Probability and Statistics
K.13 The student will gather data by counting and tallying.
K.14 The student will display gathered data in object graphs,
picture graphs, and tables, and will answer questions related to the data.
Understanding the Standard (For Teachers)
Data are pieces of information collected about people or things. The primary
purpose of collecting data is to answer questions.
Tallying is a method for gathering information. Tally marks are used to show
how often something happens or occurs. Each tally mark represents one
occurrence. Tally marks are clustered into groups of five, with four vertical
marks representing the first four occurrences and the fifth mark crossing the
first four on a diagonal to represent the fifth occurrence.
When data are presented in an organized manner, students can describe the
results of their investigation (i.e., identifying parts of the data that have
special characteristics, including categories with the greatest, the least, or
the same number of responses).
In the process of gathering data, students make decisions about what is
relevant to their investigation (e.g., when collecting data on their classmates’
favorite pets, deciding to limit the categories to common pets).
When students begin to collect data, they recognize the need to categorize,
which helps develop the understanding of "things that go together." Categorical
data are used when constructing picture graphs and bar graphs.
Object graphs are graphs that use concrete materials to represent the
categorical data that are collected (e.g., cubes stacked by the month, with one
cube representing the birthday month of each student).
Picture graphs are graphs that use pictures to show and compare information.
Tables are an orderly arrangement of data in which the data are arranged in
columns and rows in an essentially rectangular format. Tables may be used to
display some type of numerical relationship or organized lists (e.g.,
input/output functions, tables showing one candy costs five cents and two
candies cost 10 cents).
Students represent data to convey results of their investigations at a
glance, using concrete objects, pictures, and numbers to give a "picture" of the
organized data.
When data are displayed in an organized manner, children can describe the
results of their investigations.
Graphs can be used to make connections between mathematics and social studies
and/or science (e.g., job areas and the different people that work in these
areas: health — doctors and nurses; education — teachers and principals).
Statements representing an analysis and interpretation of the characteristics
of the data in the graph (e.g., similarities and differences, least and
greatest, the categories, and total number of responses) should be asked.
All students should
Pose questions and gather data.
Understand how data are collected and presented in an organized manner by
counting and tallying.
Understand that data can be represented using concrete objects, pictures, and
graphs.
Understand that different types of representations emphasize different things
about the same data.
Understand that picture graphs use pictures to show and compare information;
object graphs use concrete materials to represent categorical data; and tables
can be used to show an orderly arrangement of data in columns and rows.
Answer questions related to the gathered data from object graphs, picture
graphs, and tables.
Relate their ideas about the data to concepts such as part-part
Teaching the Standard
Books
The Great Graphing Contest. By Loreen Leedy. Illus. by Author. 2005. 32p. Holiday House. (9780823417100). Gr K+. Read about two animals who go graph crazy as they try to organize the world around them. Adorable illustrations and a great way to introduce students to all different kinds of graphs.
Tally O'Malley. By Stuart J. Murphy. Illus by Cynthia Jabar. 2004. 40p. HarperCollins. (9780060531645). GrK-2. Join the O'Malley family as they journey to the beach. What are the kids going to do on the long boring drive? Spot objects of course! Who can see the most of any certain thing and win the game?
Tiger Math: Learning to Graph from a Baby Tiger. By Ann Negada and Cindy Bikel. 2002. 32p. Owlet Paperbacks
(9780805071610). Gr K-1. This book is a little advanced for Kindergarteners, but has great examples of graphing in real world situations. Also a great way to include some science instruction into your math block.
Lessons/Activities/Centerwork
Apple Graphs. Scroll down the page and find the section on graphing apples. This activity is a great beginning to teaching sorting and graphing.
Name Graphs. This is the first graph example when you scroll down the page. I like lots of the ideas found on this page, but the name graph was very interesting. Students use graph paper to spell their names. What can your students see about their names? Is it easy to see who has the longest name? What about the shortest name? How many students have names that are the same size?
Tally Marks Hunt. Here's a fun search and find activitiy for your students to play and learn how to make and interpret tally marks.
Electronic Resources
Graphing: Fewer and More. This online activity asks students to read graphs and decide which item there is fewer of and of which there are more. Good practice to help ingrain this skill into students.
Math Data Game. Utilitarian, but mildly entertaining. Practices tally marks and creating bar and picto- graphs. Just make sure to warn students that this site uses the British spelling of some words, so they may look a little different, and to focus on what the bar graph does incorrectly. Both good bits of information for students to be aware of and watch for.
Survey Says. Use this random survey generator to give students a chance to practice sorting collected data.
Assessments
Graphing Sheet. Print out this form and give it to students along with a page containing various amounts of like stickers (ex. 4 flowers, 2 smilie faces, 3 dinosaurs) and have them count and graph the stickers. Students can either color in the blocks to make a bar graph or can come up with a picture or use given stickers to make picture or picto graphs.
Reading Bar Graphs. Use this form to assess students ability to read and interpret bar graphs.
Talley Marks. This form give students ample opportunity to demonstrate their ability to correctly use talley marks. Uses many objects and different amounts to be confident in students ability.