Range and Mode

Once children feel comfortable analyzing bar graphs, pictographs, and tally charts, they are ready to learn about two special numbers that summarize data. Introduce two new vocabulary terms: mode and range.

Materials: one post-it for each student

Preparation: none

Prerequisite Skills and Concepts: Children should have basic counting skills and be familiar with time lengths in hours. Children should be able to interpret data.

Draw the grid for a bar graph on the board. At equal intervals, write the following categories: 0 hours, about 1 hour, about 2 hours, about 3 hours, and about 4 hours.

• Say: You know that graphs and tally charts display a lot of data. Sometimes we need to summarize that data into just a few numbers. Today we will learn about two special numbers that can help us describe data shown in a bar graph, line plot, or tally.
  Write the words "mode" and "range" on the board.

• Ask: Who enjoys watching television? I'd like you to think about the amount of time you spent last night watching television. Now look at the categories shown in the graph written on the board. Decide which category best describes your television watching: 0 hours, about 1 hour, about 2 hours, about 3 hours, or about 4 hours.
  As children decide their category, distribute one post-it to each child.

• Say: As you go to the board, press your post-it above the category that best describes the amount of time you spent watching television last night.
  Allow 1 or 2 children at a time to place their post-its on the board. Urge children to build bars as for a bar graph. Continue until all children have placed their post-its on the board. Do not allow overlapping of the notes.

• Ask: Wow! Look at the bar graph we made! Can you find the most popular amount of time for watching television? How can you tell?
  Children should realize that the tallest bar represents the most popular amount of television watching time.

• Say: The most popular answer is called the mode. In this graph, the mode is the most popular amount of time spent watching television last night. It means that amount of time occurs more than any other time.
  Have children review the word "mode" in relationship to the graph on the board.

• Ask: Study our graph again. What is the shortest amount of time that someone watched television? (check the graph) What is the longest amount of time that someone watched television? (check the graph)
  Emphasize that at least one student must be in the category for it to count. If at least one student did not watch any television, then the shortest amount of time is 0 hours. If at least one student watched about 4 hours of television, then the longest amount of time is about 4 hours.

• Say: Now subtract those two hours. Your answer is called the range. It describes the spread of time intervals from the shortest to the longest.
  Have children review the word "range" in relationship to the graph on the board. Then redistribute the post-its in the graph.

• Ask: Suppose this bar graph shows the results from the third grade. What is the mode? Is it different from our class? What is the range? How do you know?
  Children should analyze the new graph and apply the meanings of the new vocabulary terms.

  Wrap-Up and Assessment Hints
  Display a line plot that shows the number of pets in 10 families. Have children find the mode and the range of the data. Remind them to subtract to find the range. Discover how they found the mode and range. Be sure to encourage children to use number sense in finding their answers as they analyze the graph.