a total of 22%.
    22% of 200 students is 44 students.
    B. 1.
    180?
    2.
    0.25 ? 360??90?
    3.
    0.33 ? 360??120?; 0.42 ? 360??150?
    4.
    5.
    Exercises
    1. a.
    13%
    b.
    66.3, or 66 businesses
    2. a.
    b.
    c.
    student total 200; green 52, purple 26,
    pink 24, blue 60, and red 38.
    3.
    Answers may vary. Sample: A circle graph
    compares parts of a whole and visually shows
    relationships of one category to another.
    A bar graph is good for ordering the data,
    but does not give a good visual of the whole.
    A line graph usually shows changes over a
    progression of time for the left to the right.
    green
    blue
    26%
    30%
    purple
    13%
    red
    19%
    pink
    12%
    Martin
    18%
    Payne
    14%
    Johnson
    18%
    Harmon
    21%
    Steel
    10%
    Anderson
    19%
    Gr.6
    33%
    Gr.7
    42%
    Gr.8
    25%

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