# 6.14 and *6.10 - Circle Graphs

6.14    The student, given a problem situation, will

a)  construct circle graphs;

b)  draw conclusions and make predictions, using circle graphs; and

c)  compare and contrast graphs that present information from the same data set.

6.10  The student, given a practical situation, will

a)  represent data in a circle graph;

b)  make observations and inferences about data represented in a circle graph; and

c)  compare circle graphs with the same data represented in bar graphs, pictographs, and line plots.

Bloom's Level:  Create, Evaluate, Apply, Analyze

### BIG IDEAS

• I can determine where my money is spent each month.
• I will be able to compare parts to the whole and make connections between fractions and percentages.

### UNDERSTANDING THE STANDARD

• To collect data for any problem situation, an experiment can be designed, a survey can be conducted, or other data-gathering strategies can be used. The data can be organized, displayed, analyzed, and interpreted to answer the problem.
• Different types of graphs are used to display different types of data.
• Bar graphs use categorical (discrete) data (e.g., months or eye color).
• Line graphs use continuous data (e.g., temperature and time).
• Circle graphs show a relationship of the parts to a whole.
• All graphs include a title, and data categories should have labels.
• A scale should be chosen that is appropriate for the data.
• A key is essential to explain how to read the graph.
• A title is essential to explain what the graph represents.
• Data are analyzed by describing the various features and elements of a graph.

·  Circle graphs are used for data showing a relationship of the parts to the whole.

-  Example: the favorite fruit of 20 students in Mrs. Jones class was recorded in the table. Compare the same data displayed in both a circle graph and a bar graph.

 Fruit Preference # of students banana 6 apple 7 pear 3 strawberry 4

·  Circle graphs can represent percent or frequency.

·  Circle graphs are not useful for representing data with large numbers of categories.

·  Teachers should be reasonable about the selection of data values. The number of data values can affect how a circle graph is constructed (e.g., 10 out of 25 would be 40%, but 7 out of 9 would be  making the construction of a circle graph more complex).  Students should have experience constructing circle graphs, but a focus should be placed on the analysis of circle graphs.

·  Students are not expected to construct circle graphs by multiplying the percentage of data in a category by 360° in order to determine the central angle measure. Limiting comparisons to fraction parameters noted will assist students in constructing circle graphs.

·  To collect data for any problem situation, an experiment can be designed, a survey can be conducted, or other data-gathering strategies can be used. The data can be organized, displayed, analyzed, and interpreted to solve the problem.

·  Categorical data can be sorted into groups or categories while numerical data are values or observations that can be measured. For example, types of fish caught would be categorical data while weights of fish caught would be numerical data.

·  Different types of graphs can be used to display categorical data. The way data are displayed often depends on what someone is trying to communicate.

–  A line plot is used for categorical and discrete numerical data and is used to show frequency of data on a number line. It is a simple way to organize data.

Example:

-  A bar graph is used for categorical and discrete numerical data (e.g., number of months or number of people with a particular eye color) and is used to show comparisons.

-  A pictograph is mainly used to show categorical data. Pictographs are used to show frequency and compare items. However, the use of partial pictures can give misleading information.

o   Example:

The Types of Pets We Have

Cat

Dog

Horse

Fish

= 1 student

·  A circle graph is used for categorical and discrete numerical data. Circle graphs are used to show a relationship of the parts to a whole.

·  All graphs must include a title, percent or number labels for data categories, and a key. A key is essential to explain how to read the graph.  A title is essential to explain what the graph represents.

·  A scale should be chosen that is appropriate for the data values being represented.

·  Comparisons, predictions, and inferences are made by examining characteristics of a data set displayed in a variety of graphical representations to draw conclusions.

The information displayed in different graphs may be examined to determine how data are or are not related, differences between characteristics (comparisons), trends that suggest what new data might be like (predictions), and/or “what could happen if” (inferences).

### ESSENTIALS

• What types of data are best presented in a circle graph?
Circle graphs are best used for data showing a relationship of the parts to the whole.

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

6.14a1  Collect, organize, and display data in circle graphs by depicting information as fractional.

·  6.10a1  Collect, organize and represent data in a circle graph.  The number of data values should be limited to allow for comparisons that have denominators of 12 or less or those that are factors of 100 (e.g., in a class of 20 students, 7 choose apples as a favorite fruit, so the comparison is 7 out of 20, , or 35%).

6.14b1  Draw conclusions and make predictions about data presented in a circle graph.

·  6.10b1  Make observations and inferences about data represented in a circle graph.

6.14c1  Compare and contrast data presented in a circle graph with the same data represented in other graphical forms.

·  6.10c1  Compare data represented in a circle graph with the same data represented in bar graphs, pictographs, and line plots.

### KEY VOCABULARY

construct, circle graph, organize, display, analyze, interpret, bar graph, line graph, trend, ascending, descending, continuous data, scale, key, title, data categories, analyze, draw conclusions, make predictions, compare, contrast

Updated: Oct 27, 2017