COLLECTING AND ANALYZING DATA: GRAPHING AND

PROBABILITY

Knight Foundation Summer Institute

Hytolia Branch, Wagner Middle School

Jennifer Fisher, Bryn Mawr College

Introduction:

To introduce the concept of collecting and analyzing data, the teacher can begin a discussion on surveys that collect information about the general population. There are surveys to decide what TV shows are well liked, and to determine how many people are in an average family. The teacher can also talk about election polls. Then the teacher can explain about samples that are taken from the general population. The people who are conducting a particular survey cannot ask every single person their questions, they take a sample of people who represent the entire population. By analyzing those, they can make generalizations about the population as a whole.

Pre-Skills:

  1. Knowledge of the letters of the alphabet
  2. Creating data tables

Objectives:

  1. To have the students learn the basic idea of probability
  2. To have the students analyze data
  3. To have the students graph the data
  4. To see how probability can be used in everyday life

Vocabulary:

Sample

Bar graph

Line plot

Mean

Median

Mode

Range

Scale

Warm Up

Exercise #1 Most Used Letter

Materials:

Procedure:

  1. Explain the directions to the students
  2. Let each student find a book and a page in that book to use for the activity
  3. Go over the results as a class and find the most used letter using every students' information

Class Activities

Exercise #2 Family Members

Materials:

Procedure:

  1. Hand out the ditto sheets and read the instructions out loud with the students
  2. Copy the table on the students' sheets onto the board or on an overhead transparency
  3. Read aloud each category in the table and ask the students to raise their hand when the topic relates to them
  4. Record the information onto the table on the board
  5. Let the students copy the information down in their own papers
  6. As a class, find the probabilities of the first category
  7. Let the students try in small groups to find the probability for the rest of the categories
  8. Distribute graph paper to the class
  9. Show them how to make a bar graph and then let each student make their own from the information in their table

 

Exercise #3 .lump Rope

Materials:

Procedure:

  1. Give each student a Jump Rope Sheet
  2. Have the students line up to jump rope
  3. After each student has jumped, tell the students to record on the sheet the number of jumps that student has completed
  4. After all of the students have had a turn, find the values for the mean, median, mode and range
  5. Help the students graph the information and let them choose what kind of graph they would prefer to use

Assessments:

The final graphs will be a good indicator of the students understanding of converting data into a graph. Each student should be able to explain every aspect of their graph and be able to reproduce one similar to it when given the appropriate information.

A vocabulary test where each student would be required to describe each word and give an example of it. For example, if the word was 'mean,' the student would have to describe that the mean is the average of a set of numbers and if a family had two children whose ages were 3 and 10, the mean age of the children in the family would be 6.5 years old.

Have the students create their own surveys. After distributing all of the surveys to the class, each student would be required to analyze the data they received and represent it graphically. Each student would then present their graph to the class.

 

Extension:

To further the students' learning about frequencies, each student could take the first hundred letters in a non-English book, Spanish for example, and compare the most frequently used letters in English to the most frequently used letters in Spanish.

Philadelphia Mathematics Content Standards:

MATHEMATICS CONTENT STANDARD 1- NUMBER SYSTEMS: ARITHMETIC, RELATIONSHIPS, AND THEORY

The graphing part of the exercise "Represents numerical relationships... in two dimensional graphs such as a bar graph." ( 1.1).

MATHEMATICS CONTENT STANDARD - USING DATA, STATISTIC, AND PROBABILITY

The standard states that each student must solve problems by interpreting data and predicting Outcomes, make decisions based on information collected, and clearly communicate the reasoning used to obtain the results."

MATHEMATICS CONTENT STANDARD - MATHEMATICAL COMMUNICATION

The standard states each student will use mathematical language and representations with appropriate accuracy including numerical tables... and charts, graphs..." (8.2).

MATHEMATICS CONTENT STANDARD 9- USE OF TOOLS AND TECHNOLOGY

The standard states that students must be able to "Organize data on charts and graphs, including scatter plots, bar, line, circle graphs and Venn Diagrams." (9.2)

Cross References

Many other areas of learning are utilized in this lesson. The process of recording data and then graphically representing it is part of the scientific method. While the students are learning about preestablished surveys and then creating their own, they are using social skills. Finally, language arts is used while finding the frequency of the letters in a particular book. While using the jump rope, the students are exercising which is also impertinent to their health.